STN(I) = Np([) (1) On the estimation of leaf size and crown geometry for tree canopies from hotspot observations

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. D24, PAGES 29,543-29,554, DECEMBER 26, 1997 On the estimation of leaf size and crown geometry for tree canopies from hotspot observations Narendra S. Goel, Wenhan Qin, and Bingquan Wang Department of Computer Science, Wayne State University, Detroit, Michigan Abstract. A computer-graphics based model for radiation interception in vegetation canopies is used to investigate the feasibility of estimating leaf size and crown size, for deciduous and coniferous trees, from canopy reflectance in the hotspot region. For deciduous trees, as represented by aspen trees, it appears that under certain conditions one can estimate leaf size; we specify optimal Sun-view geometry, wavelength, and, which can minimize the impacts of other structural parameters (e.g., leaf area, leaf angle distribution, and interplant spacing) for the most accurate estimation of leaf size. However, for coniferous trees an accurate estimation of crown size seems unlikely, except possibly for sparsely spaced canopies. 1. Introduction Leaf size has the potential to discriminate vegetation types. Tree crown sizeshape is an ecological parameter of importance in forestry; it is directly associated with the biomass and primary productivity of forestswoodlands. The canopy reflectance in the hotspot region is known to depend on the scatterer's geometric properties (leaf size and crown sizeshape), and hence in principle, these properties can be estimated from hotspot canopy reflectance [e.g., Gerstl et al., 1986]. However, optical and other structural parameters also contribute to the canopy hotspot [Qin and Goel, 1995; Qin et al., 1996], which will induce uncertainties into the estimation. We investigate the relationship between canopy hotspot and canopy geometric parameters through calculating the radiation regime in computer-generated vegetation canopies. This relationship is used to assess the feasibility of estimating leaf size for deciduous trees and crown size for coniferous trees from hotspot reflectance and the optimal conditions for most accurate estimation. The arrangement of this paper is as follows. In section 2 we describe the approach used and three types of tree canopy generated; in section 3 we analyze the result of using hotspot observations to estimate size of scatterers (leaves or tree crowns) for heterogeneous tree canopies and give some examples of such estimation. Brief conclusive remarks on applying reflectance in hotspot regions in estimating scatterer geometry are given in the final section. 2. Tree Canopies Used and the Approach The basic approach consists of three parts. 1. Generate architecturally realistic tree canopies with the extended L-systems [Goel and Rozehnal, 1992]. 2. Calculate radiation interception in the canopy using a computer graphics based model, Diana [Goel et al., 1991], which assumes Lambertian scatterers, and calculated radiation Now at Biospheric Sciences Branch, Laboratory for Terrestrial Physics, NASA Goddard Space Flight Center, Greenbelt, Maryland. Copyright 1997 by the American Geophysical Union. Paper number 97JD JD ,543 transfer in the canopy using concept of radiosity. This model explicitly gives the canopy reflectance, hotspot, and bidirectional reflectance factor (BRF); 3. Quantitatively evaluate the usefulness of canopy reflectance data for inferring scatterer size and to find the optimal Sun-view geometry combination, by using a signal-to-noise (STN) method [Leprieur et al., 1994; Goel and Qin, 1994]. The STN value is calculated as Sp(I) STN(I) = Np([) (1) where I is the measure (or ) used to