crown closure estimation of oak savannah in a dry season...

. . , 2003, . 24, . 9, 1811–1822

Crown closure estimation of oak savannah in a dry season withLandsat TM imagery: comparison of various indices throughcorrelation analysis

BING XU, PENG GONG and RUILIANG PU

Center for Assessment and Monitoring of Forest and Environmental Resources(CAMFER), 151 Hilgard Hall, University of California, Berkeley,CA 94720-3110, USA; e-mail: [email protected]

(Received 6 February 2001; in final form 19 November 2001 )

Abstract. In this paper, we assess the capability of Landsat Thematic Mapper(TM) for oakwood crown closure estimation in Tulare County, California.Measurements made from orthorectified aerial photographs for the same areawere used as a reference. The linear relationship between crown closure anddigital values of each band of the TM image was examined. TM Band 3 had thehighest correlation (r=−0.828; R2=0.687) with crown closure measurements.The simple ratio (SR) and the normalized difference vegetation index (NDVI)were generated for correlation analysis and only NDVI showed better correla-tion (r=0.836; R2=0.699) than use of single bands. An additional index(NIRN−RN )/(NIRN+RN ), called NDVIN, was experimented, NDVISQ (N=2)and NDVICUB (N=3) showed some improvements over SR and NDVI (r=0.855; R2=0.732 for N=3). Through multiple regression with all six bands, wefound that there was a considerable amount of improvement in variability explana-tion over any individual band or index tested (R2=0.803). NIR, red and bluebands were able to adequately model crown closure as using all the six TM bands(R2=0.802). Principal component analysis (PCA) and Kauth-Thomas (K-T)transform were applied to reduce multi-collinearity among bands. The thirdprincipal component and greenness in K-T transform showed similar effects tothose of NDVI. Transformation of digital numbers (DNs) to radiances kept theresults of single band and multiple band estimation the same, and did not improvethe index estimation very much. A simple radiometric correction of the TM imageimproved results for the NDVI (r=0.840; R2=0.705) and NDVISQ estimation(r=0.861; R2=0.741), but worsened estimation results of single band andmultiple bands.

1. IntroductionCrown closure is the percentage of forest canopy projected to a horizontal plane

over a unit ground area. It is an important parameter in ecological, hydrologicaland climate models. Its measurement in the field is difficult and time-consuming(Bonham 1989). This is particularly true over large areas. Although efficient samplingstrategies can be employed, such methods can be prone to error. Statistical correlationanalysis between the crown closure and spectral properties is dependent on theaccuracy of ground measured and remotely sensed data (Chen and Cihlar 1996).Therefore, we used classification results from orthorectified aerial photographs at

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online © 2003 Taylor & Francis Ltd

http://www.tandf.co.uk/journalsDOI: 10.1080/01431160210144598

Bing Xu et al.1812

1m ground resolution as ground data in this study. Landsat TM data were used asregressors after geometric registration of the air photo and the satellite image.

The correlation between tree density and TM data was explored in an oaksavannah in southern Spain (Joffre and Lacaze 1993). It was found that the greylevel values of bands 2–5 were all negatively correlated with the tree density; theNIR was the highest (r=−0.53). A recent study found a higher correlation betweensavannah vegetation cover percentage and the red band of Landsat Multi-SpectralScanner (MSS) (R2=0.88) with a relatively small sample set (n=22) in easternZambia (Yang and Prince 2000). Direct band transformation might provide a bettercorrelation. Normalized difference vegetation index (NDVI) was correlated withcanopy cover using Landsat TM (r=0.552) and MSS (r=0.698) and SPOT HRVXS (r=0.718) data (Larsson 1993). Leaf area index (LAI), a parameter directlyrelated to crown closure, could be retrieved using NDVI derived from Landsat TMdata through linear or log linear models (Spanner et al. 1990, Gong et al. 1995,Chen and Cihlar 1996). Estimation of canopy cover from multiple bands was investi-gated using airborne sensors, such as the Compact Airborne Spectrographic Imager(CASI) for forest inventory (r varies from 0.76 to 0.94) (Baulies and Pons 1995) andcrown closure estimation of conifer forest (Gong et al. 1994). Multispectral data canbe transformed using principal component analysis (PCA) from a statistical pointof view and Kauth-Thomas (K-T) transform on a physical basis (Kauth and Thomas1976). Some investigators found that redness was somehow more correlated withcanopy cover than greenness in boreal forest at high latitudes (Foster et al. 1994).K-T greenness/redness ratio (GR ratio) was found to provide a higher correlation(r=0.81) with brush canopy cover in rangeland using Landsat MSS data (Boyd1986). Among the studies, none compared a number of approaches at the samestudy site.

