Effect of Sampling Variability on Hindcast and Measured Wave Heights

Abstract

Estimates of significant wave heights made from finite record lengths have a small but important statistical sampling variability. This variability leads to positive biases in the maximum significant wave height in a storm and in design wave heights estimated from extreme value distributions fitted to the data. Since wave hindcasts are often verified by comparing the maximum hindcast and measured significant wave heights in a storm, the bias due to sampling variability can make a correct hindcast appear to be too low. In this paper we show how the magnitude of the biases can be calculated from the sample length and the shape of the wave spectrum. These theoretical calculations agree very well with results from several sets of measurements in the North Sea. We recommend that new wave measurements be recorded continuously whenever possible, and that hindcast verifications and extreme wave calculations be made with smoothed versions of the measured time series of significant wave height.