relate the measu reflectance data to the parameter of interest. In this study, the indices we used were changes in reflectance R at a given view angle or in normalized reflectance R N by that in the opposition direction (i.e., the hotspot point) within the dynamic range of the parameter of interest P in either or near-infra (NIR) wavebands. Thus the signal intensity S for each can be calculated as Sp(I) = I(Pa) - I(Pm)l, (2) where Pa and Pm are the maximum and minimum values of the parameter of interest. I is the mean value of the selected (here it is either R or RN) under all conditions studied. Three viewing planes (PP, the principal plane (plane by varying view zenith angle for a fixed view azimuth equal to solar azimuth (or plus 180ø)); PC, the principal cone (cone generated by varying view azimuth angle for a fixed view zenith equal to sun zenith); and CP, the plane perpendicular to PP) and two solar zenith angles (SZA), low (10 ø) and high (60ø), are conside for evaluation. The "noise" factors are the disturbing factors, such as leafarea (LAI) and leaf angle distribution (LAD), spatial distribution of trees, porosity of the crown, etc., which will affect the relationship between scatterer size and "signal" intensity. The noise intensity is evaluated as Np(I) = {max[if(p)] - min [If(P)]} dp (3) Pa m where max [ ] or min [ ] is the maximum or minimum value, among all cases of noise factors f, of the measure I at a value

2 29,544 GOEL ET AL.: LEAF SIZE AND CROWN GEOMETRY FROM HOTSPOT OBSERVATIONS A P of parameter of interest. If STN values are below (above) a threshold (say, 1), we infer the feasibility of estimation of scatterer geometry to be low (high). We now describe the three kinds of tree canopies generated and the noise factors for each type of canopy. 1. A canopy consisting of broadleafdeciduous tree crowns (Figure l a) is used to study the influences of canopy architecture on canopy hotspot [Qin et al., 1996] and to assess the feasibility of estimating leaf size from hotspot reflectance. 2. A coniferous tree canopy with ellipsoidal crowns (Figure lb) is used to assess the ability to estimate the crown shape size. 3. A canopy consisting of simple ellipsoidal shells (crowns as ellipsoids on sticks) with variable horizontal and vertical radii and tree height (Figure lc) is used as follows. Since canopies of this kind are like those used in most geometrical optical (GO) models [Li and Strahler, 1992], we use this type of canopy to exclude the impact of within-crown gaps on estimation of crown geometry. For the broadleaf tree canopies, two LAIs (0.6 for low and 5.5 for high) are conside, and the corresponding tree height H is about 7.0 and 11.5 m. For each LAI, three different spacing distances (SPC) between trees (small, medium, and large), equal to 0.5H (small), H (medium), and 1.5H (large) are studied. Canopies for each LAI, with medium spacing, also have three different LADs (planophile, spherical, and erectophile). Because our ultimate purpose is to estimate leaf size from BRFs in the hotspot region, a canopy with given LAI, LADSPC has three typical leaf sizes (small, medium, and large), equal to 1H, 5H, and 0.1H, on average, respectively. The optical properties of canopy components and the soil are the same as those of Goel and Qin [1994, Table 1] for aspens and are given in Table 1. For the coniferous tree canopies, three LAIs (0.5, 1.8, and 5.0) are conside, and the corresponding tree height is about 7.0 and 8.0 m (only for LAI = 5.0). The LAI is calculated by adding the areas of rectangles which represent needles. For each LAI there are also three different spacing distances between trees, specified in the same way as for the broadleaf canopy. For each LAI