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Regional analysis for the estimation of low-frequency daily rainfalls in Cheliff catchment -Algeria- BENHATTAB Karima 1 ; BOUVIER Christophe 2 ; MEDDI Mohamed 3 1 USTO Mohamed Boudiaf-Algérie 2 Hydrosciences Montpellier-France 3 ENSH BLIDA-Algérie FRIEND project - MED group;UNESCO IHP-VII (2008-13) 4th International Workshop on Hydrological Extremes 15 september 2011 LGEE

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Introduction Sizing of minor hydraulic structures is based on design Rainfall quantiles (QT) of medium to high return periods (T). If the length of the available data series is shorter than the T of interest, or when the site of interest is ungauged (no flow data available) obtaining a satisfactory estimate of QT is difficult. Regional flood Frequency analysis is one of the approaches that can be used in such situations.

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1800 m asl 0 m asl 46 rainfall stations located in the northern part of the basin: daily rainfalls records from 1968 to 2004 The Cheliff watershed, Algeria Oued Chlef 0 60 km Algeria

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Oued Chlef 0 60 km 1800 m asl 0 m asl Mean annual rainfall 1968-2004(mm) The Cheliff watershed, Algeria 2 main topographic regions : valley and hillslopes ; influence on mean annual rainfall

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Why L-moment approach? Able to characterize a wider range of distributions Represent an alternative set of scale and shape statistics of a data sample or a probability distribution. Less subject to bias in estimation More robust to the presence of outliers in the data

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Brief Intro to L-Moments Hosking [1986, 1990] defined L-moments to be linear combinations of probability-weighted moments: Let x1 x2 x3 be ordered sample. Define

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Estimating L-moments where where then the L-moments can be estimated as follows: l b0 l 2 2b1 - b0 l 3 6b2 - 6b1+ b0 4 20b3 - 30b2 + 12 b1 - b0 L-CV = l 2 / l 1 (coefficient of L-variation) L-CV = l 2 / l 1 (coefficient of L-variation) t3 = l 3 / l 2 (L-skewness) t4 = l 4 / l 2 (L-kurtosis)

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Regional Frequency Analysis Delineation of homogeneous groups and testing for homogeneity within each group Estimation of the regional frequency distribution and its parameters Estimation of precipitation quantiles corresponding to various return periods Steps for success of Regionalisation

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Heterogeneity test (H) Fit a distribution to Regional L-Moment ratios Simulation 500 H? H : is the discrepancy between L-Moments of observed samples and L- Moments of simulated samles Assessed in a series of Monte Carlo simulation : Calculate v1, v2, v3…….v500 Weighted Standard deviation of at site LCV´s

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Heterogeneity test (H) H 2 : Region is definitely heterogeneous. 1 ≤H<2 : Region is possibly heterogeneous. H<1: Region is acceptably homogeneous. The performance of H was Assessed in a series of Monte Carlo simulation experiments :

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H<1 Delineation of homogeneous groups Dendrogram presenting clusters of rainfall originated in Cheliff basin

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H>1 ! Delineation of homogeneous groups Dendrogram presenting clusters of rainfall originated in Cheliff basin

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H<1 Delineation of homogeneous groups Dendrogram presenting clusters of rainfall originated in Cheliff basin

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Delineation of homogeneous groups Dendrogram presenting clusters of rainfall originated in Cheliff basin Group1Group2Group3

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Clusters pooling 0 60 km Group1 Group2 Group3 The stations located in the valleys correspond to the group 1 (downstream valley) or 3 (upstream valleys) whereas stations located on the hillslopes correspond to the group 2.

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t4(L-Kurtosis) t3 (L-Skewness) The L-moment ratio diagram Estimation of the regional frequency distribution Hypothesis What is the appropriate Distribution?

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Estimation of the regional frequency distribution LCs–LCk moment ratio diagram for group 1.

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LCs–LCk moment ratio diagram for group 2. Estimation of the regional frequency distribution

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LCs–LCk moment ratio diagram for group 3. Estimation of the regional frequency distribution

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“Dist” refers to the candidate distribution, τ4 DIST is the average L-Kurtosis value computed from simulation for a fitted distribution. τ4 is the average L-Kurtosis value computed from the data of a given region, β4 is the bias of the regional average sample L-Kurtosis, σ v is standard deviation. A given distribution is declared a good fit if |ZDist|≤1.64 The goodness-of-fit measure ZDist

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Distribution selection using the goodness-of-fit measure GroupsNumber of stationsRegional frequency distribution Zdist 117Generalized Extreme Value0,51 216Generalized Extreme Value0,97 39Generalized Extreme Value-0,84

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Generalized Extreme Value (GEV) distribution Estimation of precipitation quantiles k= shape; = scale, ξ = location Quantile is the inverse :

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Regional Estimation Estimation of precipitation quantiles Local Estimation

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At-site and regional cumulative distribution functions (CDFs) for one representative station at each group Bougara StationAin Lelloul The regional and at-site annual rainfall group 1

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Teniet El Had station Tissemsilt station The regional and at-site annual rainfall group 2 we observe a reasonable underestimation or overestimation of quantiles estimated for the high return periods.

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Reliability of the regional approach group1 The values of RMSE is greater and the discrepancy is growing when T> 100 years.

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Conclusions and Recommendations the regional approach proposed in this study is quite robust and well indicated for the estimation of extreme storm events ; L-moments analysis is a promising technique for quantifying precipitation distributions; L-Moments should be compared with other methods (data aggregation for example).

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