int j remote sensing 2002 vol 23 no 18 3619ndash3648

Estimating leaf nitrogen concentration in ryegrass (Lolium spp)pasture using the chlorophyll red-edge theoretical modelling andexperimental observations

D W LAMBdagger M STEYN-ROSSDagger P SCHAAREsectM M HANNApara W SILVESTER and A STEYN-ROSSDagger

daggerFarrer Centre School of Science amp Technology Charles Sturt UniversityWagga Wagga NSW 2678 Australia e-mail dlambpoboxunceduauDaggerDepartment of Physics amp Electronic Engineering University of WaikatoPrivate Bag 3105 Hamilton New ZealandsectHortResearch Technology Development Group Private Bag 3123 HamiltonNew ZealandparaPO Box 4395 Hamilton New ZealandDepartment of Biological Sciences University of Waikato Private Bag 3105Hamilton New Zealand

(Received 13 November 2000 in nal form 26 July 2001)

Abstract Chlorophyll red-edge descriptors have been used to estimate leaf nitro-gen concentration in ryegrass (L olium spp) pasture Two-layer model calculationshave been used to predict the in uence of chlorophyll content and Leaf Area Index(LAI) on the shape and location of the peaks observed in the derivative spectra ofa ryegrass canopy The complex structure of the resulting derivative spectra pre-cluded extracting red-edge wavelengths by tting inverted Gaussian curves tore ectance pro les Fitting a combination of three sigmoid curves to the calculatedre ectance spectra provided a better representationof subsequentderivative spectraThe derivative spectra in the vicinity of the chlorophyll red-edge is predicted tocontain two peaks (~705 and ~725nm) which on increasing the canopy LAI isgenerally found to shift to longer wavelengths However for a canopy containingleaves of low chlorophyll content and LAIgt5 the wavelength of the rst peakbecomes insensitive to changes in LAI The same phenomenon is predicted forhigh-chlorophyll leaves of LAIgt10 The role of multiple scattering primarily dueto increased leaf transmittance at higher wavelengths has also been veri ed Insubsequent experiments the predicted shape of the derivative spectra was observedand the use of three sigmoid curves to better represent this shape veri ed Changesin the descriptors used to describe the chlorophyll red-edge were observed toexplain 60 and 65 of the variance of leaf nitrogen concentration and total leafnitrogen content respectively The resulting regression equation was found topredict leaf nitrogen concentration in the range of 2ndash55 with a standard errorof prediction (SEP) of 04 The confounding in uence of canopy biomass on thered-edge determination of leaf nitrogen concentration was found to be signi cantlyless at higher canopy biomass con rming both theoretical predictions and thepotential of using the chlorophyll red-edge as a biomass-independent means ofestimating leaf chlorophyll and hence nitrogen concentration in high-LAI ryegrasspastures

On sabbatical leave from Farrer Centre Charles Sturt University Wagga Wagga NSW2678 Australia

International Journal of Remote SensingISSN 0143-1161 printISSN 1366-5901 online copy 2002 Taylor amp Francis Ltd

httpwwwtandfcoukjournalsDOI 10108001431160110114529

D W L amb et al3620

1 IntroductionNitrogen is one of six macronutrients that are essential for pasture growth its

importance is well established (Simpson 1987) Nitrogen is necessary for the produc-tion of protein and chlorophyll and these are essential for plant development yieldpost-grazing regrowth and reproduction (Vickery 1981) On the other hand toomuch nitrogen uptake in some pasture grasses promotes accumulation of nitrogenouscompounds which are toxic to grazing animals in the grass leaves Under suchlsquounfavourablersquo conditions pastures dominated by single species such as perennialryegrasses (L olium perrenne) may be hazardous to livestock (McDonald 1981)

Nitrogen is also important from the point of view of animal nutrition Proteinor non-protein nitrogen are required by ruminant animals to sustain microbialactivity in the rumen and ensure an adequate supply of microbial protein forsubsequent digestion (McDonald et al 1975) As such one empirical measureof the chemical composition of feed generally used is Crude protein=nitrogenconcentration ()times625 (Pearson and Ison 1987)

In- eld fertilizer-response trials have long been used for determining thelsquoadequacyrsquo of nitrogen levels in pasture production however they are increasinglyexpensive and extrapolation to nearby soils is unreliable Nowadays direct measure-ment of leaf nitrogen concentration in pasture grasses either as a means of assessingpasture condition or nutritional value is completed on pasture samples in thelaboratory either by a chemical process known widely as the Kjeldahl technique orusing near-infrared (NIR) re ectance spectroscopy In the former samples are oven-dried typically overnight and then subjected to a destructive chemical extractionprocess involving Kjeldahl digestion and subsequent determination of ammonia bydistillation (Jones and Moseley 1993) NIR spectroscopy involves measuring there ectance spectra of samples in the wavelength range of 800 nm to 25 mm Prior tomeasurement samples are either oven-dried powdered and packed or chopped freshand packed into appropriate cuvettes Nanometre-resolution spectrometers are neces-sary for NIR spectroscopy as it is often derivative spectra that are utilized in thecalibration and prediction analyses The determination of nitrogen or crude proteincontent is more precise using samples of fresh grass (Murray 1986) However thisintroduces diYculties in locations where there are no readily-available laboratoryfacilities Nevertheless it is possible to calibrate for and predict crude proteincontent in foragegrasses with an R2gt095 and a standard error of prediction(SEP)lt107 g kg Otilde 1 (11) respectively (summarized by Murray 1993) Because bothKjeldahl and NIR processes involve eld sampling and preparation of pasturesamples prior to laboratory measurements the determination of nitrogen in pasturescan be time consuming and expensive especially when large numbers of samples areinvolved Furthermore the chemicals associated with the Kjeldahl technique makesit potentially hazardous to the user

Optical remote sensing of pasture nitrogen based on canopy re ectance in thevisiblendashNIR wavelengths (400ndash900 nm) is a low-cost and feasible alternative tolaboratory-based analysis Field re ectance spectroscopy is both non-destructive andis completed in situ precluding the need for time-consuming and costly eld samplingsample preparation and subsequent laboratory analysis

Nitrogen is a key component of chlorophyll and as such diVerent levels ofnitrogen in any given plant will generally be re ected in the concentration ofchlorophyll in plant leaves (Donahue et al 1983) Nitrogen de ciency results inchlorosis (yellowing) of leaves due to a drop in chlorophyll content A visible paling

Estimating leaf nitrogen concentration 3621

rst occurs in older leaves while the young and developing leaves remain green Thisis characteristic of most plants as the nitrogen de ciency initiates senescence on thelower older leaves while the metabolites from the breakdown of their proteins andchlorophyll are transported to the upper younger leaves (Devlin 1969 Atwell et al1999) Adequate nitrogen also produces thinner cell walls in plant leaves resultingin tender more succulent plants (Donahue et al 1983)

Since plant canopy re ectance in visiblendashNIR wavelengths is predominantlyin uenced by chlorophyll-related plant pigments (400ndash700nm) and leaf cell structure(600ndash900 nm) (Bonham-Carter 1987 Campbell 1996) plant nitrogen levels wouldbe expected to in uence canopy re ectance in these wavelengths

To date re ectance spectroscopy involving visiblendashNIR wavelengths has concen-trated on the delineation of canopy chlorophyll content using features of the chloro-phyll red-edge The chlorophyll red-edge describes the region of steep positivegradient in the re ectance spectra of chlorophyll-containing plants in the range690ndash740 nm ( gure 1(a)) The region of low red re ectance (~690 nm) resultsfrom chlorophyll absorption and high NIR re ectance (~740nm) results frominter-cellular scattering within the leaves (Bonham-Carter 1987 Campbell 1996)

The lsquored-edge wavelengthrsquo is de ned as that wavelength within the range690ndash740 nm corresponding to the maximum slope in the re ectance pro le Thepoint of maximum slope is displaced towards longer wavelengths with increasingchlorophyll concentration (Horler et al 1983 Buschmann and Nagel 1993 Pinarand Curran 1996) Because of the link between chlorophyll concentration and plantgrowth and development (for example Danks et al 1983) the location of the red-edge wavelength has been used to estimate nutritional status and developmentalstage (Horler et al 1983 Boochs et al 1990 Filella and Penuelas 1994) and yield(Munden et al 1994) of agricultural crops and grasses

The structure of the chlorophyll red-edge is best observed by plotting dRdl the rst derivative with respect to wavelength ( gure 1(b)) A common approach forlocating the red-edge wavelength has been to manually or computationally locatethe highest peak in the derivative spectra (Horler et al 1983 Booschs et al 1990Buschmann and Nagel 1993 Filella and Penuelas 1994 Munden et al 1994)Alternatively researchers t a portion of a single Gaussian curve to the red-edgeand extract the maximum-slope wavelength from the resulting analytical expression(Bonham-Carter 1987 Miller et al 1990 Pinar and Curran 1996) The limitation ofboth techniques is the implicit assumption that there is only a single maximum inthe gradient of the red-edge In fact the chlorophyll red-edge has been observed tocontain two (or more) gradient maxima and consequently two (or more) peaks inthe derivative spectrum (Horler et al 1983 Booschs et al 1990 Miller et al 1990Filella and Penuelas 1994) Experimental results suggest the rst peak in the derivat-ive spectrum at around 705nm is in uenced by chlorophyll concentration while asecond peak at approximately 725nm is in uenced by the combination of chloro-phyll concentration and multiple scattering within the plant canopy (Horler et al1983 Boochs et al 1990) the latter related to leaf biomass

The relative magnitudes of both peaks in the derivative spectrum depends on thecombination of chlorophyll concentration and the amount of multiple scatteringwithin the canopy In a procedure where the wavelength of the largest peak in thederivative spectra is recorded as a function of chlorophyll concentration for a plantcanopy lsquogapsrsquo or lsquosudden transitionsrsquo are observed in scatterplots of red-edge wave-length versus chlorophyll content This occurs when the relative magnitude of the

D W L amb et al3622

Figure 1 Idealized (a) re ectance and (b) derivative spectrum for typical chlorophyll-containing vegetation

peaks changes from that where the rst peak is larger (lsquophase 1rsquo) to that where thesecond peak is larger (lsquophase 2rsquo) Results suggest this transition occurs as the chloro-phyll concentration in single leaves increases or as a result of multiple scatteringbetween leaves The higher gradient of red-edge wavelength versus chlorophyll con-centration for phase 2 compared to phase 1 is likely the result of the second peakresponding to total chlorophyll content ( leaf chlorophyll concentrationtimesbiomass)

When a single Gaussian curve is tted to the chlorophyll red-edge the retrieved

Estimating leaf nitrogen concentration 3623

single red-edge wavelength will lie between the two derivative peaks as evidenced in gure 1(a) of Miller et al (1990) The retrieved lsquoaveragersquo red-edge wavelength willyield stronger correlations with chlorophyll content than chlorophyll concentration(Miller et al 1990 Pinar and Curran 1996) because the average wavelength isin uenced by the entire red-edge a combination of chlorophyll concentration ( rstpeak in the derivative spectrum) and chlorophyll concentrationleaf biomass (secondpeak in the derivative spectrum) Conversely the same phenomenon reduces thestrength of the correlation between the average red-edge wavelength and totalbiomass alone (for example Pinar and Curran 1996)

Our understanding of the in uence of chlorophyll concentration and multipleleaf scattering on the two peaks observed in the derivative spectra of plant canopiesis based on a very small number of experimental observations (Horler et al 1983Boochs et al 1990) For example Horler et al (1983) demonstrated that progressivelystacking single maize (Zea mays L) leaves resulted in a signi cant increase in themagnitude of the second peak in the derivative spectra with little change to themagnitude and wavelength of the rst peak This suggests the wavelength of the rstpeak may be insensitive to Leaf Area Index (LAI) the parameter that speci es theaverage number of leaves encountered in a vertical traverse through a canopyFurthermore derivative spectra acquired at spatial intervals along a single leafwhere changes in chlorophyll concentration would be expected showed signi cantdiVerences in the magnitude of the rst peak in the derivative spectra and no changein the second multiple scattering component Miller et al (1990) demonstratedsimilar although less dramatic results for leaf stacking using leaves of Bur oak(Quercus macrocarpa) However to date such experimental evidence is yet to besupported by plant canopy model calculations

Our own interest in the eVects of chlorophyll concentration and multiple scat-tering on the shape of the derivative spectra is motivated by our programme ofresearch investigating spectroscopic methods of estimating nitrogen content of dairypastures in the Waikato region of New Zealand (Lat 38deg S) We seek a simplemethodology for estimating leaf nitrogen concentration which avoids the need forphysical measurements of plant biophysical parameters such as biomass The chloro-phyll red-edge is a suitable candidate since plant nitrogen status is often related tochlorophyll content (Everitt et al 1985 Boochs et al 1990) and experimental resultsin unrelated plant types have suggested that the rst peak in the derivative spectramay be insensitive to changes in biomass (or LAI) (Horler et al 1983 Boochset al 1990)

Ryegrass (L olium spp) is a key component of irrigated and rain-fed dairy pasturesin the moist temperate Waikato region of New Zealand Typical Waikato dairypastures include the ryegrass and clover (T rifolium subterranean L) in various mixesranging from pure ryegrass to an approximate mix of 80 ryegrass15 cloverPasture biomass ranges from 200 to 4000kg (dry weight) per hectare LAI from 1up to as high as 12 and moisture content from 70 in summer to 85 in earlywinter (Hanna et al 1999) Typical leaf nitrogen concentrations in the ryegrasscomponent of the pasture is observed to range from 2 to 5 by mass

As a rst step in our investigation of the chlorophyll red-edge we wish to verifythe in uence of chlorophyll concentration and canopy biomass on the shape andlocation of the peaks in the derivative spectra of pure ryegrass In this paper atheoretical two-layer pasture canopy model previously reported in Hanna et al(1999) has been constructed to calculate detailed spectral re ectance curves and

D W L amb et al3624

consequently derivative spectra of a realistic ryegrass pasture canopy for varyinglevels of leaf chlorophyll concentration and biomass In these calculations canopybiomass is expressed through LAI Increasing the LAI of the top canopy for a givensingle leaf type is equivalent to xing the chlorophyll concentration but increasingtotal chlorophyll traversed by the incident radiation within the canopy In order tocon gure the model to represent a ryegrass pasture canopy detailed spectralre ectiontransmission characteristics for ryegrass and soil have also been measuredFurthermore we investigate an alternative method for extracting descriptors of thechlorophyll red-edge speci cally the peak wavelengths from the complex derivativespectra of ryegrass canopies and compare this approach with the standard approachof tting a single inverted Gaussian to the re ectance pro les The results ofthe model calculations are discussed in terms of practical requirements of usingchlorophyll red-edge to estimate leaf nitrogen concentration in ryegrass pastures

Following veri cation of the nature of the derivative spectra of ryegrass canopiesthe alternative method of extracting red-edge descriptors is then applied to measuredspectral re ectance pro les of 100 sample sites of diVerent canopy biomass and leafnitrogen levels to estimate leaf nitrogen concentration and total nitrogen content

2 Two-layer canopy re ectance modelThe two-layer canopy re ectance model previously described in Hanna et al

(1999) is based on the analytical solution of a two-stream plant canopy model(Sellers 1985) which has the governing equations

mdIldt

=Ilshy vl(1 shy bl )Il

shy vl bl I3lshy vl b0 mke Otilde kt (1)

shy mAringdI3

ldt

=I3lshy vl (1 shy bl )I3

lshy vl bl Il

shy vl (1 shy b0 )mke Otilde kt (2)

Here m is the average inverse diVuse optical depth per unit leaf area in the canopyIl and I3

l are the wavelength-dependent upward and downward diVuse uxes dividedby the incident solar ux t is the canopy LAI vl is the sum of the wavelength-dependent single leaf re ectance rl and transmittance tl bl is the wavelength-dependent backscatter distribution function for the diVuse beam b0 is the backscatterparameter for the incident beam and k is the optical depth of the direct beam perunit leaf area

The two-layer canopy model is generated by solving equations (1) and (2) for Iand I3using appropriate boundary conditions for each speci ed layer (see Appendixfor details) The wavelength-dependent canopy re ectance is computed using

RlnotIl(t=0) (3)

where t=0 corresponds to the top of the canopyA simpli ed diagram of the two-layer ryegrass pasture represented in the model

is given in gure 2 and a detailed schematic is given in gure A1 In this model wespecify the spectral characteristics and LAI of the top pasture canopy ( layer a) alayer of dead material which usually exists within the pasture pro le ( layer b) andthe re ectance characteristics of the underlying soil The LAI of the layer of deadmaterial was set to unity and the LAI of the top ryegrass was canopy varied over

Estimating leaf nitrogen concentration 3625

Figure 2 Simpli ed diagram of the two-layer ryegrass canopy represented in the model

the range of 1ndash10 to mimic the pasture conditions we observed during a number of eld visitations

3 Single-leaf and soil spectral characteristicsIn order to apply equations (1) and (2) to the model the two-layer theory

requires detailed single leaf re ectance and transmittance data for each canopy layerand re ectance data for the underlying soil In the previous work of Hanna et al(1999) involving only three re ectance wavebands (NIR red and green) the modelwas run using a combination of actual and synthetic maize data since appropriateryegrass data were unavailable In this current work however the necessary re ectionand transmission characteristics of fresh ryegrass leaves were acquired from laborat-ory measurements and soil re ectance measurements acquired from outdoormeasurements

31 Single-leaf re ectance and transmittance dataRe ectance and transmittance measurements were completed on single high- and

low-chlorophyll content chlorotic (very low chlorophyll content) and dead ryegrassleaves Single leaves were sampled from pure ryegrass plots used in a long-termfertilizer treatment program by the Dairy Research Institute Hamilton New ZealandLeaf samples of high and low chlorophyll concentration were hand-picked from400 kg ha and 0 kg ha nitrogen treatment plots respectively Chlorotic leaves thosewith agt50 surface coverage of rust and dead leaf samples were also hand-pickedfrom the 0 kg ha nitrogen plot The ryegrass samples were immediately placed in acooled black plastic bag and transported to the laboratory for subsequent analysis

Re ectance and transmittance measurements were completed using a ZeissMMS-1 Monolithic Miniature Spectrometer (Carl Zeiss OEM SensorikProzeszlig-analytik Oberkochen GmbH) The Zeiss spectrometer comprised a at- eld gratingof 366 lines mm blazed for 330 nm Coupled with a 70 mmtimes2500 mm entrance slitand a 256-pixel linear diode array the spectrometer had a useable wavelength rangeof 305 nm to 1150 nm with 33 nm resolution

For re ectance measurements ( gure 3(a)) light from a 40 W quartz tungstenhalogen source (Ocean Optics LS-1 Ocean Optics Inc Dunedin FL USA) wasdirected onto the surface of a clamped leaf specimen via a dual-optical bre couplercomprising a hollow-hexagonal array of multimode bres surrounding a centralmultimode bre (numerical aperture=02 core diameter=400 mm) The central bredirected the re ected light from the leaf surface into the input slit of the Zeissspectrometer For each measurement the leaf was clamped at on the surface ofagt99 re ectance Spectralon re ectance target (SRT-99-100 Labsphere Inc

D W L amb et al3626

Sutton NH USA) and the bre illuminationdetection bundle was placed 95 mmfrom and normal to the leaf surface using a precision spacer Spectra were averagedand recorded using lsquotec5rsquo software (Sensorik und Systemtechnik GmbH) on an IBM-compatible computer The apparent re ectance was determined from the ratio of thelight measured from the leaf surface to that measured from the exposed Spectralonpanel ( leaf removed)