and SPC, tree crowns have three vertical-to-horizontal radii ratios: 1.0, 2.0, and 4.0. Although conifer shoots are much darker than leaves in broadleaf trees, the optical properties of needles are not much different from leaves (although reflectance of needles may be slightly higher or lower than that of leaves, depending on wavelength [see Williams, 1991]). Therefore, for simplicity, we use the same optical properties as in broadleaf canopies for conifers (with optical properties of needles equal to those of leaves). For an ellipsoidal shell canopy, with a crown specified by a vertical radius v, a horizontal radius r, and a height h (vertical Table 1. Optical Properties of Canopy Components and Soil Background Used for Broadleaf Tree Canopies Band Red Near Infra Property Figure 1. Representative trees (a) broadleafdeciduous, (b) coniferous and (c) simple ellipsoidal shell. Wavelength, btm Leaf reflectance transmittance Bark reflectance Soil reflectance

3 , GOEL ET AL.: LEAF SIZE AND CROWN GEOMETRY FROM HOTSPOT OBSERVATIONS 29,545 A with low LAI andifferent LADs i'"',, i.,i: t PP, SZA=10ø(dot) and 60ø(solid) " i li, l(hs i ( NIRNIR(HS) 4 -- z I ,,= ",i i,, B with low LAI and different LADs PC, SZA=10ø(dot) and 60ø(solid) Zenith angle (o) from HS point (HS) NIR NIRNIR(HS) Z I o,,'"(,.. Jii' ' Oo. ;,.,o,,... o,,o ",.,. i'... ½,o "o% " o o o o.o I I Figure 2. Signal to noise (STN) values for broadleaf tree canopies for low leaf-area (LAI) and different leaf angle distributions (LADs):(a) principal plane (PP) and (b) principal cone (PC). HS, hotspot direction; SZA, solar zenith angle. I distance between center of ellipsoid and the ground), three different crown sizes (hv - 1.0, 3.0, and 6.0) and four different crown shapes (vr = 0.2, 0.5, 2.0, and 5.0) are conside. The optical properties of "shells" and soil background are the same as those of the first kind of canopy except the mean transmittance of "shells," which is set to 1 for bands and 0.1 for NIR bands. 3. Results We now give results for the feasibility of estimating leaf size and crown geometry from hotspot reflectance Estimation of Leaf Size for Broadleaf Trees Here we divide the discussion under two cases: canopies with different LADs and canopies with different spacings Canopies with different LADs. Several studies have shown that at a given Sun position, BRF at low-view zenith angles or in the antihotspot direction is very sensitive to LAD [Ross and Marshak, 1989; Qin and Jupp, 1993] and the sensitivity increases when SZA is also low. This means reflectance in the hotspot region at high SZA would be preferable to use to minimize the impact of LAD.

4 29,546 GOEL ET AL.' LEAF SIZE AND CROWN GEOMETRY FROM HOTSPOT OBSERVATIONS A oo.o with high LAI and different LADs PP, SZA=10ø(dot) and 60ø(solid), - Z (HS) o.o... ::::::-o--. o o o * o..-.. o :...e...e::.. ****... ::::::::::::::::::::::::::::::: :: I Zenith angle (o) from HS point wit high LAI an different LADs o o ' PC, SZA=10 (dot) and 60 (solid) i A, (HS) lo t Figure 3. Same as Figure 2 except for high LAI' (a) PP and (b) PC. Figures 2-3 are STN values at low (0.6) and high (5.5) LAI in PP and PC at the two SZAs (the result in CP is not significant and thus is not presented here). From these results, one can see that only by using the normalized reflectance RN can an acceptable estimation be obtained; R v effectively removes the impact of optical properties of scatterers to a large extent. At low LAI (Figure 2), RN in both planes (PP and PC) can yield a satisfactory estimate of leaf size. The result is almost independent of wavelength and Sun position if R v in PC are used (Figure 2b). However, in PP the result at low SZA is much better than at high SZA, and both