Why flood forecasts need uncertainty: probabilistic AI models catch the extremes deterministic ones miss

When a river rises, the difference between a safe evacuation and a deadly surprise often comes down to one number: how high the water will get. For years, the most accurate tool for predicting that number has been a deep learning architecture called the Long Short-Term Memory network, or LSTM, which has become the benchmark for rainfall–runoff modeling across the world’s catchments. But a new study published in Hydrology and Earth System Sciences argues that the single-number forecasts these models produce are fundamentally ill-suited to the events that matter most — rare, catastrophic floods — and that the fix is not a better architecture but a philosophical one: embrace uncertainty.

The research, led by Sanika Baste of the Karlsruhe Institute of Technology together with Sebastian Lerch, Daniel Klotz, and Ralf Loritz, examined how well LSTMs trained on 196 Swiss catchments handle the upper tail of the discharge distribution — the top 0.05 percent of observed flows. The verdict was stark. The deterministic LSTM, which outputs a single best-guess discharge for every time step, underestimated 97 percent of these extreme values, with a mean shortfall of roughly 28 millimeters per day of specific discharge. By contrast, a probabilistic LSTM that predicts an entire distribution of plausible outcomes placed 83 percent of those same extremes within its 99th percentile prediction interval.

The reason for this gap lies in how the models are trained. A standard LSTM is optimized with a mean squared error loss, which, in statistical terms, elicits the conditional mean of the discharge distribution. Because flood distributions are strongly right-skewed — with a long tail toward high-magnitude events — the mean sits well below the upper quantiles that define flood risk. When the relationship between rainfall and runoff is inherently ambiguous, the model regresses toward the mean and systematically underestimates extremes. The authors illustrate the ambiguity with a simple example from their training data: precipitation events of roughly 100 millimeters per day occurred 27 times during the training period, yet floods exceeding 40 millimeters per day followed in only 6 of those cases. The same storm can produce wildly different floods depending on antecedent soil moisture, snow conditions, and the internal state of the catchment — information the model’s predictors do not fully capture.

This is not merely a theoretical quibble. Earlier stress tests by the same team showed that when the most extreme precipitation events in the test period were replaced with design storms of 50-, 100-, and 300-year return intervals, the deterministic LSTM not only underestimated the flood response but hit an empirical ceiling of about 75 millimeters per day, far below its theoretical prediction limit. Previous work by Frame and colleagues in 2022 and Acuña Espinoza and colleagues in 2025 had found the same pattern: the LSTM’s advantage over traditional hydrological models erodes as flood magnitude increases. Attempts to patch the problem — more training data, modified loss functions, altered activation functions — produced only marginal gains, often at the cost of degraded performance for ordinary flows.

To test whether probabilistic modeling could break this ceiling, the team compared three approaches that represent predictive uncertainty in different ways. The Countable Mixture of Asymmetric Laplace distributions, or CMAL, predicts a weighted sum of three skewed component distributions, giving it the flexibility to capture asymmetry and multimodality in runoff. The Distributional Regression Network, or DRN, predicts the parameters of a single logistic distribution — structurally simpler but with a strong inductive bias. The Bernstein Quantile Network, or BQN, takes a nonparametric route, directly estimating the quantile function as a linear combination of Bernstein basis polynomials without assuming any distributional shape in advance. All three were built on the same LSTM backbone, differing only in their output layers, and each was trained as a five-member regional ensemble on the CAMELS-CH dataset spanning 1981 to 2020.

Evaluated with the Continuous Ranked Probability Score, the CMAL emerged as the strongest performer, with a mean catchment CRPS of 0.50 compared to 0.53 for the DRN and 0.56 for the BQN. Its advantage stems from its ability to model the skewed, heavy-tailed character of streamflow. Yet none of the models achieved perfect calibration, and each exhibited a distinct signature of miscalibration: the CMAL was consistently over-dispersed, the DRN slightly under-dispersed with overestimated upper quantiles, and the BQN under-dispersed with inflated lower quantiles. Notably, the probabilistic models came close to the deterministic LSTM on conventional point metrics — the CMAL achieved a median-catchment Nash–Sutcliffe efficiency of 0.86 against 0.87 for the deterministic model — suggesting that the richer uncertainty information comes at little practical cost in overall accuracy.

