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\begin{document}

\title{Modelling rainfall from sub-hourly to daily scale with a heavy tailed
meta-Gaussian model}



\author[1]{BOUTIGNY Marie}%
\author[2]{Pierre Ailliot}%
\author[3]{Aurore Chaubet}%
\author[4]{Philippe Naveau}%
\author[5]{Benoît Saussol}%
\affil[1]{Eau du Ponant SPL}%
\affil[2]{University of Brest}%
\affil[3]{Eau Du Ponant SPL}%
\affil[4]{IPSL-CNRS}%
\affil[5]{Universite Bretagne Occidentale}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
The time scale of usual hydrological applications can vary from a few
minutes to a few days. An accurate description of the precipitation
probability distributions at the appropriate time scale is needed to
compute meaningful summaries like return levels and periods. However few
statistical parametric models can handle the full rainfall distribution
at these different temporal scales. In this context, we propose and
study a new meta-Gaussian model which leads to a parametric model with
four parameters for the full distribution of precipitation. The main
advantage of our model is that it can be applied to a wide range of
accumulation periods. In particular, it still performs well below the
hourly scale. In addition, each parameter is linked to a different part
of the distribution: one of them describes the probability of rainfall
occurrence, two parameters are related respectively to the shape of
lower and upper tails of the distribution, and the last one is a
multiplicative scale parameter. The building block of our model is the
use of a latent Gaussian process that offers flexibility and simple
inference algorithms. The model is fitted to rain gauge data recorded in
Guipavas (France). It is shown that the proposed distribution handles
accumulation periods from 6 minutes to several days. The model
outperforms other meta-Gaussian models which have been proposed in the
literature.%
\end{abstract}%



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