are above threshold of STN = 10 and are, therefore, significant and meaningful. The useful range of view direction for such estimation is about _+ 1.5 ø away from the hotspot direction in both planes. At high LAI (Figure 3), although the result is not as good as that at low LAI, one still has an opportunity by using R N at high SZA (preferably in PP). The effective range of view zenith is about _+2.0 ø off the hotspot point or 5 ø width cente at -5 ø away from the hotspot direction in PP for bands (Figure 3a). When both LAI and LAD are unknown, the possibility of leaf size estimation exists only when the normalized reflectance at high SZA in PC is used, but the accuracy of estimation

5 GOEL ET AL.: LEAF SIZE AND CROWN GEOMETRY FROM HOTSPOT OBSERVATIONS 29,547 A with different LAIs and LADs PP, SZA=10ø(dot) and 60ø(solid) ' ' A (HS) - NIR ( NIRNIR(HS) Z 1 5.0? '... ' 3'... ::-8-:.o- 8.- '... :.::_.:.: :.: ; : ,..., : 2. : : ' '-.... x x B with different LAIs and LADs Zenith angle (o) from HS point ' ' PC, SZA=10ø(dot) and 60ø(solid) (HS) NIR O NIRNIR(HS) Z Figure 4. Same as Figure 2 except for different LAIs and LADs: (a) PP and (b) PC. decreases considerably (Figure 4). Also the effective range of tude and distribution of canopy reflectance, especially at high view direction is much narrower than those at known LAIs Sun-view zenith angles (Qin and Jupp [1993]; in a leaf canopy (about +_1.0 ø off the hotspot direction). this effect is equivalento that caused by the leaf dispersion In summary, when LAD is unknown, R N at high SZAs is pattern). Therefore we expect leaf size estimation to be much always prefer in order to estimate leaf size. The opportunity harder when SPC changes than when LAD changes (Figures is much higher when LA! is also known than when LAI is 5-7). As an analog to the study for unknown LAD, below we unknown. Usually, the optimal is RN in NIR, and use of will first explore the possibility to estimate leaf size with known the data in PC is preferable for this kind of heterogeneous LAIs (low or high), then combine them to a general case where canopy. both SPC and LA! are unknown (we choose spherical LAD for Canopies with different spacing distances between all spacing cases). trees. Spacing distance determines the heterogeneity of can- When LAI is low (Figure 5), STN values in CP are slightly opy to a large extent. It affects considerably both the magni- higher, and the range of view directions with significant STN

6 _ ß 29,548 GOEL ET AL.' LEAF SIZE AND CROWN GEOMETRY FROM HOTSPOT OBSERVATIONS A l(hs) 2 --!? -.( ß NIR NIRNIR(HS) with low LAI and different SPCs 5.0 PP'SZA=10ø(døt) and60ø(sølid) 2 o -... ø I - I F - I ß Zenith angle (o) from HS point with low LAI and different SPCs PC, SZA=10ø(dot) and 60ø(solid)... "A'"... i... (HS) 4p -- NIR i! C) NIRNIR(HS) z i OUGOOO0 '' *,...., I c 4 -- o.o - Broadleaf true canopies with low LAI and different SPCs CP, SZA-10ø(dot) and 60ø(solid) ',, -, F- N R z i o.o VZA (o) Figure 5. Same as Figure 2 cxcc t for different s acin (SPCs): (a) PP, (b) PC, and (c) plane c: cndicula: to PP (CP); VZA, view zenith I

7 GOEL ET AL.: LEAF SIZE AND CROWN GEOMETRY FROM HOTSPOT OBSERVATIONS 29,549 A 6 4 with high LAI and different SPCs ß j PP, SZA=10ø(dot) and 60ø(solid) (HS) - -( NIR NIRNIR(HS) z I- - 2.:.2... ;... ;_ :::::::::::::::::::::::... :i:: ::: : ::: --.:::::!... ' _---: Zenith angle (o) from HS point B Broadleaf true canopies withigh LAI an different SPCs ß PC, SZA=10ø(dot) and 60ø(solid) i (HS) i : NIR?!ii 0 NIPJNIR(HS) -- z I o øoo o ' I ' I - ' I 4,0 i NIR z I-- - 2,0 i with high LAI and different SPCs CP, SZA=10ø(dot) and 60ø(solid) -9 Figure VZA (o) Same as Figure 5 except for high LAI' (a) PP, (b) PC, and (c) CP.

