Improved Calculation of the Second-Order Ocean Doppler Spectrum for Sea State Inversion

We describe and exploit a reformulation, based on a recently introduced change of variables, of the double integral that describes the second-order ocean Doppler spectrum measured by high-frequency radars. We show that this alternative expression, which was primarily designed for improving the numerical inversion of the ocean wave spectrum, is also advantageous for the analytical inversion of the main sea state parameters. To this end, we revisit Barrick's Method for the estimation of the significant wave height and the mean period from the ocean Doppler spectrum. On the basis of numerical simulations we show that a better estimation of these parameters can be achieved, which necessitates a preliminary bias correction that depends only on the radar frequency. A second consequence of this improved formulation is the derivation of a simple yet analytical nonlinear approximation of the second-order ocean Doppler spectrum when the Doppler frequency is larger than the Bragg frequency. This opens up new perspectives for the inversion of directional wave spectra from high-frequency radar measurements.