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An on-board microwave radiometer can correct measurement errors due to rain attenuation for a satellite-borne microwave scatterometer, thereby allowing more accurate determination of the ocean-surface wind vector. In clear weather or when area-extensive homogeneous clouds and rain are present, corrections can be made properly even if the radiometer footprint is much larger than that of the scatterometer. When frontal or cyclonic storms are present, so that the rain and cloud distributions are nonuniform across the footprints, substantial errors remain in the "corrected" scatterometer measurements (in some cases "corrections" actually increase the errors). Simple-geometry simulations are reported here for nonidentical overlapping scatterometer and radiometer footprints with large gradients of attenuation and wind speed. In addition, examples are presented for a hurricane observed by the SEASAT-1 oceanographic satellite. These simulations demonstrate the size of the errors in wind speed (and direction for the hurricane) remaining after "correction." At higher wind speeds, the error is sometimes twice as large as the actual wind speed. The worst errors occur when the scatterometer footprint overlaps two or more radiometer footprints and the attenuation in the scatterometer footprint differs greatly from those in parts of the radiometer footprints. The presence of such large errors is inherent in systems having independent scan patterns for radiometer and scatterometer and having large radiometer footprints. A true radiometer-scatterometer system, having identical coincident footprints comparable in size with typical rain cells, could overcome this problem.