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Ecological Modelling 124 (1999) 99–119

Daily canopy photosynthesis model through temporal andspatial scaling for remote sensing applications

J.M. Chen a,*, J. Liu a, J. Cihlar a, M.L. Goulden b

a Canada Centre for Remote Sensing, 588 Booth Street, Ottawa, Ont., Canada K1A 0Y7b Department of Earth System Science, Uni6ersity of California, Ir6ine, CA 92717-3100, USA

Received 16 June 1998; received in revised form 7 June 1999; accepted 10 June 1999

Abstract

Because Farquhar’s photosynthesis model is only directly applicable to individual leaves instantaneously, consider-able skill is needed to use this model for regional plant growth and carbon budget estimations. In many publishedmodels, Farquhar’s equations were applied directly to plant canopies by assuming a plant canopy to function like abig-leaf. This big-leaf approximation is found to be acceptable for estimating seasonal trends of canopy photosynthe-sis but inadequate for simulating its day-to-day variations, when compared with eddy-covariance and gas-exchangechamber measurements from two boreal forests. The daily variation is greatly dampened in big-leaf simulationsbecause the original leaf-level model is partially modified through replacing stomatal conductance with canopyconductance. Alternative approaches such as separating the canopy into sunlit and shaded leaf groups or stratifyingthe canopy into multiple layers can avoid the problem. Because of non-linear response of leaf photosynthesis tometeorological variables (radiation, temperature and humidity), considerable errors exist in photosynthesis calculationat daily steps without considering the diurnal variability of the variables. To avoid these non-linear effects, we havedeveloped an analytical solution to a simplified daily integral of Farquhar’s model by considering the general diurnalpatterns of meteorological variables. This daily model not only captures the main effects of diurnal variations onphotosynthesis but is also computationally efficient for large area applications. Its application is then not restrictedby availability of sub-daily meteorological data. This scheme has been tested using measured CO2 data from theBoreal Ecosystem–Atmosphere Study (BOREAS), which took place in Manitoba and Saskatchewan in 1994 and1996. © 1999 Elsevier Science B.V. All rights reserved.

Keywords: Farquhar model; Canopy photosynthesis; Sunlit/shaded leaves; CO2 flux; Net primary productivity; BOREAS; Remotesensing application

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1. Introduction

In recent years, modeling net primary produc-tivity (NPP) of terrestrial ecosystems has been asubject of increasing interest because of the im-portance of terrestrial carbon cycle in global car-

* Corresponding author. Tel.: +1-613-9471266; fax: +1-613-9471406.

E-mail address: [email protected] (J.M. Chen)

0304-3800/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.

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J.M. Chen et al. / Ecological Modelling 124 (1999) 99–119100

bon budget and climate change. Several processmodels of NPP have been developed for thispurpose and applied to global landmass at spa-tial resolution of 0.5–5° (Melillo et al., 1993;Bonan, 1995; Woodward et al., 1995; Foley etal., 1996; Sellers et al., 1996). Some models (Bo-nan, 1995; Denning et al., 1996; Foley et al.,1996) are run at small time steps (minute tohours) and coarse spatial resolutions (2–5°) inconjunction with General Circulation Models(GCM). Some process models are run at moder-ate spatial resolutions (1 km and larger) but atlarge time steps from daily to monthly, with useof remote sensing data (Running et al., 1989;Liu et al., 1997) or other data (Woodward et al.,1995). For regional and global applications,modelers usually face the choice between tempo-ral and spatial resolutions, and modelingmethodologies can be very different for thesetwo choices. Hourly and sub-hourly models usu-ally treat each time step calculation as instanta-neous and no temporal integration is made, butsuch models suffer from the need for, and inac-curacy of, spatial scaling. Heterogeneity of theearth’s surface makes such scaling a considerablechallenge (Pielke et al., 1991; Hall et al., 1992;Bonan et al., 1993; Wood and Lakshmi, 1993).When run independent of GCMs, the high-tem-poral resolution models are limited by dataavailability. With the use of daily or monthlymodels, the spatial resolution can be improvedand errors due to spatial scaling can be reduced.However, many detailed canopy processes can-not be simulated at large time steps, and modelshave to become more empirical as the modelingtime step increases.

Daily models are appropriate for medium-highspatial resolution remote sensing applications be-cause of their moderate demand on computationand input data. Since the diurnal variations ofsolar radiation and temperature and the associ-ated canopy processes generally follow pre-dictable patterns, daily models, when correctlyparameterized, can capture most of the day-to-day variability in the plant canopies. Severaldaily models have been developed to considerthe non-linear effect of diurnal variation in inci-dent solar radiation on photosynthesis. Hanson

(1991) found an analytical solution to the dailyintegral of an empirical photosynthesis model asa rectangular hyperbola function of radiation.Haxeltine and Prentice (1996) developed a dailymodel using a non-rectangular hyperbola func-tion to describe the effect of radiation on photo-synthesis. Sands (1995) adjusted a light useefficiency model according to the diurnal radia-tion variation patterns. These models as well asothers with specific consideration of methods ofphotosynthesis calculation after daily andmonthly input data aggregations (Trost, 1990;Aber et al., 1996; Liu, 1996) suggest the impor-tance of considering the variability of meteoro-logical conditions within a computation timestep. However, some existing daily models usingFarquhar’s formulation (Farquhar et al., 1980),such as the BIOME-BGC (Hunt and Running,1992; Kimball et al., 1997), have not explicitlyincorporated the diurnal variation patterns in thecalculations. When we applied these daily modelsto reliable data sets obtained from BorealEcosystem–Atmosphere Study (BOREAS), wefound them to be incapable of simulating theday-to-day variations, and daily outputs are notreliable even though the annual totals can bebrought to agreement with experimental datathrough parameter adjustments. To improve thedaily modeling methodology without incurringmuch additional computation, we developed anew daily model through analytical spatial andtemporal integration of canopy photosynthesisprocesses under some assumptions. The purposeof this paper is to present this new daily modelof net primary productivity.

