Monte Carlo Simulation for Modeling Optics Wave Radiative Transfer in a Homogeneous Plane Parallel Cloud Layer

Abstract

Monte Carlo method is a stochastic technique used to solve a variety of physical problems. In all applications of the Monte Carlo method, a stochastic model is constructed in which the expected value of a certain random variable is equivalent to the value of a physical quantity to be determined. A Monte Carlo radiative transfer code is developed in order to model light transport in a homogeneous, plane-parallel cloud layer at wavelength 0.65 mum The flow chart necessary for implementation of the Monte Carlo method is provided. The simulation is based on the random walks that photons make as they travel through the cloud, which are chosen by statistically sampling the probability distributions for step size and angular deflection per scattering event according to the phase function. After propagating many photons, the net distribution of all the photon paths yields an accurate approximation to reality. Two models of phase function are used: (1) Henyey-Greenstein phase function which is the widely used in the literature. (2) Truncated phase function which is an approximation to the realistic phase function of cloud which has very sharp peak in the forward direction. Radiance computations by Monte Carlo methods are inefficient for such spiky phase functions because of significant noise. This paper computes and plots the angular distribution of the reflection and transmission of photons at boundaries, as well as to compute the total reflectance and transmittance with respect to optical depth. In addition, it makes a comparison between the asymptotic of Radiative transfer equation and Monte Carlo results.