On estimating the mean energy of sea waves from the highest waves in a record

Abstract

Abstract An analysis is made of the probability distribution of the largest values attained by a stationary random variable f(t) over a period of time containing several oscillations. Exact computations are made and asymptotic formulae are derived for the expectation and standard error of the first, second and third greatest maxima in terms of √m0, the r. m. s. deviation of f(t) about its mean value, on the assumption that successive waves are uncorrelated; an analysis is also made of the corrections necessary to allow for mutual correlation when f(t) has a narrow spectrum. The results are applied to measurements from a 24 h record of ocean waves containing some 10000 oscillations.