The role of the gravity-wave dispersion relation in HF radar measurements of the sea surface

Recent experimental and theoretical findings raise interesting questions about the applicability of the normal gravity-wave dispersion relation at wave frequencies that exceed the spectral peak frequency. The use of the dispersion relation in analysis of HF radar Doppler sea echo is examined in this paper. Drawing on the results of perturbation theory for wave-wave nonlinear interactions, we show that this relation, so essential to echo interpretation in terms of current and wave information, can be employed with no degradation in accuracy for current measurement when the dominant wave frequency is considerably less (by as much as 10) than the radar Bragg resonance frequency. This finding is supported by comparisons of currents measured by HF radar with "surface truth;" the first-order echo must only be identifiable in order to be used accurately. Wave-height directional spectral information can be extracted from the second-order echo at a given radar frequency up to the point (in wave height) where the perturbation solution employed in the inversion process fails; then a lower radar frequency must be used. On the other hand, most conventional wave measuring instruments should not use the dispersion relation for interpretation of data well beyond the spectral peak, because they do not observe wave height as a function of both space and time independently, as does HF radar.