The Statistical Evaluation of Directional Spectrum Estimates Derived from Pitch/Roll Buoy Data

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Abstract
Estimates of the ocean wave directional spectrum may be extracted from observations of surface vertical acceleration and slope made with a pitch/roll buoy. The analysis requires the specification of a parametrical model of the spectrum and a procedure by which the parameters are fixed. The statistical validity and variability of the result must then be examined. This is accomplished by formulating the hypothesis that the model spectrum is the true spectrum; the hypothesis is then rejected if the difference between observations and data computed from the model is improbably large. Otherwise, the model is accepted as statistically valid. Model variability may then be computed in terms of the variances of model parameters. One particular parametrical model and analysis scheme has received wide application in recent years; this paper examines the statistical validity and variability of results obtained with this “conventional” procedure. Explicit formulas for the data covariance matrix, which summarizes the statistics of the observations and forms the core of the statistical analysis, are presented as are formulas for the variances of derived spectral parameters.

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