In this paper we report the exploration of single band, vegetation indices, multi-band regressions, multi-spectral transformation for crown closure estimation usingLandsat TM imagery. Conversion of digital numbers (DNs) to radiance was tested.A simple radiometric correction of the image that attempted to reduce Rayleighscattering of the atmospheric effect was also applied and evaluated in this study.

2. Data acquisition and preparationOur study area is a hardwood rangeland in Tulare County, California, USA. It

is covered by oakwood, bare soil, grass and shrubs. The Landsat TM image wastaken in August 1995. The false colour composite of the TM image is shown infigure 1. Crown closure in this area is generally less than 20%. Due to theMediterranean climate in California, the sky in the summer months is usually crystalclear. Grasses are dead and dry during the dry summer months. The reflectance ofsoil and dry grasses is higher than that of oak tree leaves in the visible bands of theTM image. The red colour in figure 1 shows crown coverage. Sample pixel valuesfrom Issabelly Lake in the same TM scene were taken as dark target to do radiometriccorrection. It was assumed that radiance was inversely proportional to the 4th powerof the spectral wavelength due to Rayleigh scattering (Lillesand and Kiefer 1994).The path radiance over water bodies in each band was calculated and subtractedfrom the spectral signals of each band (Gong and Zhang 1999).

The airphoto mosaics, shown in figure 2, were taken in the dry season 2 monthslater than the satellite imagery. The airphotos (scale 1:40 000) were scanned at 1mground resolution. The scanned photographs were orthorectified using a digital

Crown closure estimation with L andsat TM imagery 1813

Figure 1. Study site in Tulare County of California in a standard false colour display of theLandsat TM imagery.

Figure 2. Aerial photograph corresponding to figure 1.

photogrammetric software package. GCPs (ground control points) measured withGPS (global positioning system) equipment were used to derive the photographicstations and they were subsequently used in stereo model development and ortho-rectification. The TM image was georeferenced with respect to the correspondingorthorectified aerial photograph. Therefore, each pixel in the TM image correspondedto 30 pixels by 30 pixels in the aerial photograph. In each ‘transparent’ mask(corresponding to one pixel ) of the TM image over the 30 pixels by 30 pixels of theaerial photograph, we were able to calculate the crown closure. Image processingsuch as image thresholding and classification was applied to derive land-cover typesfrom the aerial photographs. The surface cover classification results were used to

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calculate the percentage of crown closure, grass and soil for each correspondingpixel on the TM image. The classification results from the aerial photograph areshown in figure 3. We randomly chose 130 samples from the sunlit sites for thisstudy. Pixels on shaded sides of the scene require topographic correction, which willbe dealt with elsewhere.

3. Crown closure estimation by single band or indicesFor each of the 130 sample pixels, we extracted the DNs from the six bands of

the TM image covering the blue, green, red, near-infrared and two middle infraredspectral ranges. Linear relationships can be observed from the scatterplots (figure 4).The correlation coefficient (r), R-squared (R2 ), and residual standard errors (rse) arereported in table 1. The DN in the red band is negatively correlated with the crownclosure (r=−0.828), and explains 68.7% of data variability. The superior perform-ance of the DN in the red band of the TM image agrees with that of the MSS image(Yang and Prince 2000). However, the DN of the NIR band (band 4) has a lowcorrelation with crown closure (r=0.222). For band 4 in figure 4, the fitted linetraverses through the empty space of data clusters, compromising the cluster withno crown closures. Samples with 0% crown closure and high DNs in the red bandare mainly covered by grass, soil or both. In general, 0% crown closure should beincluded in an analysis. We also carried out analysis without sample points of 0%crown closure as pixels with 0% crown closure can be determined by image classifica-tion. It is interesting to note that removing those samples with 0% closure did notaffect much of the results except for the NIR band with which some improvementin correlation (r=0.456) was obtained. It caused a slight decrease in correlation forbands 2 and 3 (table 1).

