Ocean wave directional spectra estimation from an HF ocean radar with a single antenna array: Methodology

A method to estimate ocean wave directional spectra using a high-frequency (HF) ocean radar was developed. The governing equations of wave spectra are integral equations of first- and second-order radar cross sections. the wave energy balance equation, and the continuity equation of surface winds. The parameterization of the source function is the same as that in WAM. Furthermore, the method uses the constraints that wave spectral values are smooth in both wave frequency and direction and that the propagation terms are small. The unknowns to be estimated are surface wind vectors at radial grids whose centers are the radar position, and wave spectral values at radial and wave frequency-direction grids. The governing equations are discretized in the radial and wave frequency-direction grids and are converted into a nonlinear minimization problem. Identical twin experiments showed that the present method can estimate wave spectra and dynamically extrapolate wave spectra, even in an inhomogeneous wave field.