How rare are rapid transitions in streamflow? A conditional probability approach

Drought-to-flood transitions, where low-flow conditions are rapidly followed by high flows, are increasingly framed as compound hydrological hazards. However, it remains unclear whether such transitions are genuinely rare events or simply reflect how they are defined. Most existing studies apply uniform magnitude thresholds and fixed time windows across diverse catchments, implicitly assuming comparable extremeness. Here, we challenge this assumption by reframing transitions in probabilistic terms, quantifying the conditional likelihood of large streamflow swings across a range of severities, durations, and seasonal contexts.Using daily streamflow records from 4,299 European catchments, we perform three conditional probability experiments to assess how transition likelihood depends on threshold choice, low-flow duration, and timing within the hydrological year. We identify pronounced and spatially coherent patterns in transition probability. Very rapid transitions (e.g. within 14 days) are common in the Alps, coastal Scandinavia, and the United Kingdom, while catchments with strong hydrological memory exhibit consistently low probabilities, even over long time windows (up to 365 days). Transition probability generally decreases with increasing low-flow duration, except in snow-influenced catchments, where seasonal processes can increase the likelihood of transitions when only longer-duration low flow periods are considered. Examined continuously, low-flow events also exert a persistent influence on subsequent streamflow distributions, particularly when they occur in phase with the climatological dry season.Our results show that transition definitions commonly used in the literature correspond to frequent events in some regions and extremely rare events in others. This demonstrates that the extremeness of drought-to-flood transitions cannot be inferred from magnitude and timing alone, but must be evaluated relative to their conditional or joint probability of occurrence. We argue that compound hydrological transitions should be defined consistently with other extremes, using probability-based or impact-relevant criteria rather than uniform thresholds.