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An iterative technique to determine the near surface current velocity from time series of sea surface images

Time series of spatial wave images recorded from a nautical radar are transformed with a fast Fourier transformation to the wavenumber frequency domain resulting in a three dimensional image power spectrum. The spectral energy is localized on a shell defined by the surface wave dispersion relation. The sum of the sensor's velocity and the near surface current profile deforms the dispersion shell due to the Doppler frequency shift. An iterative least square fitting technique and an error estimation model has been implemented recently. Higher harmonics and aliasing effects are taken into account to increase the method's accuracy. The most important nonlinear mechanism leading to higher harmonics can be explained by wave shadowing due to the low grazing angles typical for ground or ship based radars. Temporal undersampling leads to aliasing. Both effects result in additional signals which are used to increase the technique's accuracy. In this paper the technique is examined analytically and with Monte Carlo simulation runs. The variation of shape of the measured or simulated three dimensional spectra-especially the peak wavenumber, the directional spread, and the main travel direction-controls the behaviour and accuracy of the technique. Comparisons with independent Doppler log current measurements are presented. With the results the technique's accuracy, its limits, and its consistency with conventional instrumentation are shown. Additional improvements are presented which lead to higher accuracy and the technique's applicability to high ship speeds.