The use of historical information for regional frequency analysis of extreme skew surge

Abstract. The design of effective coastal protections requires an adequate estimation of the annual occurrence probability of rare events associated with a return period up to 10 3 years. Regional frequency analysis (RFA) has been proven to be an applicable way to estimate extreme events by sorting regional data into large and spatially distributed datasets. Nowadays, historical data are available to provide new insight on past event estimation. The utilisation of historical information would increase the precision and the reliability of regional extreme's quantile estimation. However, historical data are from significant extreme events that are not recorded by tide gauge. They usually look like isolated data and they are different from continuous data from systematic measurements of tide gauges. This makes the definition of the duration of our observations period complicated. However, the duration of the observation period is crucial for the frequency estimation of extreme occurrences. For this reason, we introduced here the concept of “credible duration”. The proposed RFA method (hereinafter referenced as FAB, from the name of the authors) allows the use of historical data together with systematic data, which is a result of the use of the credible duration concept.

[1]  Eric Gaume,et al.  Regional flood frequency analyses involving extraordinary flood events at ungauged sites: further developments and validations , 2014 .

[2]  H. Andrieu,et al.  Information historique et étude statistique des crues extrêmes : quelles caractéristiques souhaitables pour les inventaires de crues historiques ? , 2013 .

[3]  Jery R. Stedinger,et al.  Surface water hydrology: Historical and paleoflood information , 1987 .

[4]  P. Bernardara,et al.  Formation of homogeneous regions for regional frequency analysis of extreme significant wave heights , 2014 .

[5]  D. Darling,et al.  A Test of Goodness of Fit , 1954 .

[6]  Herbert E. Allen,et al.  Flood-Frequency Analyses Manual of Hydrology: Part 3 Flood Flow Techniques , 1960 .

[7]  H. Storch,et al.  European storminess: late nineteenth century to present , 2008 .

[8]  H. Andrieu,et al.  Usefulness of historical information for flood frequency analyses: Developments based on a case study , 2011 .

[9]  B. Renard,et al.  Combining regional estimation and historical floods: A multivariate semiparametric peaks‐over‐threshold model with censored data , 2014, 1411.7782.

[10]  Fedor Baart,et al.  Using 18th century storm-surge data from the Dutch Coast to improve the confidence in flood-risk estimates , 2011 .

[11]  J. R. Wallis,et al.  Some statistics useful in regional frequency analysis , 1993 .

[12]  Manuel Garcin,et al.  How historical information can improve estimation and prediction of extreme coastal water levels: application to the Xynthia event at La Rochelle (France) , 2015 .

[13]  B. Gnedenko Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire , 1943 .

[14]  N. Pouvreau Trois cents ans de mesures marégraphiques en France : outils, méthodes et tendances des composantes du niveau de la mer au port de Brest , 2008 .

[15]  Jim Freeman,et al.  Outliers in Statistical Data (3rd edition) , 1995 .

[16]  C. Cunnane Methods and merits of regional flood frequency analysis , 1988 .

[17]  Development of a target-site-based regional frequency model using historical information , 2016 .

[18]  K. Fortuniak,et al.  Multi‐indices analysis of southern Scandinavian storminess 1780–2005 and links to interdecadal variations in the NW Europe–North Sea region , 2009 .

[19]  B. Bobée,et al.  « Utilisation de l'information historique en analyse hydrologique fréquentielle » , 1998 .

[20]  Michel Lang,et al.  Stationarity analysis of historical flood series in France and Spain (14th–20th centuries) , 2003 .

[21]  J. R. Wallis,et al.  Regional Frequency Analysis: An Approach Based on L-Moments , 1997 .

[22]  S. Coles,et al.  Likelihood-Based Inference for Extreme Value Models , 1999 .

[23]  Jonathan R. M. Hosking,et al.  The Value of Historical Data in Flood Frequency Analysis , 1986 .

[24]  J. M. Damázio,et al.  USE OF HISTORICAL DATA IN FLOOD-FREQUENCY ANALYSIS , 1987 .

[25]  Xavier Kergadallan,et al.  A two-step framework for over-threshold modelling of environmental extremes , 2014 .

