RELATING SURFACE ALBEDOS IN GCM TO REMOTELY SENSED DATA

The albedo of land surfaces is an important parameter for climate models. Observations over large areas are determined by satellite-sensed radiation from a single direction. This bidirectional reflectance is related to albedo by integration over all view angles. In the absence of observations at all view angles, a model of the radiative transfer through the atmosphere and at the surface is required to carry out this integration and to relate observations at one or a limited number of angles to surface albedo. Ideally, the same surface radiative model would be used to represent albedos in climate models. Both remote sensing and climate models require simple expressions for surface radiative models that are computationally inexpensive. We develop an analytic solution for reflection from a homogeneous leaf canopy with statistically prescribed leaf orientations. Following the approach of Hapke for planetary surfaces, this solution is used with adjustable parameters to invert observations of canopy bidirectional reflectance and define values for the model parameters. We allow for the asymmetric scattering resulting from leaf geometry and leaf-scattering properties. The former results from the product of projections of the leaf normal in the source and view directions integrated over the leaf distribution. This integration is approximated by simple analytic functions. The analytic solution is exact in the single scattering limit for the model assumed but uses a simple two-stream solution to include multiple scattering contributions to the bidirectional reflectance. The accuracy of the procedure is bench-marked using the ray-tracing model of Kimes. The analytic bidirectional reflectances agree with the numerical solution with relative errors less than 10% for near-infrared and less than 1% for visible radiation. With the use of a more accurate two-stream approach available for total fluxes, analytic albedos agree with those computed numerically with even smaller relative error. Application to remote sensing is illustrated with two examples: Kimes' lawn and Kriebel's pasture land. The inferred parameters are physically plausible. The observations are fit with an r.m.s. error of the order of 5-10%. © 1990.