Deterministic decomposition of pitch-and-roll buoy measurements

Wave-gauge arrays, current meters and pitch-and-roll buoys are widely used for the recording of directional properties of ocean waves. For the determination of directional spectra the traditional stochastic procedure usually includes the selection of a parameterized spreading function. The present theory, which is illustrated below for a pitch-and-roll buoy, decomposes the information into frequencies, amplitudes, directions, and also phases. Furthermore, this procedure requires no assumption of any function describing the expected form of the directional spread. The theory of this deterministic decomposition is described and compared to the traditional stochastic principles. Only for reasons of this comparison and presentation, the deterministically obtained directional distributions are fitted to normal distributions.Measurements taken by pitch-and-roll buoys and by current meter/wave gauge are presented and discussed. The remarkable tendency in the variation of the directional spread as a function of frequency is found for two quite different locations. To quantify the directional spread obtained from the deterministic method normal distributions are fitted, and the mean values and variances are plotted and discussed.