Simulation of Bidirectional Reflectance in Broken Clouds: From Individual Realization to Averaging over an Ensemble of Cloud Fields

Abstract

In this paper, we describe the results of simulating the bidirectional reflectance in three-dimensional (3D) cloud fields. For the calculations of reflectance, we use original statistical algorithms that ensure the effects of atmospheric sphericity and molecular absorption in the solar spectral range are accounted for. Cloud fields are simulated on the basis of a Poisson model of broken clouds; clouds are approximated by truncated paraboloids of rotation. The cloud heterogeneity effect on the averaging of reflection functions over an ensemble of cloud fields is estimated using numerical averaging of the stochastic radiative transfer equation, using a randomization. The simulation is performed for a mono-directional receiver with wavelength channels 0.55 and 2.15 µm, different realizations with small and moderate cloud fractions, and a set of sun-view geometries. With the appearance of an isolated cloud in the sky, the reflection function is determined by cloud presence/absence on the line of sight (LS), shading of LS by clouds/non-obscuration directed “toward the Sun,” and illumination of LS by cloud-reflected radiation. Passage to cloud fields gives rise to such additional factors as mutual shading and multiple scattering between clouds, which are mainly determined by cloud elements located near LS and directed “toward the Sun”. Strong fluctuations of reflectance as a function of the relative azimuth angle between sun and view directions in a specific realization are smoothed out after averaging over an ensemble of cloud fields. In interpreting the results of retrieving the cloud characteristics according to measurements of reflected radiation, it should be kept in mind that for fixed illumination conditions, the mean bidirectional reflectance may differ several-fold from bidirectional reflectance in a specific 3D cloud structure.