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

Abstract

Abstract.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 Correspondence to: F. Garavaglia (federico-externe.garavaglia@edf.fr) 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.

Evaluation of a compound distribution based on weather pattern subsampling for extreme rainfall in Norway

“…For this, three scores are computed, assessing respectively stability (SPAN) and reliability (AREA(FF) and AREA(N T )) of the fits. These scores were proposed and used in Garavaglia et al (2011) and Renard et al (2013). The SPAN criterion evaluates the stability of the return level estimation, when using data for each of the two subsamples.…”

“…We follow the split sample evaluation proposed in Garavaglia et al (2011) and Renard et al (2013). We divide the data for each station i into two subsamples, C…”

“…(7) with different choices of ξ s,k (Garavaglia et al, 2010(Garavaglia et al, , 2011: in MEWP all ξ s,k are set to 0 -in which case G is the EXP distribution -while in MGPWP, ξ s,k is free to vary in the positive range. We exclude cases ξ s,k < 0 because they give bounded GPD distributions with an upper bound at q α,s,k −σ α,s,k /ξ s,k , which is usually unrealistically low for rainfall.…”

“…In SCHADEX, heavy rainfall events are considered as 3-day centered precipitation events, being composed of a central rainfall and two adjacent rainfalls which are lower than the central one . The value for central rainfall is simulated using a fitted MEWP distribution for the extreme rainfall (Garavaglia et al, 2011), and the 2 adjacent days are simulated conditionally, using contingency tables to account for the dependence of the magnitude of the rainfall on the day before and after the peak rainfall. Given that MEWP is a probabilistic model for heavy "central" rainfall, rather than for all daily rainfall values, a pre-processing of the data was required to select the central rainfall values exceeding the precipitation received on both the preceding and following days by 1 mm or more at each station.…”

An Application of a Stochastic Semi-Continuous Simulation Method for Flood Frequency Analysis: A Case Study in Slovakia

“…5). The central rainfall is generated using the Multi-Exponential Weather Pattern (MEWP) probabilistic model developed at EDF by Garavaglia et al (2010) and thoroughly tested on datasets from France in Garavaglia et al (2011), and from Norway in Blanchet et al (2015). The model is based on both seasonal and weather pattern (WP) subsampling of rainfall series.…”