Our results in the NIR band are different from those of Joffre and Lacaze (1993),although the environments are similar. The TM data in Joffre and Lacaze (1993)were collected in late spring and the homogeneous herbaceous background hadstronger reflectance than the trees. A reduction in crown closure would increase the

Figure 3. Pseudo colour display of classification results of the aerial photograph (red: crownclosure; green: grass; white: soil ).


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Figure 4. Scatter plots of crown closure (%) against DN of each TM band.

Table 1. Statistical analysis between single bands with crown closure*.

Crown closure TM1 TM2 TM3 TM4 TM5 TM7

Correlation coefficient (r) −0.791 −0.795 −0.828 0.222 −0.733 −0.734(−0.802) (−0.794) (−0.811) (0.456) (−0.767) (−0.779)

R-squared (R2 ) 0.626 0.632 0.687 0.050 0.538 0.540(0.643) (0.630) (0.657) (0.208) (0.588) (0.607)

Residual standard error (rse) 0.191 0.189 0.175 0.304 0.212 0.212(0.201) (0.205) (0.197) (0.299) (0.216) (0.211)

*Values in brackets are after removing 0% crown closureBold number indicates the highest correlation, while italicized number indicates the lowest

correlation among different bands (columns). This notation is applicable to all the tables inthis paper.

reflectance in the NIR band. Our data were acquired in late summer when grasslandwas dead. Thus only the increase of crown closure would increase the reflectance inthe NIR. The negative correlations with other bands in our study were caused bythe dry background with greater reflectivity than the crowns. Transforming DNs toradiance with a linear model (Markham and Barker 1986) kept the correlationcoefficient with individual band the same. This is well explained by the least squarestheory (equation (1)) that the DNs multiplied by a constant c in each band will notchange the final result but the slope of the estimated line, since the absolute valuesof the regressors (brightness values in each band) are changed. The subtraction termwas so small that it could be neglected. In the equation, y is observation (crown

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closure from aerial photograph), y is estimator (crown closure to be estimated), andX is regressor (radiance or DN from the TM image).

y=cX((cX)∞(cX))−1 (cX)∞y=X(X∞X)−1X∞y (1)

Simple radiometric correction by subtracting a constant obtained by only approx-imating the Rayleigh scattering of the atmospheric condition for each band did notimprove the correlation. The slope of the estimated line was kept the same, and theintercept term was changed instead (equation (2)). The estimate result is not thesame as that without radiometric correction.

y=(X−c)((X−c)∞(X−c))−1 (X−c)∞y≠X(X∞X)−1X∞y (2)

Correlation analysis with vegetation indices was made (table 2). SR, the DN ratiobetween the NIR and the red band, did not improve the correlation when comparedwith the result from the analysis of the red band. Apparently the poor correlationbetween NIR and crown closure was the reason for the poor performance of SR.NDVI, which took advantage of both the high variability of the NIR band amongdifferent land-cover types and the relatively stable prediction of the red band, showeda slight improvement over the red band. Since NDVI showed a minor improvementover the red band and SR, we are led to speculate that the wider spectral variabilitybetween the NIR and the red band after normalization may help improve thecorrelation. This may be caused by reduction of illumination differences on the sunlitsides of the hills. It seemed to us that the spectral difference between the NIR andred bands is the primary contributor in the correlation analysis, thus we attemptedto enlarge this difference by taking the difference of powered DNs. NDVISQ,NDVICUB, NDVIN are defined in the following equations (equation (3)). TheNDVIN can be expressed by SR.

SR=NIR

R(3)

NDVIN7NIRN−RNNIRN+RN

=SRN−1

SRN+1for N=1, 2, . . .

when N=2 we have NDVISQ, when N=3 we have NDVICUB.In this exploration, we tested a number of indices. We found that NDVISQ,

NDVICUB produced better regression results than SR, NDVI and other higherordered NDVIN (N�4). We can see from the quadratic curve that the correlation

Table 2. Correlation analysis between vegetation indices derived from raw digital values andcrown closure*.

Crown closure SR NDVI NDVISQ NDVICUB Redness Greenness (G−R)/(G+R)

Correlation 0.782 0.836 0.851 0.855 −0.730 0.837 −0.822

coefficient (r) (0.748) (0.804) (0.824) (0.838) (−0.765) (0.811) (−0.804)

R-squared 0.611 0.699 0.725 0.732 0.533 0.700 0.676

(R2) (0.560) (0.646) (0.679) (0.702) (0.585) (0.657) (0.646)

Residual 0.194 0.171 0.164 0.162 0.213 0.171 0.177

standard (0.223) (0.200) (0.191) (0.183) (0.217) (0.197) (0.200)

error (rse)

*Values in brackets are after removing 0% crown closure


coefficient (r) increases as order N increases reaching its maxima when N=3, thendecreases abruptly asN further increases (figure 5 lower right). There is no significantdifference between the correlation coefficients when N is at 2 or 3, so the optimal Nis 2 and 3 (figure 5).

