Geography Research Works
Permanent URI for this collectionhttp://hdl.handle.net/1903/1641
Browse
Search Results
Item Calculation of the Angular Radiance Distribution for a Coupled Atmosphere and Canopy(Institute of Electrical and Electronics Engineers, 1993-03) Liang, Shunlin; Strahler, Alan H.The radiative transfer equations for a coupled atmosphere and canopy are solved numerically by an improved Gause-Seidel iteration algorithm. The radiation field is decomposed into three components: unscattered sunlight, single scattering, and multiple scattering radiance for which the corresponding equations and boundary conditions are set up and their analytical or iterational solutions are explicitly derived. The classic Guass-Seidel algorithm has been widely applied in atomospheric research. This is its first application for calculating the multiple scattering radiance of a coupled atmosphere and canopy. This algorithm enables us to obtain the internal radiation field as well as radiances at boundaries. Any form of bidirectional reflectance distribution function (BRDF) as a boundary condition can be easily incorporated into the iteration procedure. The hotspot effect of the canopy is accommodated by means of the modification of the extiniction coefficients of upward single scattering radiation and unscatteered sunlight using the formulation of Nilson and Kuusk. To reduce the computation for the case of large optical thickness, an improved iteration formula is derived to speed convergence. The upwelling radiances have been evaluated for different atmospheric conditions, leaf area index (LAI), leaf angle distribution (LAD), leaf size and so on. The formulation presented in this paper is also well suited to analyze the relative magnitude of multiple scattering radiance and single scattering radiance in both the visible and near infrared regions.Item An Analytic BRDF Model of Canopy Radiative Transfer and Its Inversion(Institute of Electrical and Electronics Engineers, 1993-09) Liang, Shunlin; Strahler, Alan H.Radiative transfer modeling of the bidirectional reflectance distribution function (BRDF) of leaf canopies is a powerful tool to relate multiangle remotely sensed data to biophysical parameters of the leaf canopy and to retrieve such parameters from multiangle imagery. However, the approximate approaches for multiple scattering that are used in the inversion of existing models are quite limited, and the sky radiance frequently is simply treated as isotropic. This paper presents an analytical model based on a rigorous canopy radiative transfer equation in which the multiple-scattering component is approximated by asymptotic theory and the single-scattering calculation, which requires numerical integration to properly accommodate the hotspot effect, is also simplified. Because the model is sensitive to angular variation in sky radiance, we further provide an accompanying new formulation for directional radiance in which the unscattered solar radiance and single-scattering radiance are calculated exactly, and multiple-scattering is approximated by the well-known two-stream Dirac delta function approach. A series of validations against exact calculations indicates that both models are quite accurate, especially when the viewing angle is smaller than 55 degrees. The Powell algorithm is then used to retrieve biophysical parameters from multiangle observations based on both the canopy and the sky radiance distribution models. The results using the soybean data of Ranson et al. to recover four of nine soybean biophysical parameters indicate that inversion of the present canopy model retrieves leaf area index well. Leaf angle distribution was not retrieved as accurately for the same dataset, perhaps because these measurements do not describe the hotspot well. Further experiments are required to explore the applicability of this canopy model.