On the validity of the independent pixel approximation for boundary layer clouds observed during ASTEX

The two-dimensional radiative transfer behavior of nine marine stratocumulus clouds observed by cloud radar during the Atlantic Stratocumulus Transition Experiment is examined. The cloud radar resolves the vertical structure to 37.5 m. The method of [Frisch et al., 1995] is used to convert radar reflectivities to extinction fields. Three constructions of the same cloud field help elucidate underlying causes of variability: one is fully two-dimensional, while the other two have vertically uniform extinction fields but possess either a flat cloud top or the original cloud top topography. Two-dimensional solar radiative transfer results are compared with the independent pixel approximation (IPA) result. At the scale of the domain (≈ 7km) the IPA albedo bias is small, even after including vertical structure. Locally, in contrast, the direct solar beam interaction with cloud top geometry competes with radiative smoothing as the dominant radiative process. Power spectral analysis of nadir reflectances is dominated by radiative smoothing for overhead Sun, and side illumination/shadowing of cloud top bumps for low Sun. A method that incorporates direct beam interactions with the cloud geometry, in addition to radiative smoothing, significantly improves correlations of a smoothed IPA radiance field with the 2-D reflectances. In a remote sensing application, optical depth and albedo retrieval biases from plane-parallel theory depend on the spatial scale chosen to emulate a satellite pixel size. For scales less than a few kilometers and with low Sun, cloud top topography can cause large positive optical depth biases even when averaged over the entire domain. A larger spatial scales the negative IPA bias always dominates. Domain-averaged monochromatic albedo retrieval errors remain below 0.005, a relative error of less then 1%.