REDUCING UNCERTAINTY IN EXTREME WAVES AND STORM SURGES USING A COMBINED EXTREME VALUE MODEL AND WAVELETS

Abstract

In the present study the wavelet transform is combined with non-stationary statistical models for extreme value analysis, to provide more reliable and more accurate return level estimates. The continuous wavelet transform is first used to detect the significant “periodicities” of the wave height and storm surge signals under study by means of the wavelet global and scale-averaged power spectra and then it is used to reconstruct the part of the time series, represented by these significant and prominent features. A non-stationary point process is utilized to model the extremes. A time varying threshold with a period of one year and having an approximately uniform crossing rate throughout the year is used. The reconstructed part of the series variability representing the significant non-stationarities of each signal is incorporated in the both the location and the scale parameters of the point process model, together with selected harmonic functions, formulating a number of candidate extreme value models. The quality of the fitted models is assessed by means of the Akaike Information Criterion, as well as by means of diagnostic quantile plots. The models which incorporate the reconstructed part of the wavelet transform in their location parameter, as a separate component of the parameter without any scaling coefficient, result in narrower return level confidence intervals and therefore tend to reduce uncertainty in extrapolated extremes.