3-RESULTS AND DISCUSSION 
A summary of the results using VEG and the resulting publications in regard to inferring hemispherical 
reflectance, ground cover, plant height, and view angle extension are as follows. 
3.1. Hemispherical Reflectance (Albedo) 
Kimes et al. 1991 described the first version of VEG and gave examples of VEG inferring spectral 
hemispherical reflectance. The importance of spectral and total hemispherical reflectance of terrestrial sur 
faces to biospheric and atmospheric processes has been addressed in several papers (e.g., Mintz 1984, Dic 
kinson 1983, Sellers 1985). VEG has an array of techniques for inferring hemispherical reflectance and are 
described as follows. Several techniques that use multiple off-nadir view angles taken in a single azimuth 
plane (called a string of data) have been developed by Kimes et al. (1987a,b). These techniques use a sim 
ple integration technique to calculate the spectral hemispherical reflectance of the target from any string of 
data. The Walthall and Norman (1984) technique is also included and uses any three or more off-nadir view 
angles. This technique uses a form fitting equation containing 3 unknown coefficients fitted to the data using 
a linear least squares technique. The equation and fitted coefficients are then integrated over the hemisphere 
to calculate the spectral hemispherical reflectance. Finally, a variety of techniques were developed to infer 
hemispherical reflectance from any 1 or 2 directional view angles. These techniques use a linear correction 
to calculate spectral hemispherical reflectance. The coefficients are derived from the restricted data set using 
a least squares technique. The technique is applied only to data sets of four or less data points. VEG decides 
the appropriate techniques to apply to the target data. 
VEG was applied to various kinds of surface reflectance input data, e.g. nadir only, one half string, two 
full strings, one off-nadir view angle, two off-nadir view angles, four random off-nadir view angles, etc. A 
wide variety of cover type and sun angle conditions were tested. In all cases the root goal was to infer the 
spectral hemispherical reflectance and associated error bound for visible and near infrared bands. The pur 
pose of this study was to demonstrate the utility of VEG in being able to handle any kind of input data of an 
unknown target (single view angles, scattered multiple view angles, and strings of data). VEG made all deci 
sions and inferences using the input data and knowledge bases. VEG also defined (in real time) a restricted 
data set of cover types selected from the historical database with similar percent ground cover, solar zenith 
angle, and wavelengths as the unknown target. The techniques were then applied to this restricted data set 
(with known hemispherical reflectance) to calculate a proportional rms error (Eqn. 1). This is a rigorous esti 
mate of the accuracy of a technique for targets similar to the unknown target (Kimes et al. 1991). 
The results showed a proportional rms error of between 1 and 8% for all the tests. In comparison, using 
only nadir values to estimate hemispherical reflectance directly (assuming a Lambertian target) produces 
errors as high as 45% (Kimes and Sellers 1985) It is often surprising that when using VEG with only one or 
two off-nadir view angles a relatively accurate inference can be made. However, for certain conditions (e.g., 
certain view-angle/sun-angle combinations) the inferred accuracy can be poor. Thus, a rigorous estimate of 
accuracy such as provided by VEG is a highly desirable feature. The accuracy of any particular technique is 
highly variable and depends on the specific conditions (cover type characteristics, sun angle, view angles 
available, and wavelength). 
Hemispherical reflectance estimates are required for large regions of the Earth in photosynthesis(e.g. 
FPAR) and climate studies. Ideally, one would only apply VEG over homogeneous vegetation covers. How 
ever, what is typically done in global circulation models (GCM) and related studies is to obtain an average 
hemispherical reflectance on a square grid cell (e.g. 2° x 2°). Normally, all available directional data for a 
given cell is averaged (for each view direction) and then a particular technique for inferring hemispherical 
reflectance is applied to this averaged data. This approach can potentially cause significant errors in the 
inferred hemispherical reflectance as any given grid cell can contain several surface types that directionally 
scatter radiation very differently. When averaging over a set of view angles, the resulting mean values may 
be atypical of the actual surface types that occur on the ground and the resulting inferred hemispherical 
reflectance can be in error. These errors were explored by creating a simulated scene and applying VEG to 
estimate the area-averaged hemispherical reflectance using various sampling procedures (Kimes et al. 1993) 
The reduction in the hemispherical reflectance errors provided by using VEG ranged from a factor of two to 
four, depending on conditions. This improvement represents a shift from the calculation of a hemispherical