The need for uncertainty: why probabilistic LSTMs are key to improving flood predictions and enabling learned warning rules

Abstract. Deterministic model predictions can struggle to adequately capture extreme events such as floods and droughts, which are of particular relevance in hydrology. This limitation arises because deterministic models collapse the conditional runoff distribution to a single point estimate. Probabilistic modeling provides a way to address this issue by explicitly representing uncertainty and assigning non-zero probabilities to a range of possible outcomes, including rare and extreme events, thereby capturing the full range of plausible hydrological responses. Motivated by this perspective, we examine whether probabilistic Long Short-Term Memory (LSTM) models improve the representation of extreme events in rainfall–-runoff simulations across Switzerland. Overall, the probabilistic models show good calibration, although some miscalibration remains for the extremes. Differences between models mainly manifest in how uncertainty is distributed: some approaches produce narrower and lighter-tailed distributions, while others yield broader distributions with heavier tails. These trade-offs highlight that probabilistic models differ not only in sharpness but also in how their calibration for rare events. We observe this tradeoff also in models' accuracy metrics. When evaluating the mean of the probabilistic predictions using the Nash–Sutcliffe efficiency (NSE), none of the probabilistic approaches outperform the deterministic LSTM in terms of average predictive accuracy. However, a clear advantage over the determinsitc models emerges when focusing on the tail of the discharge distribution. For the most extreme events (top 0.1 % of the discharge distribution), the deterministic LSTM underestimates more than 90 % of observed values (since it provides estimates of an expectation), whereas probabilistic predictions can capture a substantially larger fraction (67 %) of these extremes within their upper predictive bounds. Building on the additional information provided by probabilistic runoff predictions, we further show how they can be translated into actionable flood warnings using reinforcement learning. To this end, we introduce a Flood Risk Communication Agent (FRiCA) that operates on probabilistic runoff predictions and learns decision rules for issuing warnings of varying intensity. The FRiCA is implemented as an LSTM-based policy network and is trained by rewarding correct warning levels while penalizing the underestimation of flood severity. Results indicate that the FRiCA outperforms simple fixed heuristics, such as issuing warnings based on the predictive mean or a fixed high quantile (e.g., the 99th percentile). While this behavior already demonstrates the potential of reinforcement learning for improved flood risk communication, it also motivates further exploration of better reward design and policy network definition for context-dependent decision policies that adapt to varying hydrological and societal contexts.