Stochastic Modeling of Radiation Regime in Discontinuous Vegetation Canopies

A stochastic radiative transfer equation for the mean field and its solution for the case of discontinuous vegetation canopies is discussed in this article. The equation set satisfies the law of energy conservation and is amenable to numerical solution by the method of successive orders of scattering approximations. Special attention is given to analytical analysis of the effect of spatial discontinuity on the radiation field. Research indicates that a complete description of the radiation field in discontinuous media is possible, using not only average values of radiation over total space, but averages over space occupied by absorbing elements is also required. A new formula for absorbtance, which extends the formula for a homogeneous case, was obtained for the general case of discontinuous media. The internal as well as the emergent radiation fields were validated using available radiative transfer models (one- and three-dimensional) and Monte Carlo model of computer-generated maize canopy. Additionally, the canopy reflectance simulation is assessed by comparisons with field data from shrublands. In all cases, the simulations compare well with both the Monte Carlo results and the field data.