A theoretical assessment of the relation between woody canopy cover and red reflectance

ELSEVIER

A Theoretical Assessment of the Relation Between Woody Canopy Cover and Bed Reflectance Jingli Yang and Stephen D. Prince ° S e v e r a l studies have demonstrated the potential of brightness indices, especiaUy red band reflectance, from Earth resources satellite sensors" to estimate vegetation canopy cover and biomass in semiarid savannas as well as in boreal fl)rests. These studies showed that the relation between woody canopy cover and red reflectance varies with geographical location, season, and other factons. This paper nwdels the relation between woody canopy cover and red reflectance, using two simple geonwtric canopy nu)dels developed by Li-Strahler and ]asinski, respectively. Model simulations show that the relation between woo@ canopy cover and red band reflectance is sensitive to changes in background reflectance, canopy reflectance, solar zenith angle, and topography, which together determine the intercept, .slope, and linearity of the relation. The nu~del results provide a theoretical framework that serves, as a guide fi)r the most effective conditions f ) r the use of reflectance measurements" to estimate canopy cover to be selected a priori. It is predicted that woody canopy cover is best estimated with the us'e of red band measurenwnts acquired at a s'olar zenith angle less than 30 ° in a season when the contrast between background reflectance and canopy reflectance is' the largest during the year. ©Elsevier Science lnc., 1997

INTRODUCTION

Woody related woody sphere

canopy cover is an important biophysical variable to a wide range of surface conditions such as biomass and CO2 draw-down from the atmo(Olsson, 1985; Millington et al., 1989; Tietema,

° Laborato~- fur Global Remote Sensing Studies, l)epartment of Geography, University ole Mawland, College Park Address correspondence to Jingli Yang, Hughes STX, 77111 Greenbelt Boad, Suite 400, Greenbelt, MD 20770. Received 19 October 199,5; revised 4 April 1996. REMOTE SENS. ENVIRON. 59:428M39 (1997) ©Elsevier Science Inc., 1997 655 Avenue of the Americas, New York, NY 10010

1993). In semiarid savannas, the woody canopy cover, (sometimes also expressed as tree-to-grass ratio) is very, susceptible to seasonal and annual water balance and to degradation and loss of woody cover owing to truman utilization by burning, livestock husbandry, and cutting for lumber and fuel wood (Cole, 1986; Eagelson and Segarra, 1985; Jansen, 1988; Manabe, 1983). A number of studies have considered the use of optical satellite data for monitoring woody canopy cover in semiarid savannas. Although vegetation greenness indices, especially the normalized difference vegetation index (NDVI), are closely related to vegetation biomass, leaf area index, or fractional canopy cover in agricultural fields, grassland, and forest (Tucker et al., 1985; Asrar et al., 1984), they are not as well related to woody canopy cover as are brightness indices in semiarid savannas (Grif~ths and Collins, 1983; Musick, 1984, 1986; Olsson, 1984; Vujakovic, 1987; Franklin et al., 1991; Duncan et al., 1993; Larsson, 1993). Brightness indices have also been observed to be more closely related to woody canopy cover than greenness indices in boreal forest at high latitudes (Foster et al., 1994). Several brightness indices, including albedo, red band reflectance, and the Kauth-Thomas brightness, have been correlated with woody canopy cover; and, of all the brightness indices, the highest correlation was usually for red band reflectance, [e.g., multi-spectral scanner (MSS) band 5, Thematic Mapper (TM) band 3, or SPOT High Resolution Visible (SPOT HRV) band 2 (Olsson, 1984; Vujakovic, 1987; Musick, 1984; Yang, 1995; Duncan et al., 1993; Franklin et al., 1991)]. Several investigators have also demonstrated that the relation between red band reflectance and canopy cover is affected by solar zenith angle and shadows (Musick, 1986; Graetz and Gentle, 1982; Franklin et al., 1991). However, a full examination of the relation between canopy cover and red reflectance and of the sensitivity of the relation to 0034-4257/97/$17.00 Pll S0034-4257(96)0(1111-3