Since the measured intensity of the re ected light included multiple re ectionstransmissions of light from the Spectralon panel through the leaf body it wasassumed that the abaxial and adaxial surface re ectances were equal The leaf surfacere ectance was then calculated from the apparent re ectance following Methy et al(1998) using

rl=(rfrac34l+1) shy atilde (r frac34l+1)2 shy 4(r frac34l shy t2l)

2(4)

where rl is the re ectance of the leaf surface r frac34l is the apparent re ectance asmeasured by the spectrometer and tl is the measured leaf transmittance

Leaf transmittance was measured by directly illuminating the clamped leafsamples from behind using a collimated 100 W quartz tungsten halogen light sourcedirected through a 3 mm thick frosted glass diVusing plate ( gure 3(b)) Transmittedlight was collected by the central bre of the dual-optical bre bundle (describedabove) placed on the downstream side of the leaf and spaced 95 mm from andnormal to the leaf surface Transmittance was calculated by measuring the intensityof light with and without the leaf sample in place

32 Soil re ectanceIn- eld soil re ectance measurements were acquired using the Zeiss MMS-1

spectrometer mounted in a eld-portable con guration complete with arti cial targetillumination source and shroud to block ambient sunlight ( gure 4) The rigid shroudconstructed from 35 mm thick black polyethylene plastic housed the optical brebundle and foreoptic for the Zeiss spectrometer (mounted on top of the shroud) andthe arti cial light source The latter comprised two 20 W quartz tungsten halogenlight bulbs spaced 40 mm on either side of the bre foreoptic The foreoptic andlight sources were held 052 m above the ground at nadir by the rigid shroud Theforeoptic bre bundle provided the spectrometer with a 100mm diameter circularfootprint on the ground equivalent to a eld of view of approximately 55deg

Soil re ectance spectra were acquired and averaged from a number of eldlocations within the Dairy Research Institute Hamilton New Zealand

4 Results of model calculations41 Single leaf and soil spectral characteristics

Measured re ectance and transmittance spectra of single high-and low-chlorophyll chlorotic and dead ryegrass leaves are given in gure 5 The re ectancespectra of bare soil is also included in gure 5(a)

The derivative spectra of the single leaves corresponding to gure 5(a) are givenin gure 6 These were calculated using

AdR

dl Bl

=Rl

shy R(l Otilde 1)Dl

(5)

where Rlshy R(l Otilde 1) is the diVerence in re ectance measured across a single wavelength

increment centred at l and Dl is the wavelength increment of the spectrometer

Estimating leaf nitrogen concentration 3627

(a)

(b)

Figure 3 Schematic diagram showing apparatus used for single leaf (a) re ectance and(b) transmittance measurements

From the curves of gure 6 it is evident that the derivative spectra of the high-and low- chlorophyll and chlorotic leaves contain peaks at both ~705 and ~725 nmFor the low-chlorophyll and chlorotic leaves the rst feature (~705 nm) is dominantIn the high-chlorophyll leaves the second feature (~725nm) is dominant

42 Model predictionsCanopy re ectance pro les generated by the model using high-chlorophyll low-

chlorophyll and chlorotic leaves of LAI from 1 to 5 in the top canopy are givenin gure 7

D W L amb et al3628

Figure 4 Schematic diagram of the eld-portable spectrometer used for acquiring soilre ectance spectra

421 T he eVect of increasing L AI on the magnitude of peaks in the derivativespectra

Derivative spectra corresponding to gure 7 are given in gure 8 It is evidenthere that increasing the LAI of the top canopy produces a signi cant increase in themagnitude of the second peak in the derivative spectra a phenomena supported bythe experimental observations of Horler et al (1983) using maize leaves

In the case of low-chlorophyll ( gure 8(b)) and chlorotic ( gure 8(c)) leaves themagnitude of the rst peak is initially comparable to or larger than that of thesecond peak at low LAI The substantial increase in magnitude of the second peakwith increasing LAI is linked to an increase in the magnitude of the NIR plateau inthe individual re ectance pro les ( gure 7) This is attributed to signi cantly greatermultiple scattering of radiation within the canopy in NIR red wavelengths due tohigher leaf re ectance and transmittance

The eVect of multiple scattering can be veri ed by modifying the transmittancecharacteristics of one of the candidate leaf types For example if the transmittanceof a low-chlorophyll leaf is arti cially reduced at higher wavelengths as depicted in gure 9 then signi cantly smaller increases in the magnitude of the second peakwith increasing LAI are observed ( gure 10)

422 Extracting red-edge parameters from the derivative spectraExamples of modelled re ectance spectra for high and low chlorophyll-containing

ryegrass canopies (LAI=1) are reproduced in gure 11 Superimposed on there ectance and corresponding derivative spectra ( gure 12) are tted curves corres-ponding to tting a single inverted Gaussian (equation (6)mdashtable 1) and a combina-tion of three sigmoid functions (equation (7)mdashtable 1) to the re ectance pro lesThe extracted red-edge wavelengths (lP ) and the sum of squared residuals (SSR) ofthe respective tted curves are also listed in table 2

Estimating leaf nitrogen concentration 3629

(a)

(b)

Figure 5 (a) Measured re ectance spectra for single ryegrass leaves (high- and low-chlorophyll chlorotic and dead) and bare soil (b) Single-leaf transmittance spectrafor high and low chlorophyll content chlorotic and dead ryegrass leaves

It is evident from gures 11 and 12 that like the single-leaf spectra of gure 6the shape of the chlorophyll red-edge for ryegrass canopies is complex containingtwo local maxima in the gradient at approximately 705 and 725 nm respectively

Single and combinations of two three and four sigmoid functions were used toconstruct curves to reproduce the observed re ectance pro les In all cases the useof three sigmoids was found to yield the lowest SSR values and always considerablylower SSR values than the tted Gaussian curve (table 2) In most test cases thethree sigmoids resulting from the tting procedure comprised two sigmoids of positivegain and amplitude (gn and Anmdashtable 1) corresponding to the two peaks observedin the derivative spectra hitherto referred to as l1 and l2 respectively as well as athird sigmoid with a relatively small negative gain In the particular though repres-entative examples of table 2 the wavelength of the third sigmoid (in brackets)corresponds to the location of the peak chlorophyll absorption of red light where are ectance minimum is observed in the re ectance pro les ( gure 11)

D W L amb et al3630

Figure 6 Single-leaf derivative re ectance spectra (dRdl) for high- and low-chlorophylland chlorotic ryegrass

As observed in the results of Miller et al (1990) the single red-edge wavelengthpredicted by the Gaussian tting routine lies between the two peaks observed in thecomplex derivative spectra As expected (Miller et al 1990 Pinar and Curran 1996)both the single red-edge peak resulting from the Gaussian analysis and the twopeaks resulting from the sigmoid- tting procedure have shifted to higher wavelengthsin response to higher leaf nitrogen content (higher chlorophyll )

423 T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectraThe wavelengths corresponding to both peaks in the derivative spectra of the

calculated re ectance pro les were extracted following the procedure outlined aboveThe eVects of increasing LAI on the wavelengths of the two peaks are summarizedin gure 13

It is evident from these model results that increasing LAI progressively shiftsboth derivative peaks towards longer wavelengths Progressively stacking leaves willeVectively increase total chlorophyll absorption experienced by the incident radiationthrough multiple scattering thereby shifting the derivative peaks to higher wave-lengths The magnitude of the wavelength shift resulting from increasing LAI from1 to 10 is greater for the second peak ( gure 13(b)) This is not surprising given thehigher leaf transmittance and re ectance in the associated wavelength range(724ndash740nm) ( gure 5 table 3) This eVect is also observed to occur for the rstpeak ( gure 13(a)) although to a lesser extent due to lower leaf re ectance andtransmittance in the corresponding wavelength range (702ndash709nm) ( gure 5 table 3)

There is a partial overlap of the curve shoulders in gure 13 for a small range ofred-edge wavelengths The overlap of the rst peak occurs for wavelengths703ndash7042nm and for the second peak is 726ndash730nm This overlap demonstratesthe confounding in uence of leaf chlorophyll concentration and canopy LAI on

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3621

rst occurs in older leaves while the young and developing leaves remain green Thisis characteristic of most plants as the nitrogen de ciency initiates senescence on thelower older leaves while the metabolites from the breakdown of their proteins andchlorophyll are transported to the upper younger leaves (Devlin 1969 Atwell et al1999) Adequate nitrogen also produces thinner cell walls in plant leaves resultingin tender more succulent plants (Donahue et al 1983)

Since plant canopy re ectance in visiblendashNIR wavelengths is predominantlyin uenced by chlorophyll-related plant pigments (400ndash700nm) and leaf cell structure(600ndash900 nm) (Bonham-Carter 1987 Campbell 1996) plant nitrogen levels wouldbe expected to in uence canopy re ectance in these wavelengths

To date re ectance spectroscopy involving visiblendashNIR wavelengths has concen-trated on the delineation of canopy chlorophyll content using features of the chloro-phyll red-edge The chlorophyll red-edge describes the region of steep positivegradient in the re ectance spectra of chlorophyll-containing plants in the range690ndash740 nm ( gure 1(a)) The region of low red re ectance (~690 nm) resultsfrom chlorophyll absorption and high NIR re ectance (~740nm) results frominter-cellular scattering within the leaves (Bonham-Carter 1987 Campbell 1996)

The lsquored-edge wavelengthrsquo is de ned as that wavelength within the range690ndash740 nm corresponding to the maximum slope in the re ectance pro le Thepoint of maximum slope is displaced towards longer wavelengths with increasingchlorophyll concentration (Horler et al 1983 Buschmann and Nagel 1993 Pinarand Curran 1996) Because of the link between chlorophyll concentration and plantgrowth and development (for example Danks et al 1983) the location of the red-edge wavelength has been used to estimate nutritional status and developmentalstage (Horler et al 1983 Boochs et al 1990 Filella and Penuelas 1994) and yield(Munden et al 1994) of agricultural crops and grasses

The structure of the chlorophyll red-edge is best observed by plotting dRdl the rst derivative with respect to wavelength ( gure 1(b)) A common approach forlocating the red-edge wavelength has been to manually or computationally locatethe highest peak in the derivative spectra (Horler et al 1983 Booschs et al 1990Buschmann and Nagel 1993 Filella and Penuelas 1994 Munden et al 1994)Alternatively researchers t a portion of a single Gaussian curve to the red-edgeand extract the maximum-slope wavelength from the resulting analytical expression(Bonham-Carter 1987 Miller et al 1990 Pinar and Curran 1996) The limitation ofboth techniques is the implicit assumption that there is only a single maximum inthe gradient of the red-edge In fact the chlorophyll red-edge has been observed tocontain two (or more) gradient maxima and consequently two (or more) peaks inthe derivative spectrum (Horler et al 1983 Booschs et al 1990 Miller et al 1990Filella and Penuelas 1994) Experimental results suggest the rst peak in the derivat-ive spectrum at around 705nm is in uenced by chlorophyll concentration while asecond peak at approximately 725nm is in uenced by the combination of chloro-phyll concentration and multiple scattering within the plant canopy (Horler et al1983 Boochs et al 1990) the latter related to leaf biomass

The relative magnitudes of both peaks in the derivative spectrum depends on thecombination of chlorophyll concentration and the amount of multiple scatteringwithin the canopy In a procedure where the wavelength of the largest peak in thederivative spectra is recorded as a function of chlorophyll concentration for a plantcanopy lsquogapsrsquo or lsquosudden transitionsrsquo are observed in scatterplots of red-edge wave-length versus chlorophyll content This occurs when the relative magnitude of the

D W L amb et al3622

Figure 1 Idealized (a) re ectance and (b) derivative spectrum for typical chlorophyll-containing vegetation

peaks changes from that where the rst peak is larger (lsquophase 1rsquo) to that where thesecond peak is larger (lsquophase 2rsquo) Results suggest this transition occurs as the chloro-phyll concentration in single leaves increases or as a result of multiple scatteringbetween leaves The higher gradient of red-edge wavelength versus chlorophyll con-centration for phase 2 compared to phase 1 is likely the result of the second peakresponding to total chlorophyll content ( leaf chlorophyll concentrationtimesbiomass)

When a single Gaussian curve is tted to the chlorophyll red-edge the retrieved

Estimating leaf nitrogen concentration 3623

single red-edge wavelength will lie between the two derivative peaks as evidenced in gure 1(a) of Miller et al (1990) The retrieved lsquoaveragersquo red-edge wavelength willyield stronger correlations with chlorophyll content than chlorophyll concentration(Miller et al 1990 Pinar and Curran 1996) because the average wavelength isin uenced by the entire red-edge a combination of chlorophyll concentration ( rstpeak in the derivative spectrum) and chlorophyll concentrationleaf biomass (secondpeak in the derivative spectrum) Conversely the same phenomenon reduces thestrength of the correlation between the average red-edge wavelength and totalbiomass alone (for example Pinar and Curran 1996)

Our understanding of the in uence of chlorophyll concentration and multipleleaf scattering on the two peaks observed in the derivative spectra of plant canopiesis based on a very small number of experimental observations (Horler et al 1983Boochs et al 1990) For example Horler et al (1983) demonstrated that progressivelystacking single maize (Zea mays L) leaves resulted in a signi cant increase in themagnitude of the second peak in the derivative spectra with little change to themagnitude and wavelength of the rst peak This suggests the wavelength of the rstpeak may be insensitive to Leaf Area Index (LAI) the parameter that speci es theaverage number of leaves encountered in a vertical traverse through a canopyFurthermore derivative spectra acquired at spatial intervals along a single leafwhere changes in chlorophyll concentration would be expected showed signi cantdiVerences in the magnitude of the rst peak in the derivative spectra and no changein the second multiple scattering component Miller et al (1990) demonstratedsimilar although less dramatic results for leaf stacking using leaves of Bur oak(Quercus macrocarpa) However to date such experimental evidence is yet to besupported by plant canopy model calculations

Our own interest in the eVects of chlorophyll concentration and multiple scat-tering on the shape of the derivative spectra is motivated by our programme ofresearch investigating spectroscopic methods of estimating nitrogen content of dairypastures in the Waikato region of New Zealand (Lat 38deg S) We seek a simplemethodology for estimating leaf nitrogen concentration which avoids the need forphysical measurements of plant biophysical parameters such as biomass The chloro-phyll red-edge is a suitable candidate since plant nitrogen status is often related tochlorophyll content (Everitt et al 1985 Boochs et al 1990) and experimental resultsin unrelated plant types have suggested that the rst peak in the derivative spectramay be insensitive to changes in biomass (or LAI) (Horler et al 1983 Boochset al 1990)

Ryegrass (L olium spp) is a key component of irrigated and rain-fed dairy pasturesin the moist temperate Waikato region of New Zealand Typical Waikato dairypastures include the ryegrass and clover (T rifolium subterranean L) in various mixesranging from pure ryegrass to an approximate mix of 80 ryegrass15 cloverPasture biomass ranges from 200 to 4000kg (dry weight) per hectare LAI from 1up to as high as 12 and moisture content from 70 in summer to 85 in earlywinter (Hanna et al 1999) Typical leaf nitrogen concentrations in the ryegrasscomponent of the pasture is observed to range from 2 to 5 by mass

As a rst step in our investigation of the chlorophyll red-edge we wish to verifythe in uence of chlorophyll concentration and canopy biomass on the shape andlocation of the peaks in the derivative spectra of pure ryegrass In this paper atheoretical two-layer pasture canopy model previously reported in Hanna et al(1999) has been constructed to calculate detailed spectral re ectance curves and

D W L amb et al3624

consequently derivative spectra of a realistic ryegrass pasture canopy for varyinglevels of leaf chlorophyll concentration and biomass In these calculations canopybiomass is expressed through LAI Increasing the LAI of the top canopy for a givensingle leaf type is equivalent to xing the chlorophyll concentration but increasingtotal chlorophyll traversed by the incident radiation within the canopy In order tocon gure the model to represent a ryegrass pasture canopy detailed spectralre ectiontransmission characteristics for ryegrass and soil have also been measuredFurthermore we investigate an alternative method for extracting descriptors of thechlorophyll red-edge speci cally the peak wavelengths from the complex derivativespectra of ryegrass canopies and compare this approach with the standard approachof tting a single inverted Gaussian to the re ectance pro les The results ofthe model calculations are discussed in terms of practical requirements of usingchlorophyll red-edge to estimate leaf nitrogen concentration in ryegrass pastures

Following veri cation of the nature of the derivative spectra of ryegrass canopiesthe alternative method of extracting red-edge descriptors is then applied to measuredspectral re ectance pro les of 100 sample sites of diVerent canopy biomass and leafnitrogen levels to estimate leaf nitrogen concentration and total nitrogen content

2 Two-layer canopy re ectance modelThe two-layer canopy re ectance model previously described in Hanna et al

(1999) is based on the analytical solution of a two-stream plant canopy model(Sellers 1985) which has the governing equations

mdIldt

=Ilshy vl(1 shy bl )Il

shy vl bl I3lshy vl b0 mke Otilde kt (1)

shy mAringdI3

ldt

=I3lshy vl (1 shy bl )I3

lshy vl bl Il

shy vl (1 shy b0 )mke Otilde kt (2)

Here m is the average inverse diVuse optical depth per unit leaf area in the canopyIl and I3

l are the wavelength-dependent upward and downward diVuse uxes dividedby the incident solar ux t is the canopy LAI vl is the sum of the wavelength-dependent single leaf re ectance rl and transmittance tl bl is the wavelength-dependent backscatter distribution function for the diVuse beam b0 is the backscatterparameter for the incident beam and k is the optical depth of the direct beam perunit leaf area

The two-layer canopy model is generated by solving equations (1) and (2) for Iand I3using appropriate boundary conditions for each speci ed layer (see Appendixfor details) The wavelength-dependent canopy re ectance is computed using

RlnotIl(t=0) (3)

where t=0 corresponds to the top of the canopyA simpli ed diagram of the two-layer ryegrass pasture represented in the model

is given in gure 2 and a detailed schematic is given in gure A1 In this model wespecify the spectral characteristics and LAI of the top pasture canopy ( layer a) alayer of dead material which usually exists within the pasture pro le ( layer b) andthe re ectance characteristics of the underlying soil The LAI of the layer of deadmaterial was set to unity and the LAI of the top ryegrass was canopy varied over

Estimating leaf nitrogen concentration 3625

Figure 2 Simpli ed diagram of the two-layer ryegrass canopy represented in the model

the range of 1ndash10 to mimic the pasture conditions we observed during a number of eld visitations

3 Single-leaf and soil spectral characteristicsIn order to apply equations (1) and (2) to the model the two-layer theory

requires detailed single leaf re ectance and transmittance data for each canopy layerand re ectance data for the underlying soil In the previous work of Hanna et al(1999) involving only three re ectance wavebands (NIR red and green) the modelwas run using a combination of actual and synthetic maize data since appropriateryegrass data were unavailable In this current work however the necessary re ectionand transmission characteristics of fresh ryegrass leaves were acquired from laborat-ory measurements and soil re ectance measurements acquired from outdoormeasurements

31 Single-leaf re ectance and transmittance dataRe ectance and transmittance measurements were completed on single high- and

low-chlorophyll content chlorotic (very low chlorophyll content) and dead ryegrassleaves Single leaves were sampled from pure ryegrass plots used in a long-termfertilizer treatment program by the Dairy Research Institute Hamilton New ZealandLeaf samples of high and low chlorophyll concentration were hand-picked from400 kg ha and 0 kg ha nitrogen treatment plots respectively Chlorotic leaves thosewith agt50 surface coverage of rust and dead leaf samples were also hand-pickedfrom the 0 kg ha nitrogen plot The ryegrass samples were immediately placed in acooled black plastic bag and transported to the laboratory for subsequent analysis