Transforming DN to radiance did not improve the correlation with vegetationindices. We could first look at the transformation formula and the coefficients weapplied below (Markham and Barker 1986).

Radiance(i)=LMIN(i)+LMAX(i)−LMIN(i)

DNMAXDN(i) i=1, 2, . . . , 6

LMIN=(−0.15, −0.28, −0.12, −0.15, −0.037, −0.015) (4)

LMAX=(15.21, 29.68, 20.43, 20.62, 2.719, 1.438)

DNMAX=256

The corresponding coefficients of LMIN and LMAX are −0.15 and 20.62 for theNIR band, and −0.12 and 20.43 for the red band. There is a 1‰ larger scaling(slope) effect for the NIR than the red reflectance, however, a bigger cut (3%) of theintercept term for the NIR than that for the red band. The combined up-scaling anddownshifting effects of the radiance transformation would not be able to considerablyenlarge the spectral differences between the NIR and the red bands. Therefore, theNDVI and NDVIN using radiance did not improve the correlation over the DNsby much (table 2 and table 3).

The radiometric correction based on Rayleigh scattering applied a simple subtrac-tion from the transformed radiance. A larger constant was subtracted from the red

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Bing Xu et al.1818

Table 3. Correlation analysis between vegetation indices derived from radiance and crownclosure*.

Crown closure NDVI NDVISQ NDVICUB Redness Greenness (G−R)/(G+R)

Correlation 0.836 0.852 0.855 −0.693 0.839 −0.832coefficient (r) (0.803) (0.825) (0.839) (−0.732) (0.811) (−0.817)

R-squared (R2 ) 0.699 0.726 0.731 0.481 0.704 0.693(0.646) (0.680) (0.704) (0.536) (0.657) (0.668)

Residual standard 0.171 0.163 0.162 0.224 0.17 0.173error (rse) (0.200) (0.190) (0.183) (0.229) (0.197) (0.194)

*Values in brackets are after removing 0% crown closure

band, and a smaller constant was subtracted from the NIR band. It can be expectedfrom the former rationale that the transformation might be able to produce someimprovements, because we had enlarged the radiance difference between NIR andred bands. This turned out to be true (table 4).

4. Crown closure estimation by multiple bands and combination of componentsThe above analysis only took one band or a transformation between two bands

into consideration. Would additional bands further improve the correlation? Wemade use of the three visible, the NIR and the two MIR bands to do multipleregression. We had achieved a considerable amount of improvement based on theresult of a high R-squared value of 80.25% (the p-value is 0). The six-band regressionexplained the most variability among all the above-mentioned approaches, whichwas reasonable. The residual standard error, 0.170, did not drop and remained at asimilar level to that of NDVI. We knew that the degree of freedom of the multipleregression model was no longer n-2 or 130-2, but n-6 or 130-6. The residual standarderror, denoted by rse, was calculated by the following formula.

rse2=( y−Xb)T (y−Xb)/(n−p) (5)

where n is sample size, p is number of regressors and b is a p×1 vector, the estimatedcoefficient for each regressor.

There is a trade-off here between the sum of squared errors and the degree offreedom. Although the sum of squared errors may become smaller by using six bandsinstead of two bands, the degree of freedom also becomes smaller. The resulting rsemay therefore be kept at a similar level.

Based on the fact that the model estimation using bands 1, 3 and 4 only was

Table 4. Correlation analysis between crown closure and vegetation indices derived fromraw digital values after doing radiometric correction*.

Crown closure NDVI NDVISQ NDVICUB

Correlation coefficient (r) 0.840 0.861 0.856(0.841) (0.864) (0.855)

R-squared (R2 ) 0.705 0.741 0.733(0.707) (0.746) (0.732)

Residual standard error (rse) 0.169 0.159 0.161(0.169) (0.157) (0.162)

*Values in brackets are derived from radiance


statistically significant (i.e. the p-value is small enough when a is at 0.05 significancelevel in the F-test), we only chose these three bands for the regression. The multipleR2 accounted for 80.18% of the data variability, remaining at the same level as thatusing all six bands. The residual standard error was kept as low as 0.168 with 127degrees of freedom. The analysis of variance gave a p-value of 0.93 while doing a F-test for the model with all the bands and with bands 1, 3 and 4, showing no significantdifference between the two models. We conclude that the red, NIR and the blueband modelled the crown closure estimation as adequately as using all six bands.

