Return periods of extreme sea levels from short records

Extreme sea levels usually arise from a combination of the tides (assumed here to be deterministic) and storm surges (assumed stochastic). We show in this paper how tide and surge statistics derived from short (∼1 year) records can be used to predict the occurrence of extremes with much longer return periods (∼50 years). The method is based on an extension of the exceedance theory originally developed by Rice (1954) to study noise in electrical circuits. A comparison of predicted return periods with those obtained directly from a 50-year Markovian simulation of surge is used to validate the exceedance probability method. The method is next applied to the Canadian ports of Halifax and Victoria, which are dominated by semidiurnal and diurnal tides, respectively. To provide a stringent test of the method, just 1 year's data from each port are used to estimate the tide, surge statistics, and hence return periods. The predictions are found to compare well with the results of a conventional (Gumbel) extremal analysis based on more than 60 years of data provided allowance is made for (1) the anormality of the surge distribution and (2) seasonal changes of surge variance. The agreement suggests that the method may be successfully applied to other short sea level records or indeed to any partly deterministic process where return periods are of interest.