Re ectance and transmittance measurements were completed using a ZeissMMS-1 Monolithic Miniature Spectrometer (Carl Zeiss OEM SensorikProzeszlig-analytik Oberkochen GmbH) The Zeiss spectrometer comprised a at- eld gratingof 366 lines mm blazed for 330 nm Coupled with a 70 mmtimes2500 mm entrance slitand a 256-pixel linear diode array the spectrometer had a useable wavelength rangeof 305 nm to 1150 nm with 33 nm resolution

For re ectance measurements ( gure 3(a)) light from a 40 W quartz tungstenhalogen source (Ocean Optics LS-1 Ocean Optics Inc Dunedin FL USA) wasdirected onto the surface of a clamped leaf specimen via a dual-optical bre couplercomprising a hollow-hexagonal array of multimode bres surrounding a centralmultimode bre (numerical aperture=02 core diameter=400 mm) The central bredirected the re ected light from the leaf surface into the input slit of the Zeissspectrometer For each measurement the leaf was clamped at on the surface ofagt99 re ectance Spectralon re ectance target (SRT-99-100 Labsphere Inc

D W L amb et al3626

Sutton NH USA) and the bre illuminationdetection bundle was placed 95 mmfrom and normal to the leaf surface using a precision spacer Spectra were averagedand recorded using lsquotec5rsquo software (Sensorik und Systemtechnik GmbH) on an IBM-compatible computer The apparent re ectance was determined from the ratio of thelight measured from the leaf surface to that measured from the exposed Spectralonpanel ( leaf removed)

Since the measured intensity of the re ected light included multiple re ectionstransmissions of light from the Spectralon panel through the leaf body it wasassumed that the abaxial and adaxial surface re ectances were equal The leaf surfacere ectance was then calculated from the apparent re ectance following Methy et al(1998) using

rl=(rfrac34l+1) shy atilde (r frac34l+1)2 shy 4(r frac34l shy t2l)

2(4)

where rl is the re ectance of the leaf surface r frac34l is the apparent re ectance asmeasured by the spectrometer and tl is the measured leaf transmittance

Leaf transmittance was measured by directly illuminating the clamped leafsamples from behind using a collimated 100 W quartz tungsten halogen light sourcedirected through a 3 mm thick frosted glass diVusing plate ( gure 3(b)) Transmittedlight was collected by the central bre of the dual-optical bre bundle (describedabove) placed on the downstream side of the leaf and spaced 95 mm from andnormal to the leaf surface Transmittance was calculated by measuring the intensityof light with and without the leaf sample in place

32 Soil re ectanceIn- eld soil re ectance measurements were acquired using the Zeiss MMS-1

spectrometer mounted in a eld-portable con guration complete with arti cial targetillumination source and shroud to block ambient sunlight ( gure 4) The rigid shroudconstructed from 35 mm thick black polyethylene plastic housed the optical brebundle and foreoptic for the Zeiss spectrometer (mounted on top of the shroud) andthe arti cial light source The latter comprised two 20 W quartz tungsten halogenlight bulbs spaced 40 mm on either side of the bre foreoptic The foreoptic andlight sources were held 052 m above the ground at nadir by the rigid shroud Theforeoptic bre bundle provided the spectrometer with a 100mm diameter circularfootprint on the ground equivalent to a eld of view of approximately 55deg

Soil re ectance spectra were acquired and averaged from a number of eldlocations within the Dairy Research Institute Hamilton New Zealand

4 Results of model calculations41 Single leaf and soil spectral characteristics

Measured re ectance and transmittance spectra of single high-and low-chlorophyll chlorotic and dead ryegrass leaves are given in gure 5 The re ectancespectra of bare soil is also included in gure 5(a)

The derivative spectra of the single leaves corresponding to gure 5(a) are givenin gure 6 These were calculated using

AdR

dl Bl

=Rl

shy R(l Otilde 1)Dl

(5)

where Rlshy R(l Otilde 1) is the diVerence in re ectance measured across a single wavelength

increment centred at l and Dl is the wavelength increment of the spectrometer

Estimating leaf nitrogen concentration 3627

(a)

(b)

Figure 3 Schematic diagram showing apparatus used for single leaf (a) re ectance and(b) transmittance measurements

From the curves of gure 6 it is evident that the derivative spectra of the high-and low- chlorophyll and chlorotic leaves contain peaks at both ~705 and ~725 nmFor the low-chlorophyll and chlorotic leaves the rst feature (~705 nm) is dominantIn the high-chlorophyll leaves the second feature (~725nm) is dominant

42 Model predictionsCanopy re ectance pro les generated by the model using high-chlorophyll low-

chlorophyll and chlorotic leaves of LAI from 1 to 5 in the top canopy are givenin gure 7

D W L amb et al3628

Figure 4 Schematic diagram of the eld-portable spectrometer used for acquiring soilre ectance spectra

421 T he eVect of increasing L AI on the magnitude of peaks in the derivativespectra

Derivative spectra corresponding to gure 7 are given in gure 8 It is evidenthere that increasing the LAI of the top canopy produces a signi cant increase in themagnitude of the second peak in the derivative spectra a phenomena supported bythe experimental observations of Horler et al (1983) using maize leaves

In the case of low-chlorophyll ( gure 8(b)) and chlorotic ( gure 8(c)) leaves themagnitude of the rst peak is initially comparable to or larger than that of thesecond peak at low LAI The substantial increase in magnitude of the second peakwith increasing LAI is linked to an increase in the magnitude of the NIR plateau inthe individual re ectance pro les ( gure 7) This is attributed to signi cantly greatermultiple scattering of radiation within the canopy in NIR red wavelengths due tohigher leaf re ectance and transmittance

The eVect of multiple scattering can be veri ed by modifying the transmittancecharacteristics of one of the candidate leaf types For example if the transmittanceof a low-chlorophyll leaf is arti cially reduced at higher wavelengths as depicted in gure 9 then signi cantly smaller increases in the magnitude of the second peakwith increasing LAI are observed ( gure 10)

422 Extracting red-edge parameters from the derivative spectraExamples of modelled re ectance spectra for high and low chlorophyll-containing

ryegrass canopies (LAI=1) are reproduced in gure 11 Superimposed on there ectance and corresponding derivative spectra ( gure 12) are tted curves corres-ponding to tting a single inverted Gaussian (equation (6)mdashtable 1) and a combina-tion of three sigmoid functions (equation (7)mdashtable 1) to the re ectance pro lesThe extracted red-edge wavelengths (lP ) and the sum of squared residuals (SSR) ofthe respective tted curves are also listed in table 2

Estimating leaf nitrogen concentration 3629

(a)

(b)

Figure 5 (a) Measured re ectance spectra for single ryegrass leaves (high- and low-chlorophyll chlorotic and dead) and bare soil (b) Single-leaf transmittance spectrafor high and low chlorophyll content chlorotic and dead ryegrass leaves

It is evident from gures 11 and 12 that like the single-leaf spectra of gure 6the shape of the chlorophyll red-edge for ryegrass canopies is complex containingtwo local maxima in the gradient at approximately 705 and 725 nm respectively

Single and combinations of two three and four sigmoid functions were used toconstruct curves to reproduce the observed re ectance pro les In all cases the useof three sigmoids was found to yield the lowest SSR values and always considerablylower SSR values than the tted Gaussian curve (table 2) In most test cases thethree sigmoids resulting from the tting procedure comprised two sigmoids of positivegain and amplitude (gn and Anmdashtable 1) corresponding to the two peaks observedin the derivative spectra hitherto referred to as l1 and l2 respectively as well as athird sigmoid with a relatively small negative gain In the particular though repres-entative examples of table 2 the wavelength of the third sigmoid (in brackets)corresponds to the location of the peak chlorophyll absorption of red light where are ectance minimum is observed in the re ectance pro les ( gure 11)

D W L amb et al3630

Figure 6 Single-leaf derivative re ectance spectra (dRdl) for high- and low-chlorophylland chlorotic ryegrass

As observed in the results of Miller et al (1990) the single red-edge wavelengthpredicted by the Gaussian tting routine lies between the two peaks observed in thecomplex derivative spectra As expected (Miller et al 1990 Pinar and Curran 1996)both the single red-edge peak resulting from the Gaussian analysis and the twopeaks resulting from the sigmoid- tting procedure have shifted to higher wavelengthsin response to higher leaf nitrogen content (higher chlorophyll )

423 T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectraThe wavelengths corresponding to both peaks in the derivative spectra of the

calculated re ectance pro les were extracted following the procedure outlined aboveThe eVects of increasing LAI on the wavelengths of the two peaks are summarizedin gure 13

It is evident from these model results that increasing LAI progressively shiftsboth derivative peaks towards longer wavelengths Progressively stacking leaves willeVectively increase total chlorophyll absorption experienced by the incident radiationthrough multiple scattering thereby shifting the derivative peaks to higher wave-lengths The magnitude of the wavelength shift resulting from increasing LAI from1 to 10 is greater for the second peak ( gure 13(b)) This is not surprising given thehigher leaf transmittance and re ectance in the associated wavelength range(724ndash740nm) ( gure 5 table 3) This eVect is also observed to occur for the rstpeak ( gure 13(a)) although to a lesser extent due to lower leaf re ectance andtransmittance in the corresponding wavelength range (702ndash709nm) ( gure 5 table 3)

There is a partial overlap of the curve shoulders in gure 13 for a small range ofred-edge wavelengths The overlap of the rst peak occurs for wavelengths703ndash7042nm and for the second peak is 726ndash730nm This overlap demonstratesthe confounding in uence of leaf chlorophyll concentration and canopy LAI on

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3622

Figure 1 Idealized (a) re ectance and (b) derivative spectrum for typical chlorophyll-containing vegetation

peaks changes from that where the rst peak is larger (lsquophase 1rsquo) to that where thesecond peak is larger (lsquophase 2rsquo) Results suggest this transition occurs as the chloro-phyll concentration in single leaves increases or as a result of multiple scatteringbetween leaves The higher gradient of red-edge wavelength versus chlorophyll con-centration for phase 2 compared to phase 1 is likely the result of the second peakresponding to total chlorophyll content ( leaf chlorophyll concentrationtimesbiomass)

When a single Gaussian curve is tted to the chlorophyll red-edge the retrieved

Estimating leaf nitrogen concentration 3623

single red-edge wavelength will lie between the two derivative peaks as evidenced in gure 1(a) of Miller et al (1990) The retrieved lsquoaveragersquo red-edge wavelength willyield stronger correlations with chlorophyll content than chlorophyll concentration(Miller et al 1990 Pinar and Curran 1996) because the average wavelength isin uenced by the entire red-edge a combination of chlorophyll concentration ( rstpeak in the derivative spectrum) and chlorophyll concentrationleaf biomass (secondpeak in the derivative spectrum) Conversely the same phenomenon reduces thestrength of the correlation between the average red-edge wavelength and totalbiomass alone (for example Pinar and Curran 1996)

Our understanding of the in uence of chlorophyll concentration and multipleleaf scattering on the two peaks observed in the derivative spectra of plant canopiesis based on a very small number of experimental observations (Horler et al 1983Boochs et al 1990) For example Horler et al (1983) demonstrated that progressivelystacking single maize (Zea mays L) leaves resulted in a signi cant increase in themagnitude of the second peak in the derivative spectra with little change to themagnitude and wavelength of the rst peak This suggests the wavelength of the rstpeak may be insensitive to Leaf Area Index (LAI) the parameter that speci es theaverage number of leaves encountered in a vertical traverse through a canopyFurthermore derivative spectra acquired at spatial intervals along a single leafwhere changes in chlorophyll concentration would be expected showed signi cantdiVerences in the magnitude of the rst peak in the derivative spectra and no changein the second multiple scattering component Miller et al (1990) demonstratedsimilar although less dramatic results for leaf stacking using leaves of Bur oak(Quercus macrocarpa) However to date such experimental evidence is yet to besupported by plant canopy model calculations

Our own interest in the eVects of chlorophyll concentration and multiple scat-tering on the shape of the derivative spectra is motivated by our programme ofresearch investigating spectroscopic methods of estimating nitrogen content of dairypastures in the Waikato region of New Zealand (Lat 38deg S) We seek a simplemethodology for estimating leaf nitrogen concentration which avoids the need forphysical measurements of plant biophysical parameters such as biomass The chloro-phyll red-edge is a suitable candidate since plant nitrogen status is often related tochlorophyll content (Everitt et al 1985 Boochs et al 1990) and experimental resultsin unrelated plant types have suggested that the rst peak in the derivative spectramay be insensitive to changes in biomass (or LAI) (Horler et al 1983 Boochset al 1990)

Ryegrass (L olium spp) is a key component of irrigated and rain-fed dairy pasturesin the moist temperate Waikato region of New Zealand Typical Waikato dairypastures include the ryegrass and clover (T rifolium subterranean L) in various mixesranging from pure ryegrass to an approximate mix of 80 ryegrass15 cloverPasture biomass ranges from 200 to 4000kg (dry weight) per hectare LAI from 1up to as high as 12 and moisture content from 70 in summer to 85 in earlywinter (Hanna et al 1999) Typical leaf nitrogen concentrations in the ryegrasscomponent of the pasture is observed to range from 2 to 5 by mass

As a rst step in our investigation of the chlorophyll red-edge we wish to verifythe in uence of chlorophyll concentration and canopy biomass on the shape andlocation of the peaks in the derivative spectra of pure ryegrass In this paper atheoretical two-layer pasture canopy model previously reported in Hanna et al(1999) has been constructed to calculate detailed spectral re ectance curves and

D W L amb et al3624

consequently derivative spectra of a realistic ryegrass pasture canopy for varyinglevels of leaf chlorophyll concentration and biomass In these calculations canopybiomass is expressed through LAI Increasing the LAI of the top canopy for a givensingle leaf type is equivalent to xing the chlorophyll concentration but increasingtotal chlorophyll traversed by the incident radiation within the canopy In order tocon gure the model to represent a ryegrass pasture canopy detailed spectralre ectiontransmission characteristics for ryegrass and soil have also been measuredFurthermore we investigate an alternative method for extracting descriptors of thechlorophyll red-edge speci cally the peak wavelengths from the complex derivativespectra of ryegrass canopies and compare this approach with the standard approachof tting a single inverted Gaussian to the re ectance pro les The results ofthe model calculations are discussed in terms of practical requirements of usingchlorophyll red-edge to estimate leaf nitrogen concentration in ryegrass pastures

Following veri cation of the nature of the derivative spectra of ryegrass canopiesthe alternative method of extracting red-edge descriptors is then applied to measuredspectral re ectance pro les of 100 sample sites of diVerent canopy biomass and leafnitrogen levels to estimate leaf nitrogen concentration and total nitrogen content

2 Two-layer canopy re ectance modelThe two-layer canopy re ectance model previously described in Hanna et al

(1999) is based on the analytical solution of a two-stream plant canopy model(Sellers 1985) which has the governing equations

mdIldt

=Ilshy vl(1 shy bl )Il

shy vl bl I3lshy vl b0 mke Otilde kt (1)

shy mAringdI3

ldt

=I3lshy vl (1 shy bl )I3

lshy vl bl Il

shy vl (1 shy b0 )mke Otilde kt (2)

Here m is the average inverse diVuse optical depth per unit leaf area in the canopyIl and I3

l are the wavelength-dependent upward and downward diVuse uxes dividedby the incident solar ux t is the canopy LAI vl is the sum of the wavelength-dependent single leaf re ectance rl and transmittance tl bl is the wavelength-dependent backscatter distribution function for the diVuse beam b0 is the backscatterparameter for the incident beam and k is the optical depth of the direct beam perunit leaf area

The two-layer canopy model is generated by solving equations (1) and (2) for Iand I3using appropriate boundary conditions for each speci ed layer (see Appendixfor details) The wavelength-dependent canopy re ectance is computed using

RlnotIl(t=0) (3)

where t=0 corresponds to the top of the canopyA simpli ed diagram of the two-layer ryegrass pasture represented in the model

is given in gure 2 and a detailed schematic is given in gure A1 In this model wespecify the spectral characteristics and LAI of the top pasture canopy ( layer a) alayer of dead material which usually exists within the pasture pro le ( layer b) andthe re ectance characteristics of the underlying soil The LAI of the layer of deadmaterial was set to unity and the LAI of the top ryegrass was canopy varied over

Estimating leaf nitrogen concentration 3625

Figure 2 Simpli ed diagram of the two-layer ryegrass canopy represented in the model

the range of 1ndash10 to mimic the pasture conditions we observed during a number of eld visitations

3 Single-leaf and soil spectral characteristicsIn order to apply equations (1) and (2) to the model the two-layer theory

requires detailed single leaf re ectance and transmittance data for each canopy layerand re ectance data for the underlying soil In the previous work of Hanna et al(1999) involving only three re ectance wavebands (NIR red and green) the modelwas run using a combination of actual and synthetic maize data since appropriateryegrass data were unavailable In this current work however the necessary re ectionand transmission characteristics of fresh ryegrass leaves were acquired from laborat-ory measurements and soil re ectance measurements acquired from outdoormeasurements

31 Single-leaf re ectance and transmittance dataRe ectance and transmittance measurements were completed on single high- and

low-chlorophyll content chlorotic (very low chlorophyll content) and dead ryegrassleaves Single leaves were sampled from pure ryegrass plots used in a long-termfertilizer treatment program by the Dairy Research Institute Hamilton New ZealandLeaf samples of high and low chlorophyll concentration were hand-picked from400 kg ha and 0 kg ha nitrogen treatment plots respectively Chlorotic leaves thosewith agt50 surface coverage of rust and dead leaf samples were also hand-pickedfrom the 0 kg ha nitrogen plot The ryegrass samples were immediately placed in acooled black plastic bag and transported to the laboratory for subsequent analysis

Re ectance and transmittance measurements were completed using a ZeissMMS-1 Monolithic Miniature Spectrometer (Carl Zeiss OEM SensorikProzeszlig-analytik Oberkochen GmbH) The Zeiss spectrometer comprised a at- eld gratingof 366 lines mm blazed for 330 nm Coupled with a 70 mmtimes2500 mm entrance slitand a 256-pixel linear diode array the spectrometer had a useable wavelength rangeof 305 nm to 1150 nm with 33 nm resolution

For re ectance measurements ( gure 3(a)) light from a 40 W quartz tungstenhalogen source (Ocean Optics LS-1 Ocean Optics Inc Dunedin FL USA) wasdirected onto the surface of a clamped leaf specimen via a dual-optical bre couplercomprising a hollow-hexagonal array of multimode bres surrounding a centralmultimode bre (numerical aperture=02 core diameter=400 mm) The central bredirected the re ected light from the leaf surface into the input slit of the Zeissspectrometer For each measurement the leaf was clamped at on the surface ofagt99 re ectance Spectralon re ectance target (SRT-99-100 Labsphere Inc

D W L amb et al3626

Sutton NH USA) and the bre illuminationdetection bundle was placed 95 mmfrom and normal to the leaf surface using a precision spacer Spectra were averagedand recorded using lsquotec5rsquo software (Sensorik und Systemtechnik GmbH) on an IBM-compatible computer The apparent re ectance was determined from the ratio of thelight measured from the leaf surface to that measured from the exposed Spectralonpanel ( leaf removed)

Since the measured intensity of the re ected light included multiple re ectionstransmissions of light from the Spectralon panel through the leaf body it wasassumed that the abaxial and adaxial surface re ectances were equal The leaf surfacere ectance was then calculated from the apparent re ectance following Methy et al(1998) using

rl=(rfrac34l+1) shy atilde (r frac34l+1)2 shy 4(r frac34l shy t2l)

2(4)

where rl is the re ectance of the leaf surface r frac34l is the apparent re ectance asmeasured by the spectrometer and tl is the measured leaf transmittance

