Directional Surface Wave Spectra from Point Measurements of Height and Slope

We describe here a method for recovering directional ocean surface wave spectra obtained from height and slope measurements made over a small area, the Iterative Deconvolution Method (IDM). We show that IDM is a more reliable method for estimating directional wave spectra than more common spectral estimation techniques by comparing it with the widely used Maximum Entropy Method (MEM). IDM is based on the observation that pitch/roll buoys produce directional spectra that are the true spectra convolved with an angular windowing function and are therefore much broader than the true spectra. We test IDM against simulated data and find that it does a better job of retrieving the known input spectra than does MEM, which often produces false double peaks or incorrect angular widths. We compare IDM recoveries to spectra obtained using a non-standard processing technique, the Wavelet Directional Method (WDM) on data from a compact array of wave staffs on Lake Ontario. We find that IDM produces directional wave spectra very nearly identical to those obtained using WDM, verifying both techniques. Finally, we processed standard NDBC buoy directional spectra and showed that IDM recovers ocean wave spectra that narrow in the Strait of Juan de Fuca and that follow a changing wind in the expected manner. Neither of these phenomena are reliably obtained using MEM due to its tendency to produce false bimodal peaks and peaks that are too narrow. We are presently comparing spectra from NDBC buoys using IDM with directional spectra produced by the SWIM instrument on the CFOSAT satellite.