Because the Farquhar model was initially devel-oped and validated for individual leaves, consider-able skill is needed in using it for a plant canopy.Although the big-leaf approximation has beenshown to be successful for modeling evapotranspi-ration for plant canopies (Monteith andUnsworth, 1990), the same approximation may beerroneous for photosynthesis because of the addi-tional leaf internal control on carbon assimilation.For example, when stomatal conductance is re-placed by canopy conductance (usually stomatal

J.M. Chen et al. / Ecological Modelling 124 (1999) 99–119 101

conductance times leaf area index) in the big-leafmodel constructed using Farquhar’s formulation,the calculated results will be very different fromthe sum of photosynthesis of individual layers ofleaves calculated using the same formulation be-cause the internal control of leaves causes nonlin-ear response of leaf photosynthesis to stomatalconductance. From this perspective, the big-leafmethodology used by BIOME-BGC needs to befurther examined using experimental data. Manystudies have demonstrated successful use of Far-quhar’s model at the canopy level using otherapproaches, such as vertical integration againstradiation gradient (Baldocchi, 1993; Bonan, 1995)and separation of a canopy into sunlit and shadedportions (Kim and Verma, 1991; Norman, 1993;Foley et al., 1996; De Pury and Farquhar, 1997;Wang and Leuning, 1998). We adopted andmodified the latter approach because of its sim-plicity and ability to capture the major variabilitywithin the canopy. However, the effective use ofFarquhar’s model at the daily time step has notbeen demonstrated in previous studies. The objec-tives of this paper are: (1) to derive an analyticalsolution to a simplified temporal integral of Far-quhar’s photosynthesis model; (2) to validate themodel using experimental results from two majorboreal tree species; and (3) to show the advan-tages of this model over previous daily modelsand the limitations due to assumptions made inthe derivation of the integrated daily model.

2. Daily model description

NPP is an important component of the terres-trial carbon cycle. It is defined as the new carbonstored in living plants per unit time (usually annu-ally) per unit surface area. Using the same defini-tion as previous studies (see review by Melillo etal., 1996), NPP is the difference between the grossprimary productivity (GPP) and plant autotrophicrespiration (R). The emphasis of this study isplaced on the modeling of the NPP at daily step,although all other autotrophic respiration compo-nents are also calculated with the most recentlypublished results for the purpose of model valida-tion using experimental data.

2.1. Instantaneous leaf-le6el gross photosynthesis

Among models of photosynthetic CO2 assimila-tion by plant leaves, the mechanistic model pro-posed by Farquhar et al. (1980) has been widelyused. The model describes the leaf gross photo-synthesis rate at an instant of time for C3 plantsas the minimum of:

Wc=Vm

Ci−G

Ci+K(1a)

and

Wj=JCi−G

4.5Ci+10.5G(1b)

where Wc and Wj are Rubisco-limited and light-limited gross photosynthesis rates in mmol m−2

s−1, respectively. Vm is the maximum carboxyla-tion rate in mmol m−2 s−1; J is the electrontransport rate in mmol m−2 s−1; Ci is the intercel-lular CO2 concentration; G is the CO2 compensa-tion point without dark respiration; K is afunction of enzyme kinetics. The dimension forCi, G, and K can be either in Pa or in ppmv (partsper million by volume). Pa is used in this paper.Both G and K are temperature-dependentparameters. G, derived from Collatz et al. (1991),Sellers et al. (1992), can be expressed as:

G=1.92�10−4O21.75(T−25)/10 (2)

where O2 is the oxygen concentration in the atmo-sphere, being 21,000 Pa assuming that the atmo-spheric pressure is 100,000 Pa and O2 occupies21% of the air by volume. T is the air temperaturein °C. K is given by:

K=Kc(1+O2/Ko) (3)

where Kc and Ko are Michaelis–Menten constantsfor CO2 and O2, respectively in Pa. Kc=30�2.1(T−25)/10, and Ko=30,000�1.2(T−25)/10 (Col-latz et al., 1991). Vm can be expressed as afunction of temperature (Collatz et al., 1991) or afunction of both temperature and leaf nitrogencontent (Bonan, 1995):

Vm=Vm25 2.4(T−25)/10f(T)f(N) (4)

where Vm25 is Vm at 25°C, and is a variabledepending on vegetation type; f(T) and f(N) are


temperature and nitrogen limitation terms definedas:

f(T)

= (1+exp((−220,000+710(T+273))

/(Rgas(T+273))))−1 (5a)

f(N)=N/Nm (5b)

where N is the leaf nitrogen content, and Nm isthe maximum nitrogen content. J is dependent onphotosynthetic photon flux density (PPFD) ab-sorbed by the leaf (Farquhar and vonCaemmerer, 1982) and is given by:

J=JmaxPPFD/(PPFD+2.1�Jmax) (6)

where Jmax is the light-saturated rate of electrontransport in the photosynthetic carbon reductioncycle in leaf cells. According to Wullschleger(1993), it is related to the Rubisco activity by:

Jmax=29.1+1.64�Vm. (7)

To get net CO2 assimilation rate (A), daytimeleaf dark respiration (Rd) is subtracted from Eqs.(1a) and (1b):

A=min(Wc, Wj)−Rd (8)

According to Collatz et al. (1991),

Rd=0.015Vm (9)

2.2. Leaf-le6el daily integration of photosynthesisrate

The above instantaneous photosynthesis modelat leaf level defines the photosynthetic processesof individual leaves with known light illuminanceat an instant of time. Strictly, the productivityfrom a single leaf needs to be calculated continu-ously for the course of a day to obtain the dailytotal. Such a calculation for a large area is impos-sible from both viewpoints of meteorological dataavailability and computational demand. For re-gional and global applications, this original in-stantaneous model has been used to represent themean photosynthesis rate for periods of differentlengths from day to month (Woodward et al.,1995; Kimball et al., 1997). In these previousapplications, reasonable values for photosynthesiscan be obtained through appropriate parameteradjustments while ignoring the variability within

one time step. In order to avoid the excessivecomputational demand of diurnal calculationthrough numerical integration and yet to considerthe effects of diurnal variation patterns of meteo-rological variables on photosynthesis, we devel-oped an analytical solution to the simplifiedtemporal integral of Farquhar’s model for calcu-lations at daily time steps.

The net photosynthesis rate can also be de-scribed in the form (Leuning, 1990; Sellers et al.,1996):

A= (Ca−Ci)g (10)

where Ca is CO2 concentration in the atmosphere;g is the conductance to CO2 through the pathwayfrom the atmosphere outside of leaf boundarylayer in mmol m−2 s1 Pa−1 to the intercellularspace, given by:

g:106�gs/(Rgas�(T+273)) (11)

where gs is stomatal conductance; Rgas is themolar gas constant, being 8.3143 m3 Pa mol−1

K−1. After (i) substituting Ci in Eqs. (1a) and(1b) with Eq. (10), (ii) combining the results withEq. (8), and (iii) choosing the solution of thequadratic equations with the smaller roots (Leun-ing, 1990), we obtain:

Ac=12

((Ca+K)g+Vm−Rd

−((Ca+K)g+Vm−Rd)2−4(Vm(Ca−G)

−(Ca+K)Rd)g) (12a)

Aj=12

((Ca+2.3G)g+0.2J−Rd

−((Ca+2.3G)g+0.2J−Rd)2−4(0.2J(Ca

−G)− (Ca+2.3G)Rd)g) (12b)

where Ac and Aj correspond to Wc and Wj, respec-tively, after a small reduction for dark respiration(see Eq. (8)).