8 29,550 GOEL ET AL.' LEAF SIZE AND CROWN GEOMETRY FROM HOTSPOT OBSERVATIONS A -- 1 with different LAIs and SPCs PP SZA=10ø(dot) and 60ø(solid) h - ' lil X (HS) ii\l N R \ C) NIRNIR(HS) Z ' \ o 0 0,,.,.,?..... '"' _,..,...,A... ; : ::====... ' I... ' I... I... --":"' ' I ' Zenith angle (o) from HS point ,0 -- with different LAIs and SPCs. PC, SZA=10ø(dot) and 60ø(solid)! io 5. ' X (ES) _ *>.,.oo I 01 ) 16 '"'?? C) NIPJNIR(HS) o'o, o o... '" 'eøoøo l ii I o Figure 7. Same as Figure 4 except for different LAIs and spacings: (a) PP and (b) PC. values is broader than those in PP and PC, where only NIR yield a significant result, independent of the Sun-view geomereflectance at low SZA is useful, clearly contrasted to the try. The optimal range of view geometry is always within +2 ø canopies when LAD is unknown. The optimal view angle range off the hotspot direction. When both SPC and LAI are undepends on both the view plane and solar zenith. In PP the known (Figure 7), only the results (STN values) of R N in NIR optimal view directions are about _+ 2.5 ø away from the hotspot within 1 ø off the hotspot point in PP are significant. Since the point (Figure 5a). In PC it is just 1 ø off the hotspot point when STN values are much lower than those in the cases of known R in NIR is used, and is in the region from _+10 ø to +18 ø LAI, there are only a few opportunities to estimate leaf size. when the reflectance in NIR is used (Figure 5b). In CP it is In summary, for broadleaf tree canopies with different spacaround +_ 15 ø off nadir for low SZA and within _+5 ø around ings, only reflectance or normalized reflectance in NIR is usenadir for high SZA (Figure 5c). When LAI is high (Figure 6), ful, the optimal sampling domain depending upon LAI. For STN values in PP are much better than PC, and those in CP are canopies with low LAI, observations in PC or CP are more insignificant. Unlike the cases of low LAI, only R in NIR can favorable than those in PP, and a low SZA is requi, while

9 _ GOEL ET AL.: LEAF SIZE AND CROWN GEOMETRY FROM HOTSPOT OBSERVATIONS 29,551 A Coniferous tree canopies with large SPC and different LAIs PP, SZA:10ø(dot) and 60ø(solid) (HS) NIR NIRNIR(HS) 4.0 i I zenith angle (o) from HS point 5.0 Coniferous tree canopies with large SPC and different LAIs o ' 4.0 (HS) NIR C) NIRNIR(HS) 3.0 i Figure 8. Signal to noise (STN) values for coniferous tree canopies for large spacing and different LAIs: (a) PP and (b) PC. HS, hotspot. for canopies with high LAI or LAI unknown, observations in PP at high SZA are most useful for leaf size estimation. Since the STN values are so small, it is almost impossible to estimate leaf size when LAI is also unknown Estimation of Crown ShapeSize for Coniferous Trees Here we divide the discussion under two cases: canopies with different spacings and canopies with different LAIs Canopies with different spacings. Spacing is perhaps the most important factor which affects the possibility of estimating crown shapesize from B RFs. For coniferous tree canopies when LAI is high, BRF (especially in the band) is very sensitive to changes in the vertical-to-horizontal radius ratio, with sensitivity increasing as this ratio increases (more soil background is exposed to both the Sun and the viewer). However, spacing also affects BRF in a similar way: the larger the spacing, the more is the contribution of soil, which induces large "noise" into the estimation of crown geometry. Even the highest values of STN are below 1, signifying that under no conditions does there exist a possibility to get a reliable estimation if spacing is unknown, even for very dense crowns (few gaps within the crown), no matter which view plane (PP, PC, CP) is used. In order to exclude the impact of within-crown gaps on the

10 29,552 GOEL ET AL.: LEAF SIZE AND CROWN GEOMETRY FROM HOTSPOT OBSERVATIONS Coniferous tree canopies. with small SPC andifferent LAIs I o o JJ ndex PP, SZA=10 (dot) and 60 (solid) x, (HS), Nil{ C) NIRNIR(HS) er. ' --)K B zenith angle (o) from HS point - Coniferous tree canopies -- with small SPC andifferent LAIs II I IJ PC, SZA=10ø(dot)and 60ø(solid) (HS) ( NIRJNIR(HS) 0.8 '" \ '"..-" '?"A...' '...' \..." ' '...,.. G ß.... a..--.l" o.o I ' T I ' ' ' I ' I Figure 9. Same as Figure 8 except for small spacing: (a) PP and (b) PC. estimation, ellipsoidal shell crowns with different spacings and conditions (e.g., at large spacing) if only LAI is unknown (Figcrown size and shape were used. Still, because of the strong ure 8). The R v in NIR at low SZA is the most preferable influence of spacing on the relationship between crown size to use. The optimal view angle is about _+ 10 ø (or within _+20 ø) shape and canopy BRF, one cannot hope to extract the crown off the hotspot point in PP (or PC). However, the possibility of geometric parameters from BRF or hotspot observations. estimation declines, and the region in which STNs are above Canopies with different LAIs. LAI mainly affects the significance level is narrowed as spacing decreases. When the porosity of a crown. However, if spacing is known, LAI's spacing is small, the region of STN larger than 1.0 is very effect on the relation between crown sizeshape and canopy narrow (_+2 ø off the hotspot point). Although the best is BRF is quite limited. In other words, there are some oppor- the same (R v in the NIR band), the optimal SZA shifts to 60 ø tunities to estimate crown geometric parameters under some (Figure 9).

