Analyzing Extreme Sea State Conditions by Time-Series Simulation

Abstract

This paper presents an extreme value analysis on data of significant wave height based on time-series simulation. A method to simulate time series with given marginal distribution and preserving the autocorrelation structure in the data is applied to significant wave height data. Then, extreme value analysis is performed by simulating from the fitted time-series model that preserves both the marginal probability distribution and the autocorrelation. In this way, the effect of serial correlation on the extreme values can be taken into account, without subsampling and de-clustering of the data. The effect of serial correlation on estimating extreme wave conditions have previously been highlighted, and failure to account for this effect will typically lead to an overestimation of extreme conditions. This is demonstrated by this study, that compares extreme value estimates from the simulated times-series model with estimates obtained directly from the marginal distribution assuming that 3-hourly significant wave heights are independent and identically distributed. A dataset of significant wave height provided as part of a second benchmark exercise on environmental extremes that was presented at OMAE 2021, has been analysed.

Analyzing Extreme Sea State Conditions by Time-Series Simulation Accounting for Seasonality

“…[41] and hence might not always be suitable. This occurred for some of the sites on the raw data (see [12]), but not for the seasonally normalized data in this study. Note also that the empirical autocorrelation functions shown in Figure 7 look very different from the autocorrelation functions of the raw data, as shown in [12], and that they now more clearly tend to zero for increasing lags.…”

“…This occurred for some of the sites on the raw data (see [12]), but not for the seasonally normalized data in this study. Note also that the empirical autocorrelation functions shown in Figure 7 look very different from the autocorrelation functions of the raw data, as shown in [12], and that they now more clearly tend to zero for increasing lags. This is obviously because the seasonal components have been removed, and the pre-processed data are much better suited for the time-series modelling proposed in this paper.…”

“…In this study, the rather crude models presented in [12] have been improved by carefully removing the systematic seasonal component before fitting the time-series models. This is believed to be important, so that the seasonal effect is not a part of the autocorrelation function.…”

“…Such modelling could also provide a means for more realistic simulation of time-series of significant wave height that could be relevant for other applications than extreme value analysis, even though the focus of this paper is estimation of extreme conditions. A preliminary analysis of these types of models was presented at OMAE 2022 [12]. However, in this…”