Analysis of the extreme value distribution’s tail of coastal water levels: influence of independence criteria, sea level rise and convolution of astronomic and storm surge components
Willems, P.; Verwaest, T. (2008). Analysis of the extreme value distribution’s tail of coastal water levels: influence of independence criteria, sea level rise and convolution of astronomic and storm surge components, in: McKee Smith, J. (Ed.) (2009). Proceedings of the 31st International Conference on Coastal Engineering 2008, Hamburg, Germany, 31 August to 5 September 2008.
In: McKee Smith, J. (Ed.) (2009). Proceedings of the 31st International Conference on Coastal Engineering 2008, Hamburg, Germany, 31 August to 5 September 2008. World Scientific: Hackensack, NJ (USA). ISBN 978-981-4277-36-5. 5 vol. pp., more
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| Available in | Authors |
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Document type: Conference paper
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| Keywords |
Analysis
Analysis > Mathematical analysis > Convolution
Coastal zone
Levels > Water levels
Surges > Surface water waves > Storm surges
Temporal variations > Long-term changes > Sea level changes
ANE, Belgium, Oostende [Marine Regions]
Marine/Coastal |
| Abstract |
Based on a 76 years time series of high water levels along the Belgian Coast at Ostend, the extreme value distribution of total water levels is investigated, as well as the separate distributions for the astronomic component and the storm surge levels. The series were derived by Technum-IMDC-Alkyon (2002) in a previous research study for the Flanders Hydraulics Research Laboratory. The extreme value analysis makes use of the recently developed QQR method based on regression in quantile plots (Beirlant et al., 2005). This method allows the tail heaviness of the extreme value distribution to be investigated and a generalized extreme value distribution to be fitted to water levels above an optimal threshold. Extremes were extracted from the series using three methods: the classical method with annual maxima, the full series of water level maxima during tidal periods, and through derivation of a partial-duration-series (PDS) with nearly independent extremes defined by independence criteria. The criteria are based on the independence period (4 to 10 tidal cycles) and the accuracy in the calculation of the astronomic water level component. Different PDS series were derived considering weak and strong independence. It is shown in Willems et al. (2007) that the different series need to converge asymptotically towards the same ext reme value distribution’s tail; see the results for Ostend in the Figure. The 76 years series is subject to a trend due to sea level rise. The effect of this historical sea level rise on the extreme value distribution’s tail was investigated. This was done comparing extreme water level quantiles (water levels for given exceedance probabilities, return periods or mean recurrence intervals) with and without detrending the different extreme water level series (taking the most recent year as reference). It is concluded that the detrending affects the water level quantiles only in a minor way (Figure). Derivation of coastal extreme value distributions is traditionally done through convolution of the distribution of stochastic storm surges and the deterministically known astronomic tidal levels. This paper, however, shows that this convolution does not lead to more accurate results in comparison with the direct use of total water levels. The authors explain this by the linear relation that exists between the total water level quantiles and the storm surge level quantiles in the tail of the extreme value distribution. Based on the parametric bootstrapping technique, it is furthermore shown that the asymptotic tail distribution, in coastal engineering used on the basis of extrapolations to higher return periods (e.g. to 10000 years in the Belgian coastal defense design), does not lead to less accurate results when convolution is not applied. This conclusion has important advantages for future coastal design applications; extreme value distributions can be derived in a far more simplified way, and with a more parsimonious model |
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