Local and regional estimation of extreme hydrological events Lyon 2003 FLOODS IN FRANCE Is there a change? Hélène NIEL & Laurie GIRAUD
Objective To answer questions raised by society and the scientific community faced withextreme events that occurred in France for the last few years (Nîmes 1988, Ouvèze 1992, Aude 1999, Somme 2000-2001, Gardons and Vidourle 2002) Is there a change in the French flood regime? Is theresignificant change of floods in frequency, in magnitude or in shape? in the global change context
PNRH Detection of possible changes in the flood regime of a sample of French rivers Scientific team : Cemagref LTHE Météo-France UMR HydroSciences soon EDF Today A survey of statistical methods used to detect changes as trend or shift Power analysis of some univariate tests First applications to a few long time-series
The different steps to detect a possible non-stationarity Application of univariate tests at each individual station Use of multivariate tests Drawing maps of test results to identify some possible spatial modeling approaches Looking for possible links between non-stationarity of flood records and rainfall time-series variability
Data 78 reliable gauging stations for catchments with a surface area from 20 km² to 110 000 km² 54 catchments with a surface area of more than 900 km² More than 40 years long for 51 of them More than 60 years long for 34 of them Large catchments : daily discharges Data supplied by Compagnie Nationale du Rhône (CNR) and the data base HYDRO with the agreement of MEDD
Location of the gauging stations for the large catchments
Loire, Garonne, Adour, Rhône and Var catchments Gauging station (area km²) River Main river Observation period Bas-en-Basset (3 234) Loire 1919-2001 83 yrs Vieille-Brioude (2 269) Palais-sur-Vienne (2 296) Allier Vienne Loire Loire 1919-2001 83 yrs 1923-2002 80 yrs Montjean (109 930) Loire 1863-2002 134 yrs Bort-les-Orgues (1 010) Laguépie (1 530) Dordogne Viaur Garonne Aveyron 1918-2001 84 yrs 1937-2002 66 yrs Brive-la-Gaillarde (947) Corrèze Vézère 1918-2002 85 yrs Montignac (3 125) Foix (1 340) St Pierre-des-Tripiers (925) Vézère Ariège Tarn Dordogne Garonne Garonne 1900-2002 103 yrs 1906-2002 97 yrs 1913-2002 90 yrs Pont de Berenx (2 575) Gave de Pau Adour 1924-2002 79 yrs Goumois (1 060) Doubs Saône 1956-2002 47 yrs Glère (1 240) Couzon-au-Mont-d'Or (29 900) Doubs Saône Saône Rhône 1959-2002 44 yrs 1921-2001 81 yrs Argentière-la-Bessée (984) Durance Rhône 1952-2002 51 yrs Malaussène (1 830) Var 1948-2001 54 yrs
Characteristic variables Flood shape Qmax Time of rise defined as the duration between Qmax/2 or Qmax/3 and Qmax Maximum mean discharge over x days Flood occurrences Number of floods per year Date of the floods Are floods becoming more severe? Is the flood shape changing? Are floods becoming more frequent? Is there some variation in the occurrence process? Annual maximum sampling / over-threshold sampling Hydrological year
Statistical methods univariate Tests to detect linear trend or abrupt changes in the mean of time-series Tests to detect changes in extreme values Tests used for series of peaks over threshold multivariate Permutation test Parametric approaches (Gaussian linear model)
Univariate tests Tests for linear trend Rank correlation test Linear regression as a function of time and parametric test for the slope Tests for abrupt change One change-point : Pettitt s test (1979), Buishand s U test (1982, 1984), Lee & Heghinian s bayesian method (1977) Several change-points : segmentation procedure (Hubert et al, 1989)
Permutation test Application at each individual station test for stationarity floods described by more than one variable one a priori change-point Table X variables Group 1 1 0 Table Y indexes Change-point? units Group 2 1 0 0 0 1 1 units What is the effect of table X on table Y? Can Y be explained by X?
