Multivariate frequency analysis of threshold-defined streamflow droughts: a mixed-tail framework for duration, severity, and minimum-flow magnitude

Abstract. Threshold-defined streamflow droughts are commonly described by duration, deficit volume, and minimum-flow magnitude, but these characteristics pose a specific mixed-tail problem for multivariate frequency analysis. Duration and deficit volume increase with drought extremity, whereas minimum-flow magnitude decreases. A consistent trivariate return-period framework for these event characteristics therefore cannot be formulated as a simple upper-tail exceedance problem. Here, we develop an event-based multivariate frequency framework that jointly models drought duration (D), deficit volume or severity (S), and minimum-flow magnitude (M) within Yevjevich's threshold approach. Annual event series are constructed by selecting, in each water year, the drought with the largest deficit volume and extracting D, S, and the minimum discharge M for the same event. Marginal distributions are represented by zero-augmented Weibull models where applicable, and dependence is modelled using a regular vine copula. Analytical AND and OR probabilities are formulated for the resulting mixed upper-/lower-tail setting, representing compound exceedance and at-least-one exceedance risk, respectively. The framework is applied to 46 years of streamflow observations from 235 Austrian catchments, with a focus on the 2003 and 2015 droughts. The analysis provides strengthened trivariate evidence of compound severity in 2003, with 31 % of stations showing T_AND >50 years, whereas 2015 exhibits fewer compound extremes but localized northern hotspots. Non-parametric bootstrap intervals show substantially wider uncertainty for rare AND events than for OR events, reflecting limited information in the joint tail. The multivariate assessment re-ranks events relative to univariate analyses and identifies compound drought hotspots that are not apparent from individual characteristics alone. The framework provides a transferable basis for mixed-tail frequency analysis of streamflow droughts and other threshold-defined environmental extremes.