Statistics of wave groups measured in the northern North Sea: comparisons between time series and spectral predictions

Abstract

This paper presents an analysis of wave time-series data collected from storms in the northern North Sea. Statistics of run and group lengths obtained for each of 852 20-min records are compared with predictions of a Markov chain model. The Markov chain transition probabilities have been estimated in five ways. The first method, estimating directly from the data, makes minimal assumptions and shows that the Markov chain model can accurately predict mean run and group lengths. The four remaining methods assume the bivariate Rayleigh distribution for consecutive waveheights and estimate a correlation parameter to calculate the transition probabilities. Two time-series based approaches give relatively good estimates of the transition probabilities whilst a simple spectral approach under-estimates them somewhat. A second, more complex, spectral approach gives good estimates of the transition probabilities when the data are band-pass filtered but poor estimates when they are not.