The diurnal variation in plant photosynthesis iscaused by several meteorological variables includ-ing (1) incident solar irradiance which determinesstomatal conductance and J in the photosynthesismodel; (2) air temperature which affects Vm, G,and K ; and (3) air humidity which influencesstomatal conductance and hence Ci. Completetemporal integration of Eqs. (12a) and (12b) re-


quires consideration of the temporal patterns ofall three variables, but no analytical solutions tothis complete daily integral are possible. Throughour numerical experiments with the daily integral,we found that the diurnal variation in photosyn-thesis is mostly caused by the diurnal variation instomatal conductance as the synthetic variable ofthe solar irradiance and vapor pressure deficitunder given soil moisture conditions. The effect ofthe air temperature variation is secondary andgenerally occurs in a similar pattern to solarradiation. This is agreeable since solar radiation isthe driving force for diurnal changes in othermeteorological variables. Incident solar irradi-ance, air temperature and humidity at a givenlocation are usually highly correlated. Our tempo-ral scaling approach is therefore focused on thediurnal integration of changes caused by stomatalconductance. For the calculation of diurnalcourse of stomatal conductance, we made thefollowing assumptions.

1. The daily course of solar radiation follows acosine function of solar zenith angle with a peakat solar noon. That is:

Sg=Sg,n cos� u−un

p/2−un

p

2�

(13)

where Sg is the instantaneous global solar radia-tion; Sg,n is the global solar radiation at noon; u isthe solar zenith angle; un is the solar zenith angleat noon. This equation is applied to sunlit leafcalculations on all weather conditions. A cloudyday follows the same pattern as a clear day butwith smaller magnitudes.

2. Solar radiation variation determines the di-urnal pattern of stomatal conductance. Since airhumidity has a similar diurnal pattern, the firstorder effect of humidity is automatically broughtinto account in this way. However, considerableerrors can still remain after considering these vari-ations because under water-stressed conditions,plants usually exhibit mid-day depression in pho-tosynthesis as a result of low leaf water potential.Such effects causing irregular diurnal patterns aredifficult to be considered at daily step calcula-tions, but the water potential effect will enter intothe calculation through making the mid-day stom-

atal conductance dependent on the daily meanwater potential.

3. Vm, K and J in Eqs. (12a) and (12b) changeapproximately linearly with environmental factorsduring the day so that daily mean values for themcan be used. We realize that Vm and K are non-linear functions of temperature. However, duringthe active photosynthesis period in the day, thetemperature generally vary within a small range(5–10°C), and the departure from the linearity issmall within such a small range. The sunlit andshaded leaf separation described below is the crit-ical step towards minimizing the non-linear effectof the spatial variability of PPFD in the canopyon J, but the effect of temporal variability stillremains. However, the most important effect ofPPFD temporal variability on stomatal conduc-tance is considered.

4. The ratio of sunlit to shaded leaf area isconstant during a day. This ratio does vary duringthe day and decreases with increasing solar zenithangle. This simplification is made to avoid exces-sive complexity of the model. The simplificationcauses some suppression of diurnal variation,which is compensated by assuming the sinusoidalvariations in the direct and diffuse irradiance onleaf surfaces.

Theoretically, diurnal integration of Eqs. (12a)and (12b) for daily total photosynthesis should bemade with respect to time. Our attempt to obtainan analytical solution to such integration was notsuccessful because of the complication induced bythe non-linear relationship between time andstomatal conductance, which is approximately si-nusoidal. We therefore found an alternative byintegrating with respect to conductance (g) asfollows:

Ac=m

2(gn−gmin)& gn

g min

((Ca+K)g+Vm−Rd

−((Ca+K)g+Vm−Rd)2−4(Vm(Ca−G)

−(Ca+K)Rd)g)dg (14a)

Aj=m

2(gn−gmin)& gn

g min

((Ca+2.3G)g+0.2J−Rd

−((Ca+2.3G)g+0.2J−Rd)2−4(0.2J(Ca

−G)− (Ca+2.3G)Rd)g) dg (14b)


where gn is the conductance at noon, and gmin isthe minimum conductance before sunrise or aftersunset and is set to zero in this study. The under-lying assumption of direct integration with respectto g rather than time is that g changes linearlywith time in both directions from noon. Since thediurnal solar radiation variation pattern is moresinusoidal than linear, such an assumption canincur errors in the final integration. If gn is cor-rectly calculated from the total daily radiationand leaf water potential using the sinusoidal pat-tern, the linear variation would cause underesti-mation in the daily photosynthesis. There are twoways to remedy this: (1) to calculate gn under thesame linear assumption, (2) to make an adjust-ment according to the difference between thesetwo integration schemes. The first is not a goodchoice because it would produce gn which is unre-alistic and cannot be compared with measure-ments. We choose to correct the bias by makingan adjustment. The parameter m is therefore mul-tiplied to the integral. It can be calculated from

m=1

0.5p/2& p/2

0

cos u du=4p:1.27 (15)

The result is to increase the linearly-integratedvalue by 27%. The appropriateness of the linearintegration and this adjustment lies in the factthat the relationship between Ac (or Aj) and g isessentially linear (Ball, 1988) except for very largeg values (Leuning, 1990; Dang et al., 1998). Withthis simplification in our approach, these twoequations can be analytically integrated and pre-sented in the following form:

A=1.27

2(gn−gmin)�a1/2

2(gn

2 −gmin2 )+c1/2(gn−gmin

2 )

−2agn+b

4ad+

2agmin+b4a

e1/2

+b2−4ac

8a3/2 ln2agn+b+2a1/2d

2agmin+b+2a1/2e�

(16)

where for Ac, a= (K+Ca)2, b=2(2G+K−Ca)Vm+ 2(Ca+K)Rd and c= (Vm−Rd)2 and forAj, a= (2.3G+Ca)2, b=0.4(4.3G−Ca)J+ 2(Ca

+ 2.3G)Rd, and c= (0.2J−Rd)2. For both, d=(agn

2 +bgn+c)1/2 and e= (ag2min+bgmin+c)1/2.

