How extreme are transitions in streamflow? A conditional probability approach

Abstract Drought-to-flood transitions, events in which droughts are quickly followed by floods, are increasingly studied as compound hydrological hazards. Yet, it remains unclear whether such transitions represent genuinely rare events. Existing studies typically define transitions using uniform magnitude thresholds and fixed time windows across many catchments, implicitly assuming comparable extremeness. Here, we challenge this assumption and re-conceptualize transitions by relaxing threshold criteria and quantifying the probability of occurrence of large swings in streamflow across a range of severity levels and timescales. We also quantify the influence of low-flow events on subsequent exceedance probability. Using daily streamflow data from 4299 catchments in Europe, we conduct three conditional probability experiments to evaluate how transition likelihood varies with threshold level choice, low-flow duration, and seasonal context. We identify spatially coherent patterns in transition probability, with the highest likelihoods of quick transitions (e.g. ≤ 14 days) concentrated in the Alps, coastal Scandinavia, and the United Kingdom. In contrast, catchments with strong hydrological memory exhibit consistently low transition probabilities, even for long time windows (e.g. 365 days). These spatial patterns are robust across both strict and relaxed threshold definitions and persist for longer low-flow durations. Transition probability generally decreases with increasing low-flow duration, except in snow-influenced catchments, where seasonal dynamics can increase transition likelihood following longer duration low-flows. When examined continuously, low-flow anomalies also condition the subsequent streamflow distribution for extended periods, particularly when they occur in phase with the dry season. Overall, we show that transition definitions frequently used in the literature correspond to common events in some regions and rare events in others. We argue that drought-to-flood transitions should be defined in a manner consistent with other hydrological extremes: using context-appropriate probabilities, or impact-based criteria, rather than uniform thresholds.