595 
is sparse, a physical model that explains remotely sensed data will have to accommodate both upper and lower 
layers. In that event, the lower boundary may be modeled fully by a separate physical model, or its behavior 
may be characterized empirically. 
1.4. Atmospheric Effects 
For satellite or aircraft observations of radiance, the atmosphere influences both solar irradiance reaching the 
surface and reflected radiance leaving the surface. Beam radiation is scattered into diffuse surface irradiance, 
smoothing reflectance anisotropy; scattering adds path radiance, augmenting the surface radiance received by 
the sensor; and absorption reduces the surface radiance on its path to the sensor. Unfortunately, atmospheric 
effects are not independent of the surface. As surface brightness increases, multiple scattering between the 
surface and the atmosphere increases, boosting path radiance and diffuse irradiance. The influence of the 
atmosphere varies with wavelength. 
Because the atmosphere modifies land-leaving radiance, an inversion strategy that estimates the 
physical descriptors of the surface BRDF from remotely sensed radiance measurements must include atmo 
spheric effects. For applications in which atmospheric scattering is small compared to surface scattering, a 
simple path radiance correction may be all that is required (or that is practical, given limited knowledge about 
the state of the atmosphere at the time of data acquisition). However, for hazy atmospheres or shorter wave 
bands, some form of coupled-model approach is preferable, in which a combined surface-atmosphere model is 
fitted to the top-of-atmosphere radiances (Liang and Strahler, 1993a, 1993b; Rahman et ah, 1993a, 1993b). 
Note that the addition of an atmospheric model adds both a new set of physical parameters and a higher 
degree of complexity to any inversion process applied to remotely sensed data. 
2 - SOME RECENT DEVELOPMENTS IN VEGETATION CANOPY REFLECTANCE MODELING 
The following discussion documents a number of advances in vegetation canopy reflectance modeling that 
have occurred within the past two to three years. The treatment is not designed to be exhaustive or even fairly 
complete; rather it is designed to identify examples of new developments within the major subfields of canopy 
reflectance modeling. 
2.1. Radiative Transfer Canopy Models 
The modeling of the BRDF of vegetation canopies using radiative transfer (RT) theory has been significantly 
enhanced in the past few years by Myneni with coworkers. One line of research has been to extend the radia 
tive transfer formulation of the finite leaf scattering medium to three dimensions, expressing leaf area density 
within the medium first as a polynomial (Myneni et al., 1990), then as an external parameterization derived by 
fractal simulation (Myneni, 1991; Myneni et al., 1992a). The radiation field is solved numerically by extending 
the discrete ordinates method to three dimensions. The model fits a number of angular vegetation reflectance 
datasets quite well, although it slightly overestimates near-infrared reflectance. 
Another contribution has been to model the hotspot effect from first principles (Myneni and Ganopol, 
1991; Myneni et al., 1991; Myneni and Asrar, 1991; Knyazikhin et al., 1992), using an approach that describes 
the canopy as a medium containing regions of scattering phytoelements (e. g., branchlets with leaves) alternat 
ing with convoluted voids lacking scatterers. Technical advances to the solution of the radiative transfer equa 
tion for the leaf canopy are provided by Ganapol and Myneni (1991a, 1991b). Their formulations increase the 
accuracy of the solutions, especially those obtained by the discrete ordinates method. 
The 3-D model of Myneni (1991) has been simplified somewhat and extended to simulate the case of a 
canopy of sparse vegetation clumps, rather like a desert shrub landscape (Asrar, et al., 1992; Myneni et al., 
1992b). The model demonstrates that the directional reflectance behavior of the 3-D canopy is quite different 
from that of the equivalent 1-D canopy. However, the fraction of absorbed photosynthetically active radiation 
(FAPAR), canopy photosynthetic efficiency and stomatal efficiency are all well predicted by simple relation 
ships with the normalized difference vegetation index (NDVI) for either case. 
Iaquinta and Pinty (1994) recently modified the physical model of Verstraete et al. (1990) along the 
lines of radiative transfer to include a (Lambertian) lower soil boundary, thus allowing its application to opti 
cally thin canopies. The radiance field is divided into uncollided, singly-scattered, and multiply-scattered radi 
ance, with the multiple scattering component evaluated numerically using a single-angle discrete ordinates 
method. Calculation is rapid enough to allow inversion through forward iteration, and when tested with data 
simulated using other radiative transfer models, optical properties and the hotspot parameter are well 
retrieved. Leaf area index and soil albedo inference, however, are sensitive to the leaf area index value. 
2.2. Coupled Atmosphere-Canopy Radiative Transfer Models 
A number of models couple the atmosphere and plant canopy together. Coupled models are particularly 
suited to exploring satellite sensing scenarios, since orbital measurements are always influenced by the atmo 
sphere. Because radiative transfer models of the vegetation canopy lend themselves readily to atmospheric