Eq. (16) is the final equation for calculating thedaily averaged A as the minimum of Ac and Aj. Itis applied to sunlit and shaded leaves separately.It is noted that: (1) no additional parameters areintroduced in this daily model, and all the con-stants are determined by the leaf biochemicalparameters in the original Farqhuar model; (2)although Eq. (16) appears to be complex, it isnumerically stable, and no numerical problemshave been encountered in using this equation forremote sensing applications for large areas ofextreme conditions; (3) the analytical integrationgiven by Eq. (16) is computationally efficient andavoids a daily loop using a numerical integrationmethod.

In principle, Eq. (16) should be applied forevery leaf in a canopy in order to get daily ormonthly total canopy photosynthesis. In thisstudy, we choose to stratify a canopy into sunlitand shaded leaf groups and apply this equation tothese two groups separately. We prefer this tostratification by canopy layers because the great-est difference in leaf illumination in the canopyexists between sunlit and shaded leaves. The pur-pose of the multiple layer calculation is to con-sider the general decreasing trend of radiationwith the increasing depth into the canopy. It is animprovement from the big-leaf model, in whichthe canopy is treated as one layer of leaves.However, within a layer at a given time the differ-ence in illumination between sunlit and shadedleaves is very large and using the mean illumina-tion value to represent the layer can result inconsiderable errors in modeled results. With theseparation of sunlit and shaded leaf groups, thetotal canopy photosynthesis (Acanopy) can be cal-culated as (Norman, 1982):

Acanopy=AsunLAIsun+AshadeLAIshade (17)

where the subscripts ‘sun’ and ‘shade’ denote thesunlit and shaded components of photosynthesisand LAI. The method of Norman (1982) forcalculating LAIsun and LAIshade is adopted in thisstudy but modified to consider the effect of foliageclumping index (V) on the canopy radiationregime:


LAIsun=2 cos u(1−exp(−0.5VLAI/cos u))(18a)

LAIshade=LAI−LAIsun (18b)

where LAI is the leaf area index, and u is the solarzenith angle. V for boreal forests is �0.5 forconifers and 0.7 for deciduous species, respectively(Chen, 1996a; Chen et al., 1997). The larger V

departure from unity, the more non-random is thefoliage spatial distribution. It is critically impor-tant to consider this in productivity models be-cause foliage clumping alters the way plantsinteract with incident radiation. Increasing foliageclumping (decreasing V value) allows more radia-tion penetrated through the canopy without beingintercepted by the foliage and therefore decreasessunlit LAI and increases shaded LAI. The clumpedarchitecture of forest canopies makes the stratifica-tion between sunlit and shaded leaves essentialbecause the fraction of the shaded leaves is muchlarger in clumped canopies than in randomcanopies and shaded leaves play an important rolein forest productivity (Goulden et al., 1997).

2.3. Sunlit leaf irradiance and shaded leafirradiance

Sunlit leaf irradiance and shaded leaf irradianceare important variables in Eq. (16) because of theireffects on both g and J. In order to estimate them,the total solar radiation above the plant canopy(Sg) is partitioned using an empirical formula ofErbs et al. (1982), which was modified and vali-dated by Black et al. (1991) for northern environ-ment. The fraction of diffuse radiation in the totalis determined by:

Sdif

Sg

=

>0.943+0.734R−4.9R2+1.796R3+2.058R4

0.13RB0.8R\0.8 (19)

where Sg is the global solar radiation in W m−2.R is a ratio equal to Sg/(So cos u) where So is thesolar constant (=1367 W m−2). The direct radia-tion fraction above the canopy (Sdir) is the remain-der of the diffuse fraction.

With Sdif, and therefore Sdir determined fromEq. (19), the sunlit leaf irradiance (Ssun) is calcu-

lated as (Norman, 1982):

Ssun=Sdir cos a/cos u+Sshade (20)where a is mean leaf-sun angle. a=60° for acanopy with spherical leaf angle distribution,which is found to be also a good approximationfor boreal canopy in u range from 30 to 60° (Chen,1996b). Because Sdir is proportional to cos u, Ssun

changes little in a day. With the consideration offoliage clumping effect, a different method forestimating the mean shaded leaf irradiance (Sshade)is developed based on radiative transfer physics. Itis summarized as follows:

Sshade= (Sdif−Sdif,under)/LAI+C (21)

where Sdif,under is diffuse radiation under the plantcanopy; and C arises from multiple scattering ofdirect radiation (Norman, 1982):

C=0.07VSdir(1.1−0.1LAI) exp(−cos u) (22)

Eq. (21) states that diffuse irradiance on shadedleaves originates from two sources: sky irradianceand multiple scattering of the incident radiationwithin the canopy. The first term in Eq. (21) makesthe average of the total intercepted diffuse radia-tion from the sky for the total LAI involved (sunlitleaves also contribute to the interception). Thediffuse radiation reaching to the forest floor iscalculated using the simple equation with the con-sideration of the clumping effect (V):

Sdif,under=Sdif exp(−0.5VLAI/cos u) (23)

where u is a representative zenith angle for diffuseradiation transmission and slightly dependent onleaf area index:

cos u=0.537+0.025LAI (24)

This is a simple but an effective way to calculatethe transmitted diffuse radiation. It avoids theintegration of the sky irradiance for the hemisphereby using a representative transmission zenith angleu, which is obtained through a numerical experi-ment with the complete integration. Under theassumption of isotropic sky radiance distribution,it is near a constant of 57.5° but also a weakfunction of LAI. This angle is larger than the meanof 45° because the hemisphere is more heavilyweighted against the lower hemisphere in the inte-


gration. The dependence on LAI is found becauseit modifies slightly the weight distribution.

2.4. Stomatal conductance

Plants respond to their environment throughstomatal movement that can be quantified interms of stomatal conductance. To simulate thisresponse, one approach is to reduce a species-de-pendent maximum by the environmental condi-tions departed from the optimum (Jarvis andMorison, 1981; Running and Coughlan, 1988).The environmental factors usually include photo-synthetic photon flux density (PPFD), tempera-ture (T), vapor pressure deficit (VPD), and others,i.e.

gs=max(gmax�f(PPFD)�f(T)�f(VPD), gmin)(25)

where the environmental functions are scalars be-tween 0 and 1 which are formed in the same wayas in BIOME-BGC. These functions are expressedas:

f(PPFD)

=PPFD�PPFDcoef/(1+PPFD�PPFDcoef) (26a)

f(T)

=ÍÃ

Ã

Á

Ä

ln(T)/ln(Topt)

cos�p

2(T−Topt)/(Trange−Topt)

�0

TBTopt

T\Topt

TB1(26b)

f(VPD)=

ÍÁ

Ä

1(VPDclose−VPD)/(VPDclose−VPDopen)0

VPDBVPDopen

VPDopenBVPDBVPDclose

VPD\VPDclose

(26c)

The meaning of the symbols in these equationsand their values and units are found in Table 1.