[26]  M. Hubert,et al.  Outlier detection for skewed data , 2008 .

[27]  M. Leese,et al.  Use of censored data in the estimation of Gumbel distribution parameters for annual maximum flood series , 1973 .

[28]  R. Allan,et al.  Fluctuations in autumn–winter severe storms over the British Isles: 1920 to present , 2009 .

[29]  Nathalie Giloy,et al.  How frequent is storm-induced flooding in the central part of the Bay of Biscay? , 2014 .

[30]  R. Allan,et al.  New Insights into North European and North Atlantic Surface Pressure Variability, Storminess, and Related Climatic Change since 1830 , 2008 .

[31]  T. Ouarda,et al.  Use of Systematic, Palaeoflood and Historical Data for the Improvement of Flood Risk Estimation. Review of Scientific Methods , 2004 .

[32]  F. Zwiers,et al.  Trends and low-frequency variability of storminess over western Europe, 1878–2007 , 2011 .

[33]  D. P. Stone The Intergovernmental Panel on Climate Change (IPCC) , 2015 .

[34]  J. Weiss Analyse régionale des aléas maritimes extrêmes , 2014 .

[35]  P. Bernardara,et al.  Application of regional frequency analysis to the estimation of extreme storm surges , 2011 .

[36]  Anthony C. Davison,et al.  Statistics of Extremes , 2015, International Encyclopedia of Statistical Science.

[37]  J. Pickands Statistical Inference Using Extreme Order Statistics , 1975 .

[38]  P. Bernardara,et al.  Modeling intersite dependence for regional frequency analysis of extreme marine events , 2014 .

[39]  I. Prosdocimi German tanks and historical records: the estimation of the time coverage of ungauged extreme events , 2018, Stochastic Environmental Research and Risk Assessment.

[40]  Jean-François Breilh Les surcotes et les submersions marines dans la partie centrale du Golfe de Gascogne : les enseignements de la tempête Xynthia , 2014 .

[41]  K. Pearson On the χ 2 Test of Goodness of Fit , 1922 .

[42]  Claire-Marie Duluc,et al.  Regional frequency analysis of extreme storm surges along the French coast , 2011 .

[43]  J. Stedinger,et al.  Use of historical information in a maximum-likelihood framework , 1987 .

[44]  J. H. Ward Hierarchical Grouping to Optimize an Objective Function , 1963 .

[45]  E. Garnier,et al.  La tempête Xynthia face à l'histoire ; submersions et tsunamis sur les littoraux français du Moyen Âge à nos jours , 2010 .

[46]  Jonathan R. M. Hosking,et al.  Paleoflood Hydrology and Flood Frequency Analysis , 1986 .

[47]  Jery R. Stedinger,et al.  Bayesian MCMC flood frequency analysis with historical information , 2005 .

[48]  Yasser Hamdi,et al.  Use of historical information in extreme-surge frequency estimation: the case of marine flooding on the La Rochelle site in France , 2014 .

[49]  Eric P. Smith,et al.  An Introduction to Statistical Modeling of Extreme Values , 2002, Technometrics.

[50]  W. G. Cochran The $\chi^2$ Test of Goodness of Fit , 1952 .

[51]  Thomas Gouriou Evolution des composantes du niveau marin à partir d'observations de marégraphie effectuées depuis la fin du 18ème siècle en Charente-Maritime , 2012 .

[52]  M. A. Benson Use of historical data in flood-frequency analysis , 1950 .

[53]  Pieter van Gelder,et al.  A new statistical model for extreme water levels along the Dutch coast , 1996 .

[54]  Robert Condie,et al.  Flood frequency analysis with historic information , 1982 .

[55]  J. Stedinger,et al.  Flood Frequency Analysis With Historical and Paleoflood Information , 1986 .

[56]  D. Idier,et al.  How historical information can improve extreme coastal water levels probability prediction: application to the Xynthia event at La Rochelle (France) , 2014 .

[57]  F. Zwiers,et al.  Trends and variability of storminess in the Northeast Atlantic region, 1874–2007 , 2008 .