Woody Canopy Cover and Red Reflectance 429

other factors, such as background reflectance, topograplay, leaf area index, and tree geometry, is lacking. In this paper, we assess the relation between red band reflectance and woody canopy cover in an African savanna, using two geometric canopy models developed by Li and Strahler and by Jasinski, independently. The canopy models enable the functional relation between canopy cover and red band reflectance to be simulated and the effects of background reflectance, solar zenith angle, topography, leaf area index, and tree geometry to be evaluated. Thus these canopy models provide a mechanistic approach to the use of reflectance data to estimate canopy cover. METHODS

Several simple geometric canopy models have been developed to calculate pixel reflectance for a given vegetation cover and geometry of radiometric interaction (Otterman, 1984; Li and Strahler, 1985; Jasinski and Eagleson, 1990). In simple geometric canopy models, the canopy is assumed to consist of a ground surface (of known reflective properties) with geometric objects or protrusions, of prescribed shapes, (e.g., cylinders, cones, ellipsoids, or spheres), dimensions, and optical properties (reflectance, transmittance, and absorptance), placed on the surface in a defined manner. The interception of light and the consequent shadowing by the protrusions and reflectance from the ground surface are analyzed to determine the reflectance of the composite canopies. Otterman (1981) assumed that the protrusions were vertical cylinders of variable height and negligible cross section (diameter to height ratio is much smaller than 1), and the protrusions were numerous. Otterman's model is, therefore, not directly applicable to the open woodland canopies in which the protrusions (trees) can be low in density or relatively large or both (Goel, 1987). The Jasinski and Li-Strahler models assume trees to be randomly spaced cylinders or ellipsoids on sticks, which seems likely to be an appropriate description of discontinuous tree canopies with continuous grass cover.

Franklin and Turner, 1992):

S=Ag.G +(1-Ag).Xo

(1)

where S=the pixel-level reflectance, X0=the average reflectance of a plant and its associated shadow, referred to as figure reflectance, G=the reflectance of sunlit background, Ag=sunlit background cover. If it is assumed that tree size is log normally distributed and the spacing of trees can be described by a Poisson distribution, the figure cover (tree crown plus shaded background) can be calculated by using an overlap model (Strahler et al., 1988). 1-A~= 1 - e ,,,r

(2)

where m is the product of the density and the average squared crown radius divided by the pixel area, which is proportional to the nonoverlapping plant cover in the pixel, nm. For plant cover with overlap, m is related to the vertical projection of canopy cover, C: m-

-ln(1-C)

(3)

F is the area of the figure cover created by an ellipsoid of unit radius and is a function of plant shape (the ratio of r to b) and solar zenith angle 0: 7~

F=n+cos0S-Ao

(4)

and

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2 sin (2fliJ\

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if (b +h)tan0>r[1 + (1/cos0')], otherwise A0=0.

and Li-Strahler Geometric Canopy Model Li and Strahler (1985, 1986, 1988) developed a family of geometric models of the reflectance of a vegetation canopy composed of discontinuous woody cover. Pixel-level reflectance is modeled as the area-weighted sum of the reflectance of four components: sunlit canopy crown, sunlit background, shaded crown, and shaded background. Trees are modeled as solid, opaque ellipsoids on sticks, parameterized by h; stick height; r, the horizontal radius; and b, the vertical radius. In many situations, the model was simplified to a two-component mixture owing to the difficulties of measuring or estimating refleetanees of sunlit and shaded canopy crown (Strahler et al., 1988;

0,=tan

ta4

When topography is included in the model, F is adjusted by using the following formula (Wu and Strahler, 1994): F' = n + (F-n) c°sac°sO

cos(0-e) where e=tan-l(tana eosq~) a is the slope angle, and fp is the difference between slope and solar azimuth.