11 GOEL ET AL.' LEAF SIZE AND CROWN GEOMETRY FROM HOTSPOT OBSERVATIONS 29,553 A 1.00 Estimation of leaf size for broadleaf tree canopies with different LAIs and LADs NIR, PC (HS+0.2 ø) SZA=60 ø a = 1.04, b = 3 R , ( 2= 2.61E A Estimation of crown sizeshape for coniferous tree canopies with small SPC and different LAIs NIR, PP (HS-1.0 ø) SZA=60 ø 0.98 ß a = 0.78, b = 7 R 2= 0.95, o 2= 9.15E-05 3 ' low & hori ( low & sph -{- low & erect LAI 'k O ß, high & hod high & sph high & erect -h 0.s ( 1.8 -{- :) ' I ' I relative leaf size vr Estimation of leaf size for broadleaf tree canopies with different LAIs and SPCs NIR, PP (HS-0.2 ø) SZA=60 ø ß a = 1.03, b = 2 R 2= 0.64, c?= 8.09E-05 B Estimation of crown sizeshape for coniferous tree canopies with large SPC an different LAIs PP (HS+8.2 ø) - NIR, SZA= 10 ø.i r + o LAI & spc a = 0.91, b = low & small r ( low & medium -{- low & large 'k O ß, high & small high & medium high & large , -A relative leaf size Figure 10. Relationship betweenormalized reflectance and relative leaf size (for estimating leaf size from reflectances in hotspot region): (a) different LAIs and LADs and (b) different LAIs and spacings ' I ' I ' I ' I vr Figure 11. Relationship betwee normalized reflectance and ratio of crown's vertical to horizontal radii (for estimating crown sizeshape from canopy reflectance): (a) small spacing and (b) large spacing Practical Estimation of Leaf Size and Crown SizeShape From Hotspot Observations From the above discussion, we have obtained the optimal and Sun-view geometry for estimating scatterer geometric parameters in various vegetation types, LAIs, LADs, and spacings. Using those results, below we will explore the practical estimation of leaf size and crown sizeshape in different scenarios Leaf size estimation. For broadleaf tree canopies dealt with in this study, we have the scenarios of two combinations: different LAIs and LADs and different LAIs and spacings. A stable exponential relationship between R v and the relative leaf size (l* L = tlh) is found as l}- exp [-(a - R v)b], (4) where a fluctuates around 1.0 and b varies from 1 to 0.1, depending on the canopy structure (Figure 10). Leaf size can be retrieved from R v in NIR in the range of +2.0 ø around the hotspot point in PC if only LAD is unknown or in PP or PC, or even CP (depending on values of LAI), if spacing is unknown. But if LAI is also unknown at the same time, only if spacing is kept fixed may one obtain an acceptable estimate of leaf size by selecting PC and high SZA. When both spacing and LAI are unknown (even LAD is kept fixed), one should not hope to obtain the reliable estimation result. For the case where both LAI and LAD are unknown, constant a and b = 25 and the square correlation coefficients R 2 = 0.89,

12 29,554 GOEL ET AL.: LEAF SIZE AND CROWN GEOMETRY FROM HOTSPOT OBSERVATIONS while in the case where neither LAI nor spacing is known, a = 1.03 and b = 2 and R 2 is only equal to 0.64, much lower than that for the first case, implying that there are only a few opportunities to estimate leaf size Crown sizeshape estimation. In section we noted that only for the case where spacing is known does there exist a possibility to estimate crown sizeshape from BRF by using R N in NIR region (mostly at low SZA). The relationship between that and the ratio of the crown's vertical to horizontal radius can be expressed as vr - exp [-(c - R v)d], where constant c fluctuates between 0.7 and 1.0 and d varies from 6 to 9, depending on spacing (Figure 11). Here R 2 is above 0.88, and the residual mean square o is less than 4.5 x Conclusions The simulations presented in this paper suggest that for broadleaf or deciduous trees, for the purpose of estimating leaf size from canopy reflectance in the hotspot region, in