Satellite-based scatterometers, for historical reasons, have been used mainly to derive the wind forcing term for oceanography applications in the form of the near-surface wind field. However, the scatterometer is sensitive to the surface roughness, which is related to the wind stress field, which is in turn related to the wind field at the bottom of the troposphere but not just at 10 meters above the surface { indeed, in organized systems such as tropical cyclones, the surface roughness is highly correlated with the wind at altitudes much higher than 10 meters. We show how to assimilate this data as a function of the vertical principal components of the wind rather than the oversimplified alternative. We derive the empirical correlations between simulated scatterometer observations and underlying columns of wind produced by a numerical weather prediction model and derive an observation operator based on these correlations. We then present the results of the subsequent assimilation.
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