To determine PPFD at noon, the solar zenith

angle at noon is first calculated from the latitudeof the location (8) and the day of year (D) (Oke,1990):

cos un=sin(−23.4 cos(360(D+10)/365)) sin 8

+cos(−23.4 cos(360(D+10)/365)) cos 8

(27)

The arguments in the trigonometry functions inEq. (27) are in degrees. According to Eq. (13),

Sg, day

Daylength=

1p

2−un

& 2/p

u n

Sg,n cos� u−un

p/2−un

p

2�

du

= (2/p)Sg,n (28)

where Sq,day is the daily total solar radiation in Jday−1 m−2. Therefore, with the PAR-energy ratioof 4.55 mmol/J and the visible shortwave radiationfraction of 0.5, PPFD at noon (in mmol m−2 s−1)is:

PPFDn=1.1p(Sg, day/Daylength) (29)

2.5. Daily autotrophic respiration

Conventionally, autotrophic respiration (Ra) isseparated into maintenance respiration (Rm) andgrowth respiration (Rg) (Running and Coughlan,1988; Ryan, 1990, 1991):

Ra=Rm+Rg=%i

(Rm,i+Rg,i) (30)

where i is an index for different plant compo-nents, (1 for leaf, 2 for stem, and 3 for root).Maintenance respiration is temperature-dependent:

Rm,i=Mirm,iQ10(T−Tb)/10 (31)

where Mi is the biomass (sapwood for stems) ofplant component i ; rm,i is maintenance respirationcoefficient for component i, or the respiration rateat the base temperature; Q10 is the temperaturesensitivity factor, and Tb is the base temperature.Growth respiration is generally considered to beindependent of temperature and is proportional toGPP:

Rg,i=rg,i ra,iGPP (32)

where rg,i is a growth respiration coefficient forplant component i ; and ra,i is the carbon alloca-tion fraction for plant component i.


3. Experimental data for model validation

An old black spruce site located at 55.879° Nand 98.484° W in Manitoba, Canada, is chosen asthe major site to validate the daily model. Thissite was one of tower measurement sites duringthe BOREAS in 1994 (Sellers et al., 1997). Blackspruce (Picea mariana) is the dominant species inthe BOREAS study region. The overstory at thesite was dominated with dense, 10 m tall, 75-year-old trees in upland areas, and sparse, 1 to 6-mtall, 90-year-old trees in lowland areas. The un-derstory was composed of 45% feather moss(Pleurozium schreberi ), 45% Sphagnum moss(Sphagnum fuscum), and 10% fen within 500 m of

the tower. The site was level, and consisted ofpoorly drained silt and clay.

In 1996, simultaneous CO2 flux measurementswere made above and below the canopy. Theabove-canopy measurements were made using aneddy-covariance method, and the below-canopywas made using closed clear chambers on theforest floor including the understory grass andmoss. Two chambers were used for feather moss(chambers 2 and 3 referred by Goulden and Crill,1997), and three for sphagnum moss (chambers 8,9, 10). The chamber measurements were madeautomatically at 3-h intervals. Daily total fluxesfor the stand were obtained by giving 50% weightto the average of chambers 2 and 3 for feather

Table 1The parameters, their descriptions, and values at the old black spruce site for NPP calculation

Value ReferenceDescriptionUnitSymbol

General4Leaf area indexLAI Chen et al. (1997)m2/m2

Latitude 55.8798 Goulden et al. (1997)° N

Photosynthesismm s−1 Maximum stomatal conductance 1.6 Dang et al. (1997), Running andgmax

Coughlan (1988)gmin Minimum stomatal conductancemm s−1 0.0 This studyNleaf Based on Kimball et al. (1997)1.2Leaf nitrogen content%

1.5Maximum leaf nitrogen content Bonan (1995)%Nm

Maximum carboxylation rate at 25°C 33Vm,25 Bonan (1995), Dang et al. (1998)mmol m−2 s−1

mmol m−2 s−1 Coefficient in a relationship between gs and 0.01 Kimball et al. (1997)PPFDcoef

PPFD (Eq. (26a))°CTopt Optimal temperature 25 Kimball et al. (1997)

Maximum temperature range Kimball et al. (1997)°C 40Trange

kPa Vapour pressure deficit at stomatal openingVPDopen 0.2 Dang et al. (1997)VPDclose kPa Vapour pressure deficit at stomatal closure 2 Dang et al. (1997)

RespirationQ10 – Temperature sensitivity factor 2.3 Kimball et al. (1997)

kg C m−2 Biomass of leafMleaf 0.4 Gower et al. (1977)Mstem kg C m−2 Sapwood carbon of stem 0.28 Kimball et al. (1997)Mroot kg C m−2 Biomass of root 1.4 Steele et al. (1997)

day−1 Leaf maintenance respiration coefficientrm,leaf 0.002 at 20°C Kimball et al. (1997)Stem maintenance respiration coefficientg g−1day Kimball et al. (1997)rm,stem 0.001 at 20°CCoarse root maintenance respiration coeffi-rm,rootc 0.001 at 20°C Kimball et al. (1997)g g−1daycient

g g−1dayrm,rootf Fine root maintenance respiration coefficient 0.002 at 20°C Kimball et al. (1997)Ryan (1991)0.25Overall growth respiration coefficientrg g g−1day

g g−1day Root growth respiration coefficientrg,root 0.25 Ryan (1991)Root carbon allocation fractionra,root – Running and Coughlan (1988)0.40


moss, and 50% weight to the average of chambers8, 9 and 10 for sphagnum moss. This weightdistribution reflects the percentage coverage ofthese two moss types on the forest floor. The datawere checked for quality in processing (Gouldenand Crill, 1997) and good measurements from 28May to 21 October, 1996 were used in this study.Similar above-canopy measurements in 1994 andbelow-canopy measurements in 1995 were de-scribed in detail by Goulden et al. (1997), Gouldenand Crill (1997), respectively.

