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A Regional Scale‐Invariant Extreme Value Model of Rainfall Intensity‐Duration‐Area‐Frequency Relationships
Author(s) -
Mélèse Victor,
Blanchet Juliette,
Creutin JeanDominique
Publication year - 2019
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2018wr024368
Subject(s) - maxima , return period , storm , generalized extreme value distribution , range (aeronautics) , extreme value theory , environmental science , duration (music) , scale (ratio) , sampling (signal processing) , spatial distribution , meteorology , statistics , climatology , geography , mathematics , geology , cartography , computer science , physics , art , materials science , filter (signal processing) , archaeology , acoustics , composite material , flood myth , computer vision , art history , performance art
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‐km 2 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 km 2 . 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.