A method for computing calibrated ocean wave spectra from measurements with a nautical X-band radar

The radar backscatter from the ocean surface, called sea clutter, is modulated due to the surface wave field. The modulation introduces a spatio-temporal correlation of the sea clutter signal. A three-dimensional wavenumber frequency spectrum of the sea clutter is calculated from a time series of radar images with an FFT algorithm. Because of the non-linearity of the imaging process the image spectrum contains harmonics in addition to the linear fundamental mode. These modes are localized at distinct surfaces in the wave number frequency space corresponding to the scaled dispersion relation of surface gravity waves. Because of the localization of the spectral energy on dispersion shells, the aliasing effect due to a temporal undersampling can be overcome. The dispersion shells are reconstructed over the Nyquist frequency barrier and for negative frequencies. The dispersion shells are used as spectral filters to separate the modes from the clutter noise pedestal of radar image spectra. This pedestal shows the effect of the impulse response due to the finite spatial resolution of the radar. The spectral energy of the wavenumber frequency spectrum is integrated over the frequency coordinate axis, with the positive solution of the dispersion relation of surface gravity waves as signal filter. With this spectral filter method an unambiguous wave number image spectrum is selected. The fundamental image spectrum is related to the surface wave spectrum by an image transfer function. An empirical calibration procedure is presented. This procedure is based on the correlation of the signal to noise ratio with the significant wave height. The applicability of the method is shown using a radar and buoy data set. The spectral energies of fundamental mode, first harmonic, and the clutter component are compared.