The flux measurements at these two levels can beused to differentiate between the overstory and thebackground (understory, moss and soil) in theirrole in the carbon cycle. The fluxes at the top of thecanopy and from the forest floor are composed ofseveral terms defined as follows:

FLUXT=POVER+ROVER,ABOVE+ROVER,ROOT

+PUNDER+RUNDER+RSOIL (33)

FLUXC=ROVER,ROOT+PUNDER+RUNDER

+RSOIL (34)

where P and R denote photosynthesis and respira-tion fluxes, respectively. Subscripts T and C standfor tower and chamber measurements, respectively.The subscripts OVER, UNDER, SOIL indicateoverstory, understory and soil, respectively. Thesubscripts ABOVE and ROOT are for aboveground, and root of the overstory, respectively. Wedefine downward fluxes as positive and upwardfluxes as negative so that photosynthesis is alwayspositive and respiration is always negative. There-fore, NPP of the overstory, defined as Pover+Rover,above+Rover,root, can be then be obtained bytaking the difference between Eqs. (33) and (34).The final expression becomes

NPP=FLUXT−FLUXC+ROVER,ROOT (35)

The root respiration term remains in the expressionbecause of the transport of some fraction of carbonassimilates to roots from the overstory. Since thefluxes measured correspond to the instantaneousphotosynthesis and respiration processes, NPP cal-culated in this way is considered to be instanta-neous. Meteorological variables including solarradiation, temperature and humidity used as the

model input were measured on the tower above thecanopy (Goulden et al., 1997).

A deciduous forest site located at 53.629° N,106.2° W in the BOREAS region is used to furthervalidate the daily model. The overstory at the sitewas mature aspen (Populus tremuloides). The sameprinciples given above are also used to obtain theoverstory NPP from simultaneous eddy-covariancemeasurements at heights above the forest andbetween the overstory and understory. More detailsof the measurement procedures and the data set in1994 are found in Black et al. (1996).

3.1. Parameterization for the old black spruce site

Table 1 summarizes all the parameters used forcalculating photosynthesis, maintenance respira-tion, growth respiration and total root respirationat the old black spruce site.

3.1.1. Maximum stomatal conductance (gmax)The observed stomatal conductance for black

spruce during BOREAS reached 0.05 mol m−2 s−1

in the field and 0.055 mol m−2 s−1 in the labora-tory (Dang et al. 1997). It is �1.3–1.4 mm s−1.Although the gmax was reduced to 1.0 mm s−1 inBIOME-BGC from 1.6 mm s−1 in the FOREST-BGC for conifer forest (Kimball et al., 1997), weconsider 1.6 mm s−1 is more reasonable for gmax.It is slightly larger than the largest value found inobservation because the optimum conditions sel-dom occurred in the field.

3.1.2. Maximum carboxylation rate at 25°C(Vm,25)

Vm,25 is a very important parameter that stronglyinfluences the magnitude of photosynthesis. Com-paring the observed Vm values (Dang et al. 1998)with Vm values calculated using the methods ofBonan (1995), Kimball et al. (1997) and Sellers etal. (1992), it is found that Bonan’s method and theassociated Vm,25 fit observations best, while theothers tend to overestimate Vm and the photosyn-thetic rate.

3.1.3. Maintenance respiration coefficientsAs discussed above, plant maintenance respira-

tion is determined by: (1) biomass of plant compo-nents; (2) respiration coefficients at the base


Fig. 1. Response of biochemical parameters in Farquhar’s model to meteorological variables. Vm is the maximum carboxylation rate;J is the electron transport rate; gamma (G) is the CO2 compensation point without dark respiration; and K is a function of enzymekinetics.

temperature; (3) Q10; and (4) base temperature.The biomass of the plant components at the sitecan be obtained from the literature, while deter-mining the maintenance respiration coefficients,Q10 values, and the base temperature is difficult.After carefully examining previous studies (Run-ning and Coughlan, 1988; Foley, 1994; Bonan,1995; Ruimy et al., 1996; Kimball et al. 1997),we chose the equations and associated parame-ters of BIOME-BGC (Kimball et al. 1997). Thisis because: (1), as stated by Ruimy et al. (1996),BIOME-BGC is the only model using ‘uncali-brated’ coefficients; and (2) the derived autores-piration based on the coefficients agrees closelywith measurements for the site (Ryan et al.,1997).

4. Results and discussion

To illustrate the importance of proper dailyintegration for stand-level and ecosystem-levelmodeling of photosynthesis, the response of severalFarquhar model parameters to meteorologicalvariables are shown in Fig. 1. The effects oftemperature on the model parameters including k,G and Vm are not linear, causing non-linearresponse to temperature over the full range.However, during daytime the temperature usuallyvaries within a small range and a linearapproximation would not incur large errors. Alinear approximation justifies the use of meandaytime temperature for one step dailyphotosynthesis calculations. The response of J toillumination is highly non-linear. During the


daytime, plant leaves experience the full range ofillumination. At a given time, leaves at differentlocations in the canopy can have very differentillumination levels. These large temporal and spa-tial variations in radiation can cause large errorsin daily photosynthesis calculations if ignored.

Meteorological conditions at the site during thegrowing season of 1996 are shown in Figs. 2 and3. In Fig. 2, the values of the mean irradiance atnoon on sunlit and shaded leaves were calculatedusing Eqs. (20)–(24). The day-to-day variationsare caused by cloud conditions. Large day-to-dayvariations in air temperature and VPD are alsoevident in Fig. 3. The daily mean air temperatureranged from −3 to 23°C, while the daily meanVPD ranged from 0 to 16 mbar. In addition tothe seasonal variation of the temperature from theend of May to the beginning of September, therewere two distinct step changes in temperature atDOY:250 and DOY:270. The seasonal varia-tion of the vapor pressure deficit follows a patternsimilar to the temperature variation.

The seasonal course of daily CO2 fluxes mea-sured above and below the black spruce standusing eddy-covariance and chamber techniques

are shown in Fig. 4. These data series are the firstsimultaneously paired measurements for blackspruce, which allow the separation of the over-story NPP from above-canopy flux measurementson a daily basis after making an allowance for theroot respiration as described in Eqs. (31) and (32).No previous models were tested with similar datasets. However, the fact that root respiration isinvolved causes some uncertainties in the conver-sion of these time series into an overstory NPPseries. We therefore closely examined the magni-tude of root respiration as a function of soiltemperature and the root biomass. Using theavailable data for root biomass measured at thesite and suggested coefficients (Running andCoughlan, 1988; Steele et al., 1997; Kimball et al.,1997; Ryan, 1991; Ryan et al., 1997), we obtainedthe best possible daily values of root respiration(Fig. 5). The total autotrophic respiration withoutthe daytime leaf respiration is also shown forcomparison. The root respiration is responsiblefor 60% of the total plant respiration. This ratio isin agreement with the value of 62% for the sitereported by Ryan et al. (1997).

Fig. 2. Canopy photosynthetically active photon flux density (PPFD) on sunlit and shaded leaves at noon in comparison with thetotal PPFD at noon.