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Jasinski Geometric C a n o p y Model In Jasinski and Eagleson's model (Jasinski, 1990; Jasinski and Eagleson, 1990), woody plants are represented by solid blocks (or cylinders) arranged spatially in a Poisson distribution and superposed on a horizontal background. Pixel-level reflectance is modeled as a linear mixture of sunlit canopy tops, sunlit background (or understory), and shadows:

R(,~) = c.tL(,~) + s.tL(,~) +B.R,(,~)

(5)

where R(2)=pixel reflectance in 2 waveband, R,.(2)=sunlit canopy reflectance in 2 waveband, R~(2)=shadow reflectance in 2 waveband, Rb(2)=baekground reflectance in 2 waveband, C=canopy cover, S=shadowed background cover, B = sunlit background cover. To calculate shadowed background cover, Jasinski (1990) derived a functional relation among subpixel canopy cover, shadow, and illuminated background for large samples (pixel size>30X30 m2): S=I-C-(1-C/',+~)

(6)

q is a nondimentional solar geometric parameter, defined as the ratio of the shadow area cast by a single tree without overlap, A, to the vertical projected canopy area of that tree, At. For the specific case of cylinders, r/=2H tan0

(7)

7rr

where H and r are the height and the radius of the cylinder, respectively, and 0 is the solar zenith angle. Because B+C+S=I, B can be calculated as :

B=I-C-S For a nonhorizontal surface, */ can be modified accordingly, as in the Li-Strahler model. Comparison o f the Li-Strahler and the Jasinski Models As presented above, calculated of the pixel-level reflectance is very similar in the Li-Strahler and the Jasinski geometric models, although the number of reflectance components in the calculation and assumed tree shape are different in the two models. Comparison of the LiStrahler model and the Jasinski model showed that equations for calculating the figure cover in both models are the same, as demonstrated below. In the Li-Strahler model, the figure cover is calculated as follows ([see Eqs. (2) and (3)]: 1 -Av = 1 - e -'''r = l_jh,i~ c/ F

=1-(1-c>

In the Jasinski model, the figure cover is calculated as follows [see Eq. (6)]:

S+C=I-(1-C)I'+~ ! Based on the definition of F in the Li-Strahler model and t/in the Jasinski model, it is easy to see that F/x is equivalent to q + l , which is the ratio of the figure cover of a single tree to the vertical projected canopy area of that tree. Model Parameterization Data Sources The canopy models were parameterized by using field measurements made in the South Luangwa National Park (SLNP) in the Luangwa Valley of eastern Zambia (Fig. 1). The Luangwa Valley is one of the few areas in Africa where savanna vegetation exhibits great variation in form and composition in a small area, owing to the variation in rainfall caused by the deep rift valley and the presence of large alluvial areas as well as faulted sediinentary rocks of the Karroo System. The vegetation communities in the Luangwa Valley represent a wide range of savanna types in central and southern Africa (Werger and Coetzee, 1978; Huntley, 1982; Menaut, 1983; White, 1983; Cole, 1986). For example, miombo woodland dominated by species of Brachystegia, Isoberlinia, and Julbernardia is present in several growth germs in Luangwa and also covers the greater part of the level terrain of the plateau in central and southern Africa. Another major woodland vegetation, mopane woodland, almost exclusively composed of a single tree species, Colophosperwmm mopane, exists in the wide, flat valley bottoms of all the larger rivers--notably the Zambezi, Luangwa, Shire, Limpopo, Okavango, and Cunene in south-central Africa (Cole, 1986). A wide variety." of soil types developed from different sedimentary rocks of the Karroo System grits, sandstones, mudstones, silts, and alluvium can be found in the Valley and its surrounding areas (Wilson and Lee, 1968; Astle, 1969; Trapnell, 1953). Soil colors vmy from relatively bright gray silt to brown sandstone soil and to black vertisols (Wilson and Lee, 1968). Astle (1988) mapped vegetation in the SLNP into four major types: miombo woodland, mopaue woodland, scrubland, and grassland. Twenty-nine sites in the SLNP, representative of different vegetation and background types in the SLNP, were visited in October 1993, and tree density and height were measured (Yang, 1995). At each site, ground radiometric data were collected, using an Exotech 100 BX hand-held radiometer with a 15° field of view and Landsat Thematic Mapper (TM) spectral configuration (0.450.52 /lm, 0.52-0.60 /mL 0.63-0.69 /tin, 0.76-0.90 /am). Radiometric measurements were made at 5 meter intervals 'along transects of 100 m to 200 m at each site. Befleeted radiances were collected from the field target and a BaSO4 standard reflectance panel, and reflectance valnes were subsequently calculated by taking the ratio of

