Numerical analysis of the sea state bias for satellite altimetry

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Abstract
Theoretical understanding of the dependence of sea state bias (SSB) on wind wave conditions has been achieved only for the case of a unidirectional wind‐driven sea [Jackson, 1979; Rodriguez et al., 1992; Glazman and Srokosz, 1991]. Recent analysis of Geosat and TOPEX altimeter data showed that additional factors, such as swell, ocean currents, and complex directional properties of realistic wave fields, may influence SSB behavior. Here we investigate effects of two‐dimensional multimodal wave spectra using a numerical model of radar reflection from a random, non‐Gaussian surface. A recently proposed ocean wave spectrum is employed to describe sea surface statistics. The following findings appear to be of particular interest: (1) Sea swell has an appreciable effect in reducing the SSB coefficient compared with the pure wind sea case but has less effect on the actual SSB, owing to the corresponding increase in significant wave height. (2) Hidden multimodal structure (the two‐dimensional wavenumber spectrum contains separate peaks, for swell and wind seas, while the frequency spectrum looks unimodal) results in an appreciable change of SSB. (3) For unimodal, purely wind‐driven seas, the influence of the angular spectral width is relatively unimportant; that is, a unidirectional sea provides a good qualitative model for SSB if the swell is absent. (4) The pseudo wave age is generally much better for parametrizing the SSB coefficient than the actual wave age (which is ill‐defined for a multimodal sea) or wind speed. (5) SSB can be as high as 5% of the significant wave height, which is significantly greater than predicted by present empirical model functions tuned on global data sets. (6) Parameterization of SSB in terms of wind speed is likely to lead to errors due to the dependence on the (in practice, unknown) fetch.

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