For a few decades, climate models are used to provide future scenarios of precipitation with increasingly higher spatial resolution. However, this resolution is not yet sufficient to describe efficiently what happens at local scale. Dynamical and statistical methods of downscaling have been developed and allow us to make the link between two levels of resolution and enable us to get values at a local scale based on large-scale information from global or regional climate models. Nevertheless, both the extreme behavior and the spatial structures are not well described by these downscaling methods. We propose a two-step methodology, called spatial hybrid downscaling (SHD), to solve this problem. The first step consists in applying a univariate (i.e., one-dimensional) statistical downscaling to link the high- and low-resolution variables at some given locations. Once this 1d-link is performed, a conditional simulation algorithm of max-stable processes adapted to the extremal t process enables us to get conditional distributions of extreme precipitation at any point of the region. An application is performed on precipitation data in the south of France where extreme (Cevenol) events have major impacts (e.g., floods). Different versions of the SHD approach are tested. Most of them show particularly good results regarding univariate and multivariate criteria and overcome classical downscaling techniques tested in comparison. Furthermore, these conclusions are robust to the choice of the 1d-link functions tested and to the choice of the conditioning points to drive the conditional local-scale simulations performed by the SHD approach.
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