Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount

Abstract

Precipitation amounts at daily or hourly scales are skewed to the right, and heavy rainfall is poorly modeled by a simple gamma distribution. An important yet challenging topic in hydrometeorology is to find a probability distribution that is able to model well low, moderate, and heavy rainfall. To address this issue, we present a semiparametric distribution suitable for modeling the entire range of rainfall amount. This model is based on a recent parametric statistical model called the class of extended generalized Pareto distributions (EGPDs). The EGPD family is in compliance with extreme value theory for both small and large values, while it keeps a smooth transition between these tails and bypasses the hurdle of selecting thresholds to define extremes. In particular, return levels beyond the largest observation can be inferred. To add flexibility to this EGPD class, we propose to model the transition function in a nonparametric fashion. A fast and efficient nonparametric scheme based on Bernstein polynomial approximations is investigated. We perform simulation studies to assess the performance of our approach. It is compared to two parametric models: a parametric EGPD and the classical generalized Pareto distribution (GPD), the latter being only fitted to excesses above a high threshold. We also apply our semiparametric version of EGPD to a large network of 180 precipitation time series over France.

A universal Standardized Precipitation Index candidate distribution function for observations and simulations

“…As a result, many studies that use SPI directly fit the gamma (Mo and Lyon, 2015;Ma et al, 2015;Yuan and Wood, 2013;Quan et al, 2012;Yoon et al, 2012) or the Pearson type III distribution (Ribeiro and Pires, 2016) without assessing the normality of SPI's resulting distribution with goodness-of-fit tests or other statistical analyses beforehand. The selected PDF, however, is of critical importance because the choice of this PDF is the key decision involved in the calculation of SPI, and indeed many authors have urged investigating the adequacy of distribution functions for new datasets and regions before applying them (Blain et al, 2018;Stagge et al, 2015;Touma et al, 2015;Sienz et al, 2012). Neglecting such an investigation has potentially far-reaching consequences in terms of a biased drought description (Guenang et al, 2019;Sienz et al, 2012).…”

“…A biased drought description would result from an inadequacy of the fitted distribution function to describe precipitation. Such an inadequacy has been identified for the gamma (Lloyd-Hughes and Saunders, 2002;Naresh Kumar et al, 2009;Sienz et al, 2012;Blain and Meschiatti, 2015;Stagge et al, 2015;Touma et al, 2015;Blain et al, 2018;Guenang et al, 2019) as well as the Pearson type III distribution (Blain and Meschiatti, 2015;Blain et al, 2018;Stagge et al, 2015) in many parts of the world. This led to the request for further investigations of candidate distribution functions (Blain and Meschiatti, 2015;Blain et al, 2018;Stagge et al, 2015;Touma et al, 2015;Sienz et al, 2012;Lloyd-Hughes and Saunders, 2002;Guttman, 1999).…”

“…Two additional studies analyzed the adequacy of different candidate PDFs fitted onto simulated precipitation while focusing on drought occurrence probabilities in climate projections (Touma et al, 2015;Sienz et al, 2012). Touma et al (2015) is the only study that tested candidate PDFs globally.…”

“…Two additional studies analyzed the adequacy of different candidate PDFs fitted onto simulated precipitation while focusing on drought occurrence probabilities in climate projections (Touma et al, 2015;Sienz et al, 2012). Touma et al (2015) is the only study that tested candidate PDFs globally. However, they solely provide highly aggregated results that are globally averaged for accumulation periods between 3 and 12 months and conclude that the gamma distribution is overall best suited to calculate SPI.…”

“…Testing the performance of three-parameter distributions introduces the risk of overfitting (Stagge et al, 2015;Sienz et al, 2012), which could explain the focus on two-parameter distributions in recent studies. As a consequence of this one-sided focus in combination with the inability of twoparameter PDFs to perform sufficiently well in different locations and for different accumulation periods concurrently, many studies have proposed a multi-distribution approach (Guenang et al, 2019;Blain and Meschiatti, 2015;Touma et al, 2015;Sienz et al, 2012;Lloyd-Hughes and Saunders, 2002). Such an approach recommends the use of a set of PDFs.…”