Leaf transmittance was measured by directly illuminating the clamped leafsamples from behind using a collimated 100 W quartz tungsten halogen light sourcedirected through a 3 mm thick frosted glass diVusing plate ( gure 3(b)) Transmittedlight was collected by the central bre of the dual-optical bre bundle (describedabove) placed on the downstream side of the leaf and spaced 95 mm from andnormal to the leaf surface Transmittance was calculated by measuring the intensityof light with and without the leaf sample in place

32 Soil re ectanceIn- eld soil re ectance measurements were acquired using the Zeiss MMS-1

spectrometer mounted in a eld-portable con guration complete with arti cial targetillumination source and shroud to block ambient sunlight ( gure 4) The rigid shroudconstructed from 35 mm thick black polyethylene plastic housed the optical brebundle and foreoptic for the Zeiss spectrometer (mounted on top of the shroud) andthe arti cial light source The latter comprised two 20 W quartz tungsten halogenlight bulbs spaced 40 mm on either side of the bre foreoptic The foreoptic andlight sources were held 052 m above the ground at nadir by the rigid shroud Theforeoptic bre bundle provided the spectrometer with a 100mm diameter circularfootprint on the ground equivalent to a eld of view of approximately 55deg

Soil re ectance spectra were acquired and averaged from a number of eldlocations within the Dairy Research Institute Hamilton New Zealand

4 Results of model calculations41 Single leaf and soil spectral characteristics

Measured re ectance and transmittance spectra of single high-and low-chlorophyll chlorotic and dead ryegrass leaves are given in gure 5 The re ectancespectra of bare soil is also included in gure 5(a)

The derivative spectra of the single leaves corresponding to gure 5(a) are givenin gure 6 These were calculated using

AdR

dl Bl

=Rl

shy R(l Otilde 1)Dl

(5)

where Rlshy R(l Otilde 1) is the diVerence in re ectance measured across a single wavelength

increment centred at l and Dl is the wavelength increment of the spectrometer

Estimating leaf nitrogen concentration 3627

(a)

(b)

Figure 3 Schematic diagram showing apparatus used for single leaf (a) re ectance and(b) transmittance measurements

From the curves of gure 6 it is evident that the derivative spectra of the high-and low- chlorophyll and chlorotic leaves contain peaks at both ~705 and ~725 nmFor the low-chlorophyll and chlorotic leaves the rst feature (~705 nm) is dominantIn the high-chlorophyll leaves the second feature (~725nm) is dominant

42 Model predictionsCanopy re ectance pro les generated by the model using high-chlorophyll low-

chlorophyll and chlorotic leaves of LAI from 1 to 5 in the top canopy are givenin gure 7

D W L amb et al3628

Figure 4 Schematic diagram of the eld-portable spectrometer used for acquiring soilre ectance spectra

421 T he eVect of increasing L AI on the magnitude of peaks in the derivativespectra

Derivative spectra corresponding to gure 7 are given in gure 8 It is evidenthere that increasing the LAI of the top canopy produces a signi cant increase in themagnitude of the second peak in the derivative spectra a phenomena supported bythe experimental observations of Horler et al (1983) using maize leaves

In the case of low-chlorophyll ( gure 8(b)) and chlorotic ( gure 8(c)) leaves themagnitude of the rst peak is initially comparable to or larger than that of thesecond peak at low LAI The substantial increase in magnitude of the second peakwith increasing LAI is linked to an increase in the magnitude of the NIR plateau inthe individual re ectance pro les ( gure 7) This is attributed to signi cantly greatermultiple scattering of radiation within the canopy in NIR red wavelengths due tohigher leaf re ectance and transmittance

The eVect of multiple scattering can be veri ed by modifying the transmittancecharacteristics of one of the candidate leaf types For example if the transmittanceof a low-chlorophyll leaf is arti cially reduced at higher wavelengths as depicted in gure 9 then signi cantly smaller increases in the magnitude of the second peakwith increasing LAI are observed ( gure 10)

422 Extracting red-edge parameters from the derivative spectraExamples of modelled re ectance spectra for high and low chlorophyll-containing

ryegrass canopies (LAI=1) are reproduced in gure 11 Superimposed on there ectance and corresponding derivative spectra ( gure 12) are tted curves corres-ponding to tting a single inverted Gaussian (equation (6)mdashtable 1) and a combina-tion of three sigmoid functions (equation (7)mdashtable 1) to the re ectance pro lesThe extracted red-edge wavelengths (lP ) and the sum of squared residuals (SSR) ofthe respective tted curves are also listed in table 2

Estimating leaf nitrogen concentration 3629

(a)

(b)

Figure 5 (a) Measured re ectance spectra for single ryegrass leaves (high- and low-chlorophyll chlorotic and dead) and bare soil (b) Single-leaf transmittance spectrafor high and low chlorophyll content chlorotic and dead ryegrass leaves

It is evident from gures 11 and 12 that like the single-leaf spectra of gure 6the shape of the chlorophyll red-edge for ryegrass canopies is complex containingtwo local maxima in the gradient at approximately 705 and 725 nm respectively

Single and combinations of two three and four sigmoid functions were used toconstruct curves to reproduce the observed re ectance pro les In all cases the useof three sigmoids was found to yield the lowest SSR values and always considerablylower SSR values than the tted Gaussian curve (table 2) In most test cases thethree sigmoids resulting from the tting procedure comprised two sigmoids of positivegain and amplitude (gn and Anmdashtable 1) corresponding to the two peaks observedin the derivative spectra hitherto referred to as l1 and l2 respectively as well as athird sigmoid with a relatively small negative gain In the particular though repres-entative examples of table 2 the wavelength of the third sigmoid (in brackets)corresponds to the location of the peak chlorophyll absorption of red light where are ectance minimum is observed in the re ectance pro les ( gure 11)

D W L amb et al3630

Figure 6 Single-leaf derivative re ectance spectra (dRdl) for high- and low-chlorophylland chlorotic ryegrass

As observed in the results of Miller et al (1990) the single red-edge wavelengthpredicted by the Gaussian tting routine lies between the two peaks observed in thecomplex derivative spectra As expected (Miller et al 1990 Pinar and Curran 1996)both the single red-edge peak resulting from the Gaussian analysis and the twopeaks resulting from the sigmoid- tting procedure have shifted to higher wavelengthsin response to higher leaf nitrogen content (higher chlorophyll )

423 T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectraThe wavelengths corresponding to both peaks in the derivative spectra of the

calculated re ectance pro les were extracted following the procedure outlined aboveThe eVects of increasing LAI on the wavelengths of the two peaks are summarizedin gure 13

It is evident from these model results that increasing LAI progressively shiftsboth derivative peaks towards longer wavelengths Progressively stacking leaves willeVectively increase total chlorophyll absorption experienced by the incident radiationthrough multiple scattering thereby shifting the derivative peaks to higher wave-lengths The magnitude of the wavelength shift resulting from increasing LAI from1 to 10 is greater for the second peak ( gure 13(b)) This is not surprising given thehigher leaf transmittance and re ectance in the associated wavelength range(724ndash740nm) ( gure 5 table 3) This eVect is also observed to occur for the rstpeak ( gure 13(a)) although to a lesser extent due to lower leaf re ectance andtransmittance in the corresponding wavelength range (702ndash709nm) ( gure 5 table 3)

There is a partial overlap of the curve shoulders in gure 13 for a small range ofred-edge wavelengths The overlap of the rst peak occurs for wavelengths703ndash7042nm and for the second peak is 726ndash730nm This overlap demonstratesthe confounding in uence of leaf chlorophyll concentration and canopy LAI on

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3623

single red-edge wavelength will lie between the two derivative peaks as evidenced in gure 1(a) of Miller et al (1990) The retrieved lsquoaveragersquo red-edge wavelength willyield stronger correlations with chlorophyll content than chlorophyll concentration(Miller et al 1990 Pinar and Curran 1996) because the average wavelength isin uenced by the entire red-edge a combination of chlorophyll concentration ( rstpeak in the derivative spectrum) and chlorophyll concentrationleaf biomass (secondpeak in the derivative spectrum) Conversely the same phenomenon reduces thestrength of the correlation between the average red-edge wavelength and totalbiomass alone (for example Pinar and Curran 1996)

Our understanding of the in uence of chlorophyll concentration and multipleleaf scattering on the two peaks observed in the derivative spectra of plant canopiesis based on a very small number of experimental observations (Horler et al 1983Boochs et al 1990) For example Horler et al (1983) demonstrated that progressivelystacking single maize (Zea mays L) leaves resulted in a signi cant increase in themagnitude of the second peak in the derivative spectra with little change to themagnitude and wavelength of the rst peak This suggests the wavelength of the rstpeak may be insensitive to Leaf Area Index (LAI) the parameter that speci es theaverage number of leaves encountered in a vertical traverse through a canopyFurthermore derivative spectra acquired at spatial intervals along a single leafwhere changes in chlorophyll concentration would be expected showed signi cantdiVerences in the magnitude of the rst peak in the derivative spectra and no changein the second multiple scattering component Miller et al (1990) demonstratedsimilar although less dramatic results for leaf stacking using leaves of Bur oak(Quercus macrocarpa) However to date such experimental evidence is yet to besupported by plant canopy model calculations

Our own interest in the eVects of chlorophyll concentration and multiple scat-tering on the shape of the derivative spectra is motivated by our programme ofresearch investigating spectroscopic methods of estimating nitrogen content of dairypastures in the Waikato region of New Zealand (Lat 38deg S) We seek a simplemethodology for estimating leaf nitrogen concentration which avoids the need forphysical measurements of plant biophysical parameters such as biomass The chloro-phyll red-edge is a suitable candidate since plant nitrogen status is often related tochlorophyll content (Everitt et al 1985 Boochs et al 1990) and experimental resultsin unrelated plant types have suggested that the rst peak in the derivative spectramay be insensitive to changes in biomass (or LAI) (Horler et al 1983 Boochset al 1990)

Ryegrass (L olium spp) is a key component of irrigated and rain-fed dairy pasturesin the moist temperate Waikato region of New Zealand Typical Waikato dairypastures include the ryegrass and clover (T rifolium subterranean L) in various mixesranging from pure ryegrass to an approximate mix of 80 ryegrass15 cloverPasture biomass ranges from 200 to 4000kg (dry weight) per hectare LAI from 1up to as high as 12 and moisture content from 70 in summer to 85 in earlywinter (Hanna et al 1999) Typical leaf nitrogen concentrations in the ryegrasscomponent of the pasture is observed to range from 2 to 5 by mass

As a rst step in our investigation of the chlorophyll red-edge we wish to verifythe in uence of chlorophyll concentration and canopy biomass on the shape andlocation of the peaks in the derivative spectra of pure ryegrass In this paper atheoretical two-layer pasture canopy model previously reported in Hanna et al(1999) has been constructed to calculate detailed spectral re ectance curves and

D W L amb et al3624

consequently derivative spectra of a realistic ryegrass pasture canopy for varyinglevels of leaf chlorophyll concentration and biomass In these calculations canopybiomass is expressed through LAI Increasing the LAI of the top canopy for a givensingle leaf type is equivalent to xing the chlorophyll concentration but increasingtotal chlorophyll traversed by the incident radiation within the canopy In order tocon gure the model to represent a ryegrass pasture canopy detailed spectralre ectiontransmission characteristics for ryegrass and soil have also been measuredFurthermore we investigate an alternative method for extracting descriptors of thechlorophyll red-edge speci cally the peak wavelengths from the complex derivativespectra of ryegrass canopies and compare this approach with the standard approachof tting a single inverted Gaussian to the re ectance pro les The results ofthe model calculations are discussed in terms of practical requirements of usingchlorophyll red-edge to estimate leaf nitrogen concentration in ryegrass pastures

Following veri cation of the nature of the derivative spectra of ryegrass canopiesthe alternative method of extracting red-edge descriptors is then applied to measuredspectral re ectance pro les of 100 sample sites of diVerent canopy biomass and leafnitrogen levels to estimate leaf nitrogen concentration and total nitrogen content

2 Two-layer canopy re ectance modelThe two-layer canopy re ectance model previously described in Hanna et al

(1999) is based on the analytical solution of a two-stream plant canopy model(Sellers 1985) which has the governing equations

mdIldt

=Ilshy vl(1 shy bl )Il

shy vl bl I3lshy vl b0 mke Otilde kt (1)

shy mAringdI3

ldt

=I3lshy vl (1 shy bl )I3

lshy vl bl Il

shy vl (1 shy b0 )mke Otilde kt (2)

Here m is the average inverse diVuse optical depth per unit leaf area in the canopyIl and I3

l are the wavelength-dependent upward and downward diVuse uxes dividedby the incident solar ux t is the canopy LAI vl is the sum of the wavelength-dependent single leaf re ectance rl and transmittance tl bl is the wavelength-dependent backscatter distribution function for the diVuse beam b0 is the backscatterparameter for the incident beam and k is the optical depth of the direct beam perunit leaf area

The two-layer canopy model is generated by solving equations (1) and (2) for Iand I3using appropriate boundary conditions for each speci ed layer (see Appendixfor details) The wavelength-dependent canopy re ectance is computed using

RlnotIl(t=0) (3)

where t=0 corresponds to the top of the canopyA simpli ed diagram of the two-layer ryegrass pasture represented in the model

is given in gure 2 and a detailed schematic is given in gure A1 In this model wespecify the spectral characteristics and LAI of the top pasture canopy ( layer a) alayer of dead material which usually exists within the pasture pro le ( layer b) andthe re ectance characteristics of the underlying soil The LAI of the layer of deadmaterial was set to unity and the LAI of the top ryegrass was canopy varied over

Estimating leaf nitrogen concentration 3625

Figure 2 Simpli ed diagram of the two-layer ryegrass canopy represented in the model

the range of 1ndash10 to mimic the pasture conditions we observed during a number of eld visitations

3 Single-leaf and soil spectral characteristicsIn order to apply equations (1) and (2) to the model the two-layer theory

requires detailed single leaf re ectance and transmittance data for each canopy layerand re ectance data for the underlying soil In the previous work of Hanna et al(1999) involving only three re ectance wavebands (NIR red and green) the modelwas run using a combination of actual and synthetic maize data since appropriateryegrass data were unavailable In this current work however the necessary re ectionand transmission characteristics of fresh ryegrass leaves were acquired from laborat-ory measurements and soil re ectance measurements acquired from outdoormeasurements

31 Single-leaf re ectance and transmittance dataRe ectance and transmittance measurements were completed on single high- and

low-chlorophyll content chlorotic (very low chlorophyll content) and dead ryegrassleaves Single leaves were sampled from pure ryegrass plots used in a long-termfertilizer treatment program by the Dairy Research Institute Hamilton New ZealandLeaf samples of high and low chlorophyll concentration were hand-picked from400 kg ha and 0 kg ha nitrogen treatment plots respectively Chlorotic leaves thosewith agt50 surface coverage of rust and dead leaf samples were also hand-pickedfrom the 0 kg ha nitrogen plot The ryegrass samples were immediately placed in acooled black plastic bag and transported to the laboratory for subsequent analysis

Re ectance and transmittance measurements were completed using a ZeissMMS-1 Monolithic Miniature Spectrometer (Carl Zeiss OEM SensorikProzeszlig-analytik Oberkochen GmbH) The Zeiss spectrometer comprised a at- eld gratingof 366 lines mm blazed for 330 nm Coupled with a 70 mmtimes2500 mm entrance slitand a 256-pixel linear diode array the spectrometer had a useable wavelength rangeof 305 nm to 1150 nm with 33 nm resolution

For re ectance measurements ( gure 3(a)) light from a 40 W quartz tungstenhalogen source (Ocean Optics LS-1 Ocean Optics Inc Dunedin FL USA) wasdirected onto the surface of a clamped leaf specimen via a dual-optical bre couplercomprising a hollow-hexagonal array of multimode bres surrounding a centralmultimode bre (numerical aperture=02 core diameter=400 mm) The central bredirected the re ected light from the leaf surface into the input slit of the Zeissspectrometer For each measurement the leaf was clamped at on the surface ofagt99 re ectance Spectralon re ectance target (SRT-99-100 Labsphere Inc

D W L amb et al3626

Sutton NH USA) and the bre illuminationdetection bundle was placed 95 mmfrom and normal to the leaf surface using a precision spacer Spectra were averagedand recorded using lsquotec5rsquo software (Sensorik und Systemtechnik GmbH) on an IBM-compatible computer The apparent re ectance was determined from the ratio of thelight measured from the leaf surface to that measured from the exposed Spectralonpanel ( leaf removed)

Since the measured intensity of the re ected light included multiple re ectionstransmissions of light from the Spectralon panel through the leaf body it wasassumed that the abaxial and adaxial surface re ectances were equal The leaf surfacere ectance was then calculated from the apparent re ectance following Methy et al(1998) using

rl=(rfrac34l+1) shy atilde (r frac34l+1)2 shy 4(r frac34l shy t2l)

2(4)

where rl is the re ectance of the leaf surface r frac34l is the apparent re ectance asmeasured by the spectrometer and tl is the measured leaf transmittance

Leaf transmittance was measured by directly illuminating the clamped leafsamples from behind using a collimated 100 W quartz tungsten halogen light sourcedirected through a 3 mm thick frosted glass diVusing plate ( gure 3(b)) Transmittedlight was collected by the central bre of the dual-optical bre bundle (describedabove) placed on the downstream side of the leaf and spaced 95 mm from andnormal to the leaf surface Transmittance was calculated by measuring the intensityof light with and without the leaf sample in place

32 Soil re ectanceIn- eld soil re ectance measurements were acquired using the Zeiss MMS-1

spectrometer mounted in a eld-portable con guration complete with arti cial targetillumination source and shroud to block ambient sunlight ( gure 4) The rigid shroudconstructed from 35 mm thick black polyethylene plastic housed the optical brebundle and foreoptic for the Zeiss spectrometer (mounted on top of the shroud) andthe arti cial light source The latter comprised two 20 W quartz tungsten halogenlight bulbs spaced 40 mm on either side of the bre foreoptic The foreoptic andlight sources were held 052 m above the ground at nadir by the rigid shroud Theforeoptic bre bundle provided the spectrometer with a 100mm diameter circularfootprint on the ground equivalent to a eld of view of approximately 55deg

Soil re ectance spectra were acquired and averaged from a number of eldlocations within the Dairy Research Institute Hamilton New Zealand

4 Results of model calculations41 Single leaf and soil spectral characteristics

Measured re ectance and transmittance spectra of single high-and low-chlorophyll chlorotic and dead ryegrass leaves are given in gure 5 The re ectancespectra of bare soil is also included in gure 5(a)

The derivative spectra of the single leaves corresponding to gure 5(a) are givenin gure 6 These were calculated using

AdR

dl Bl

=Rl

shy R(l Otilde 1)Dl

(5)

where Rlshy R(l Otilde 1) is the diVerence in re ectance measured across a single wavelength

increment centred at l and Dl is the wavelength increment of the spectrometer

Estimating leaf nitrogen concentration 3627

(a)

(b)

Figure 3 Schematic diagram showing apparatus used for single leaf (a) re ectance and(b) transmittance measurements

From the curves of gure 6 it is evident that the derivative spectra of the high-and low- chlorophyll and chlorotic leaves contain peaks at both ~705 and ~725 nmFor the low-chlorophyll and chlorotic leaves the rst feature (~705 nm) is dominantIn the high-chlorophyll leaves the second feature (~725nm) is dominant

42 Model predictionsCanopy re ectance pro les generated by the model using high-chlorophyll low-

chlorophyll and chlorotic leaves of LAI from 1 to 5 in the top canopy are givenin gure 7

D W L amb et al3628

Figure 4 Schematic diagram of the eld-portable spectrometer used for acquiring soilre ectance spectra

