Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection

Philippe Naveau, Raphaël Huser, Pierre Ribereau, Alexis Hannart

Research output: Contribution to journalArticlepeer-review

86 Scopus citations


In statistics, extreme events are often defined as excesses above a given large threshold. This definition allows hydrologists and flood planners to apply Extreme-Value Theory (EVT) to their time series of interest. Even in the stationary univariate context, this approach has at least two main drawbacks. First, working with excesses implies that a lot of observations (those below the chosen threshold) are completely disregarded. The range of precipitation is artificially shopped down into two pieces, namely large intensities and the rest, which necessarily imposes different statistical models for each piece. Second, this strategy raises a nontrivial and very practical difficultly: how to choose the optimal threshold which correctly discriminates between low and heavy rainfall intensities. To address these issues, we propose a statistical model in which EVT results apply not only to heavy, but also to low precipitation amounts (zeros excluded). Our model is in compliance with EVT on both ends of the spectrum and allows a smooth transition between the two tails, while keeping a low number of parameters. In terms of inference, we have implemented and tested two classical methods of estimation: likelihood maximization and probability weighed moments. Last but not least, there is no need to choose a threshold to define low and high excesses. The performance and flexibility of this approach are illustrated on simulated and hourly precipitation recorded in Lyon, France.
Original languageEnglish (US)
Pages (from-to)2753-2769
Number of pages17
JournalWater Resources Research
Issue number4
StatePublished - Apr 9 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Part of this work has been supported
by the ANR-DADA, LEFE-INSU-Multirisk,
Extremoscope projects. The authors
acknowledge Meteo France for the
Lyon precipitation time series that
available to anyone upon request. Part
of the work was done when the first
author was visiting the IMAGE-NCAR
group in Boulder, CO, USA. The
authors would also like very much to
credit the contributors of the R Core
Team [2013]. The data are freely
available by sending an email to
Philippe Naveau (

ASJC Scopus subject areas

  • Water Science and Technology


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