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Changes in the concentration of greenhouse gases within the atmosphere lead to changes in radiative fluxes within the atmosphere and at its boundaries. This paper describes an experiment within the...

Since three-dimensional (3-D) radiative transfer in cloudy atmospheres is too expensive for large-scale atmospheric models, approximate radiative transfer methods are used. The accuracy of these approximations for a large sample of realistic cloud fields has not been determined. This study examines 150 fields of small marine tropical cumulus to assess the magnitude of 3-D effects on domain average solar fluxes and to evaluate the accuracy of these approximations in actual cumulus fields. The cloud fields are derived from Moderate-Resolution Imaging Spectroradiometer Airborne Simulator (MAS) visible and thermal infrared imagery. Domain average broadband solar fluxes in these fields are simulated with a Monte Carlo radiative transfer model using four radiative transfer methods: full three-dimensional, the independent pixel approximation (IPA), the tilted IPA, and the plane-parallel approximation. The average 3-D radiative effects of these cumulus cloud fields are small, with mean reflected flux errors up to 3 W/m2 for overhead Sun and less than 1 W/m2 for the daytime average. The mean errors for column-absorbed fluxes are less than 0.3 W/m2 for all Sun angles. The small absolute flux errors are a result of the average field having small cloud fraction (10%), low cloud optical depth (4.4), and shallow clouds. Some individual fields have large 3-D absolute reflected flux effects, and the normalized reflected flux errors are significant. The errors correlate well with the cloud fraction; so it may be possible to make corrections to the approximations.

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%.