Hodographic analysis of gravity waves: Relationships among Stokes parameters, rotary spectra and cross-spectral methods

The elliptical rotation with height of horizontal velocities produced by gravity waves provides considerable information about the wave field. Methods of statistically characterizing velocity ellipses from data currently fall into three main categories: (1) hodographic analyses, (2) cross-spectral analyses, and (3) rotary spectral analyses. The three methods have some intuitive similarities, yet precise interrelationships among them are presently unclear. The three techniques are interrelated here using the so-called ''Stokes parameters'' of the wave field, which initially provide a concise description of the hodographic analysis method (1). On Fourier transforming the Stokes parameters, standard formulae employed in rotary-spectral and cross-spectral analysis methods can then be expressed in terms of the resulting ''Stokes-parameter spectra.'' The results highlight some drawbacks in the use of cross-coherence spectra between velocity components to verify the existence of a coherent wave motion. A more robust measure is suggested, based on the ''degree of polarization'' of classical hodograph-based Stokes-parameter analysis, which can be generalized to provide an analogous spectral measure for evaluation in rotary-spectral and cross-spectral analyses.