There are currently large numbers of rainfall retrieval algorithms based upon passive microwave radiances. Most of these algorithms are physically based in that they use explicit physical assumptions to derive relationships between brightness temperatures (Tb's) and rainfall. If these assumptions involve observable quantities, then the physical basis of the algorithms can be extended to determine fundamental uncertainties in the retrieved precipitation fields. In this paper this process begins

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... y examining the largest uncertainty in many of the physical models-the homogeneous rainfall assumption. Four months of Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment shipborne radar data is used to describe the horizontal characteristics of rain. The vertical hydrometeor structures needed to simulate the upwelling Tb are taken from a dynamical cloud model. Radiative transfer computations were performed using a fully three-dimensional Monte Carlo solution in order to test all aspects of the beamfilling problem. Results show that biases as well as random errors depend upon the assumed vertical structure of hydrometeors, the manner in which inhomogeneity is modeled in the retrieval, and the manner in which the radiative transfer problem is handled. Unlike previous works, the goal of this paper is not to determine a mean beamfilling correction or a vertical hydrometeor profile that should be applied to specific retrieval algorithms. Rather, it is to explore the impact of inhomogeneous rainfall upon the predicted brightness temperatures so that these relations may eventually be used to develop a physically based error model for microwave precipitation retrievals. Because the predicted Tb's depend upon assumed cloud vertical structures, the paper offers a procedure to account for the uncertainty introduced by rainfall inhomogeneity rather than a general result. The impact of inhomogeneous rainfall upon specific algorithms must still be investigated within the context of that specific algorithm.