Abstract
AbstractA statistical model to analyze different time scales of the variability of extreme high sea levels is presented. This model uses a time-dependent generalized extreme value (GEV) distribution to fit monthly maxima series and is applied to a large historical tidal gauge record (San Francisco, California). The model allows the identification and estimation of the effects of several time scales—such as seasonality, interdecadal variability, and secular trends—in the location, scale, and shape parameters of the probability distribution of extreme sea levels. The inclusion of seasonal effects explains a large amount of data variability, thereby allowing a more efficient estimation of the processes involved. Significant correlation with the Southern Oscillation index and the nodal cycle, as well as an increase of about 20% for the secular variability of the scale parameter have been detected for the particular dataset analyzed. Results show that the model is adequate for a complete analysis of seasonal-to-interannual sea level extremes providing time-dependent quantiles and confidence intervals.
Highlights
The knowledge of the statistical distribution of extreme sea levels is of practical importance for many purposes, including coastal management, flooding of urban areas and valuable ecosystems, and the design of maritime works
The model is based on the time-dependent generalized extreme value distribution for independent monthly maxima series
Nonstationarity is introduced in the model in terms of different time scales—such as seasonality, interdecadal climate variability and astronomical modulations, sea level rise, and secular trends—that are parameterized as functions of time or covariates (e.g., Southern Oscillation index (SOI))
Summary
The knowledge of the statistical distribution of extreme sea levels is of practical importance for many purposes, including coastal management, flooding of urban areas and valuable ecosystems, and the design of maritime works. This approach is widely used in time series analysis and has been used recently for predicting extreme high water levels in San Francisco (SFO), California (Sobey 2005) This data precondition is not necessary because the time-dependent generalized extreme value distribution can describe the variability as a function of time or other covariates (see, e.g., Coles 2001, chapter 6; Smith 2001, chapter 8; Katz et al 2002). The model is applied to a well-known large hourly tidal gauge series (San Francisco) showing the characteristics of the seasonal-to-interannual time scales at this particular site This approach is useful when historical information is not hourly recorded, provided that daily or monthly high-water data are known (Bijl et al 1999). For nonstationary or time-dependent GEV parameters, the calculation of “effective” design values can be carried out using Eq (10), so that the quantity varies depending on the time of the year (Katz et al 2002)
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