Woody Canopy Cover and Red Reflectance 431

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these radiances. Multiple measurements at the same site were averaged to calculate the average reflectance of the background. Reflectances of leafless tree branches were measured by piling the branehes on the ground to create an optically impermeable layer. Reflectanees of tree shadow of each vegetation type were measured in October 1988 by W. L. Astle, using a Milton hand-held radiometer, with spectral band passes in the red (0.6-0.7 /zm) and NIR (0.75-1.05/zm) wave bands (Milton, 1980). The red bandwidth of the Milton radiometer is a little wider than the red bandwidth of TM (0.63-0.7/lm), but the difference is usually considered to be neglible (Marhkam et al., 1980; Crist and Cieone, 1984).

Because direct measurements of canopy refleetance were not available, canopy refectance was estimated by using a canopy radiative transfer model, the SAIL (Scattering by Arbitrarily Inclined Leaves) model (Verhoef, 1984). It is assumed that the canopy could be treated as a homogeneous, turbid medium, so the SAIL model could be applied to estimate the average canopy reflectance and canopy transmittance. The inputs to SAIL are leaf area index (LAD, the optical properties (reflectance and transmittance) of single leaves, the leaf angle distribution, and the reflectance of branches. The assumption was made that the leaves are distributed in a spherical fashion (Monteith and Unsworth,

432

Yangand Prince

1990). Previous studies (e.g., Goward and Hummerich, 1992) have shown that, compared with other factors, SAIL model is not very sensitive to changes in leaf angle distribution. Leaf reflectance in the red band was assumed to be 0.06, and leaf transmittance was assumed to be equal to leaf reflectance, whieb is a reasonable approximation for a wide range of leaf types and species (Gates et al., 1965; Elvidge, 1990). Leaf area index was calculated from canopy transmittance, using the Beer-Lambert law, which assumes a negative exponential relatkm between transmitted light and LAI (Spanner et al., 1994): LAI =

-In(r) k

where k is a light extinction coefficient, and r is the canopy transmittance. At solar zenith angle 0=0, k=O.5. When 0>0, k becomes (Monteith and Unsworth, 1990): k =~ cos0 2 r was calculated from the Milton hand-held radiometer measurements of sunlit background and tree-shadowed background, assuming the reflectance of sunlit and shadowed background were the same: RI, K where Rj, and//~ are the radiances measured from sunlit background and tree shadow, respectively.

Tree Geometry Estimation Model simulations were done ibr three major woodland types in the SLNP (i.e., mopane woodland, scrubland, and miombo woodland). Tree height for different vegetation types was calculated by averaging the heights of trees over 3.05 meters at three field sites representative of mopane woodland, scrub, and miombo woodland, respectively. Tree densities were measured in October 1993 (Yang, 1995). Visual observation of woodland and serubland crowns indicates that they contain a mixture of" oblate- (major axis is perpendicular to the ground) and prolate- (major axis is parallel to the ground) shaped canopies sueh that, on average, tree crowns can be treated as spherical. Because crown geoinetry measurements were not available, the assumption of spherical crown shape has been made throughout the analysis. The horizontal erown radius was estimated from 35 mm photographs taken with the ICAR (Integrated Camera and Radiometer) (Prince et al., 1988). The ICAR was flown during a period of high spectral contrast between tree and ground layers. Individual trees were visible in photographs and their crown dimensions could be measured. Only those elose to nadir have been used to calculate the average radius typical of the vegetation types as a whole (Fuller, 1994). The LAI for mopane trees was assumed

