A Functionalized Monte Carlo 3D Radiative Transfer Model: Radiative Effects of Clouds Over Reflecting Surfaces

In the Earth Sciences, the 3D radiative transfer equation is often solved for by Monte Carlo (MC) methods. They can, however, be computationally taxing, and that can narrow their range of application and limit their use in explorations of model parameter spaces. A novel family of MC algorithms is investigated here in which single simulations provide estimates of both radiative quantities A for a set of parameters (x) over cap, as usual, as well as the overarching functional A(x) that can be evaluated, extremely efficiently, at any x. One such algorithm is developed and demonstrated for horizontally averaged broadband solar radiative fluxes as functions of surface albedo for uniform Lambertian surfaces beneath inhomogeneous cloudy atmospheres. Simulations for a high-resolution synthetic cloud field, at various solar zenith angles, illustrate the potential of the method to gain insights into the nature of 3D radiative effects for complicated atmosphere-surface conditions using information specially derived from the MC simulation. For simulations performed with a single surface albedo it is found that as surface albedo increases, 3D radiative effects increase, too, with maxima occurring at middling to large values, and then decrease. By utilizing the derived coefficients that describe A(x) it was established that these 3D effects stem from differences in fractions of radiation entrapped at successive orders of internal multiple reflections for 1D and 3D transfer.