A common problem associated with scaceborne scatterometry, including SASS, NSCAT and ERS-1, is that retrieval algorithms often compute wind vectors per retrieval cell. Only one wind vector per retrieval cell corresponds to the true solution while the others are aliases that arise from symmetries in the response of small scale surface waves to wind forcing. The NSCAT retrieval algorithm ranks each ambiguous wind vector within a retrieval cell according to the likelihood that the wind vector is the true solution. Although the most likely wind vectors are usually correct, in approximately 40% of the retrieval cells an alias is ranked first. Based on the mathematical properties of these likelihood assignments errors, an ambiguity removal algorithm is derived that utilizes a nonlinear circular median filter (CMF) to select the true solution in each retrieval cell. The CMF algorithm was tested by analyzing twelve simulated wind fields with an average likelihood assignment error rate of 389 per 1000 retrievals. After processing by the CMF algorithm, the error rate was significantly reduced to an average of only 36 per 1000. To better understand the performance of the CMF algorithm under operational conditions, the analysis was extended by adding spatially correlated likelihood assignment errors to one of the simulated wind fields. A re-analysis of this wind field showed that the performance of the CFM algorithm may decrease significantly if the likelihood assignment errors are correlated over several retrieval cells. In addition to deriving an ambiguity removal algorithm, a wind field smoothing technique that utilizes a circular median filter is derived and tested on one of the resolved wind fields. The results showed that CMF smoothing technique increases the spatial coherency between the true and resolved wind fields. Based on these analyses, specific recommendations are made for monitoring the performance of the wind retrieval process and for improving the accuracy of the retrieved wind fields. ¿ American Geophysical Union 1990