Table 1. Tree Parameters Measured and Calculated for Dill)rent Vegetation Types in the South Luangwa National Park Vegetation Type

Tree Hei~,ht (m)

Crown tladius (m)

LAI

Mopane woodland Scrubland Miombo woodland

9.5 4.36 7.05

2.3 1.66 2.45

0.01 0.91 2.00

to be 0.01, because mopane trees tire ahnost leafless in late dry, season. The LAI for scrub and miombo woodland was calculated by using the Beer-Lambert equation. Table 1 lists the parameter values used for the dirt)rent vegetation types in the SLNP.

RESULTS Simulation of the Relation between Red Reflectance and Woody Canopy Cover Both the Li-Strahler and the Jasinski eanopy models were used to simulate the relation between woody canopy cover and red reflectance tbr three major vegetation types in the SLNP. The solar zenith angle used in the model sinmlation (36 °) was for a Landsat overpass at the SLNP in early October when the ground radiometer data were collected. The view zenith angle was set to zero because Landsat, like most of the earth resource satellite sensors, has an ahnost nadir view (Lillesand and Kiefer, 1987). Fignre 2 shows the relations between canopy cover and red reflectance obtained, using the Jasinski and the Li-Strahler canopy simulations. Negative relations were sinmlated for all three vegetation types. The slope of the simulated relation tbr mopane woodland was nmch smaller than those for scrub and miomho woodland, because canopy reflectance of mopane woodland was higher than that of scrub and miombo woodland due to the thet that mopane trees were ahnost leafless in early October. Because the canopy reflectance and shadow reflectance of" miolnbo woodland were the lowest, eompared with those of mopane woodland and scrub, the slope of the relation between canopy cover and red reflectance tor miombo woodland was the highest. The negative relation between canopy cover and red reflectance may be explained by wiriations of the fraction of sunlit background cover and shadow cover as the fraction of canopy cover increases. Figure .3 shows modelsimulated canopy cover, shadow cow~r, and sunlit background cover for mopane woodland. As canopy cover increased, the shadow eover increased until canopy cover reached 0.4-0.5 and then decreased as canopy cover increased. Sunlit background cover decreased curvilinearly as canopy cover increased. Both models gave similar relations between canopy cover, shadow cover, and sunlit background cover except that, lbr the saine canopy

Woody Canopy Cover and Red Reflectance 433

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cover, the Jasinski m o d e l shadow covers w e r e larger than those o f the Li-Strahler model. This is p r o b a b l y b e c a u s e the Jasinski m o d e l assumes that each plant is a cylinder and t h e r e f o r e shadow cover is likely to b e overestimated. Based on the fraction o f sunlit background, shadow, and canopy cover, pixel-level r e d reflectance can be calculated, which is the w e i g h t e d average o f the r e d refleetances of these t h r e e components. T h e sunlit b a c k g r o u n d had the highest r e d reflectance; shadow and canopy cover h a d m u c h lower r e d reflectance. Thus, as canopy cover increased, sunlit b a c k g r o u n d cover d e c r e a s e d and the pixel-level r e d reflectance decreased. Although both c a n o p y models simulated negative relations b e t w e e n canopy cover and r e d reflectance for different vegetation types, the Jasinski m o d e l relation was less linear than that o f the Li-Strahler model, p r o b a b l y because the Jasinski m o d e l overestimates shadow cover. The o t h e r difference b e t w e e n the two models is that, in the Li-Strahler c a n o p y m o d e l simulation, the r e d reflec-

