Resolving directional errors in ocean wave spectra estimated from marine radars on moving vessels

The ability to estimate ocean surface wave propagation direction from sequences of marine radar backscatter imagery is well established. The general procedure is to compute the 3D Fourier transform of a time sequence of 2D images in (x,y), yielding a transform cube in (k_x ,k_y,ω). In this 3D spectrum, wave energy lies in regions that are consistent with the relevant dispersion relation for those waves. These regions are symmetric about the origin. When this spectrum is integrated over positive frequencies, only one branch of the dispersion relation is selected and hence a true propagation direction of the waves may be found. The correct operation of this algorithm assumes that all measured waves fall on or near the theoretical dispersion relation, and that the sampling scheme is “perfect” for the spatial and temporal scales involved. Marine radar used from ships in motion violates both these assumptions. The relatively slow sampling rate of the radar causes aliasing and the motion of the ship causes distortion of the dispersion relation