Duration of Measurements and Long‐Term Wave Statistics

Abstract

Small sample size and high sample variability go hand in hand in statistical analyses. In this study, the uncertainties in extrapolations of wave heights from small‐size samples to large return‐intervals are investigated and results are obtained for cases where wave statistics are expressed by the Weibull distribution. A nondimensional error for prediction of rare events corresponding to any required confidence level is derived as a function of the number of years of observations, frequency of observations and wave climatological characteristics. It follows that the number of years of wave measurement necessary to determine an extreme event of high return‐interval within a certain confidence level and accuracy can be established. The study shows that shortterm wave measurements of a few years are not sufficient for engineering accuracy, and can be used only to verify or complement wave height estimation given by other methods such as hindcasting. Wave measurement programs have to be conceived as a long‐term investment and commitment for future generations.