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A Regional Scale‐Invariant Extreme Value Model of Rainfall Intensity‐Duration‐Area‐Frequency Relationships

We propose in this article a regional study of intensity‐duration‐area‐frequency (IDAF) relationships of annual rainfall maxima in southern France. For this we develop a regional extreme value IDAF model based on space‐time scale invariance hypotheses. The model allows us to link the statistical distributions of rainfall maxima over any duration and area. It provides in particular an analytical expression of the areal reduction factor, which expresses how the statistical distribution of rainfall maxima changes as the area increases, for any fixed duration. It also provides an analytical expression of areal return level for the continuum of area and duration. The model is applied to radar reanalysis data covering a 13,000‐km2 region of southern France featuring contrasted rainfall regimes (2008–2015). We estimate the IDAF relationships centered on any radar pixel of the region in the range 3–48 hr and 1–2,025 km2. We obtain in particular a spatial distribution of the areal reduction factor, which allows us to distinguish different rainfall regimes in the region. The overall IDAF model provides also a regional quantification of areal rainfall risk by allowing the computation of rainfall return level maps for any area and duration in the applicable range. Despite inevitable sampling issues due to the shortness of the data sample, we highlight important differences in the spatial distribution of areal rainfall risk depending on the area and duration, illustrating that a comprehensive storm risk evaluation should consider the continuum of area and duration rather than arbitrarily predefined ones.