The real test came with individual flood events. During a summer flood on the river Reuss in June 2019, triggered by a 30-year return precipitation event, the deterministic LSTM underestimated the peak by 6 millimeters per day, while all three probabilistic models placed the observed peak within their 99th percentile. A winter flood on the Allondon in January 2004, with a peak of about 51 millimeters per day approaching a 10-year flood, was similarly underestimated by the deterministic model at 37 millimeters per day, but captured by the probabilistic predictions. Most dramatically, an autumn flood on the Saltina at Brig — driven by more than 100-year return precipitation on two consecutive days and producing a 30-year flood of about 87 millimeters per day — saw the deterministic LSTM predict only 50 millimeters per day, while the CMAL’s 99th percentile reached 117 millimeters, comfortably above the observed peak.

But a probability distribution, however accurate, does not itself save lives. Operational flood management requires discrete decisions: a warning is issued at a specific level, or it is not. Choosing the mean or median risks missing extremes; relying blindly on high quantiles generates crippling false alarms. To bridge this gap, the team introduced FRiCA, a Flood Risk Communication Agent built on reinforcement learning, which observes a seven-day sequence of predictive distributions and lagged discharge and learns to issue warnings across six severity classes based on Swiss design-flood thresholds ranging from 2-year to 300-year return periods. Trained with the Proximal Policy Optimization algorithm and a reward function that penalizes both under- and over-warning in proportion to their ordinal distance from the true severity, FRiCA learned a risk-aware policy that outperformed both the deterministic LSTM rule and a fixed 99th-percentile heuristic.

The numbers tell the story. For flood events, FRiCA achieved 414 hits compared to 301 for the deterministic rule and just 124 for the 99th-percentile rule, though at the cost of more false alarms than the deterministic approach. For extreme floods of 10-year return period and above, FRiCA detected 27 of 128 events with only 10 false alarms, while the 99th-percentile rule captured 28 events but generated 90 false alarms — operationally impractical. The learned policy thus strikes a balance between sensitivity and specificity that neither static rule achieves, and unlike fixed thresholds, it can in principle be updated as new flood events are observed, closing a feedback loop that conventional warning systems cannot.

The authors are careful to frame FRiCA as a proof of concept rather than a finished operational tool. The learned policies showed sensitivity to random initialization, no systematic hyperparameter optimization was performed, and the team observed the risk of reward hacking, where the agent achieves high nominal reward by collapsing to the dominant warning class and ignoring rare but consequential events. They point to inverse reinforcement learning — inferring the reward structure from historical forecaster decisions — as a promising path forward. But the broader message stands: the fundamental limitation in extreme flood prediction may lie not in the neural network architecture but in the information content of the training data itself. When predictors cannot uniquely determine the runoff response, any deterministic model is forced to collapse a distribution of plausible outcomes into a single number. Probabilistic models that estimate the full conditional distribution, paired with learned decision rules that translate uncertainty into action, offer a pathway toward warning systems that are not only more accurate but genuinely risk-aware.

Subject of Research: Probabilistic LSTM models and reinforcement learning for improved flood prediction and warning communication

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

Article References: Baste, S., Lerch, S., Klotz, D., & Loritz, R. (2026). The need for uncertainty: why probabilistic LSTMs are key to improving flood predictions and enabling learned warning rules. Hydrology and Earth System Sciences, 30(20), 6339-6358. https://doi.org/10.5194/hess-30-6339-2026

Image Credits: AI Generated

DOI: 10.5194/hess-30-6339-2026

Keywords: flood forecasting, LSTM, probabilistic modeling, reinforcement learning, hydrology, uncertainty quantification, deep learning, early warning systems, need, uncertainty, probabilistic, LSTMs