Climate Publications

Knyazikhin, Yu., and A. Marshak, 2000: Mathematical aspects of BRDF modeling: Adjoint problem and Greens function. Remote Sens. Rev., 18, 263-280.

Abstract
Adjoint formulation of three-dimensional radiative transfer and the Green's function concept
have been developed in neutron transport several decades ago. This is not merely yet another method of simulating the radiative transfer process, but a method of reformulating the problem
to better incorporate existing radiation models into a particular research. In the case of photon
transport in vegetation canopies, the Green's function is a canopy radiative response to a point monodirectional source located outside the canopy. The Green's function, therefore, has
intrinsic canopy information. It can be evaluated by using existing canopy radiation models. The problem-dependent adjoint formulation of radiative transfer allows us to express a particular canopy radiation efect in terms of the Green's function and, as a consequence, to better adjust the existing models to the solution of a specific radiation problem. Application of this technique to the retrieval of biophysical parameters from remotely sensed data (the table
look-up method) was discussed in (Kimes et al., this issue). In this paper, we will illustrate how
this concept can be applied to the estimation of cloud optical properties from ground-based measurements of spectral zenith radiance above the vegetation canopy under broken cloud conditions. In spite of different physical formulations of these problems, both of them use the
Green's function to describe radiation fields due to the interaction between the canopy ground
and the canopy and the canopy -clouds interaction. This technique allows us not only to extend
an applicability range of existing canopy - radiation models, but also to incorporate of various
approaches developed in other fields of physics into BRDF modeling and its applications.
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