Manual on sea level measurement and ... - unesdoc - Unesco

Sea Level Measurement and Interpretationsea levels. It begins with the classical method of AnnualExtremes, which first appeared in the early 1960s andcontinued to be developed for some time thereafter.Following this, the Joint Probability Method, which wasdeveloped in the late 1970s, is considered. This makesmore efficient use of data by incorporating our extensiveknowledge of the tides and storm surges, whichare the two main components of sea level, as a part ofthe estimation procedure.More recent work on the Annual Exceedance Method isdiscussed, followed by a revision of the Joint ProbabilityMethod to correct its deficiencies in areas where the sealevel is dominated by the meteorological surge component.Finally, very recent work on the spatial estimationof extremes is mentioned. References are given at eachstage so that the reader can examine any of the methodsin greater depth. Although extreme high sea levelsare considered, results for extreme low sea levels can beobtained in an analogous way.2.8.2 The Annual Maximum Method (AMM)This is the classical general method of analysis ofextremes having been applied to sea level estimationsince 1963 (Lennon, 1963; Suthons, 1963). It is basedon a result from probabilistic extreme value theorywhich states: if X 1 ,... X n is a sequence of independentand identically distributed random variables, thenmax(X 1 ,... X n ), suitably linearly normalized, convergesas n ∞ , to a random variable with a distributionfunction which is one of the so called extremevaluedistributions. The general case is known as theGeneralized Extreme Value (GEV) distribution. Animportant special case is the Gumbel distribution.The Annual Maximum Method takes the GEV to bethe distribution function of the maximum sea level ina year. Therefore, for a place of interest, the annualmaximum for each year is extracted from hourly observationsand is used as data to estimate the parametersof the distribution that they follow. From the estimateddistribution one can obtain the sea level correspondingto a chosen ‘Return Period’. In practice, return periodsof 50, 100 and 1,000 years are common. The basicmethod assumes that there is no trend in the data, butit can be extended to deal with those cases where atrend is present.A recent extension of the annual maximum methodinvolves using probabilistic extreme value theory toobtain the asymptotic joint distribution of a fixed number(r) of the largest independent extreme values, forexample the five largest in each year. Essentially theapproach is the same as above except that more relevantdata are included in the analysis thereby improvingthe estimation. Care must be taken to ensure that thenumber of annual maxima ‘r’ is not excessive, such thatthe lower extremes fall outside the tail of the extremevalue distribution.This method of estimating sea level extremes is highlyinefficient in its use of data, since it extracts very fewvalues from each yearly record. This is particularly importantwhen the sea level record is short, since it yieldsreturn level estimates with unacceptably large standarderrors. In addition, it makes no use of our knowledge ofthe sea level and storm surge processes. However, theadvantage of annual maxima methods is that they donot require knowledge of tide–surge interaction whichcan sometimes be a significant feature of the data.Consequently the methods are relatively straightforwardto apply.2.8.3 The Joint Probabilities Method (JPM)This method of analysis was introduced to exploit ourknowledge of the tide in short data sets to which theannual maxima method could not be applied (Pughand Vassie, 1979). At any time, the observed sea level,after averaging out surface waves, has three components:mean sea level, tidal level and meteorologicallyinduced sea level. The latter is usually referred to as astorm surge. Using standard methods, the first two ofthese components can be removed from the sea levelsequence leaving the surge sequence, which is just thetime-series of non-tidal residuals. For simplicity these areassumed to be stationary. Because the tidal sequenceis deterministic, the probability distribution for all tidallevels can be generated from tidal predictions. Thisdistribution can be accurately approximated using 18.6years of predictions.The probability distribution of hourly sea levels can beobtained either directly using an empirical estimate orby combining the tidal and surge probability densityfunctions (pdf). The latter is preferable, as it smoothesand extrapolates the former. However the nature ofthe combination of the pdf’s depends on whetherthere is dependence between the tide and surgesequences. Initially, consider the case in which theyare independent.By combining the pdf’s of tide and surge, the distributionfunction of hourly (instantaneous) sea levels is obtained.From this, the distribution function of the annual maximais required. If hourly values were independent, whichis approximately the case where the tide dominates theregime, then this is straightforward.The method has been widely applied. It makes betteruse of the data and of our extensive knowledge of thetides, and accounts for surges that could have occurredon high tide but by chance did not. Most successfulapplications have been to sites which have several yearsof hourly records (>10 years) and where the site is tidallydominant, i.e. where the tidal range is large in comparisonto the surge amplitude. Least successful applicationshave been to sites with both short lengths of data andwhere the site is surge dominant.8IOC <strong>Manual</strong>s and Guides No 14 vol IV