Effect of Spatial Organization on Solar Radiative Transfer in Three-Dimensional Idealized Stratocumulus Cloud Fields

Abstract

To relate the error associated with 1D radiative calculations to the geometrical scales of cloud organization and/or in-cloud optical inhomogeneities, a new idealized methodology, based on a Fourier statistical technique, has been developed. Three-dimensional cloud fields with variability over a selected range of horizontal spatial scales and consistent vertical structure can be obtained and controlled by a small number of parameters, which relate directly to the dynamical and thermodynamical meteorology of the situation to be examined. This initial study deals with marine stratocumulus. Two experiments are conducted: an overcast situation and a broken cloud case with maximum cloud cover of 80%. For each experiment, five cloud fields are generated with the dominant organizational scale changing from 1.4 to 22 km, while all other quantities—such as cloud cover, cloud liquid water, and total water variance—remain constant. For each scene, three radiative calculations are performed for solar zenith angles of 08 and 608: a plane parallel (PP) calculation, similar to that commonly implemented in general circulation models; an independent pixel approximation (IPA); and a full 3D calculation. The ‘‘PP bias’’ (IPA-PP) is used to assess cloud optical homogeneity approximation, while the ‘‘IPA bias’’ (3D-IPA) measures the impact of horizontal photon transport. For the overcast scenes, the neglect of horizontal photon transport was found to be unimportant, and the IPA calculation gives accurate results. For the broken cloud case, this was only true for clouds with dominant horizontal spatial scales exceeding 10 km. With a scale of 2 km or less, the IPA bias in reflectivity, transmissivity, and absorption could exceed 5%. This indicates that even for shallow cloud systems, cloud geometry can play an important role. The sign of the bias depends critically on the solar angle, with IPA over- (under) estimating reflectivity for high (low) sun angles. The PP bias in reflectivity was also found to be around 5% for both cases, comparable to the IPA bias, and smaller than previous estimates for this cloud type. Additional sensitivity tests prove this to be due to the vertical cloud structure. Vertically resolving the subcloud adiabatic liquid profile leads to a more opaque cloud upper boundary, reducing photon penetration into the cloud layer, and thus also PP biases. Additionally, for the broken cloud case it was found that changes in cloud fraction with height are translated by cloud overlap rules into effective horizontal variability in the liquid water path, further reducing biases. Taking a vertically uniform slab with identical integrated properties led to much larger PP biases comparable to previous estimates. Thus, models with sufficient vertical resolution are likely to suffer from smaller PP biases than previously estimated.