Monte Carlo Simulation of Solar Reflectances for Cloudy Atmospheres

Abstract

Monte Carlo simulations of solar radiative transfer were performed for a well-resolved, large, three-dimensional (3D) domain of boundary layer cloud simulated by a cloud-resolving model. In order to represent 3D distributions of optical properties for ∼2 × 106 cloudy cells, attenuation by droplets was handled by assigning each cell a cumulative distribution of extinction derived from either a model or an assumed discrete droplet size spectrum. This minimizes the required number of detailed phase functions. Likewise, to simulate statistically significant, high-resolution imagery, it was necessary to apply variance reduction techniques. Three techniques were developed for use with the local estimation method of computing reflectance ρ. First, small fractions of ρ come from numerous, small contributions of ζ computed at each scattering event. Terminating calculation of ζ when it falls below ζmin ≈ 10−3 was found to impact estimates of ρ minimally but reduced computation time by ∼10%. Second, large fractions of ρ come from infrequent realizations of large ζ. When sampled poorly, they boost Monte Carlo noise significantly. Removing ζ − ζmax, storing them in a domainwide reservoir, adding ζmax to local estimates of ρ, and, at simulation's end, distributing the reservoir across the domain in proportion to local ρ, tends to reduce variance much. This regionalization technique works well when the number of photons per unit area is small (nominally ≲ 50 000). A value of ζmax ≈ 100 reduces variance of ρ greatly with little impact on estimates of ρ. Third, if ζ are computed using exact (e.g., Mie) phase functions for the first N scattering events, and thereafter a blunt-nosed corresponding phase function (e.g., Henyey–Greenstein) is used, production of large ζ is thwarted resulting in reduced variance and time required to achieve accurate estimates of ρ.