The Saône river at Couzon-au-Mont-d Or Flood monthly distribution from 1922 to 2001 number of floods 30 25 20 15 10 5 0 Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
TheSaône river at Couzon-au-Mont-d Or Annual maxima of daily discharge Mean : 1 633 m 3 /s Standard deviation : 372 m 3 /s Maximum : 2 820 m 3 /s Minimum : 800 m 3 /s Median : 1 640 m 3 /s Standardized annual maxima of daily discharge 4 3 2 1 0-1 1921 1931 1941 1951 1961 1971 1981 1991-2 -3
The Saône river at Couzon-au-Mont-d Or 10-year mean of the standardized annual maxima of daily discharge 06 04 02 0-02 -04 1920/30 1930/40 1940/50 1950/60 1960/70 1970/80 1980/90 1990/00 decades
Peak discharges and flood occurrences Qmax Gauging station Sampling Annual over-threshold Number of floods per year Bas-en-Basset shift ~1946 (-40%) Vieille-Brioude shift ~1945 (-39%) Palais-sur-Vienne Montjean shift ~1905 (52%) Bort-les-Orgues shift ~1962 (-21%) shift ~1962 shift ~1941 (-44%) Laguépie Brive-la-Gaillarde shift ~1962 (-19%) shift ~1970 (-45%) Montignac shift ~1964 (-19%) shift ~1941 (-34%) Foix shift ~1940 (-19%) shift ~1942/1985 (-22/-36%) St Pierre-des-Tripiers Pont de Berenx Goumois Glère Couzon-au-Mont-d'Or shift ~1976 (14%) Argentière-la-Bessée shift ~1977 (-15%) shift ~1978 (-65%) Malaussène shift ~1964 (-45%) shift ~1961 shift ~1978 (12%)
Other variables Time of rise : between Qmax/2 and Qmax Annual maximum of mean discharge over different durations d Dates of flood occurrences Gauging station Time of rise (over-threshold sampling) Annual maximum of mean discharge over d days Dates of flood occurrences (over-threshold sampling) Montjean Brive-la-Gaillarde shift ~1934 St Pierre-des-Tripiers Goumois "d Glère "d Couzon-au-Mont-d'Or shift~1977 si d<25 days Argentière-la-Bessée shift ~1986 "d Malaussène shift ~1965 "d
Application of the permutation test Change-point (abrupt change) from univariate analysis Application with 3 possible groups of variables : - all the variables - the shape variables (Qmax, time of rise, annual maximum of mean discharge over the duration d ) - the occurrence variables (number of floods per year, dates of flood occurrences) Null hypothesis H0 : Statistic of the test derived from Principal Component Analysis with respect to Instrumental Variables (PCAIV) H0 rejected if : exceedance probability of the test statistic < significance level of the test Approximation of the test statistic by a Gaussian, Pearson III, Beta distribution
Results of the permutation test Station Date of possible change Variables Exceedance probability of the test statistic under the hypothesis of the following distribution: Gauss Pearson III Malaussène 1964 shape occurrence 88 10-7 20 10-4 46 10-4 94 10-3 1978 shape occurrence 016 44 10-8 015 13 10-3 Brive-la-Gaillarde 1962 shape occurrence 52 10-5 39 10-2 24 10-3 63 10-2 1970 shape occurrence 42 10-4 99 10-4 58 10-3 16 10-3 Argentière-la-Bessée 1977 shape occurrence 015 60 10-4 015 12 10-2 1986 shape occurrence 32 10-3 13 10-8 17 10-2 11 10-3 Couzon-au-Mont-d'Or 1976 shape occurrence 28 10-3 77 10-2 14 10-2 90 10-2
In the world Stationarity of the flood regime in the UK and of the low flows in Europe Decrease of the flood volumes Increase of the mean discharges, concordance with the rainfall signal Less severe low flows, no trend for floods Floods? Low flows? Abrupt change in the annual max discharges in the 50 s Abrupt change in the mean discharges, more severe than for rainfall From ESauquet PNRH Group