Research papersA regional model for extreme rainfall based on weather patterns subsampling
Introduction
Design of water-related infrastructures often applies weather generators as a probabilistic tool to assess risks related to extreme events. Among the great variety of weather generators, an important class of models makes the link between the generating physical processes of meteorological events and statistical models via a limited number of weather “types” or “patterns” (Ailliot et al., 2015). Following the assumption that such classification generally improves the statistical homogeneity of fitted observations, MEWP (Garavaglia et al., 2010, Garavaglia et al., 2011) categorizes rainfall events according to sub-populations corresponding to eight atmospheric circulation patterns identified at a large scale (e.g. over Western Europe). For each sub-population and season, an exponential distribution is fitted to a Peak-Over-Threshold (POT) sample composed of the largest rainfall events, i.e. exceeding a pre-determined quantile (e.g. the 0.7-quantile at a daily scale). The global MEWP distribution is obtained by combining the exponential distributions.
Several studies in France (Garavaglia et al., 2010, Garavaglia et al., 2011), Canada, Austria (Brigode et al., 2013) and Norway (Blanchet et al., 2015) show that MEWP often outperforms other distributions commonly used to model extreme rainfall (e.g. Gumbel, GPD and GEV distributions) in terms of reliability and robustness. However, the assumption of severe rainfall events being exponentially distributed can be put into question, especially in regions where flash-floods are likely to occur (e.g. the South-East of France, see Veysseire et al., 2012, Neppel et al., 2014). For this reason, we propose to apply the MDWP model, for which the exponential distribution can be replaced by distributions with a heavier tail, such as the GPD. Unfortunately, local applications of the MDWP model reveal a lack of robustness and overfitting issues (Garavaglia et al., 2011). Indeed, the application of heavy-tailed distributions to short record lengths of rainfall extremes leads to potential estimation biases (Papalexiou and Koutsoyiannis, 2013, Serinaldi and Kilsby, 2014).
To solve these estimation issues, we propose to apply a regionalized version of MDWP. A regional frequency analysis (RFA) is developed in order to increase the sample size for each season and weather pattern (WP). The RFA approach (Hosking and Wallis, 2005) combines observations at a given site with the information gathered in a region around this site. While the RFA approach has been extensively applied to annual rainfall maxima (for recent applications see, e.g. Carreau et al., 2013, Du et al., 2014), fewer applications to POT rainfall series can be found, with the notable exceptions of Madsen et al., 1997, Roth et al., 2012, and Mailhot et al. (2013). In this paper, we develop a RFA methodology specific to the MDWP model and study the impact of several choices (scale factor, homogeneity tests) on its performances. The regionalized MDWP is expected to show a significant gain of robustness when heavy-tailed distributions are applied, while preserving the reliability qualities of the MEWP model in regions where the local MEWP shows adequate performances. In addition, the possibility of extending the application of MDWP to ungauged sites is of strong interest.
The development of the RFA methodology is based on an extensive dataset of 773 daily rainfall series. Neighborhoods around each site are considered, following the concept of regions-of-influence (RoI) proposed by Burn (1990). The paper is organized as follows: The rainfall dataset and the localization of the meteorological stations are presented in Section 2. Section 3 discusses the nonstationarity of rainfall extremes in France. Section 4 details the local MDWP model and Section 5 the regional MDWP model. A bottom-up algorithm for the selection of RoIs is proposed, different options of scale factors are tested and several statistical homogeneity tests are reviewed. Section 6 describes the criteria used to evaluate the reliability and robustness of the different probabilistic models. Section 7 assesses the performance of local and regional models, when different alternatives to the exponential distribution are considered. Section 8 concludes and draws some perspectives.
Section snippets
Data
Daily rainfall observations from rain gauges belonging to EdF (Électricité de France), the French meteorological office Météo-France and the Italian meteorological Service are used in this study. Only rain gauges with at least 20 years of records over the period 1948–2013 have been selected, most of the stations having more than 50 years of data (see Table 1). These stations are mainly located in the South-Eastern part of France and at borders (see Fig. 1). Rain gauges networks are
Nonstationarity of rainfall extremes in France
According the last IPCC report (IPCC, 2014), some properties of rainfall extremes clearly exhibit a trend. For example, it has been confirmed that the number of heavy precipitation events has globally increased in land regions. Therefore, the nonstationarity of rainfall extremes cannot be ignored and must be discussed.
In Europe, the frequency and intensity of heavy precipitation events has likely increased (IPCC, 2014). However, for extreme precipitation, van den Besselaar et al. (2013) report
Ingredients
MEWP is a rainfall probabilistic model used in SCHADEX (Paquet et al., 2013), a stochastic simulation process of floods which is operationally applied at EdF for extreme flood estimation. More precisely, MEWP model is the distribution applied to the central rainfall events. Central rainfalls are extracted from rainfall series by selecting the largest observation in 3-day rainfall events, a minimum threshold being set to 1 mm. Central rainfalls are thus expected to be nearly independent (Blanchet
Regional MDWP
RFA methods have been originally developed and applied to flood frequency analysis (Hosking et al., 1985, Cunnane, 1988). However, numerous applications to rainfall (Bonnin et al., 2004, Trefry et al., 2005) and rainfall extremes (Buishand, 1991, Durrans and Kirby, 2004, Roth et al., 2012, Mailhot et al., 2013, Carreau et al., 2013) exist. One of the funding principle of RFA methods is the index-flood procedure (Dalrymple, 1960), which assumes that site-dependent scaled data from different
Performance criteria
In this paper, the focus is put on the extreme upper tail of the distributions and its ability to describe the most extreme events. Different criteria have been developed to compare the predictive performances of different statistical models. Following Garavaglia et al. (2011) and Renard et al. (2013), we apply a split-sampling procedure. For each station i, rainfall measurements are divided in two sub-samples and , which correspond to an equal number of years randomly chosen. Let
Results
Different MDWP models are compared: when seasons and weather patterns are considered, distribution tails of the 16 sub-components are either exponential (), generalized Pareto () or Weibull (). For each model version, the split-sampling procedure presented in Section 6 is repeated 100 times. 100 scores are then obtained, which represent the variability of the performances due to the choice of calibration and validation periods. This section presents the results obtained for
Conclusions
In this paper, a regional version of a daily extreme rainfall model (MDWP) based on a seasonal and weather pattern sub-sampling is proposed. The different steps of a RFA methodology are examined in details. We review the power of homogeneity tests, and provide insights for the selection of Hosking-Wallis-based tests only. Different choices of at-site scale factors are empirically tested, the global average of central rainfalls being considered as an adequate option.
Local and regional MDWP
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