Fig. 3. Daily mean air temperature and vapor pressure deficit (VPD) measured at a micrometeorological tower above a mature blackspruce stand at the height of 29 m.

Results from several models are compared withthe ‘measured daily NPP’ values obtained fromthe above- and below-canopy flux measurementsand root respiration estimates (Fig. 6). Threetypes of models were used: (1) Farquhar’s modelwith the daily integration and sunlit–shaded leafseparation as shown in Section 2; (2) Farquhar’smodel with sunlit–shaded leaf separation withoutthe daily integration; and (3) big-leaf Farqhuar’smodel as formulated by BIOME-BGC. The valuesfor the model parameters of k, G and Vm arefound to be the most suitable for the species(Collatz et al., 1991; Bonan, 1995; Dang et al.,1998) and are the same for all three types ofmodels. The relationship between Vm and Jmax isalso the same. The differences in the modeledresults are therefore entirely due to the differentmathematical manipulation of the Farquhar equa-tions. In all these models, the soil water balance,precipitation, and evapotranspiration are consid-ered and stomatal conductance is calculated notonly from radiation but also from temperatureand humidity as outlined in Eqs. (25), (26a), (26b)and (26c)–(29). Several important points aredemonstrated.

(1) The big-leaf model is able to simulate thegeneral seasonal variation pattern with approxi-mately correct total for the season, but it is notable to mimic the day-to-day variation. Much ofthe day-to-day variation in photosynthesis wascaused by changes in radiation regimes as well asin humidity and temperature. The effects of thechanges in radiation and humidity are mostlyconsidered through their influences on stomatalconductance and partly in the value of J. How-ever, in the big-leaf formulation, canopy conduc-tance as a surrogate of stomatal conductance isonly a relative small part of the control of theflow of CO2 from the free air to photosyntheticapparatus in leaf cells, and the canopy photosyn-thesis is not very sensitive to changes in canopyconductance. The fundamental problem with big-leaf models is that when stomatal conductance isreplaced by canopy conductance, the big-leaf in-ternal controls, as reflected by the parameters k,G, Vm and Jmax, should not remain the same. Forexample, if G is considered as the CO2 compensa-tion point per unit leaf area, in the big-leaf modelit should become per unit ground surface area,and then the value should be increased by a factor


equal to LAI because more leaf area producesmore photorespiration. By the same argument,Vm and Jmax should also be increased accordingly.We conducted numerical experiments by increas-ing these parameters by a factor of LAI andfound that the day-to-day variation indeed be-comes much larger and follows the general pat-tern of measured NPP. Although this seems to bean improvement to the big-leaf formulation, itdoes not solve the problem because these adjust-ments do not have biological foundation andmakes the model too highly sensitive to the inputLAI value. In reality, canopy photosynthesis hasdiminished response to LAI increase at large LAIvalues. A further improvement can perhaps bemade by allowing Vm and Jmax to vary at differentlayers. This then will eventually turn a big-leafmodel into a multiple layer model. The problemwith big-leaf models can also be seen from an-other perspective. In a canopy, individual leavesoperate in parallel, but big-leaf models conceptu-ally force them to operate in a partial parallelmode after multiplying the stomatal conductanceby LAI. When stomatal conductance is replacedby canopy conductance in Farquhar’s model, the

simulated leaf internal CO2 concentration (Ci)becomes unrealistic (in some cases values veryclose to external concentration Ca can be pro-duced in big-leaf simulation). This is because theharmony of the original model for individualleaves is disrupted when used in this way.

(2) The simple separation of sunlit and shadedleaves at noon results in much greater day-to-dayvariability compared with the big-leaf model, andthe pattern of the variation is similar to thatexhibited in the measured data. However, themagnitude of the modeled NPP is too large com-pared with measured values. The difference farexceeds the uncertainty range in the root respira-tion estimation. The overestimation is caused byoptimizing the radiation control on photosynthe-sis in the process of taking the mean irradiancefor the day. For example, in hourly calculations,sunlit leaves are often saturated by direct irradi-ance, but when the mean of the day is taken, thesaturation never occurs. In this case, the radiationuse efficiency is too high, resulting in the overesti-mation. Fig. 7 is shown in support of this argu-ment. The modelled daily total gross primaryproductivity (GPP), as defined by Eqs. (1a) and

Fig. 4. Daily total CO2 fluxes measured using an eddy-covariance technique above the canopy (29 m) and below the canopy usingchambers. Note downward flux is defined as positive.


Fig. 5. Estimated daily root respiration and total plant respiration for the growing season for a mature black spruce stand.

(1b), depends strongly on the computation timestep, within which the tower-measured meteoro-logical variables (radiation, temperature and hu-midity) are aggregated before modelling. Themodelled values increases with the increasing timestep from 1/2, 2, 4 to 24 h, although the differencebetween 1/2 and 2 h steps is small.

(3) The integrated daily model not only has theappropriate variability but also has the right mag-nitude. This model not only avoids the flaws ofthe big-leaf model, allowing good response ofpredicted photosynthesis to weather conditions,but also remedies the overestimation problem ofsunlit–shaded leaf model without considering thediurnal variation pattern.

Another problem with big leaf models usingFarquhar’s formulation is the tendency to invokefrequent temperature limitations and infrequentradiation limitations to photosynthesis. When ei-ther the incident radiation or the absorbed radia-tion of the big-leaf is used in the models, theestimated electronic transport rate almost alwaysexceeds the Rubisco activity, i.e. the radiationlevel is higher than the minimum required by theRubisco activity and often becomes irrelevant forcanopy photosynthesis estimation. As both photo-

synthesis and autotrophic respiration vary withtemperature in similar patterns, the NPP, as thedifference between GPP and autotrophic respira-tion, becomes insensitive not only to radiation butalso to temperature variation. The big-leaf modelis therefore not able to capture productive sunnyand humid days or non-productive overcast orrainy days. After sunlit and shaded leaves areseparated, it is often found that sunlit leaves arecontrolled by temperature and shaded leaves byradiation, and therefore the sensitivity of the cal-culated NPP to meteorological changes is greatlyimproved.