421 T he eVect of increasing L AI on the magnitude of peaks in the derivativespectra

Derivative spectra corresponding to gure 7 are given in gure 8 It is evidenthere that increasing the LAI of the top canopy produces a signi cant increase in themagnitude of the second peak in the derivative spectra a phenomena supported bythe experimental observations of Horler et al (1983) using maize leaves

In the case of low-chlorophyll ( gure 8(b)) and chlorotic ( gure 8(c)) leaves themagnitude of the rst peak is initially comparable to or larger than that of thesecond peak at low LAI The substantial increase in magnitude of the second peakwith increasing LAI is linked to an increase in the magnitude of the NIR plateau inthe individual re ectance pro les ( gure 7) This is attributed to signi cantly greatermultiple scattering of radiation within the canopy in NIR red wavelengths due tohigher leaf re ectance and transmittance

The eVect of multiple scattering can be veri ed by modifying the transmittancecharacteristics of one of the candidate leaf types For example if the transmittanceof a low-chlorophyll leaf is arti cially reduced at higher wavelengths as depicted in gure 9 then signi cantly smaller increases in the magnitude of the second peakwith increasing LAI are observed ( gure 10)

422 Extracting red-edge parameters from the derivative spectraExamples of modelled re ectance spectra for high and low chlorophyll-containing

ryegrass canopies (LAI=1) are reproduced in gure 11 Superimposed on there ectance and corresponding derivative spectra ( gure 12) are tted curves corres-ponding to tting a single inverted Gaussian (equation (6)mdashtable 1) and a combina-tion of three sigmoid functions (equation (7)mdashtable 1) to the re ectance pro lesThe extracted red-edge wavelengths (lP ) and the sum of squared residuals (SSR) ofthe respective tted curves are also listed in table 2

Estimating leaf nitrogen concentration 3629

(a)

(b)

Figure 5 (a) Measured re ectance spectra for single ryegrass leaves (high- and low-chlorophyll chlorotic and dead) and bare soil (b) Single-leaf transmittance spectrafor high and low chlorophyll content chlorotic and dead ryegrass leaves

It is evident from gures 11 and 12 that like the single-leaf spectra of gure 6the shape of the chlorophyll red-edge for ryegrass canopies is complex containingtwo local maxima in the gradient at approximately 705 and 725 nm respectively

Single and combinations of two three and four sigmoid functions were used toconstruct curves to reproduce the observed re ectance pro les In all cases the useof three sigmoids was found to yield the lowest SSR values and always considerablylower SSR values than the tted Gaussian curve (table 2) In most test cases thethree sigmoids resulting from the tting procedure comprised two sigmoids of positivegain and amplitude (gn and Anmdashtable 1) corresponding to the two peaks observedin the derivative spectra hitherto referred to as l1 and l2 respectively as well as athird sigmoid with a relatively small negative gain In the particular though repres-entative examples of table 2 the wavelength of the third sigmoid (in brackets)corresponds to the location of the peak chlorophyll absorption of red light where are ectance minimum is observed in the re ectance pro les ( gure 11)

D W L amb et al3630

Figure 6 Single-leaf derivative re ectance spectra (dRdl) for high- and low-chlorophylland chlorotic ryegrass

As observed in the results of Miller et al (1990) the single red-edge wavelengthpredicted by the Gaussian tting routine lies between the two peaks observed in thecomplex derivative spectra As expected (Miller et al 1990 Pinar and Curran 1996)both the single red-edge peak resulting from the Gaussian analysis and the twopeaks resulting from the sigmoid- tting procedure have shifted to higher wavelengthsin response to higher leaf nitrogen content (higher chlorophyll )

423 T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectraThe wavelengths corresponding to both peaks in the derivative spectra of the

calculated re ectance pro les were extracted following the procedure outlined aboveThe eVects of increasing LAI on the wavelengths of the two peaks are summarizedin gure 13

It is evident from these model results that increasing LAI progressively shiftsboth derivative peaks towards longer wavelengths Progressively stacking leaves willeVectively increase total chlorophyll absorption experienced by the incident radiationthrough multiple scattering thereby shifting the derivative peaks to higher wave-lengths The magnitude of the wavelength shift resulting from increasing LAI from1 to 10 is greater for the second peak ( gure 13(b)) This is not surprising given thehigher leaf transmittance and re ectance in the associated wavelength range(724ndash740nm) ( gure 5 table 3) This eVect is also observed to occur for the rstpeak ( gure 13(a)) although to a lesser extent due to lower leaf re ectance andtransmittance in the corresponding wavelength range (702ndash709nm) ( gure 5 table 3)

There is a partial overlap of the curve shoulders in gure 13 for a small range ofred-edge wavelengths The overlap of the rst peak occurs for wavelengths703ndash7042nm and for the second peak is 726ndash730nm This overlap demonstratesthe confounding in uence of leaf chlorophyll concentration and canopy LAI on

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3624

consequently derivative spectra of a realistic ryegrass pasture canopy for varyinglevels of leaf chlorophyll concentration and biomass In these calculations canopybiomass is expressed through LAI Increasing the LAI of the top canopy for a givensingle leaf type is equivalent to xing the chlorophyll concentration but increasingtotal chlorophyll traversed by the incident radiation within the canopy In order tocon gure the model to represent a ryegrass pasture canopy detailed spectralre ectiontransmission characteristics for ryegrass and soil have also been measuredFurthermore we investigate an alternative method for extracting descriptors of thechlorophyll red-edge speci cally the peak wavelengths from the complex derivativespectra of ryegrass canopies and compare this approach with the standard approachof tting a single inverted Gaussian to the re ectance pro les The results ofthe model calculations are discussed in terms of practical requirements of usingchlorophyll red-edge to estimate leaf nitrogen concentration in ryegrass pastures

Following veri cation of the nature of the derivative spectra of ryegrass canopiesthe alternative method of extracting red-edge descriptors is then applied to measuredspectral re ectance pro les of 100 sample sites of diVerent canopy biomass and leafnitrogen levels to estimate leaf nitrogen concentration and total nitrogen content

2 Two-layer canopy re ectance modelThe two-layer canopy re ectance model previously described in Hanna et al

(1999) is based on the analytical solution of a two-stream plant canopy model(Sellers 1985) which has the governing equations

mdIldt

=Ilshy vl(1 shy bl )Il

shy vl bl I3lshy vl b0 mke Otilde kt (1)

shy mAringdI3

ldt

=I3lshy vl (1 shy bl )I3

lshy vl bl Il

shy vl (1 shy b0 )mke Otilde kt (2)

Here m is the average inverse diVuse optical depth per unit leaf area in the canopyIl and I3

l are the wavelength-dependent upward and downward diVuse uxes dividedby the incident solar ux t is the canopy LAI vl is the sum of the wavelength-dependent single leaf re ectance rl and transmittance tl bl is the wavelength-dependent backscatter distribution function for the diVuse beam b0 is the backscatterparameter for the incident beam and k is the optical depth of the direct beam perunit leaf area

The two-layer canopy model is generated by solving equations (1) and (2) for Iand I3using appropriate boundary conditions for each speci ed layer (see Appendixfor details) The wavelength-dependent canopy re ectance is computed using

RlnotIl(t=0) (3)

where t=0 corresponds to the top of the canopyA simpli ed diagram of the two-layer ryegrass pasture represented in the model

is given in gure 2 and a detailed schematic is given in gure A1 In this model wespecify the spectral characteristics and LAI of the top pasture canopy ( layer a) alayer of dead material which usually exists within the pasture pro le ( layer b) andthe re ectance characteristics of the underlying soil The LAI of the layer of deadmaterial was set to unity and the LAI of the top ryegrass was canopy varied over

Estimating leaf nitrogen concentration 3625

Figure 2 Simpli ed diagram of the two-layer ryegrass canopy represented in the model

the range of 1ndash10 to mimic the pasture conditions we observed during a number of eld visitations

3 Single-leaf and soil spectral characteristicsIn order to apply equations (1) and (2) to the model the two-layer theory

requires detailed single leaf re ectance and transmittance data for each canopy layerand re ectance data for the underlying soil In the previous work of Hanna et al(1999) involving only three re ectance wavebands (NIR red and green) the modelwas run using a combination of actual and synthetic maize data since appropriateryegrass data were unavailable In this current work however the necessary re ectionand transmission characteristics of fresh ryegrass leaves were acquired from laborat-ory measurements and soil re ectance measurements acquired from outdoormeasurements

31 Single-leaf re ectance and transmittance dataRe ectance and transmittance measurements were completed on single high- and

low-chlorophyll content chlorotic (very low chlorophyll content) and dead ryegrassleaves Single leaves were sampled from pure ryegrass plots used in a long-termfertilizer treatment program by the Dairy Research Institute Hamilton New ZealandLeaf samples of high and low chlorophyll concentration were hand-picked from400 kg ha and 0 kg ha nitrogen treatment plots respectively Chlorotic leaves thosewith agt50 surface coverage of rust and dead leaf samples were also hand-pickedfrom the 0 kg ha nitrogen plot The ryegrass samples were immediately placed in acooled black plastic bag and transported to the laboratory for subsequent analysis

Re ectance and transmittance measurements were completed using a ZeissMMS-1 Monolithic Miniature Spectrometer (Carl Zeiss OEM SensorikProzeszlig-analytik Oberkochen GmbH) The Zeiss spectrometer comprised a at- eld gratingof 366 lines mm blazed for 330 nm Coupled with a 70 mmtimes2500 mm entrance slitand a 256-pixel linear diode array the spectrometer had a useable wavelength rangeof 305 nm to 1150 nm with 33 nm resolution

For re ectance measurements ( gure 3(a)) light from a 40 W quartz tungstenhalogen source (Ocean Optics LS-1 Ocean Optics Inc Dunedin FL USA) wasdirected onto the surface of a clamped leaf specimen via a dual-optical bre couplercomprising a hollow-hexagonal array of multimode bres surrounding a centralmultimode bre (numerical aperture=02 core diameter=400 mm) The central bredirected the re ected light from the leaf surface into the input slit of the Zeissspectrometer For each measurement the leaf was clamped at on the surface ofagt99 re ectance Spectralon re ectance target (SRT-99-100 Labsphere Inc

D W L amb et al3626

Sutton NH USA) and the bre illuminationdetection bundle was placed 95 mmfrom and normal to the leaf surface using a precision spacer Spectra were averagedand recorded using lsquotec5rsquo software (Sensorik und Systemtechnik GmbH) on an IBM-compatible computer The apparent re ectance was determined from the ratio of thelight measured from the leaf surface to that measured from the exposed Spectralonpanel ( leaf removed)

Since the measured intensity of the re ected light included multiple re ectionstransmissions of light from the Spectralon panel through the leaf body it wasassumed that the abaxial and adaxial surface re ectances were equal The leaf surfacere ectance was then calculated from the apparent re ectance following Methy et al(1998) using

rl=(rfrac34l+1) shy atilde (r frac34l+1)2 shy 4(r frac34l shy t2l)

2(4)

where rl is the re ectance of the leaf surface r frac34l is the apparent re ectance asmeasured by the spectrometer and tl is the measured leaf transmittance

Leaf transmittance was measured by directly illuminating the clamped leafsamples from behind using a collimated 100 W quartz tungsten halogen light sourcedirected through a 3 mm thick frosted glass diVusing plate ( gure 3(b)) Transmittedlight was collected by the central bre of the dual-optical bre bundle (describedabove) placed on the downstream side of the leaf and spaced 95 mm from andnormal to the leaf surface Transmittance was calculated by measuring the intensityof light with and without the leaf sample in place

32 Soil re ectanceIn- eld soil re ectance measurements were acquired using the Zeiss MMS-1

spectrometer mounted in a eld-portable con guration complete with arti cial targetillumination source and shroud to block ambient sunlight ( gure 4) The rigid shroudconstructed from 35 mm thick black polyethylene plastic housed the optical brebundle and foreoptic for the Zeiss spectrometer (mounted on top of the shroud) andthe arti cial light source The latter comprised two 20 W quartz tungsten halogenlight bulbs spaced 40 mm on either side of the bre foreoptic The foreoptic andlight sources were held 052 m above the ground at nadir by the rigid shroud Theforeoptic bre bundle provided the spectrometer with a 100mm diameter circularfootprint on the ground equivalent to a eld of view of approximately 55deg

Soil re ectance spectra were acquired and averaged from a number of eldlocations within the Dairy Research Institute Hamilton New Zealand

4 Results of model calculations41 Single leaf and soil spectral characteristics

Measured re ectance and transmittance spectra of single high-and low-chlorophyll chlorotic and dead ryegrass leaves are given in gure 5 The re ectancespectra of bare soil is also included in gure 5(a)

The derivative spectra of the single leaves corresponding to gure 5(a) are givenin gure 6 These were calculated using

AdR

dl Bl

=Rl

shy R(l Otilde 1)Dl

(5)

where Rlshy R(l Otilde 1) is the diVerence in re ectance measured across a single wavelength

increment centred at l and Dl is the wavelength increment of the spectrometer

Estimating leaf nitrogen concentration 3627

(a)

(b)

Figure 3 Schematic diagram showing apparatus used for single leaf (a) re ectance and(b) transmittance measurements

From the curves of gure 6 it is evident that the derivative spectra of the high-and low- chlorophyll and chlorotic leaves contain peaks at both ~705 and ~725 nmFor the low-chlorophyll and chlorotic leaves the rst feature (~705 nm) is dominantIn the high-chlorophyll leaves the second feature (~725nm) is dominant

42 Model predictionsCanopy re ectance pro les generated by the model using high-chlorophyll low-

chlorophyll and chlorotic leaves of LAI from 1 to 5 in the top canopy are givenin gure 7

D W L amb et al3628

Figure 4 Schematic diagram of the eld-portable spectrometer used for acquiring soilre ectance spectra

421 T he eVect of increasing L AI on the magnitude of peaks in the derivativespectra

Derivative spectra corresponding to gure 7 are given in gure 8 It is evidenthere that increasing the LAI of the top canopy produces a signi cant increase in themagnitude of the second peak in the derivative spectra a phenomena supported bythe experimental observations of Horler et al (1983) using maize leaves

In the case of low-chlorophyll ( gure 8(b)) and chlorotic ( gure 8(c)) leaves themagnitude of the rst peak is initially comparable to or larger than that of thesecond peak at low LAI The substantial increase in magnitude of the second peakwith increasing LAI is linked to an increase in the magnitude of the NIR plateau inthe individual re ectance pro les ( gure 7) This is attributed to signi cantly greatermultiple scattering of radiation within the canopy in NIR red wavelengths due tohigher leaf re ectance and transmittance

The eVect of multiple scattering can be veri ed by modifying the transmittancecharacteristics of one of the candidate leaf types For example if the transmittanceof a low-chlorophyll leaf is arti cially reduced at higher wavelengths as depicted in gure 9 then signi cantly smaller increases in the magnitude of the second peakwith increasing LAI are observed ( gure 10)

422 Extracting red-edge parameters from the derivative spectraExamples of modelled re ectance spectra for high and low chlorophyll-containing

ryegrass canopies (LAI=1) are reproduced in gure 11 Superimposed on there ectance and corresponding derivative spectra ( gure 12) are tted curves corres-ponding to tting a single inverted Gaussian (equation (6)mdashtable 1) and a combina-tion of three sigmoid functions (equation (7)mdashtable 1) to the re ectance pro lesThe extracted red-edge wavelengths (lP ) and the sum of squared residuals (SSR) ofthe respective tted curves are also listed in table 2

Estimating leaf nitrogen concentration 3629

(a)

(b)

Figure 5 (a) Measured re ectance spectra for single ryegrass leaves (high- and low-chlorophyll chlorotic and dead) and bare soil (b) Single-leaf transmittance spectrafor high and low chlorophyll content chlorotic and dead ryegrass leaves

It is evident from gures 11 and 12 that like the single-leaf spectra of gure 6the shape of the chlorophyll red-edge for ryegrass canopies is complex containingtwo local maxima in the gradient at approximately 705 and 725 nm respectively

Single and combinations of two three and four sigmoid functions were used toconstruct curves to reproduce the observed re ectance pro les In all cases the useof three sigmoids was found to yield the lowest SSR values and always considerablylower SSR values than the tted Gaussian curve (table 2) In most test cases thethree sigmoids resulting from the tting procedure comprised two sigmoids of positivegain and amplitude (gn and Anmdashtable 1) corresponding to the two peaks observedin the derivative spectra hitherto referred to as l1 and l2 respectively as well as athird sigmoid with a relatively small negative gain In the particular though repres-entative examples of table 2 the wavelength of the third sigmoid (in brackets)corresponds to the location of the peak chlorophyll absorption of red light where are ectance minimum is observed in the re ectance pro les ( gure 11)

D W L amb et al3630

Figure 6 Single-leaf derivative re ectance spectra (dRdl) for high- and low-chlorophylland chlorotic ryegrass

As observed in the results of Miller et al (1990) the single red-edge wavelengthpredicted by the Gaussian tting routine lies between the two peaks observed in thecomplex derivative spectra As expected (Miller et al 1990 Pinar and Curran 1996)both the single red-edge peak resulting from the Gaussian analysis and the twopeaks resulting from the sigmoid- tting procedure have shifted to higher wavelengthsin response to higher leaf nitrogen content (higher chlorophyll )

423 T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectraThe wavelengths corresponding to both peaks in the derivative spectra of the

calculated re ectance pro les were extracted following the procedure outlined aboveThe eVects of increasing LAI on the wavelengths of the two peaks are summarizedin gure 13

It is evident from these model results that increasing LAI progressively shiftsboth derivative peaks towards longer wavelengths Progressively stacking leaves willeVectively increase total chlorophyll absorption experienced by the incident radiationthrough multiple scattering thereby shifting the derivative peaks to higher wave-lengths The magnitude of the wavelength shift resulting from increasing LAI from1 to 10 is greater for the second peak ( gure 13(b)) This is not surprising given thehigher leaf transmittance and re ectance in the associated wavelength range(724ndash740nm) ( gure 5 table 3) This eVect is also observed to occur for the rstpeak ( gure 13(a)) although to a lesser extent due to lower leaf re ectance andtransmittance in the corresponding wavelength range (702ndash709nm) ( gure 5 table 3)

There is a partial overlap of the curve shoulders in gure 13 for a small range ofred-edge wavelengths The overlap of the rst peak occurs for wavelengths703ndash7042nm and for the second peak is 726ndash730nm This overlap demonstratesthe confounding in uence of leaf chlorophyll concentration and canopy LAI on

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3625

Figure 2 Simpli ed diagram of the two-layer ryegrass canopy represented in the model

the range of 1ndash10 to mimic the pasture conditions we observed during a number of eld visitations

3 Single-leaf and soil spectral characteristicsIn order to apply equations (1) and (2) to the model the two-layer theory

requires detailed single leaf re ectance and transmittance data for each canopy layerand re ectance data for the underlying soil In the previous work of Hanna et al(1999) involving only three re ectance wavebands (NIR red and green) the modelwas run using a combination of actual and synthetic maize data since appropriateryegrass data were unavailable In this current work however the necessary re ectionand transmission characteristics of fresh ryegrass leaves were acquired from laborat-ory measurements and soil re ectance measurements acquired from outdoormeasurements

31 Single-leaf re ectance and transmittance dataRe ectance and transmittance measurements were completed on single high- and

low-chlorophyll content chlorotic (very low chlorophyll content) and dead ryegrassleaves Single leaves were sampled from pure ryegrass plots used in a long-termfertilizer treatment program by the Dairy Research Institute Hamilton New ZealandLeaf samples of high and low chlorophyll concentration were hand-picked from400 kg ha and 0 kg ha nitrogen treatment plots respectively Chlorotic leaves thosewith agt50 surface coverage of rust and dead leaf samples were also hand-pickedfrom the 0 kg ha nitrogen plot The ryegrass samples were immediately placed in acooled black plastic bag and transported to the laboratory for subsequent analysis