most cases, the ratio of NIR reflectance for a given view angle to the hotspot reflectance at a high sun zenith angle is the best. A statistically significant negative exponential relationship (1) between this and the relative leaf size exists which can be used to estimate leaf size. The accuracy of estimation is better at a smaller LAI than for a higher LAI canopy. At high LAI, PP works better, and for low LAI, PC works better; unfortunately, in remote sensing, one may not know LAI, and other simultaneous observations could help here. Unfortunately, the result is not positive about the possibility of estimating crown sizeshape for a coniferous canopy because of the strong influence (noise) of spacing between trees on the hotspot reflectance. That is, it appears that an accurate estimation of crown sizeshape seems unlikely except when spacing between trees is a priori known. It should be noted that preliminary results of simulating hotspots for row-planted crops, e.g., corn, show that under certain conditions the estimation of leaf size is possible. We plan to present details in a future publication. For completeness, we should also note that typical computer time for calculating canopy reflectance is between 14 and 1 hour (on a SUN SPARC station, higher for more polygons for higher LAIs). (s) Acknowledgments. This research was partially supported by NASA. W.Q.'s work is in part supported by the Chinese National Science Foundation through grant References Gerstl, S. A. W., C. Simmer, and B. J. Powers, The canopy hotspot as crop identifier, in Proceedings of Symposium on Remote Sensing Resources Development and Environmental Management, Enschede, Netherlands, pp , A. A. Balkema, Brookfield, Vt., Aug Goel, N. S., and W. Qin, Influences of canopy architecture on relationships between various vegetation indices and LAI and FPAR: A computer simulation, Remote Sens. Rev., 10, , Goel, N. S., and I. Rozehnal, A high-level language for L-system and its applications, in In the Footsteps of L: L-145se Studies to the Memory of Aristid Lindenmeyer , edited by G. Rozenberg and A. Salomaa, pp , Springer-Verlag, New York, Goel, N. S., I. Rozehnal, and R. L. Thompson, A computer graphics based model for scattering from objects of arbitrary shapes in the optical region, Remote Sens. Environ., 36, , Leprieur, C., M. M. Verstraete, and B. Pinty, Evaluation of the performance of various vegetation indices to retrieve vegetation cover from AVHRR data, Remote Sens. Rev., 10, , Li, X., and A. H. Strahler, Geometric-optical modeling of the discretecrown vegetation canopy: Effect of crown shape and mutual shadowing, IEEE Trans. Geosci. Remote Sens., 30, , Qin, W., and N. S. Goel, An evaluation of hotspot models for vegetation canopies, Remote Sens. Rev., 13, , Qin, W., and D. L. B. Jupp, An analytical and computationally efficient reflectance model for leaf canopies, Agric. For. Meteorol., 66, 31-64, Qin, W., N. S. Goel, and B. Wang, The hotspot effect in heterogeneous vegetation canopies and performances of various hotspot models, Remote Sens. Rev., 14, , Ross, J., and A. Marshak, The influence of leaf orientation and the specular components of leaf reflectance on the canopy bidirectional reflectance, Remote Sens. Environ., 27, , Williams, D. L., A comparison of spectral reflectance properties at the needle, branch, and canopy level for selected conifer species, Remote Sens. Environ., 35, 79-93, N. S. Goel and B. Wang, Department of Computer Science, Wayne State University, 413 State Hall, Detroit, MI ( ngoel@tiger.cs.wayne.edu) W. Qin, Biospheric Sciences Branch, Laboratory for Terrestrial Physics, NASA Goddard Space Flight Center, Greenbelt, MD ( wqin@ltpmail.gsfc.nasa.gov) (Received April 29, 1996; revised March 7, 1997; accepted March 12, 1997.)