1 october 2009 Regional Frequency Analysis (RFA) Cong Mai Van Ferdinand Diermanse

1 october 2009 Problem definition

1 october 2009 Trading space for time  Available time series are “by definition” too short for extreme value analysis  consequence: large uncertainties  combining data from different stations (trading space for time) can reduce the uncertainties

1 october 2009 RFA Principle:  pooling data by using information from neighbouring locations, which are considered from homogeneous regions The main stages: 1.screening of data; 2.identification of homogeneous regions; 3.test for discordant stations 4.choice of a regional frequency distribution; 5.estimation of the regional frequency distribution.

1 october 2009 How to combine? Popular method: the Index Flood Method: distributions in all locations are assumed to be multiples of the “average” distribution (the regional growth curve) -> shape is the same for al stations f regional growth curve Q r (f) Q Q i (f)= µ i Q r (f),

1 october 2009 derivation of regional growth curve  normalise data: divide data by mean (µ) -> new mean = 1  derive fits of normalised data for each station  regional growth factor = “mean” of all fits e.g.: omean of the parameters of the distribution functions ofor each frequency: mean of the quantiles (mean [Q i (f)])

1 october 2009 L-moments approach in RFA  described by Hosking and Wallis, 1997 (the “bible of RFA”)  L-moments (linear moments) are alternative estimates of the classic statistical moments (mean, standard deviation, skewness and curtosis)  found to be “superior” in estimating parameters of distribution functions in many applications

1 october 2009 coefficients of L-mean for n=20 *1/20 1/n*(X 1 +X 2 + … + X n )

1 october 2009 Concept of L-variance: example with 2 observations measure for “spread” X 2 – X 1

1 october 2009 coefficients of L-variance for n=50 *1/50

1 october 2009 Concept of L-skewness: example with 3 observations measure for “spread” X 3 -2X 2 + X 1

1 october 2009 coefficients of L-skewness for n=50 *1/50

1 october 2009 coefficients of L-kurtosis for n=50 *1/50

1 october 2009 selection of distribution function based on L-moments Skewness and Kurtosis provide information about the shape

1 october 2009 Identification of discordant stations Wilks’ discordancy test

1 october 2009 Region homogeneity test  simulate a homogeneous region with same L-moments as the observed region  sample large number of simulated series in all stations  derive measure of heterogenity for each sampled set of simulated series.  compare observed meaure of heterogeneity with measures of simulated series

1 october 2009 example

1 october 2009 Original fits (lines are crossing, large diversity)

1 october 2009 RFA fits (no crossing lines, smaller diversity)

1 october 2009 compare original and RFA fit

1 october 2009 Wave recording locations along the Dutch coast StationAbbrev. 1. Eierlandse GatELD 2. Euro PlatformEUR 3. K13A PlatformK13 4. Lichteleiland GoereeLEG 5. Noordwijk MeetpostMPN 6. Scheur WestSCW 7. Schiermonnikoog NoordSON 8. SchouwenbankSWB 9. Ijmuiden Munitie StortplaatsYM6 Application 1: Dutch coast North sea

1 october 2009 StationND(I) SCW MPN SWB LEG330.9 ELD EUR K SON YM Wave data Dutch Coast Discordance tests of the datasets

1 october 2009 Homogeneity tests Wave data Dutch Coast

1 october 2009 Goodness of fit to find a “bestfit” Distribution Wave data L-Kurt.Z Value GEN. LOGISTIC GEN. EXTREME VALUE GEN. NORMAL PEARSON TYPE III GEN. PARETO *

1 october 2009 RFA of waves data, Dutch coast conventional fit

1 october 2009 Application 2: Vietnam coast StationAbbrev. PhuLe NamDinhPhule VanUc ThaiBinhVanuc DoSon HaiPhongDoson CuaCam HaiPhongCuacam HonDau HaiPhongHondau VanLy NamDinhNamdinh BinhMinh NinhBinhNinhbinh BaLat-SongHongBalat AnPhu HaiPhongAnphu

1 october 2009 Discordance & homogeneity test StationND(I) Phule Vanuc Doson Cuacam Hondau Namdinh Ninhbinh Balat Anphu

1 october 2009 RFA of storm surge data, Vietnam coast conventional fit

1 october 2009 Discussions The GPD appears to be the optimal regional fit for the POT extreme sea datasets. Uncertainty of the quantile estimates with RFA for both application cases is found smaller than conventional data fitting methods Differences between the at-site quantile estimates and the regional quantile estimates can be quite high (up to ~1.0m for the extreme extrapolations of years). It is better to rely on the regional quantile estimates for decision making, as suggestion in Hosking and Wallis (1997). A convex curvature is presented in the normalized regional growth curves for both wave and storm surge data. This would lead to a regional upper limit of the extreme value for waves and surges, which is more physical relevant. Adding more sites to the existing databases for each data type may result in more accurate predictions of the extreme quantiles.