Ocean Engng, Vol. 14, No 4, pp. 295-311, 1987. 0029-8018/87 $3.00 + .00 Printed in Great Britain. Pergamon Journals Ltd. JOINT DISTRIBUTIONS OF WAVE HEIGHT AND PERIOD: A CRITICAL COMPARISON M.A. SROKOSZ and P.G. CHALLENOR Institute of Oceanographic Science, Wormley, Godalming, Surrey, GU8 5UB, U.K. Abstract--Three theoretical joint distributions of wave height and period are compared with data. Both crest-to-trough waves and zero-upcrossing waves are considered. The data consist of two long Waverider records (of 12 and 8 hr) and a shorter record taken from a reservoir. It is found that a distribution based on the theory of Gaussian processes fits the crest-to-trough waves well in all cases. In contrast, the two narrow band approximations only fit the data from the reservoir, which is more narrow band. The effect of high frequency cut-off on the distribution of height and period are considered. CCA CLH f f~ h h. h~ H mn PcA(h,t) PLH(h,t) stf~ t tc tz T Tz Tl v ~a t~ b NOMENCLATURE Constant in Cavani6's distribution Constant in Longuet-Higgins' distribution Frequency (in Hz) Peak frequency Normalised waveheight Crest-to-trough waveheight Zero-upcrossing waveheight Waveheight Significant waveheight nth spectral moment Cavani6's distribution of h and t Longuet-Higgins' distribution of h and t Frequency spectrum Normalised period Crest-to-trough period Zero-upcrossing period Period Average zero-upcrossing period "Mean" period (inverse of mean frequency) JONSWAP peak enhancement factor Bandwidth parameter Bandwidth parameter JONSWAP spectral parameter JONSWAP spectral parameter 1. INTRODUCTION FOR MANY years the study of ocean waves has been dominated by Gaussian statistics. This approach involves modelling the sea surface as a random Gaussian process and has proved remarkably successful. One notable example of this sticcess is the derivation of the probability distribution of crest heights by Cartwright and Longuet-Higgins (1956). A problem that has remained unsolved until fairly recently, however, is the joint distribution of waveheight and period. This is of both practical and theoretical 295