Some Relevant Calculations of Geometry Function with Area Scattering Phase Functions Related to Vegetative Radiative Transfer Equations in the Vegetative Canopy Scattering Medium

Abstract

The theory of Vegetative Radiative Transfer Equation (VRTE) in canopy scattering medium is the major mathematical tool enabling researchers to investigate and analyze mathematically essential ingredients to understand how to use remote sensing data for the canopy vegetative medium. VRTE involves geometry functions or G-functions associated with leaf normal distribution functions and a major constituent of the important Area Scattering Phase functions (ASPF) which governs the scattering pattern in any vegetative scattering medium. Almost all these functions are mathematically defined on the basis of Leaf Normal Distribution Function (LNDF), probability of distribution of normals to a particular leaf with respect to a particular direction, say, zenith direction. The VRTE started its evolution on the basis of four experimentally designed LNDF model with specific normalization conditions. In this article, we have presented various new models based on previous field survey but not reported in Biswas (JQSRT 108:197–219, 2007, [1]) and linear combinations of basic four models of LNDF with somewhat detailed mathematical sketch of these important mathematical functions and computer-generated simulations relevant for the realistic problems in these fields of study.