The directional resolution characteristics of sparse wave gage arrays in the measurement of directional wave spectra is investigated. The resolution capability of the maximum-likelihood-method (MLM) is compared with the standard (FFT) approach via computer simulated wave correlation data. The performances are contrasted graphically and quantified by a suitable "figure of merit". The effects of wavelength, array size and geometry, and noise on resolution are discussed.
The spectral descriptions of the time history describing the surface wave elevation at an arbitrary point are fairly well developed and are widely used (cf Hasselmann, 1973 and 1976, and Pierson, 1976). However, the issue as to how the spectrum is distributed over direction is by no means resolved and current knowledge of the angular spreading of wave energy is minimal. A majority of "suggested" directional spreading models are based on measurements and analyses that are incapable of resolving narrower structure. Huntington and Thompson (1976) have shown the importance of taking the directionality into consideration when attempting to extract response amplitude- operators from measurements in short crested seas. The incorporation of directional wave spectra into the interpretation of full scale experimental data is urgently needed.
Essential to the analysis of open water experiments and the establishment of a data base are spectral estimation techniques of sufficient resolution. With the advent of the Fast-Fourier Transform (FFT) and the Maximum Likelihood Method (MLM) of spectral analysis (Capon, 1969), the directional spectrum may now be computed efficiently and routinely along with the point spectrum. This "data adaptive" spectral analysis technique is known to be far superior in computational efficiency and resolution to the conventional or "direct" approach. It is also free of certain mathematical problems inherent in the "direct" and Fourier series approaches (cf Panicker, 1974). Directional spectra naturally involve spatial transforms and spatial cross correlations rom observations, typically over a small portion of the wave field. Relatively few observation or recording points can cause poor angular resolution of the spectral estimate. This may be observed in the following examples.
MLM directional wave spectra estimates were determined from measurements obtained in San Francisco Bay and extensively reported in Chou, et al, 1974. Two contour plots of wave energy density spectra S(? ?) are shown in Figures (1) and (2) where frequency increases radially and wave direction corresponds to the angular variable. Both examples suggest that there was a considerable amount of directional spreading of the wave energy. On the other hand, observers at the time were impressed by the relative narrowness of the wave distribution and the lack of spectral energy from directions other than the principle wind wave sources.