tance d e c r e a s e d over the full range o f canopy cover; whereas, in the Jasinski m o d e l simulation, the decrease in r e d reflectance b e c a m e very small when canopy covers were high, and r e d reflectance even showed little increase w h e n canopy cover increased from 0.9 to 1.0 (Fig. 2). This is because canopy reflectance was usually higher than that of the shadow reflectance, and therefore pixellevel reflectance at a canopy cover o f 1.0 could b e higher than that at a canopy cover of 0.9. In the Li-Strahler model, b e c a u s e the canopy cover and shadow cover were c o m b i n e d , pixel r e d reflectance c o n t i n u e d to decrease as canopy cover increased for all t h r e e vegetation types. Generally speaking, a concave curved relation b e t w e e n canopy cover and r e d reflectance was simulated from b o t h canopy models. This may explain wily Olsson (1984) o b t a i n e d the b e s t correlation b e t w e e n MSS r e d b a n d m e a s u r e m e n t s and c a n o p y cover by using the square root o f canopy cover.

background cover, and shadow cover for mopane woodland: (a) Jasinski model; (b) Li-Strahler model.

434 Yang and Prince

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The simulated relations between red reflectance and figure cover (sum o f canopy cover and shadow cover) for three different vegetation type are shown in Figure 4. Both the Li-Strahler and the Jasinsld models simulated linear relations between figure cover and red reflectance ibr three vegetation types. This result suggests a linear response of red reflectance to the sum of canopy cover and shadow cover and probably explains why a more linear relation resulted when TM red reflectance was correlated with the sum of canopy cover and shadow cover instead of canopy cover alone (Franklin et al., 1991). Analysis

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Effect of Background Reflectance Figure 5a shows the effect of different background reflectances on the simulated relation between canopy cover and red reflectance. The background refleetanees used in the model simulation were representative of different ground layers in the S L N P and its neighboring areas. Background reflectance had a large effect on the simulated red reflectance when canopy cover was low. As canopy cover increased, simulated red reflectance values for different background reflectances converged. Figure 5b shows the effect of seasonal variation in background reflectance on the simulated relation between canopy cover and red reflectance. The seasonal background refleetances used in the model simulation were measured by W. L. Astle at a scnlb miombo site

Woody Canopy Cover and Red Reflectance 435

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in 1988. Owing to the large variations in seasonal background reflectance in the SLNP caused mainly by seasonal changes in herbaceous cover and soil moisture, the relation between canopy cover and red reflectance showed significant variation from May to October. Tim slope of the relation between canopy cover and red reflectance was the highest in October, when the contrast between background reflectance and canopy reflectance was the largest.

Effect of Solar Zenith Angle The effect of solar zenith angle on the model-simulated results is shown in Figure 6. The highest red reflectance at any given canopy cover was for solar zenith angle of 0 °. When solar zenith angle is 0 °, there is no shadow on the ground, and the relation between canopy cover and red reflectance is linear. As solar zenith angle increased, the simulated red reflectance a t a n y given canopy cover decreased as the shadow cover increased. Because Earth observation satellites cross the equator either in the morning (e.g., Landsat, SPOT) or in the afternoon (e.g., NOAA-even satellites) (Lillesand and Kiefer, 1987), the solar zenith angle at the time when satellite data are collected in usually not zero. Greater sensitivity of canopy cover detection is obtained with higher solar zenith angles, but the relation saturates at progressively lower canopy covers.

