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

Deterministic model predictions can struggle to adequately capture extreme events such as floods and droughts, which are of particular importance in hydrology. This limitation arises because deterministic models collapse the conditional discharge 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 all possible outcomes, including extreme events, thereby capturing the entire conditional discharge distribution. 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. The differing degree of flexibility in the models leads to different degrees and distinct patterns of miscalibration in the predictive distributions. For the extreme discharges (top 0.05 % of the marginal discharge distribution), the deterministic LSTM systematically underestimates 97 % of these events, whereas 83 % of these fall within the probabilistic model's 99th percentile prediction interval. Given the rarity of these events, representing them as outcomes near the upper tail of the predictive distribution is both expected and statistically consistent. 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 risk-aware decision rules for issuing warnings of varying intensity. Results indicate that the FRiCA outperforms simple fixed heuristics, such as issuing warnings based on the deterministic LSTM predictions or a fixed high quantile (e.g., the 99th percentile). The learnt behavior demonstrates the potential of reinforcement learning as a decision layer for improved flood risk communication, and motivates further exploration of better reward design and policy network optimization for context-dependent decision policies that adapt to varying hydrological and societal contexts.