Re ectance and transmittance measurements were completed using a ZeissMMS-1 Monolithic Miniature Spectrometer (Carl Zeiss OEM SensorikProzeszlig-analytik Oberkochen GmbH) The Zeiss spectrometer comprised a at- eld gratingof 366 lines mm blazed for 330 nm Coupled with a 70 mmtimes2500 mm entrance slitand a 256-pixel linear diode array the spectrometer had a useable wavelength rangeof 305 nm to 1150 nm with 33 nm resolution

For re ectance measurements ( gure 3(a)) light from a 40 W quartz tungstenhalogen source (Ocean Optics LS-1 Ocean Optics Inc Dunedin FL USA) wasdirected onto the surface of a clamped leaf specimen via a dual-optical bre couplercomprising a hollow-hexagonal array of multimode bres surrounding a centralmultimode bre (numerical aperture=02 core diameter=400 mm) The central bredirected the re ected light from the leaf surface into the input slit of the Zeissspectrometer For each measurement the leaf was clamped at on the surface ofagt99 re ectance Spectralon re ectance target (SRT-99-100 Labsphere Inc

D W L amb et al3626

Sutton NH USA) and the bre illuminationdetection bundle was placed 95 mmfrom and normal to the leaf surface using a precision spacer Spectra were averagedand recorded using lsquotec5rsquo software (Sensorik und Systemtechnik GmbH) on an IBM-compatible computer The apparent re ectance was determined from the ratio of thelight measured from the leaf surface to that measured from the exposed Spectralonpanel ( leaf removed)

Since the measured intensity of the re ected light included multiple re ectionstransmissions of light from the Spectralon panel through the leaf body it wasassumed that the abaxial and adaxial surface re ectances were equal The leaf surfacere ectance was then calculated from the apparent re ectance following Methy et al(1998) using

rl=(rfrac34l+1) shy atilde (r frac34l+1)2 shy 4(r frac34l shy t2l)

2(4)

where rl is the re ectance of the leaf surface r frac34l is the apparent re ectance asmeasured by the spectrometer and tl is the measured leaf transmittance

Leaf transmittance was measured by directly illuminating the clamped leafsamples from behind using a collimated 100 W quartz tungsten halogen light sourcedirected through a 3 mm thick frosted glass diVusing plate ( gure 3(b)) Transmittedlight was collected by the central bre of the dual-optical bre bundle (describedabove) placed on the downstream side of the leaf and spaced 95 mm from andnormal to the leaf surface Transmittance was calculated by measuring the intensityof light with and without the leaf sample in place

32 Soil re ectanceIn- eld soil re ectance measurements were acquired using the Zeiss MMS-1

spectrometer mounted in a eld-portable con guration complete with arti cial targetillumination source and shroud to block ambient sunlight ( gure 4) The rigid shroudconstructed from 35 mm thick black polyethylene plastic housed the optical brebundle and foreoptic for the Zeiss spectrometer (mounted on top of the shroud) andthe arti cial light source The latter comprised two 20 W quartz tungsten halogenlight bulbs spaced 40 mm on either side of the bre foreoptic The foreoptic andlight sources were held 052 m above the ground at nadir by the rigid shroud Theforeoptic bre bundle provided the spectrometer with a 100mm diameter circularfootprint on the ground equivalent to a eld of view of approximately 55deg

Soil re ectance spectra were acquired and averaged from a number of eldlocations within the Dairy Research Institute Hamilton New Zealand

4 Results of model calculations41 Single leaf and soil spectral characteristics

Measured re ectance and transmittance spectra of single high-and low-chlorophyll chlorotic and dead ryegrass leaves are given in gure 5 The re ectancespectra of bare soil is also included in gure 5(a)

The derivative spectra of the single leaves corresponding to gure 5(a) are givenin gure 6 These were calculated using

AdR

dl Bl

=Rl

shy R(l Otilde 1)Dl

(5)

where Rlshy R(l Otilde 1) is the diVerence in re ectance measured across a single wavelength

increment centred at l and Dl is the wavelength increment of the spectrometer

Estimating leaf nitrogen concentration 3627

(a)

(b)

Figure 3 Schematic diagram showing apparatus used for single leaf (a) re ectance and(b) transmittance measurements

From the curves of gure 6 it is evident that the derivative spectra of the high-and low- chlorophyll and chlorotic leaves contain peaks at both ~705 and ~725 nmFor the low-chlorophyll and chlorotic leaves the rst feature (~705 nm) is dominantIn the high-chlorophyll leaves the second feature (~725nm) is dominant

42 Model predictionsCanopy re ectance pro les generated by the model using high-chlorophyll low-

chlorophyll and chlorotic leaves of LAI from 1 to 5 in the top canopy are givenin gure 7

D W L amb et al3628

Figure 4 Schematic diagram of the eld-portable spectrometer used for acquiring soilre ectance spectra

421 T he eVect of increasing L AI on the magnitude of peaks in the derivativespectra

Derivative spectra corresponding to gure 7 are given in gure 8 It is evidenthere that increasing the LAI of the top canopy produces a signi cant increase in themagnitude of the second peak in the derivative spectra a phenomena supported bythe experimental observations of Horler et al (1983) using maize leaves

In the case of low-chlorophyll ( gure 8(b)) and chlorotic ( gure 8(c)) leaves themagnitude of the rst peak is initially comparable to or larger than that of thesecond peak at low LAI The substantial increase in magnitude of the second peakwith increasing LAI is linked to an increase in the magnitude of the NIR plateau inthe individual re ectance pro les ( gure 7) This is attributed to signi cantly greatermultiple scattering of radiation within the canopy in NIR red wavelengths due tohigher leaf re ectance and transmittance

The eVect of multiple scattering can be veri ed by modifying the transmittancecharacteristics of one of the candidate leaf types For example if the transmittanceof a low-chlorophyll leaf is arti cially reduced at higher wavelengths as depicted in gure 9 then signi cantly smaller increases in the magnitude of the second peakwith increasing LAI are observed ( gure 10)

422 Extracting red-edge parameters from the derivative spectraExamples of modelled re ectance spectra for high and low chlorophyll-containing

ryegrass canopies (LAI=1) are reproduced in gure 11 Superimposed on there ectance and corresponding derivative spectra ( gure 12) are tted curves corres-ponding to tting a single inverted Gaussian (equation (6)mdashtable 1) and a combina-tion of three sigmoid functions (equation (7)mdashtable 1) to the re ectance pro lesThe extracted red-edge wavelengths (lP ) and the sum of squared residuals (SSR) ofthe respective tted curves are also listed in table 2

Estimating leaf nitrogen concentration 3629

(a)

(b)

Figure 5 (a) Measured re ectance spectra for single ryegrass leaves (high- and low-chlorophyll chlorotic and dead) and bare soil (b) Single-leaf transmittance spectrafor high and low chlorophyll content chlorotic and dead ryegrass leaves

It is evident from gures 11 and 12 that like the single-leaf spectra of gure 6the shape of the chlorophyll red-edge for ryegrass canopies is complex containingtwo local maxima in the gradient at approximately 705 and 725 nm respectively

Single and combinations of two three and four sigmoid functions were used toconstruct curves to reproduce the observed re ectance pro les In all cases the useof three sigmoids was found to yield the lowest SSR values and always considerablylower SSR values than the tted Gaussian curve (table 2) In most test cases thethree sigmoids resulting from the tting procedure comprised two sigmoids of positivegain and amplitude (gn and Anmdashtable 1) corresponding to the two peaks observedin the derivative spectra hitherto referred to as l1 and l2 respectively as well as athird sigmoid with a relatively small negative gain In the particular though repres-entative examples of table 2 the wavelength of the third sigmoid (in brackets)corresponds to the location of the peak chlorophyll absorption of red light where are ectance minimum is observed in the re ectance pro les ( gure 11)

D W L amb et al3630

Figure 6 Single-leaf derivative re ectance spectra (dRdl) for high- and low-chlorophylland chlorotic ryegrass

As observed in the results of Miller et al (1990) the single red-edge wavelengthpredicted by the Gaussian tting routine lies between the two peaks observed in thecomplex derivative spectra As expected (Miller et al 1990 Pinar and Curran 1996)both the single red-edge peak resulting from the Gaussian analysis and the twopeaks resulting from the sigmoid- tting procedure have shifted to higher wavelengthsin response to higher leaf nitrogen content (higher chlorophyll )

423 T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectraThe wavelengths corresponding to both peaks in the derivative spectra of the

calculated re ectance pro les were extracted following the procedure outlined aboveThe eVects of increasing LAI on the wavelengths of the two peaks are summarizedin gure 13

It is evident from these model results that increasing LAI progressively shiftsboth derivative peaks towards longer wavelengths Progressively stacking leaves willeVectively increase total chlorophyll absorption experienced by the incident radiationthrough multiple scattering thereby shifting the derivative peaks to higher wave-lengths The magnitude of the wavelength shift resulting from increasing LAI from1 to 10 is greater for the second peak ( gure 13(b)) This is not surprising given thehigher leaf transmittance and re ectance in the associated wavelength range(724ndash740nm) ( gure 5 table 3) This eVect is also observed to occur for the rstpeak ( gure 13(a)) although to a lesser extent due to lower leaf re ectance andtransmittance in the corresponding wavelength range (702ndash709nm) ( gure 5 table 3)

There is a partial overlap of the curve shoulders in gure 13 for a small range ofred-edge wavelengths The overlap of the rst peak occurs for wavelengths703ndash7042nm and for the second peak is 726ndash730nm This overlap demonstratesthe confounding in uence of leaf chlorophyll concentration and canopy LAI on

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3626

Sutton NH USA) and the bre illuminationdetection bundle was placed 95 mmfrom and normal to the leaf surface using a precision spacer Spectra were averagedand recorded using lsquotec5rsquo software (Sensorik und Systemtechnik GmbH) on an IBM-compatible computer The apparent re ectance was determined from the ratio of thelight measured from the leaf surface to that measured from the exposed Spectralonpanel ( leaf removed)

Since the measured intensity of the re ected light included multiple re ectionstransmissions of light from the Spectralon panel through the leaf body it wasassumed that the abaxial and adaxial surface re ectances were equal The leaf surfacere ectance was then calculated from the apparent re ectance following Methy et al(1998) using

rl=(rfrac34l+1) shy atilde (r frac34l+1)2 shy 4(r frac34l shy t2l)

2(4)

where rl is the re ectance of the leaf surface r frac34l is the apparent re ectance asmeasured by the spectrometer and tl is the measured leaf transmittance

Leaf transmittance was measured by directly illuminating the clamped leafsamples from behind using a collimated 100 W quartz tungsten halogen light sourcedirected through a 3 mm thick frosted glass diVusing plate ( gure 3(b)) Transmittedlight was collected by the central bre of the dual-optical bre bundle (describedabove) placed on the downstream side of the leaf and spaced 95 mm from andnormal to the leaf surface Transmittance was calculated by measuring the intensityof light with and without the leaf sample in place

32 Soil re ectanceIn- eld soil re ectance measurements were acquired using the Zeiss MMS-1

spectrometer mounted in a eld-portable con guration complete with arti cial targetillumination source and shroud to block ambient sunlight ( gure 4) The rigid shroudconstructed from 35 mm thick black polyethylene plastic housed the optical brebundle and foreoptic for the Zeiss spectrometer (mounted on top of the shroud) andthe arti cial light source The latter comprised two 20 W quartz tungsten halogenlight bulbs spaced 40 mm on either side of the bre foreoptic The foreoptic andlight sources were held 052 m above the ground at nadir by the rigid shroud Theforeoptic bre bundle provided the spectrometer with a 100mm diameter circularfootprint on the ground equivalent to a eld of view of approximately 55deg

Soil re ectance spectra were acquired and averaged from a number of eldlocations within the Dairy Research Institute Hamilton New Zealand

4 Results of model calculations41 Single leaf and soil spectral characteristics

Measured re ectance and transmittance spectra of single high-and low-chlorophyll chlorotic and dead ryegrass leaves are given in gure 5 The re ectancespectra of bare soil is also included in gure 5(a)

The derivative spectra of the single leaves corresponding to gure 5(a) are givenin gure 6 These were calculated using

AdR

dl Bl

=Rl

shy R(l Otilde 1)Dl

(5)

where Rlshy R(l Otilde 1) is the diVerence in re ectance measured across a single wavelength

increment centred at l and Dl is the wavelength increment of the spectrometer

Estimating leaf nitrogen concentration 3627

(a)

(b)

Figure 3 Schematic diagram showing apparatus used for single leaf (a) re ectance and(b) transmittance measurements

From the curves of gure 6 it is evident that the derivative spectra of the high-and low- chlorophyll and chlorotic leaves contain peaks at both ~705 and ~725 nmFor the low-chlorophyll and chlorotic leaves the rst feature (~705 nm) is dominantIn the high-chlorophyll leaves the second feature (~725nm) is dominant

42 Model predictionsCanopy re ectance pro les generated by the model using high-chlorophyll low-

chlorophyll and chlorotic leaves of LAI from 1 to 5 in the top canopy are givenin gure 7

D W L amb et al3628

Figure 4 Schematic diagram of the eld-portable spectrometer used for acquiring soilre ectance spectra

421 T he eVect of increasing L AI on the magnitude of peaks in the derivativespectra

Derivative spectra corresponding to gure 7 are given in gure 8 It is evidenthere that increasing the LAI of the top canopy produces a signi cant increase in themagnitude of the second peak in the derivative spectra a phenomena supported bythe experimental observations of Horler et al (1983) using maize leaves

In the case of low-chlorophyll ( gure 8(b)) and chlorotic ( gure 8(c)) leaves themagnitude of the rst peak is initially comparable to or larger than that of thesecond peak at low LAI The substantial increase in magnitude of the second peakwith increasing LAI is linked to an increase in the magnitude of the NIR plateau inthe individual re ectance pro les ( gure 7) This is attributed to signi cantly greatermultiple scattering of radiation within the canopy in NIR red wavelengths due tohigher leaf re ectance and transmittance

The eVect of multiple scattering can be veri ed by modifying the transmittancecharacteristics of one of the candidate leaf types For example if the transmittanceof a low-chlorophyll leaf is arti cially reduced at higher wavelengths as depicted in gure 9 then signi cantly smaller increases in the magnitude of the second peakwith increasing LAI are observed ( gure 10)

422 Extracting red-edge parameters from the derivative spectraExamples of modelled re ectance spectra for high and low chlorophyll-containing

ryegrass canopies (LAI=1) are reproduced in gure 11 Superimposed on there ectance and corresponding derivative spectra ( gure 12) are tted curves corres-ponding to tting a single inverted Gaussian (equation (6)mdashtable 1) and a combina-tion of three sigmoid functions (equation (7)mdashtable 1) to the re ectance pro lesThe extracted red-edge wavelengths (lP ) and the sum of squared residuals (SSR) ofthe respective tted curves are also listed in table 2

Estimating leaf nitrogen concentration 3629

(a)

(b)

Figure 5 (a) Measured re ectance spectra for single ryegrass leaves (high- and low-chlorophyll chlorotic and dead) and bare soil (b) Single-leaf transmittance spectrafor high and low chlorophyll content chlorotic and dead ryegrass leaves

It is evident from gures 11 and 12 that like the single-leaf spectra of gure 6the shape of the chlorophyll red-edge for ryegrass canopies is complex containingtwo local maxima in the gradient at approximately 705 and 725 nm respectively

Single and combinations of two three and four sigmoid functions were used toconstruct curves to reproduce the observed re ectance pro les In all cases the useof three sigmoids was found to yield the lowest SSR values and always considerablylower SSR values than the tted Gaussian curve (table 2) In most test cases thethree sigmoids resulting from the tting procedure comprised two sigmoids of positivegain and amplitude (gn and Anmdashtable 1) corresponding to the two peaks observedin the derivative spectra hitherto referred to as l1 and l2 respectively as well as athird sigmoid with a relatively small negative gain In the particular though repres-entative examples of table 2 the wavelength of the third sigmoid (in brackets)corresponds to the location of the peak chlorophyll absorption of red light where are ectance minimum is observed in the re ectance pro les ( gure 11)

D W L amb et al3630

Figure 6 Single-leaf derivative re ectance spectra (dRdl) for high- and low-chlorophylland chlorotic ryegrass

As observed in the results of Miller et al (1990) the single red-edge wavelengthpredicted by the Gaussian tting routine lies between the two peaks observed in thecomplex derivative spectra As expected (Miller et al 1990 Pinar and Curran 1996)both the single red-edge peak resulting from the Gaussian analysis and the twopeaks resulting from the sigmoid- tting procedure have shifted to higher wavelengthsin response to higher leaf nitrogen content (higher chlorophyll )

423 T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectraThe wavelengths corresponding to both peaks in the derivative spectra of the

calculated re ectance pro les were extracted following the procedure outlined aboveThe eVects of increasing LAI on the wavelengths of the two peaks are summarizedin gure 13

It is evident from these model results that increasing LAI progressively shiftsboth derivative peaks towards longer wavelengths Progressively stacking leaves willeVectively increase total chlorophyll absorption experienced by the incident radiationthrough multiple scattering thereby shifting the derivative peaks to higher wave-lengths The magnitude of the wavelength shift resulting from increasing LAI from1 to 10 is greater for the second peak ( gure 13(b)) This is not surprising given thehigher leaf transmittance and re ectance in the associated wavelength range(724ndash740nm) ( gure 5 table 3) This eVect is also observed to occur for the rstpeak ( gure 13(a)) although to a lesser extent due to lower leaf re ectance andtransmittance in the corresponding wavelength range (702ndash709nm) ( gure 5 table 3)

There is a partial overlap of the curve shoulders in gure 13 for a small range ofred-edge wavelengths The overlap of the rst peak occurs for wavelengths703ndash7042nm and for the second peak is 726ndash730nm This overlap demonstratesthe confounding in uence of leaf chlorophyll concentration and canopy LAI on

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3627

(a)

(b)

Figure 3 Schematic diagram showing apparatus used for single leaf (a) re ectance and(b) transmittance measurements

From the curves of gure 6 it is evident that the derivative spectra of the high-and low- chlorophyll and chlorotic leaves contain peaks at both ~705 and ~725 nmFor the low-chlorophyll and chlorotic leaves the rst feature (~705 nm) is dominantIn the high-chlorophyll leaves the second feature (~725nm) is dominant

42 Model predictionsCanopy re ectance pro les generated by the model using high-chlorophyll low-

chlorophyll and chlorotic leaves of LAI from 1 to 5 in the top canopy are givenin gure 7

D W L amb et al3628

Figure 4 Schematic diagram of the eld-portable spectrometer used for acquiring soilre ectance spectra

421 T he eVect of increasing L AI on the magnitude of peaks in the derivativespectra

Derivative spectra corresponding to gure 7 are given in gure 8 It is evidenthere that increasing the LAI of the top canopy produces a signi cant increase in themagnitude of the second peak in the derivative spectra a phenomena supported bythe experimental observations of Horler et al (1983) using maize leaves

In the case of low-chlorophyll ( gure 8(b)) and chlorotic ( gure 8(c)) leaves themagnitude of the rst peak is initially comparable to or larger than that of thesecond peak at low LAI The substantial increase in magnitude of the second peakwith increasing LAI is linked to an increase in the magnitude of the NIR plateau inthe individual re ectance pro les ( gure 7) This is attributed to signi cantly greatermultiple scattering of radiation within the canopy in NIR red wavelengths due tohigher leaf re ectance and transmittance

