Efficient Monte Carlo methods for radiative transfer modeling

Demands for Monte Carlo radiative transfer modeling have grown with the increase in computational power in recent decades. This method provides realistic simulations of radiation processes for various types of application, including radiation budgets in cloudy conditions and remote measurements of clouds, aerosols, and gases. Despite many advantages, such as explicit treatment of three-dimensional radiative transfer, issues of numerical efficiency can make the method intractable, especially in radiance calculations. The commonly used local estimation method requires computationally intensive ray tracing at each collision. Furthermore, the realistic phase function of Mie scattering by cloud and aerosol particles has very sharp peaks in the forward direction. Radiance computations by Monte Carlo methods are inefficient for such spiky phase functions because of significant noise. Moreover, in optically thin regions, sampling of radiance contributions is so rare that long computing times are required to reduce noise. To solve these issues, several variance reduction methods have been proposed. This paper discusses a modified local estimation method, a truncation approximation for a highly anisotropic phase function, a collision-forcing method for optically thin media, a numerical diffusion technique, and several related topics. Numerical experiments demonstrated significant improvements in efficiency for solar radiance calculations in a limited number of cloudy cases.