To get rid of the high correlation among different bands, we orthogonalized thecolumns of the regression bases formed by the spectral values of the samples andestablished a new set of orthogonal coordinates system. The approaches we appliedhere were PCA and K-T transform. Distribution variability of land-cover types wasneeded to enlarge the contrast between group signatures. The linear regression usingeach component is shown in figure 6. The 3rd principal component shows the bestfitting result, which is almost the same as that of the red band among all sixcomponents (r=−0.825; R2=0.681). When we used all six components together,we found that the only significant term in the regression was the 3rd principalcomponent. When we combined the 3rd principal component with the 2nd principalcomponent to model the crown closure, we got a similar result to that using the redand the NIR band directly. The R2 and the rse were 78.92% and 0.173. PCA, pickingthe principal components by putting the data variance in order, did not lead to abetter estimation for crown closure than that of the original six bands. The compon-ents explaining greater sample variability (such as the 1st and 2nd components) arenot better at predicting variables for crown closure estimation.

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Figure 6. Regression between crown closure (%) and principal components.

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The K-T transform is orthogonal and endows physical meaning to each axis. Wepicked up redness and greenness. Greenness, supposed to be an indicator ofvegetation vigour, showed a rather good prediction of crown closure. The estimationresult of greenness is similar to that of NDVI as shown in table 2, table 3 andfigure 7. (G-R)/(G+R) estimation, where G indicates greenness and R indicatesredness, did not improve the result of the single component estimation. This indicatesthat the idea of NDVI could not be simply borrowed here.

5. Summary and conclusionsData preparation and ground data generation is critical to crown closure estima-

tion. Careful classification of the aerial photographs and sample selection was doneto reduce possible errors. Based on the experiments of this study, we have thefollowing conclusions for the savannah type of oakwood lands during the dry season:

1. The red band in the TM image is the best for crown closure estimationamong the six individual bands.

2. The NIR band itself is the last band one should use to predict crown closuredue to the high variability among different land-cover types. Removingsamples with crown closure of 0% only increases the predicting power ofthis band, and slightly improves the correlation with the two middle infraredbands. However, it degenerates the differentiating power of other bands andof the combined use with other bands.

3. NDVI, the combined use of the NIR and red bands, may improve theestimation results over the red band by a small amount.

4. Our newly proposed index, NDVISQ and NDVICUB (NDVIN, when N=2 and N=3) produced better results than NDVI (a special case of NDVIN,when N=1). Enlarging the variability of NIR and the red to some extentand stretching the difference between the two bands were helpful in crownclosure estimation.

5. The six bands of the TM image give us the best estimation in terms ofencompassing variability. However, the contribution of three of the bandswas insignificant, indicating multi-collinearity among the six bands.

6. The NIR, red and blue band adequately modelled the crown closure andslightly reduced residual standard error in comparison with the use of allsix bands.

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Figure 7. Regression between crown closure (%) and redness, greenness and (G−R)/(G+R)derived from K-T transform.


7. The third principal component in the PCA works similarly to the red band.The combined use of the third and the second principle component givesa similar result to that of NDVI in terms of variability explanation andstandard error.

8. The greenness in a K-T transform achieves similar estimation results to thatof NDVI.

9. Transformation of the DNs to radiance will not significantly improve theestimation due to the inadequate increase in differentiating power of the NIRand the red band by applying the coefficients provided.

10. Simple radiometric correction slightly improves NDVI and NDVISQestimation. However, it degrades single band and multiple band regression.

Further research on radiometric correction needs to be done to provide a moreaccurate estimation and to explain how atmospheric condition influences the solarradiance in each band of the TM image. More research on transformation of originalbands is needed to further improve the estimation results. The shadow problemcaused by topography needs to be solved before we can make use of the shaded sideof the imagery for crown closure estimation.

AcknowledgmentsThis research was partially supported by NASA (NCC5-492) and the Integrated

Hardwood Rangeland Management Program of California.

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