The eVect of multiple scattering can be veri ed by modifying the transmittancecharacteristics of one of the candidate leaf types For example if the transmittanceof a low-chlorophyll leaf is arti cially reduced at higher wavelengths as depicted in gure 9 then signi cantly smaller increases in the magnitude of the second peakwith increasing LAI are observed ( gure 10)

422 Extracting red-edge parameters from the derivative spectraExamples of modelled re ectance spectra for high and low chlorophyll-containing

ryegrass canopies (LAI=1) are reproduced in gure 11 Superimposed on there ectance and corresponding derivative spectra ( gure 12) are tted curves corres-ponding to tting a single inverted Gaussian (equation (6)mdashtable 1) and a combina-tion of three sigmoid functions (equation (7)mdashtable 1) to the re ectance pro lesThe extracted red-edge wavelengths (lP ) and the sum of squared residuals (SSR) ofthe respective tted curves are also listed in table 2

Estimating leaf nitrogen concentration 3629

(a)

(b)

Figure 5 (a) Measured re ectance spectra for single ryegrass leaves (high- and low-chlorophyll chlorotic and dead) and bare soil (b) Single-leaf transmittance spectrafor high and low chlorophyll content chlorotic and dead ryegrass leaves

It is evident from gures 11 and 12 that like the single-leaf spectra of gure 6the shape of the chlorophyll red-edge for ryegrass canopies is complex containingtwo local maxima in the gradient at approximately 705 and 725 nm respectively

Single and combinations of two three and four sigmoid functions were used toconstruct curves to reproduce the observed re ectance pro les In all cases the useof three sigmoids was found to yield the lowest SSR values and always considerablylower SSR values than the tted Gaussian curve (table 2) In most test cases thethree sigmoids resulting from the tting procedure comprised two sigmoids of positivegain and amplitude (gn and Anmdashtable 1) corresponding to the two peaks observedin the derivative spectra hitherto referred to as l1 and l2 respectively as well as athird sigmoid with a relatively small negative gain In the particular though repres-entative examples of table 2 the wavelength of the third sigmoid (in brackets)corresponds to the location of the peak chlorophyll absorption of red light where are ectance minimum is observed in the re ectance pro les ( gure 11)

D W L amb et al3630

Figure 6 Single-leaf derivative re ectance spectra (dRdl) for high- and low-chlorophylland chlorotic ryegrass

As observed in the results of Miller et al (1990) the single red-edge wavelengthpredicted by the Gaussian tting routine lies between the two peaks observed in thecomplex derivative spectra As expected (Miller et al 1990 Pinar and Curran 1996)both the single red-edge peak resulting from the Gaussian analysis and the twopeaks resulting from the sigmoid- tting procedure have shifted to higher wavelengthsin response to higher leaf nitrogen content (higher chlorophyll )

423 T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectraThe wavelengths corresponding to both peaks in the derivative spectra of the

calculated re ectance pro les were extracted following the procedure outlined aboveThe eVects of increasing LAI on the wavelengths of the two peaks are summarizedin gure 13

It is evident from these model results that increasing LAI progressively shiftsboth derivative peaks towards longer wavelengths Progressively stacking leaves willeVectively increase total chlorophyll absorption experienced by the incident radiationthrough multiple scattering thereby shifting the derivative peaks to higher wave-lengths The magnitude of the wavelength shift resulting from increasing LAI from1 to 10 is greater for the second peak ( gure 13(b)) This is not surprising given thehigher leaf transmittance and re ectance in the associated wavelength range(724ndash740nm) ( gure 5 table 3) This eVect is also observed to occur for the rstpeak ( gure 13(a)) although to a lesser extent due to lower leaf re ectance andtransmittance in the corresponding wavelength range (702ndash709nm) ( gure 5 table 3)

There is a partial overlap of the curve shoulders in gure 13 for a small range ofred-edge wavelengths The overlap of the rst peak occurs for wavelengths703ndash7042nm and for the second peak is 726ndash730nm This overlap demonstratesthe confounding in uence of leaf chlorophyll concentration and canopy LAI on

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3628

Figure 4 Schematic diagram of the eld-portable spectrometer used for acquiring soilre ectance spectra

421 T he eVect of increasing L AI on the magnitude of peaks in the derivativespectra

Derivative spectra corresponding to gure 7 are given in gure 8 It is evidenthere that increasing the LAI of the top canopy produces a signi cant increase in themagnitude of the second peak in the derivative spectra a phenomena supported bythe experimental observations of Horler et al (1983) using maize leaves

In the case of low-chlorophyll ( gure 8(b)) and chlorotic ( gure 8(c)) leaves themagnitude of the rst peak is initially comparable to or larger than that of thesecond peak at low LAI The substantial increase in magnitude of the second peakwith increasing LAI is linked to an increase in the magnitude of the NIR plateau inthe individual re ectance pro les ( gure 7) This is attributed to signi cantly greatermultiple scattering of radiation within the canopy in NIR red wavelengths due tohigher leaf re ectance and transmittance

The eVect of multiple scattering can be veri ed by modifying the transmittancecharacteristics of one of the candidate leaf types For example if the transmittanceof a low-chlorophyll leaf is arti cially reduced at higher wavelengths as depicted in gure 9 then signi cantly smaller increases in the magnitude of the second peakwith increasing LAI are observed ( gure 10)

422 Extracting red-edge parameters from the derivative spectraExamples of modelled re ectance spectra for high and low chlorophyll-containing

ryegrass canopies (LAI=1) are reproduced in gure 11 Superimposed on there ectance and corresponding derivative spectra ( gure 12) are tted curves corres-ponding to tting a single inverted Gaussian (equation (6)mdashtable 1) and a combina-tion of three sigmoid functions (equation (7)mdashtable 1) to the re ectance pro lesThe extracted red-edge wavelengths (lP ) and the sum of squared residuals (SSR) ofthe respective tted curves are also listed in table 2

Estimating leaf nitrogen concentration 3629

(a)

(b)

Figure 5 (a) Measured re ectance spectra for single ryegrass leaves (high- and low-chlorophyll chlorotic and dead) and bare soil (b) Single-leaf transmittance spectrafor high and low chlorophyll content chlorotic and dead ryegrass leaves

It is evident from gures 11 and 12 that like the single-leaf spectra of gure 6the shape of the chlorophyll red-edge for ryegrass canopies is complex containingtwo local maxima in the gradient at approximately 705 and 725 nm respectively

Single and combinations of two three and four sigmoid functions were used toconstruct curves to reproduce the observed re ectance pro les In all cases the useof three sigmoids was found to yield the lowest SSR values and always considerablylower SSR values than the tted Gaussian curve (table 2) In most test cases thethree sigmoids resulting from the tting procedure comprised two sigmoids of positivegain and amplitude (gn and Anmdashtable 1) corresponding to the two peaks observedin the derivative spectra hitherto referred to as l1 and l2 respectively as well as athird sigmoid with a relatively small negative gain In the particular though repres-entative examples of table 2 the wavelength of the third sigmoid (in brackets)corresponds to the location of the peak chlorophyll absorption of red light where are ectance minimum is observed in the re ectance pro les ( gure 11)

D W L amb et al3630

Figure 6 Single-leaf derivative re ectance spectra (dRdl) for high- and low-chlorophylland chlorotic ryegrass

As observed in the results of Miller et al (1990) the single red-edge wavelengthpredicted by the Gaussian tting routine lies between the two peaks observed in thecomplex derivative spectra As expected (Miller et al 1990 Pinar and Curran 1996)both the single red-edge peak resulting from the Gaussian analysis and the twopeaks resulting from the sigmoid- tting procedure have shifted to higher wavelengthsin response to higher leaf nitrogen content (higher chlorophyll )

423 T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectraThe wavelengths corresponding to both peaks in the derivative spectra of the

calculated re ectance pro les were extracted following the procedure outlined aboveThe eVects of increasing LAI on the wavelengths of the two peaks are summarizedin gure 13

It is evident from these model results that increasing LAI progressively shiftsboth derivative peaks towards longer wavelengths Progressively stacking leaves willeVectively increase total chlorophyll absorption experienced by the incident radiationthrough multiple scattering thereby shifting the derivative peaks to higher wave-lengths The magnitude of the wavelength shift resulting from increasing LAI from1 to 10 is greater for the second peak ( gure 13(b)) This is not surprising given thehigher leaf transmittance and re ectance in the associated wavelength range(724ndash740nm) ( gure 5 table 3) This eVect is also observed to occur for the rstpeak ( gure 13(a)) although to a lesser extent due to lower leaf re ectance andtransmittance in the corresponding wavelength range (702ndash709nm) ( gure 5 table 3)

There is a partial overlap of the curve shoulders in gure 13 for a small range ofred-edge wavelengths The overlap of the rst peak occurs for wavelengths703ndash7042nm and for the second peak is 726ndash730nm This overlap demonstratesthe confounding in uence of leaf chlorophyll concentration and canopy LAI on

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3629

(a)

(b)

Figure 5 (a) Measured re ectance spectra for single ryegrass leaves (high- and low-chlorophyll chlorotic and dead) and bare soil (b) Single-leaf transmittance spectrafor high and low chlorophyll content chlorotic and dead ryegrass leaves

It is evident from gures 11 and 12 that like the single-leaf spectra of gure 6the shape of the chlorophyll red-edge for ryegrass canopies is complex containingtwo local maxima in the gradient at approximately 705 and 725 nm respectively

Single and combinations of two three and four sigmoid functions were used toconstruct curves to reproduce the observed re ectance pro les In all cases the useof three sigmoids was found to yield the lowest SSR values and always considerablylower SSR values than the tted Gaussian curve (table 2) In most test cases thethree sigmoids resulting from the tting procedure comprised two sigmoids of positivegain and amplitude (gn and Anmdashtable 1) corresponding to the two peaks observedin the derivative spectra hitherto referred to as l1 and l2 respectively as well as athird sigmoid with a relatively small negative gain In the particular though repres-entative examples of table 2 the wavelength of the third sigmoid (in brackets)corresponds to the location of the peak chlorophyll absorption of red light where are ectance minimum is observed in the re ectance pro les ( gure 11)

D W L amb et al3630

Figure 6 Single-leaf derivative re ectance spectra (dRdl) for high- and low-chlorophylland chlorotic ryegrass

As observed in the results of Miller et al (1990) the single red-edge wavelengthpredicted by the Gaussian tting routine lies between the two peaks observed in thecomplex derivative spectra As expected (Miller et al 1990 Pinar and Curran 1996)both the single red-edge peak resulting from the Gaussian analysis and the twopeaks resulting from the sigmoid- tting procedure have shifted to higher wavelengthsin response to higher leaf nitrogen content (higher chlorophyll )

423 T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectraThe wavelengths corresponding to both peaks in the derivative spectra of the

calculated re ectance pro les were extracted following the procedure outlined aboveThe eVects of increasing LAI on the wavelengths of the two peaks are summarizedin gure 13

It is evident from these model results that increasing LAI progressively shiftsboth derivative peaks towards longer wavelengths Progressively stacking leaves willeVectively increase total chlorophyll absorption experienced by the incident radiationthrough multiple scattering thereby shifting the derivative peaks to higher wave-lengths The magnitude of the wavelength shift resulting from increasing LAI from1 to 10 is greater for the second peak ( gure 13(b)) This is not surprising given thehigher leaf transmittance and re ectance in the associated wavelength range(724ndash740nm) ( gure 5 table 3) This eVect is also observed to occur for the rstpeak ( gure 13(a)) although to a lesser extent due to lower leaf re ectance andtransmittance in the corresponding wavelength range (702ndash709nm) ( gure 5 table 3)

There is a partial overlap of the curve shoulders in gure 13 for a small range ofred-edge wavelengths The overlap of the rst peak occurs for wavelengths703ndash7042nm and for the second peak is 726ndash730nm This overlap demonstratesthe confounding in uence of leaf chlorophyll concentration and canopy LAI on

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3630

Figure 6 Single-leaf derivative re ectance spectra (dRdl) for high- and low-chlorophylland chlorotic ryegrass

As observed in the results of Miller et al (1990) the single red-edge wavelengthpredicted by the Gaussian tting routine lies between the two peaks observed in thecomplex derivative spectra As expected (Miller et al 1990 Pinar and Curran 1996)both the single red-edge peak resulting from the Gaussian analysis and the twopeaks resulting from the sigmoid- tting procedure have shifted to higher wavelengthsin response to higher leaf nitrogen content (higher chlorophyll )

423 T he eVect of increasing L AI on the wavelengths of peaks in the derivative spectraThe wavelengths corresponding to both peaks in the derivative spectra of the

calculated re ectance pro les were extracted following the procedure outlined aboveThe eVects of increasing LAI on the wavelengths of the two peaks are summarizedin gure 13

It is evident from these model results that increasing LAI progressively shiftsboth derivative peaks towards longer wavelengths Progressively stacking leaves willeVectively increase total chlorophyll absorption experienced by the incident radiationthrough multiple scattering thereby shifting the derivative peaks to higher wave-lengths The magnitude of the wavelength shift resulting from increasing LAI from1 to 10 is greater for the second peak ( gure 13(b)) This is not surprising given thehigher leaf transmittance and re ectance in the associated wavelength range(724ndash740nm) ( gure 5 table 3) This eVect is also observed to occur for the rstpeak ( gure 13(a)) although to a lesser extent due to lower leaf re ectance andtransmittance in the corresponding wavelength range (702ndash709nm) ( gure 5 table 3)

There is a partial overlap of the curve shoulders in gure 13 for a small range ofred-edge wavelengths The overlap of the rst peak occurs for wavelengths703ndash7042nm and for the second peak is 726ndash730nm This overlap demonstratesthe confounding in uence of leaf chlorophyll concentration and canopy LAI on

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3631

(a)

(b)

(c)

Figure 7 Model-derived re ectance spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3632

(a)

(b)

(c)

Figure 8 Model-derived derivative spectra for a ryegrass canopy containing a lower deadlayer (LAI=1) and a top canopy of (a) high-chlorophyll (b) low-chlorophyll and(c) chlorotic ryegrass leaves of LAI from 1 to 5

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3633

Figure 9 Low-chlorophyll leaf transmittance pro les used in model calculations theactual pro le measured in the laboratory (from gure 5(b)) and a synthesized pro lecalculated using

Ctfrac34l=t

l l aring 715 nm

t frac34l=Gt

l= 715 nm+1

10tlH lgt715 nm

Dwhere t frac34

l=synthesized transmittance t

l=actual transmittance

red-edge wavelength particularly at lower values of LAI Here it would be possibleto determine total chlorophyll content but not chlorophyll concentration unless anadditional measurement of canopy LAI (or biomass) was completed

The wavelengthLAI plots of both red-edge peaks tends to saturate at higherLAI This is in keeping with the fact that due to scattering and absorption progress-ively less incident radiation interacts with additional leaves deeper within the canopyas the radiation traverses vertically through the canopy This is also supported bythe trends observed in the re ectance spectra with increasing LAI ( gure 7) ForLAIgt10 for the high-chlorophyll leaves and LAIgt5 for the low-chlorophyll andchlorotic leaves the wavelengths of both derivative peaks are no longer sensitive tochanges in LAI The wavelength of the rst peak of the chlorotic leaves appearsalways insensitive to changes in LAI

5 Experimental observationsThe ryegrass plots studied in this work were located at the Dairy Research

Institute Hamilton New Zealand (Lat 37deg 47ecirc S Long 175deg 17 ecirc E) Detailed canopyre ectance measurements were completed at 100 locations comprising a range ofcanopy biomass and leaf nitrogen levels Field samples were taken for laboratorydissection and analysis of nitrogen content

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3634

Figure 10 Calculated derivative spectra using actual and synthetic leaf transmittance data

51 Measurement of canopy re ectanceIn- eld measurements of canopy re ectance were acquired using the spectrometer

described in sect32Canopy re ectance was calculated by taking the ratio of the measured radiance

re ected oV the canopy to that re ected oV agt99 re ectance Spectralon re ectancetarget (SRT-99-100 Labsphere Inc Sutton NH USA) In order to minimize theeVect of illuminationsensor azimuth on the measured radiance canopy measure-ments were averaged for two readings each taken at a relative azimuth of w=0degand 90deg

52 Collection and dissection of eld samplesImmediately following each re ectance measurement the precise area correspond-

ing to the footprint of the eld spectrometer was harvested to soil level and packedin bags for laboratory dissection into live leaf live stem chlorotic leaf dead leafand lsquoother speciesrsquo sub-groups All samples were subsequently oven dried at 75degCovernight and each sub-group weighed for total biomass

53 Nitrogen analysisApproximately 1 mg portions of each dried live-leaf sub-group was ground and

re-weighed Leaf nitrogen concentration expressed as a percentage of leaf dry weightand total nitrogen content expressed in grams were determined by Kjeldahl digestionand subsequent determination of ammonia by distillation (Ministry of AgricultureFisheries and Food 1986)

54 Extracting chlorophyll red-edge parameters f rom spectral pro lesThe appropriateness of the three-sigmoid curve- tting methodology described in

sect422 was checked using representative measured re ectance spectra Again the

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3635

(a)

(b)

Figure 11 Modelled and tted re ectance pro le for a (a) high-chlorophyll and (b) chloroticryegrass canopy of LAI=1

measured re ectance spectra were also characterized using the standard procedureof tting portions of a Gaussian curve (table 1) to the spectra In addition to red-edge wavelengths described in table 1 the height of the red-edge step was calculatedfrom the area under each derivative spectrum using the analytical expression ttedto each of the re ectance pro les according to

step height=P l= 780 nm

l= 670 nm

dRldl

dl=R780 shy R670 (6)

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3636

(a)

(b)

Figure 12 Derivative re ectance spectra of modelled and tted curves for the (a) high-chlorophyll and (b) chlorotic ryegrass canopy of gure 11

Here R670 and R780 are the calculated re ectances at 670 and 780 nm respectivelyMultiple linear regression analyses based on least squares were completed usingcombinations of the extracted red-edge descriptors and measured leaf nitrogen con-centration and total leaf nitrogen content (nitrogen concentrationtimesleaf dry weight)

6 Results of experimental observations and discussion61 Extracting red-edge parameters f rom the measured derivative spectra

Examples of measured re ectance spectra for known high and low nitrogen-containing ryegrass canopies are given in gure 14 Corresponding derivative spectragiven in gure 15 were calculated using equation (5) Superimposed on there ectance and derivative spectra are tted curves corresponding to equations (1)

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3637

Table 1 Two curve- tting procedures evaluated for extracting red-edge wavelengths (lP )from measured re ectance pro les

Equation type andprocedure Formula

1 Fit single Rl=Rmax shy (Rmax shy Rmin)e Otilde (l0 Otilde l)22s (6)

Gaussian to Rmax=average re ectance of NIR plateaure ectance pro le Rmin=re ectance at peak red absorption

l0=wavelength (nm) of peak absorption (corresponding towavelength of Rmin )s=width (nm) of Gaussian pro lelP=l0+s=wavelength (nm) of the point of in ection in Rl(corresponding to the peak in derivative spectrum)

2 Fit n sigmoids to Rl=Sn On+An1+eOtilde gn(lOtilde lp) (7)

re ectance pro le On=re ectance oVset of sigmoid nAn=amplitude of sigmoid ngn=gain of sigmoid nlP=wavelength (nm) of the point of in ection in sigmoid n(corresponding to a peak in the derivative spectrum)

Table 2 Red-edge wavelengths and SSR values for tted curves of gure 11

High chlorophyll Chlorotic

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7197nm (6751nm) 7132nm (6751nm)7036nm 7036nm7293nm 7240nm

SSR 192times10Otilde 3 108times10 Otilde 5 120times10 Otilde 4 199times10Otilde 5

and (2) (table 1 ) The extracted red-edge wavelengths (lP ) and SSR of the respective tted curves are also listed in table 4

