| This thesis discusses two separate topics. First, the statistics of sequences of large ocean waves are investigated, and observations are compared to theories based on the assumption of a Gaussian process. The results are applicable to threshold crossings in a random process. Second, several methods for estimating the number of phase coupled sinusoids in a nonGaussian random process are investigated.;Wave group statistics were obtained from observations of ocean waves in the Pacific and Atlantic oceans. Comparison of the observations to numerical simulations of linear wave fields shows that the observed groups are not inconsistent with the assumption of a Gaussian sea surface. In addition, observed and numerically simulated wave fields were compared to predictions of two analytic models (approximating linear theory) which predict wave group statistics given the power spectrum of sea-surface elevation. One model accounts for correlations between two successive waves, while the other accounts for correlations between waves separated by an arbitrary number of intervening waves. The model based on one-wave correlations underpredicts the average number of sequential large waves occurring with narrow power spectra and significant multiwave correlations. The multiwave correlation model has improved accuracy for these very narrow power spectra. Both approximations overpredict the lengths of groups of high waves for very broad and/or multipeaked spectra because the underlying assumption of Rayleigh distributed wave heights breaks down.;Subspace-based algorithms for obtaining parametric estimates of the bispectrum of a random process determine the number of phase-coupled frequencies from the number of singular values (i.e., the rank) in the third-moment matrix. Three algorithms to determine the rank of the third-moment matrix of finite-length processes in the presence of noise, which produces spurious singular values, are compared and contrasted. Subspace-based estimates of the bispectrum of short random processes with coupled and uncoupled sinusoids perform better than estimates made with parametric models. |