Having shown shortcomings of the big-leaf for-mulation for canopy photosynthesis, we need toanalyze the reason for the widespread success ofbig-leaf evapotranspiration (ET) model (Monteithand Unsworth, 1990). For transpiration, leaves indifferent layers also operate in parallel, but chang-ing the formulation from the parallel to partialparallel mode in big-leaf models only incurs asmall error due to the control of leaf air boundarylayer resistance which is in series with stomatalresistance. If the boundary layer resistance is ab-sent, there is no difference between parallel (mul-tiple layers) and big-leaf (single layer)


formulations This is because the flow of watervapor remains the same whether or not it isdivided into multiple channels (stomates) as longas the total conductance is the same. This may beunderstood by imagining the case of water flow ina pipe: the flow rate is independent of the numberof divisions of the pipe into mini-pipes if thefriction on the walls of the mini-pipes is ignored.The friction resembles the boundary layer resis-tance. Because it is usually one order of magni-tude smaller than the stomatal resistance, anysimple treatment of this effect does not causeconsiderable errors. The basic reason for the suc-cess of ET big-leaf models is that there is no leafinternal control beyond stomates on the watervapor flux, i.e. the stomatal pores are 100% wet.On the other hand, in photosynthesis, CO2 instomatal pores can be assimilated at very differentrates depending on the rate of Rubisco activity orthe electron transport. In mathematical terms,there is a large additional resistance to the CO2

flow inside the leaf that is in series with stomatalresistance and should be adjusted accordinglywhen stomatal conductance is replaced by canopy

conductance. From this point of view, it can beinferred that big-leaf NPP models would workwell for thin canopies with LAI close to unity, butas the LAI increases the error of big-leaf modelswill likely to increase. If a model of this type iscalibrated using measurements from a sitethrough adjustment of parameters (such as Vmax

and G), it can still be inaccurate for other standsof different LAI values or under different climateregimes. In other words, the level of simplificationin our modeling methodologies should be compat-ible with the complexity of the gas type involvedin the biological processes, and it is undesirable tosimplify the photosynthesis process using big-leafmodels if both simplicity and generality of modelsare required.

The results from the big-leaf and daily-inte-grated models are compared with the measureddaily NPP values in one-to-one plots (Fig. 8) forfurther analysis. The lack of response of the big-leaf model to the changes in the measured valuesis evident from the small slope and low R2 value.The response is greatly increased after the sun–shade leaf separation and the daily integration,

Fig. 6. Daily variations of overstory NPP obtained from tower and chamber measurements in comparison with modeled results. Forall three modeling methodologies the same values were used for Vm, G and other coefficients in Farquhar’s model. The samerelationship between Vm and Jmax was also used.


Fig. 7. The effect of pre-modelling data aggregation on daily gross primary productivity (GPP) calculations for a mature blackspruce stand. The calculations are made using the sunlit–shaded leaf model without considering the variability of meteorologicalconditions within a time step. The data aggregation steps are 0.5, 2, 4 and 24 h.

but the deviation from the one-to-one line is stillsignificant and the R2 value is still low (0.46).Much of the scatter in the plot results from theuncertainties in chamber measurements becausethe five chambers used might have not well repre-sented the average conditions of the stand undervarying weather conditions. Some of the scatter isdue to irregular sub-daily variations in weatherconditions, especially on cloudy days when thediurnal radiation pattern deviates from the sinu-soidal pattern assumed in the model. For thepurpose of differentiating errors due to sub-dailyvariability from those due to measurement, dailyNPP values (i.e. Y) calculated at daily steps usingthe sun–shade model with daily integration (Eqs.(16) and (17)) were compared with those (i.e. X)calculated at half hourly steps using a sun–shadeleaf model (Eqs. (12a), (12b) and (17)). The resultof the comparison is Y=0.94X+0.38, with R2=0.72. This means that the sub-daily variabilitycaused about half of the data scatter and the otherhalf was due to measurement errors. The system-atic difference between modeled values at thesetwo time steps is about 22%, suggesting that thereis still room for improvement in the integrateddaily model. The most needed improvement maybe to develop a way to determine the frequency oftemperature or radiation control on photosynthe-

sis for sunlit and shaded leaves separately in dailysteps under variable weather conditions.

To further validate the daily model for applica-tions to boreal landscape of various cover types,we also simulated a data set obtained from anaspen site. Fig. 9 shows a summary of the model-ing results for this site. Again, the big-leaf modelhas the same problem, but the results for thedaily-integrated model are better than that for theblack spruce site shown in Fig. 8 in terms of thescatter and slope. The scatter is reduced because ofthe better spatial representativeness of the eddy-covariance technique used for measuring fluxesfrom the understory and soil. However, the modelis still not able to simulate the days with large NPPvalues for the same reason as discussed for Fig. 8.

5. Conclusions

With the unprecedented simultaneous CO2 fluxmeasurements above and below forest canopies,we are able for the first time to examine variouscanopy photosynthesis models at daily steps. Big-leaf canopy photosynthesis models are the simplestand are shown to be capable of simulating theseasonal photosynthesis trends. However, wefound such models greatly dampen day-to-day


variations in canopy photosynthesis simulationswhen compared with the measurements. Big-leafphotosynthesis models disrupted the harmony ofthe original leaf-level photosynthesis modelthrough the replacement of stomatal conductancewith canopy conductance. They do not ade-quately represent the flow of CO2 in plantcanopies because stomatal conductance is onlypart of the control of CO2 flow from the free airto the photosynthetic apparatus inside leaf cells.Sunlit–shaded leaf separation is an improvementover big-leaf models, but models of this type canbe in error in daily step calculations if the diurnalvariability is ignored. Non-linear response of leafphotosynthesis to meteorological variables makesit inaccurate to use daily mean meteorologicalinputs to calculate the daily total photosynthesiswithout considering the diurnal variabilities. Thefirst-order effects of the diurnal variabilities areconsidered in this study by performing a sim-plified analytical temporal integration of the Far-quhar’s model under the assumption of a

sinusoidal radiation variation pattern. A newdaily canopy photosynthesis model is thereforederived and validated with experimental data.This model captures the effects of diurnal vari-abilities on photosynthesis and is efficient forcomputation, and therefore is suitable for remotesensing applications.

Acknowledgements

We thank Dr T.A. Black of University ofBritish Columbia for the permission to use thedata from the aspen site for model validation. Thesenior author is indebted to Dr J. Norman ofUniversity of Wisconsin at Madison and Dr J.Berry of Stanford University for useful discus-sions concerning the importance of shaded leavesin boreal photosynthesis. We are grateful toMichael Sarich for his assistance in dataprocessing.

Fig. 8. One-to-one comparison of the measured NPP with the modeled NPP for a mature black spruce stand. (a) big-leaf model,and (b) daily integrated model with sunlit–shaded leaf separation.


Fig. 9. One-to-one comparison of the measured NPP with the modeled NPP for a mature aspen stand. (a) big-leaf model, and (b)daily integrated model with sunlit–shaded leaf separation.

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