The multi-scale rarity matrix – a comprehensive tool to analyze the space-time severity of meteorological drought, with application to France

Droughts are recurrent phenomena that present a large variety of space and time patterns making rather difficult the assessment of their rarity and the comparison between events. Our study focuses on the space-time “memory effect” of meteorological drought over France using gridded precipitation from the SAFRAN reanalysis over 1950-2022. The proposed easy tool of rarity matrix analyzes how drought events build and persist across time and space. The approach is purely statistic, assuming that drought consequences over a given area depend on the probability of non exceedance (“rarity”) of antecedent rainfall accumulations. In order to cover a large spectrum of “memory effects”, we consider a continuum of accumulation periods ranging from a few weeks to several years and moving windows of size 80x80 to 480x480 km2 over France. The rarity matrix of a given year displays the most severe rarity values encountered during the year as a function of the various accumulation periods and the various spatial scales. Over the study period of 1950-2022 we show how the shape of rarity matrix discriminate short- and long-term historical droughts, as well as regional to national droughts. As an additional asset, the rarity matrix is also able to analyze the rarity of precipitation excess over several weeks to months or years, as it was the case in fall 2023 in France.