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Reliability and robustness of rainfall compound distribution model based on weather pattern sub-sampling

Abstract : Garavaglia et al. (2010) ont introduit un nouveau modèle probabiliste MEWP pour l'étude de la distribution des pluies journalières extrêmes. Il est basé sur la composition de huit lois exponentielles, chacune étant relative aux pluies issues d'un type de temps. Cet article présente l'étude des performance de ce modèle, à partir d'un jeu de données de 37 longues séries (période 1904-2003) et un jeu régional de 478 stations (période commune 1954-2005), sur la France, l'Espagne et la Suisse. Les performances du modèle ont été évaluées en terme : (i) de justesse (en vérifiant l'adéquation entre probabilités théorique et empirique), et (ii) de robustesse (à partir de plusieurs sous-échantillons). Le modèle MEWP a été comparé aux modèles saisonniers GEV et GPD et à une extension du modèle MEWP par composition de huit lois GPD. Les principaux résultats obtenus montrent : (i) l'intérêt d'un échantillonnage par type de temps qui améliore la justesse des estimations ; (ii) la faible robustesse des approches locales GEV et GPD (cf. paramètre de forme) ; (iii) le bon comportement du modèle MEWP à la fois robuste et juste. / A new probabilistic model for daily rainfall, named MEWP (Multi Exponential Weather Pattern) distribution, has been introduced in Garavaglia et al. (2010). This model provides estimates of extreme rainfall quantiles using a mixture of exponential distributions. Each exponential distribution applies to a specific sub-sample of rainfall observations, corresponding to one of eight typical atmospheric circulation patterns that are relevant for France and the surrounding area. The aim of this paper is to validate the MEWP model by assessing its reliability and robustness with rainfall data from France, Spain and Switzerland. Data include 37 long series for the period 19042003, and a regional data set of 478 rain gauges for the period 19542005. Two complementary properties are investigated: (i) the reliability of estimates, i.e. the agreement between the estimated probabilities of exceedance and the actual exceedances observed on the dataset; (ii) the robustness of extreme quantiles and associated confidence intervals, assessed using various sub-samples of the long data series. New specific criteria are proposed to quantify reliability and robustness. The MEWP model is compared to standard models (seasonalised Generalised Extreme Value and Generalised Pareto distributions). In order to evaluate the suitability of the exponential model used for each weather pattern (WP), a general case of the MEWP distribution, using Generalized Pareto distributions for each WP, is also considered. Concerning the considered dataset, the exponential hypothesis of asymptotic behaviour of each seasonal and weather pattern rainfall records, appears to be reasonable. The results highlight : (i) the interest of WP sub-sampling that lead to significant improvement in reliability models performances; (ii) the low level of robustness of the models based on at-site estimation of shape parameter; (iii) the MEWP distribution proved to be robust and reliable, demonstrating the interest of the proposed approach.
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Submitted on : Monday, September 5, 2011 - 10:44:42 AM
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F. Garavaglia, M. Lang, E. Paquet, J. Gailhard, R. Garçon, et al.. Reliability and robustness of rainfall compound distribution model based on weather pattern sub-sampling. Hydrology and Earth System Sciences Discussions, European Geosciences Union, 2011, 15 (2), p. 519 - p. 532. ⟨10.5194/hess-15-519-2011⟩. ⟨hal-00619041⟩

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