712 
3.3. Integration 
All of the integrations performed in the experiments discussed below have been evaluated numerically on a 
regular grid of 5° increments in both azimuth and zenith angle. Whilst this grid is quite coarse, we estimate that 
the simulated albedo values are accurate to three significant figures, which is sufficient for these experiments. 
4 - RESULTS AND DISCUSSION 
4.1. Trends in Albedo as a Function of Solar Elevation 
Simulations were performed of the (instantaneous spectral) albedo of the land cover types, described above, at 
662 nm and 826 nm, using equations (3), (5) and (6), with directional sky radiance and direct solar irradiance 
data provided by the Zibordi-Voss model for typical mid-latitude Summer atmospheric conditions with a relatively 
low concentration of continental aerosols (atmosphere 1). The simulations at 826 nm are presented in Figure 3; 
the 662 nm data show similar trends. It should be noted that these curves are somewhat different from those 
obtained when calculating L c from equation (21) (as published in Ahmad and Deering (1992)). The reason for 
this appears to be that the method used by Ahmad and Deering to account for diffuse irradiance effects. The 
magnitude of parameters A and B (as defined in equation (21)) that they obtain from model inversions are much 
higher than one would expect, showing that this empirical term is indeed, as the authors suspected, providing a 
good fit to the measurements by compensating for various approximations made in the BRDF model formulation. 
Despite this, the parameter values obtained by Ahmad and Deering can still be expected to provide reasonable 
estimates of BRDF and hence albedo for the various cover types, as most of the model parameters fit within a 
range one would expect for these cover types. 
Figure 3 Albedo (ociQj,,,,)) of various land Figure 4 Variations in albedo introduced by 
cover types at 826 nm for atmosphere 1. different irradiance conditions 
(atmosphere 1 (Al) and atmosphere 2 (A2)) 
From Figure 3, we can see that the albedo tends to decrease as the solar elevation increases for most of these 
cover types. These results are consistent with measurements made by several authors (e.g. Pinty and Ramond 
(1986), Eck and Deering (1990)), but are, in fact the opposite trend to that calculated by Ahmad and Deering. 
Again, this seems to be associated with the way in which Ahmad and Deering account for diffuse irradiance. 
The magnitude of the variation in albedo with Sun angle is summarized in Table I, and one can see that the 
variations can be quite large for many cover types. Again, this is backed up by experimental observations. 
Figure 5 shows calculated values of R H for the various cover types. It can be seen that the variation between 
R H for 662 nm and 826 nm is generally quite small, which would seem to suggest that a parameterization of 
R H is worth considering as a wavelength-independent function describing the relative variation in albedo as a 
function of sun angle. This will need to be tested further for other cover types and at different wavelengths, 
but if this finding were generally true, it would have significant implications for albedo products as the 
formulations of p 3 and p 4 would require only p 2 to be specified as a function of wavelength for spectral 
albedo, and wavelength-integration of this to yield broadband albedo would be considerably simplified. The 
form of these functions (as well as experience with the quadratic formulation used by Ahmad and Deering 
(1992) to model albedo) suggest that they might well be modelled empirically through the use of a quadratic 
function in solar elevation, though again, the form of such a model would need to be further investigated.