Effect of Topography Figure 7 shows the effect of topography (slope and aspect) on the simulated relation between canopy cover a n d red reflectance. The simulated red reflectance was a little higher when the slope was facing the sun at 30 ° or 50 ° than when the surface was f i a t . This is because the solar zenith angle used in the model simulation was 36 ° , a n d a slope facing the sun at a 30 ° or 50 ° angle has less shadow on the ground than does a flat surface. With a slope facing away from the sun at 30 ° or 50 °, there is

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Effect of Tree Geometry and LAI Figure 8 shows the effect of tree canopy geometry (tree height and crown radius) of mopane woodland, scrubland, and miombo woodland on the simulated relation between canopy cover and red reflectance. The LAI was held constant for different savanna types. Tree geometries did not have much effect on the simulated relation. The red reflectances calculated for mopane woodland were a little lower than those for scrub and miombo woodland at any canopy cover because trees (such as mopane) with tall stems cast more shadow on the ground than do those with short stems (such as scrub and miombo trees) (Franklin and Turner, 1992).

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Figure 9. Sensitivity of the Li-Strahler canopy modelsimulated relation between canopy cover and red reflectance to leaf area index.

The effect of LAI on the simulated relation between canopy cover and red reflectance is shown in Figure 9. As the LAI for each canopy cover increased, canopy reflectance and shadow reflectance decreased; therefore, the calculated red reflectance decreased. Variations in LAI over seasons therefore have some effect on the canopy cover and red reflectance relation. The higher the LAI, the lower the canopy and shadow reflectances and, therefore, the larger the slope and the greater the sensitivity of the relation between canopy cover and red reflectance. DISCUSSION

AND CONCLUSIONS

Both the Li-Strahler and the Jasinski canopy models simulated similar negative relations between canopy cover and red reflectance for several major savanna vegetation types in the SLNP and its neighboring areas. The modeled relations tbr miombo and scrub vegetation types were similar but, because the canopy reflectance of leafless mopane woodland was higher than that of the scrub and miombo woodland, the relation between reflectance and canopy cover was weaker for mopane woodland. At the time of the field measurements (October), the canopy cover for leafless mopane woodland is usually below 20%, and so one relation between canopy cover and red reflectance may be used for all three vegetation types, with some scatter in the relation due to differences ill background and canopy reflectances (Fig. 2). This may explain why Yang (1995) observed a high correlation coefficient (r=0.94) between field-measured canopy cover and MSS band 5 measurements for all major woodland types pooled in the SLNP. Both the Li-Strahler and the Jasinski geometric-optical canopy models are well suited to the discontinuous tree or shrub cover in savannas. In fact, equations for calculating the pixel-level reflectance and the percent

component covers are the same in both models, as demonstrated in the section comparing the Li-Strahler and Jasinski models. The differences between the two models lie in their different assmnptions about tree shape and the number of" distinct reflectance components. First, if the number of trees and solar geometry are the same, cylindrical trees cast more shadows than do ellipsoids on sticks, and the calculated pixel red reflectance will consequently be lower; as a result, the Jasinski model-simulated relation between canopy cover and red reflectance was more nonlinear than that of the Li-Strahler canopy model. Second, the Li-Strahler model used in this paper had only two reflectance components (the sunlit background and figure cover, which includes sunlit canopy, shadowed crown, and shadowed background), whereas the Jasinski model included three ground components (sunlit canopy, sunlit background, and shadows), which gave more realistic results when canopy cover vahles were high (>80%; Fig. 2). The four-component LiStrahler model would overcome the shortcomings of both the two-component Li-Strahler model and the Jasinski model. However, more parameters and more field measurements are needed for the four-component LiStahler model. Both models showed that the simulated relation between canopy cover and red reflectance is sensitive to changes in solar zenith angle and topography. When solar zenith angle was zero the model-simulated relation between canopy cover and red reflectance was linear; but, when solar zenith angle was not zero, the relation became nonlinear owing to the ei}~et of shadows. By the same token, variations in topography cause changes in the amount of shadows cast on the ground and therefore affect the linearity of the relation, ttowever, fbr an area with canopy cover values below 80%, solar zenith angle below 30 ° , and moderate typographical variations (slope<30), a linear equation can be used to approximate the relation. This probably explains why linear relations have generally been reported for semiarid savanna vegetation that usually has less than 80% canopy cover and fbr which terrain variation is usually small (Vujakovic, 1987; Yang, 1995; Duncan et al., 1993). The simulations also showed that the relation between canopy cover and red reflectance is sensitive to changes in background reflectance, canopy reflectance, and shadow reflectance. Seasonal variations of background reflectance, canopy reflectance, and shadow reflectance would cause the relation between canopy cover and red reflectance to vary. The larger the difference between background reflectance and canopy reflectance, the greater the slope and the sensitivity of the relation between canopy cover and red reflectance. This result parallels that noted by others (Li and Stahler, 1985; Franklin and Strahler, 1988) that the ability to estimate tree density., which is another vegetation structure measurement, is greater when the dif{)rence between the

