Bridging rarity of drought-flood abrupt alternation events with reverse distributions or reverse copulas

Floods and droughts have received substantial attention in the hydro-meteorological community as isolated phenomena. However, abrupt transitions between these two extremes-termed Drought-Flood Abrupt Alternation Events (DFAAEs)-remain understudied despite their heightened destructiveness, often resulting in more severe impacts than standalone droughts or floods. Accurate identification and classification of DFAAEs are critical for risk assessment and forecasting, yet existing methods suffer from technical limitations such as reliance on empirical parameters and unboundedness. To address these gaps, this study introduces a novel framework for identifying and classifying DFAAEs by assessing the statistical rarity of combinatorial events constructed from successive hydro-meteorological indices. This rarity is bridged with reverse distributions-and further refined through reverse copulas-obtained via reverse integration of the corresponding probability density function. Ultimately, we propose a metric based on drought-to-flood and flood-to-drought specific reverse distributions/copulas. This framework demonstrates significant improvements over conventional methods across multiple dimensions. Using it to characterize DFAAEs in Anhui Province (middle-lower Yangtze River) over 123 years, our analysis reveals a marked increase in DFAAE frequency and intensity, underscoring the urgent need for enhanced preparedness and mitigation strategies in response to escalating DFAAE risks.