Abstract 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 , as usual, as well as the overarching functional ( 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 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.
Plain Language Summary The general aim of this study is to improve our understanding of a particular process that occurs in the atmosphere, that is, how radiation (light) is affected by the presence of clouds. It focuses on the role that the ground reflectivity plays on the radiative effect of cumulus clouds. To that end, we extend the so‐called MC methods—which are often used in the community to simulate light–cloud interactions and estimate the resulting radiative fluxes—so that one simulation yields not only the result for a given surface reflectivity, but also the overarching functional that expresses the full dependency of the flux on the surface reflectivity. It is much faster than running one simulation per value of surface reflectivity, and also gives access to new information usually not available in standard MC simulations. This modified “Functional” MC method is applied to solar radiation in a virtual 3D cloud field. By analysis of the resulting functionals, it is demonstrated that surface reflectivity plays a major role in the intensity of a process called entrapment of light.
Key Points Functionalized Monte Carlo methods that estimate functional forms instead of scalar quantities are presented Solar fluxes are estimated as polynomial functions of surface albedo with a single simulation Surface albedo plays a major role in 3D effects of cumulus clouds through the entrapment process