Towards a Unified Treatment of Stochastic Radiative Transfer of Solar Radiation in Clouds

Abstract

The new era of European Copernicus Sentinel nadir atmospheric sensors will provide an unprecedented high spatial resolution of about 7 km by 7 km in combination with improved radiometric sensor performance as compared to current satellite spectrometers. Thus, for trace gas retrievals it may turn out important to account for sub-pixel cloud inhomogeneity, or at least, to assess the effect of such inhomogeneities on spectral radiances at the top of the atmosphere. The radiative transfer (RT) through such inhomogeneous media can be described by stochastic RT models, in which new transport equations, relating the statistical parameters of the clouds to those of the radiance field, are derived. We present both a coherent framework for treating stochastic RT in three-, two- and one-dimensional broken cloud fields with arbitrary statistics as well as a unified treatment of closure schemes to determine the resulting covariance terms between the fluctuations of the radiance and the cloud random indicator fields. For computational purposes, the resulting stochastic model is discretized in discrete ordinate space and solved via the discrete ordinate with matrix exponential (DOME) formalism. The powerful DOME tool is used here to solve the stochastic RT equation for a bounded cascade cloud model. Our simulations represent a scenario typical for a nadir-looking UV/VIS spectrometer. In the wavelength region 325-335 nm, with Sun in the zenith and a surface albedo of 0.2, we consider a one-dimensional cloud model based on the cellular statistical model of broken clouds (Alexandrov et al., 2010). As a benchmark solution to this problem, ensemble averaged results based on two-dimensional SHDOM simulations are used. Also some ideas for the future inter-comparison of results from stochastic RT models with those from ensemble averaged conventional three- dimensional RT model data will be discussed.