It is evident from gures 14 and 15 that the shape of the chlorophyll red-edgefor ryegrass canopies is complex containing two local maxima in the gradient atapproximately 700 and 720 nm respectively The shapes of the derivative spectra in gure 15 particularly the relative magnitudes of the two peaks corresponding tohigh and low nitrogen content leaves are similar to that predicted by the earliermodel calculations involving a canopy of rye grass containing leaves of high andlow chlorophyll concentration respectively ( gure 8) As in evaluating the earliersynthesized derivative spectra the use of three sigmoids was again found to yieldthe lowest SSR values of either a single or combinations of two three or four sigmoidfunctions Again considerably lower SSR values result from using the three-sigmoidcombination compared to the tted Gaussian curve (table 4) Again the single red-edge wavelength predicted by the Gaussian tting routine lies between the two peaksobserved in the complex derivative spectra Furthermore both the single red-edgepeak resulting from the Gaussian analysis and the two peaks resulting from thesigmoid- tting procedure have shifted to higher wavelengths in response to higherleaf nitrogen content (higher chlorophyll )

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3638

(a)

(b)

Figure 13 Extracted wavelengths corresponding to the (a) rst and (b) second peaks in thederivative spectra for varying LAI

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3639

Table 3 Single wavelength transmittance and re ectance values extracted from gure 5 andcalculated absorption coeYcient (a) assuming a=1 shy r shy t

Transmittance t Re ectance r a=1 shy rshy t

l=706 nmHigh chlorophyll 0028 0256 0716Low chlorophyll 0044 0320 0636Chlorotic 0068 0379 0553

l=729 nmHigh chlorophyll 0063 0589 0348Low chlorophyll 0074 0605 0321Chlorotic 0096 0657 0247

62 Red-edge wavelength and canopy nitrogen contentThe results of multiple linear regression analyses involving both red-edge wave-

lengths and step height and leaf nitrogen concentration () and total leaf nitrogencontent (g) respectively are summarized in table 5

The two red-edge wavelengths used to describe the chlorophyll red-edge explain52 and 65 of the variance in leaf nitrogen concentration and total leaf nitrogencontent respectively A higher level of explanation is achieved with total leaf nitrogenbecause changes in canopy biomass in response to diVerent nitrogen levels are alsoaVecting the measured spectral signature This conclusion is further supported whenthe step height at the red edge (equation (6)) is also included in the regressionanalyses The step height is related to the Vegetation Index which has been shownto correlate strongly with biomass (Hanna et al 1999) On its own R780 shy R670explains 33 of the variance observed in changes in total leaf nitrogen content andonly 11 of changes in leaf nitrogen concentration However incorporatingR780 shy R670 into the regression analyses involving leaf nitrogen concentrationincreases R2 by acting to include changes in leaf biomass On the other handincluding R780 shy R670 in the total leaf nitrogen content analyses does not change R2values because the biomass in uence has already been accounted for in the measureof total leaf nitrogen content (total leaf nitrogen=leaf nitrogen concentrationtimesleafdry weight)

Regression equations involving all three descriptors and both measured nitrogenconcentration () and total nitrogen content (g) are listed in table 6 According to thecriteria discussed by Whitlock et al (1982) FFcrit 4 and R2 1 should formbenchmark requirements for using remotely sensed radiance in a linear regressionanalysis Both regression equations in table 6 are signi cant and accordingly show areasonable predictive utility In order to estimate the error in using the regressionequations to estimate nitrogen concentration (N) and content (Ntot) the data wasrandomly assigned into calibration and test sets The calibration test set was used togenerate regression equations for nitrogen concentration and content respectivelyThese equations were then used to estimate nitrogen concentration and content for thetest data based on the spectral measurements Comparison between the estimated andactual test data produced an average diVerence of plusmn04 in estimating nitrogenconcentration in the range 0ndash5 and plusmn0006g in estimating nitrogen content in therange 002ndash005g Scatterplots comparing the nitrogen concentration and content estim-ated by the respective regression equations and the actual values are given in gure 16

Generally a signi cant proportion of the total canopy nitrogen exists in the

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3640

(a)

(b)

Figure 14 Measured and tted re ectance pro le for a (a) high-nitrogen and (b) low-nitrogenryegrass canopy

upper-canopy leaves due to increased competition for available sunlight especiallywhen the plant is nitrogen-stressed (Wolfe et al 1988) Leaves of higher nitrogencontent have a lower transmittance and higher re ectance at NIR wavelengths( gure 5) Consequently the detected scattered radiation could be predominantlyin uenced by the upper canopy higher nitrogen content leaves The scatterplots of

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3641

(a)

(b)

Figure 15 Derivative re ectance spectra of measured and tted pro les for a (a) high-nitrogenand (b) low-nitrogen ryegrass canopy

gure 16 do show that nitrogen concentration is overestimated although only atlower nitrogen levels This phenomenon is the subject of further investigation

63 Con rming the in uence of canopy biomass on red-edge determination of leafnitrogen concentration

Earlier model calculations (sect423) predicted that the in uence of canopy LAI orin this case biomass on the location of the red-edge wavelengths would progressively

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3642

Table 4 Red-edge wavelengths and SSR values for tted curves of gure 14

High nitrogen Low nitrogen

Gaussian t Three-sigmoid t Gaussian t Three-sigmoid t

lP 7112nm (6733nm) 7071nm (6751nm)6996nm 6978nm7225nm 7196nm

SSR 262times10Otilde 3 149times10Otilde 5 324times10Otilde 4 736times10 Otilde 5

Table 5 Results of multiple linear regression analyses between combinations of red-edgeparameters leaf nitrogen concentration and total leaf nitrogen content

Leaf nitrogen concentration Total leaf nitrogen( leaf dry weight) content (g)

Red-edge feature R2 R2

Principal red-edge wavelengths 060 065(l1 l2 ) and R780 shy R670

l1 and l2 052 064l1 040 062l2 052 062R780 shy R670 011 033

Table 6 Linear multiple regression equations generated using red-edge parameters andmeasured leaf nitrogen concentration () and total leaf nitrogen content (g)

Regression equation FFcrit R2

N=shy 174shy 00005l1+00029l2 shy 00006 (R780 shy R670) 1216 Plt1times10 Otilde 15 060Ntot=shy 648shy 00070l1+00022l2 shy 000006 (R780 shy R670) 1557 Plt1times10Otilde 17 065

Table 7 Pearson correlation coeYcients (R) for red-edge wavelength and nitrogen con-centration () for three canopy biomass levels (high 15ndash27 g medium 10ndash15 glow 05ndash10 g) Correlation coeYcients relating total green matter and leaf nitrogenconcentration are also included (italics)

Principal Nitrogen Total greenTotal green red-edge concentration biomass (g)biomass level wavelength R R

High (shy 020)15ndash28 g l1 061 0008

l2 055 0002

Medium (032)10ndash15 g l1 071 035

l2 082 040

Low (030)05ndash10 g l1 045 028

l2 072 035

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3643

(a)

(b)

Figure 16 (a) Leaf nitrogen concentration () estimated by the regression equation comparedto actual leaf nitrogen concentration (test dataset) (b) Leaf nitrogen content (g)estimated by the regression equation compared to actual leaf nitrogen content (testdataset) Solid lines represent a zero error of prediction (SEP=0)

diminish with increasing biomass When the eld-plot data is subsequently strati edaccording to low (05ndash10 g) medium (10ndash15 g) and high (15ndash28 g) values of totalgreen biomass (total green biomass=live leaf+live stem fractions) (table 7) correla-tions between the two principal red-edge wavelengths (l1 700 nm l2 720 nm) andtotal green biomass are almost zero for the high biomass grouping

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3644

7 ConclusionA two-layer canopy re ectance model has been constructed to generate detailed

re ectance spectra and corresponding derivative spectra of a realistic ryegrasspasture canopy comprising an upper layer of varying LAI a middle layer of deadmaterial and underlying soil Detailed spectral re ectance and transmittance valuesfor high-chlorophyll low-chlorophyll chlorotic and dead single ryegrass leaves andre ectance data for underlying soil were acquired to initialize the model A moreaccurate method of extracting red-edge wavelengths from complex derivative spectrainvolving a combination of three sigmoid functions was proposed Model calculationsdemonstrated the confounding eVects of chlorophyll content and LAI on the locationand shape of peaks in the derivative spectra at low LAI Increasing LAI in thecanopy is found to signi cantly increase the magnitude of the second peak due tohigher leaf transmittance at these wavelengths The wavelength of both peaks shiftto longer wavelengths with increasing LAI as a result of the increase in totalchlorophyll absorption by multiple scattering of incident radiation between indi-vidual leaves This is found to occur to a greater extent with the longer-wavelengthsecond peak as increased leaf re ectance and transmittance makes it more sensitiveto multiple scattering eVects

The complex shape of the derivative spectra of ryegrass was also observed in eld measurements and the appropriateness of tting three sigmoid curves tore ectance pro les in order to extract chlorophyll red-edge descriptors was veri edIn subsequent measurements the descriptors of the chlorophyll red-edge explained60 and 65 of the variance respectively in leaf nitrogen concentration and totalleaf nitrogen content The resulting regression equation was found to predict leafnitrogen concentration in the range 2ndash5 with a SEP of 04 The confoundingin uence of varying canopy biomass on the red-edge determination of leaf nitrogenconcentration was found to be signi cantly less at higher canopy biomass therebyverifying model predictions The tendency of the red-edge wavelengths to becomeinsensitive to changes in LAI at high values of LAI suggests that under appropriate eld conditions the red-edge wavelength could be a LAI (biomass)-independentindicator of leaf chlorophyll concentration in ryegrass pasture canopies For low-chlorophyll leaves calculations predicted this may occur for LAI as low as 5 althoughthe chlorotic leaf data suggests that this gure may be even lower

Leaf area index values of up to 12 are encountered in some Waikato pastures(Hanna et al 1999) albeit in irrigated elds Therefore provided a quantitative linkbetween LAI and canopy biomass is established and suYcient correlation existsbetween leaf chlorophyll concentration and nitrogen content the use of the chloro-phyll red-edge as a biomass-independent measure of pasture nitrogen status is quitepossible in the Waikato region of New Zealand

AcknowledgmentsThe authors gratefully acknowledge the assistance of Alec McGowen and Linda

Trolove (Agricultural Research Institute Hamilton New Zealand) in the acquisitionand dissection of pasture samples and Duncan Miers (Department of BiologicalSciences University of Waikato Hamilton New Zealand) for completion of leafnitrogen analyses The support of staV of the HortResearch Technology DevelopmentGroup in the acquisition of plant and soil spectral characteristics and the receipt ofa Special Studies Program Grant from Charles Sturt University (DL) are alsoacknowledged

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3645

Appendix Solution of the two-stream model for a two-layer canopyFollowing the schematic of gure A1

Ila=wavelength-dependent upward-directed ux at the top of layer a divided byincident solar uxI3la=wavelength-dependent downward-directed ux at top of layer a divided by

incident solar uxIlb=wavelength-dependent upward directed ux at the top of layer b divided byincident solar uxI3lb=wavelength-dependent downward-directed ux at top of layer b divided by

incident solar ux

Solution of equations (1) and (2) for the two canopy layers yields

L ayer a

Ila (t)=Canaexat+Dauae Otilde xat+Eae Otilde kt

I3la (t)=Cauaexat+Danae Otilde xat+Fae Otilde kt

L ayer b

Ilb (t)=Cbnbexbt+Dbube Otilde xbt+Ebe Otilde kt

I3lb (t)=Cbubexbt+Dbnbe Otilde xbt+Fbe Otilde kt

Re ectance at the top canopy (top of layer a) for each wavelength l is given by

RlanotIla (t=0)

Boundary conditions to determine the unknown coeYcients C D E and F

I3la (t=0)=0 no downward ux at top of layer a (t=0)

Ila (t=ta )=Ilb (t=ta ) continuity of upward ux at interface between layers

I3la (t=ta )=I3

lb (t=ta ) continuity of downward ux at interface between layers

Ilb (t=ta+tb )=rle Otilde k(ta+ tb)+I3lb (ta+tb )

re ected ux at soil surface=upward ux at t=ta+tb

Figure A1 Detailed schematic diagram of the two-layer ryegrass canopy represented in themodel

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

D W L amb et al3646

Equation coeYcients relevant to the solution of Ila

Cb=Dba1+a2Ca=shy Dava

uashy

Faua

Da=a5 (a6 shy a4 )

a3 shy a5+a6 Db=

a6 shy a4a3 shy a5

Ea=aa+b1a

2Eb=

ab+b1b2

Fa=aa shy b1a

2Fb=

ab shy b1b2

na=1

2A1+S 1shy va1shy vaga

B ua=1

2A1 shy S 1 shy va1 shy vaga

Bva=ra+ta ga=1 shy 2 ba=

[ra+ta+(ra shy ta )cos2h]

ra+ta

nb=1

2A1+S 1shy vb1shy vbgb

B ub=1

2A1 shy S 1 shy vb1 shy vbgb

Bvb=rb+tb gb=1 shy 2 bb=

[rb+tb+(rb shy tb )cos2h]

rb+tb

aa=Z2a

k2 shy x2a

xa=S (1shy vaga ) (1shy va )

m2

b1a=Z1a

k2 shy x2a

S1=vamkb0Z2a=k (S1 shy S2 )

mshy

(S1+S2 ) (1 shy vaga )

m2

S2=vamk (1 shy b0 )Z1a=k (S1+S2 )

mshy

(S1 shy S2 ) (1 shy va )

m2

ab=Z2b

k2 shy x2b

xb=S (1shy vbgb ) (1shy vb )

m2

b1b=Z1b

k2 shy x2b

S3=vbmkb0Z2b=k (S3 shy S4 )

mshy

(S3+S4 ) (1 shy vbgb )

m2

S4=vbmk (1 shy b0 )Z1b=k (S3+S4 )

mshy

(S3 shy S4 ) (1 shy vb )

m2

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration 3647

a1=Arsnb shy ubnb shy rsub

Be Otilde 2xb(ta+ tb)

a2=Ars(1+Fb )shy Ebnb shy rsub

Be Otilde (k+ xb) (ta+ tb)

a3=Ca1nbexbta+ube Otilde xbta

uaexbta shy An2a

uaB exataD

a4=Ca2nbexbta+AFanaua

B exata+(Eb shy Ea )e Otilde kta

uae Otilde xata shy An2a

uaB exata D

a5=Ca1ubexbta+nbe Otilde xbtana (eOtilde xata shy exata ) D

a6=Ca2ubexbta+Faexata+(Fb shy Fa )e Otilde ktana (e Otilde xata shy exata ) D

For each canopy (a) k=05 for leaves having random orientations (b) m=cosh=plusmn1 where h is the zenith angle for diVuse ux h=0deg for upward directed ux and180deg for downward directed ux (c) G(m)=km=plusmn05 (d) m=aacute mG dm=1 for leaveshaving random orientations (e) h=45deg is the average leaf angle relative to thehorizontal and (f ) b0=05 is the backscatter parameter for the incident beam

ReferencesAtwell B J Kriedemann P E and TurnbullC G N 1999 Plants in Action Adaptation

in Nature Performance in Cultivation (Sydney Macmillan Education)Bonham-Carter G F 1987 Numerical procedures and computer program for tting an

inverted Gaussian model to vegetation re ectance data Computers and Geosciences14 339ndash356

Boochs F Kupfer G Dockter K and Kuhbauch W 1990 Shape of the red-edge asa vitality indicator for plants International Journal of Remote Sensing 11 1741ndash1753

Buschmann C and Nagel E 1993 In vivo spectroscopy and internal optics of leaves asbasis for remote sensing of vegetation International Journal of Remote Sensing 14711ndash722

Campbell J B 1996 Introduction to Remote Sensing 2nd edn (London The Guilford Press)Danks S M Evans E H and Whittaker P A 1983 Photosynthetic Systems Structure

Function and Assembly (New York John Wiley)Devlin R M 1969 Plant Physiology 2nd edn (New York Van Nostrand Reinhold)Donahue R L Miller R W and Shickluna J C 1983 Soils an Introduction to Soils

and Plant Growth 5th edn (Englewood CliVs New Jersey Prentice Hall)Everitt J H Richardsen A J and Gausman H W 1985 Leaf re ectancendashchlorophyll

relations in buVelgrass Photogrammetric Engineering and Remote Sensing 51 463ndash466Filella I and Pen~uelas J 1994 The red-edge position and shape as indicators of plant

Estimating leaf nitrogen concentration3648

chlorophyll content biomass and hydric status InternationalJournal of Remote Sensing15 1459ndash1470

Hanna M M Steyn-Ross D A and Steyn-Ross M 1999 Estimating biomass for NewZealand pasture using optical remote sensing techniques Geocarto International 1489ndash94

Horler D N H Dockray M and Barber J 1983 The red-edge of plant leaf re ectanceInternational Journal of Remote Sensing 4 273ndash288

Jones D I H and Moseley G 1993 Laboratory methods for estimating nutritive qualityIn Sward Measurement Handbook 2nd edn edited by A Davies R D Baker S AGrant and A S Laidlaw (Reading British Grassland Society) pp 265ndash283

McDonald I W 1981 Detrimental substances in plants consumed by grazing ruminantsIn Grazing Animals edited by F H W Morley (Amsterdam Elsevier) pp 349ndash360

McDonald P Edwards R A and Greenhalgh J F D 1975 Animal Nutrition 2ndedn (London Longman)

Methy M Joffre R and Ourcival J M 1998 Two ways of assessing absorbance offresh leaves from near-infrared re ectance spectroscopy International Journal ofRemote Sensing 19 1741ndash1750

Miller J R Hare E W and Wu J 1990 Quantitative characterization of the vegetationred-edge re ectance 1 An inverted Gaussian re ectance model International Journalof Remote Sensing 11 1755ndash1773

Ministry of Agriculture Fisheries and Food 1986 T he Analysis of Agricultural Materials3rd edn (London Her Majestyrsquos Stationery OYce)

Munden R Curran P J and Catt J A 1994 The relationship between red-edge andchlorophyll concentration in the Broadbank winter wheat experiment at RothamstedInternational Journal of Remote Sensing 15 705ndash709

Murray I 1986 Near infrared analysis of forages In Recent Advances in Animal Nutritionmdash1986 edited by W Haresign and D J A Cole (London Butterworths) pp 141ndash156

Murray I 1993 Forage analysis by near infrared spectroscopy In Sward MeasurementHandbook 2nd edn edited by A Davies R D Baker S A Grant and A S Laidlaw(Reading British Grassland Society) pp 285ndash312

Pearson C J and Ison R L 1987 Agronomy of Grassland Systems (Cambridge CambridgeUniversity Press)

Pinar A and Curran P J 1996 Grass chlorophyll and the re ectance red-edgeInternational Journal of Remote Sensing 17 351ndash357

Sellers P J 1985Canopy re ectancephotosynthesisand transpirationInternationalJournalof Remote Sensing 6 1335ndash1372

Simpson J R 1987 Nitrogen nutrition of pastures In T emperate Pastures T heir ProductionUse and Management edited by J L Wheeler C J Pearson and G E Robards(Australia CSIRO) pp 143ndash154

Vickery P J 1981 Pasture growth under grazing In Grazing Animals edited by F H WMorley (Amsterdam Elsevier) pp 55ndash78

Wolfe D W Henderson D W Hsiao T C and Alvino A A 1988 Interactive waterand nitrogen eVects on the senescence of maize II Photosyntheticdecline and longevityof individual leaves Agronomy Journal 80 865ndash870

Whitlock C H Kuo C Y and LeCroy S R 1982 Criteria for the use of regressionanalysis for remote sensing of sediment and pollutants Remote Sensing of Environment12 151ndash168