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.
Highlights
Within a general framework of assessing risk of coastal flooding, uncertainty analysis is nowadays regarded as a crucial component in the decision-making process
The quality of the fitted models is assessed by means of the AIC (Akaike Information Criterion), as well as by means of diagnostic quantile plots
In the present work a non-stationary point-process model is combined with a signal processing technique, the wavelet transform, inquiring a possible reduction in uncertainty of extreme quantiles when prominent “periodicities” of the marine variables examined are included in the extremal analysis
Summary
Within a general framework of assessing risk of coastal flooding, uncertainty analysis is nowadays regarded as a crucial component in the decision-making process. They note that uncertainty can arise from a) Statistical variation e.g. random error in direct measurements of a quantity, b) Systematic error e.g. bias in the measuring apparatus and experimental procedure, c) Subjective judgment e.g. for quantities where empirical data is largely unavailable, d) Linguistic imprecision e.g. translation of verbal phrases into numerical probabilities, e) Variability e.g. quantities that vary over time or space, or from one person to another, f) Inherent randomness or unpredictability, which cannot be reduced by further research, g) Disagreement e.g. among multiple experts, h) Approximation e.g. due to limits in the spatial resolution of a model and i) Uncertainty about the most appropriate model to represent some phenomenon. The later can be divided in parameter uncertainty and distribution type uncertainty
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