Woody Canopy Cover and Red Reflectance

background and the canopy reflectance is larger: For the SLNP savannas, the slope of the relation between canopy cover and red reflectance was largest in the middle to late dry season when the contrast between the background and the canopy reflectance was largest. This explains why canopy cover may be best estimated from satellite data acquired in late dry season rather than in any other season, as observed in empirical studies (Olsson, 1984; Vujakovie, 1987). Because the background reflectance, canopy reflectance, shadow reflectance, and solar zenith angle vary geographically, no universal relation between canopy cover and red reflectance exists. The greatest variation of the relation is likely to be caused by variations in canopy, background, and shadow reflectance; the effect of solar zenith angle can be reduced to some extent by selection of time of day and year for observation. Although several studies have addressed the spatial and seasonal variations of canopy and background reflectances at local scales (e.g., Franklin et al., 1993; Fuller, 1994), knowledge of the variability of the canopy and background optical properties of savannas at large scale is still poor. Future studies are needed to assess the variation of background reflectance, canopy reflectance, and shadow reflectance for savannas and other vegetation systems globally. Finally, the relation between canopy cover and red reflectance appeared not to be very sensitive to changes in tree geometry of different woodland types in the SLNP. Thus the same relation between canopy cover and red reflectance may be appropriate for several major African savanna types of different tree geometry. Further studies are needed to evaluate the effect of tree geometry of other vegetation types, such as boreal forests and other savanna types, on the relations between canopy cover and red reflectance. This work has shown that the empirical results obtained in several studies of savanna canopy cover (Griffiths and Collins, 1983; Musick, 1984, 1986; Olsson, 1984; Vujakovic, 1987; Franklin et al., 1991; Duncan et al., 1993; Larsson, 1993) can be explained by the simple geometric canopy model simulations. The modeling study suggested that different linear relations between canopy cover and red reflectance (Vujakovic, 1987; Musick, 1984; Yang, 1995; Duncan et al., 1993; Franklin et al., 1991) are probably due to geographical and seasonal variations in canopy, background, shadow reflectance, and solar zenith angle. The model study also shows that the theoretical relation between canopy cover and red reflectance is eurvilinear; but, under certain conditions, a linear equation may be used to approximate the relation. Thus the modeling framework outlined here can guide the selection of the optimum time of year and time of day for measurement of canopy cover, using remotely sensed reflectanees, and indicate the significance of any uncontrolled variables such as background and canopy reflectances.

437

The paper is part of a research project supported by a grant from the National Aeronautics and Space Administration under Global Change Fellowship (NGT-30168). We w(ntM like to thank Drs. John Townshend, Ralph Dubayah, and Naill Hanan for their critical comments" on canopy model simulations. We would also like to thank Dr. Karl Huemmrich fi)r this valuable discussion about simple geometric canopy models. Thanks also go to two anonymous reviewers.

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Woody Canopy Cover and Red Reflectance 439

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Yang, J. (1995), Remote sensing of savanna vegetation structure and its change in eastern Zambia, Ph.D. dissertation, Department of Geography, University of Maryland, College Park.