A stochastic radiative transfer model of a discontinuous vegetation canopy

From the viewpoint of interaction with electromagnetic radiation, a vegetation canopy can be considered to be a stochastically macro-nonhomogeneous scattering medium characterized by a random geometric structure and a stochastic internal structure, such as the macroscale fluctuations in optical properties and dimensions of leaves. To model this interaction, the most promising approach is the use of a stochastic radiative transfer equation, whose coefficients are random scalar fields of the optical parameters of the elementary volumes of plant crowns. By averaging the stochastic transfer equation over the ensemble of realizations of the stochastic canopy field, the authors can thus obtain the lower-order moments of the stochastic radiation field, such as its mean and variance. The authors formulate the radiative transfer equation for the ensemble average radiance based on a two-component random mixture model from kinetic theory. The resulting model can account for non-Markovian statistics as well as both vertical and lateral variations in the canopy. The key parameters of this model include the ratio of the height of the plant crown to its horizontal dimension and the percentage coverage of crowns on the ground. In addition are parameters of the ordinary one-dimensional canopy radiative transfer model. The radiative transfer equation for this model is solved most accurately using the Gauss-Seidel iteration algorithm; the asymptotic solution is comparable to that of the deterministic model the authors have developed earlier