Wave spectral moments and Stokes drift estimation

The relationships between the moments of wave spectra and Stokes drift velocity are calculated for empirical spectral shapes and a third-generation wave model. From an assumed spectral shape and only an estimate of wave period and significant wave height, one may determine: the leading-order Stokes drift, other wave period estimates, and all spectral moments. The conversion factors are tabulated for quick reference for the common empirical spectral shapes. The different spectral shapes considered are shown to exhibit similar spectral moment relationships. Using these relationships, uncertainty in Stokes drift may be decomposed into the uncertainty in spectral shape and a much greater uncertainty due to significant wave height and wave period discrepancies among ERA40/WAM, satellite altimetry, and CORE2 reanalysis-forced WAVEWATCH III simulations. Furthermore, using ERA40 or CORE2 winds and assuming fully-developed waves results in discrepancies that are unable to explain the discrepancies in modeled Stokes drift; the assumption of fully-developed waves is likely the culprit.