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

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 1904-2003, and a regional data set of 478 rain gauges for the period 1954-2005. 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.