Articles | Volume 30, issue 20
https://doi.org/10.5194/hess-30-6339-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-30-6339-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
16 Oct 2026
Research article |
| 16 Oct 2026
| 16 Oct 2026
The need for uncertainty: why probabilistic LSTMs are key to improving flood predictions and enabling learned warning rules
Institute of Water and Environment, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Sebastian Lerch
Department of Mathematics and Computer Science, Marburg University, Marburg, Germany
Daniel Klotz
Machine Learning in Earth Science, Interdisciplinary Transformation University Austria, Linz, Austria
Ralf Loritz
Institute of Water and Environment, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
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Hydrol. Earth Syst. Sci., 29, 5005–5029, https://doi.org/10.5194/hess-29-5005-2025, https://doi.org/10.5194/hess-29-5005-2025, 2025
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Three process-based and four data-driven hydrological models are compared using different training data. We found that process-based models perform better with small datasets but stop learning soon, while data-driven models learn longer. The study highlights the importance of memory in data and the impact of different data sampling methods on model performance. The direct comparison of these models is novel and provides a clear understanding of their performance under various data conditions.
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The CAMELS-LUX dataset (Catchment Attributes and MEteorology for Large-sample Studies – LUXembourg) contains hydrologic, meteorologic and thunderstorm formation relevant atmospheric time series of 56 Luxembourgish catchments (2004–2021). These catchments are characterized by a large physiographic variety on a relatively small scale in a homogeneous climate. The dataset can be applied for (regional) hydrological analyses.
Eduardo Acuña Espinoza, Frederik Kratzert, Daniel Klotz, Martin Gauch, Manuel Álvarez Chaves, Ralf Loritz, and Uwe Ehret
Hydrol. Earth Syst. Sci., 29, 1749–1758, https://doi.org/10.5194/hess-29-1749-2025, https://doi.org/10.5194/hess-29-1749-2025, 2025
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Long short-term memory (LSTM) networks have demonstrated state-of-the-art performance for rainfall-runoff hydrological modelling. However, most studies focus on predictions at a daily scale, limiting the benefits of sub-daily (e.g. hourly) predictions in applications like flood forecasting. In this study, we introduce a new architecture, multi-frequency LSTM (MF-LSTM), designed to use inputs of various temporal frequencies to produce sub-daily (e.g. hourly) predictions at a moderate computational cost.
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Hydrol. Earth Syst. Sci., 29, 1277–1294, https://doi.org/10.5194/hess-29-1277-2025, https://doi.org/10.5194/hess-29-1277-2025, 2025
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Weather forecasts 14 days in advance generally have a low skill but not always. We identify reasons thereof depending on the atmospheric flow, shown by Weather Regimes (WRs). If the WRs during the forecasts follow climatological patterns, forecast skill is increased. The forecast of a cold-wave day is better when the European Blocking WR (high pressure around the British Isles) is present a few days before a cold-wave day. These results can be used to assess the reliability of predictions.
Andreas Auer, Martin Gauch, Frederik Kratzert, Grey Nearing, Sepp Hochreiter, and Daniel Klotz
Hydrol. Earth Syst. Sci., 28, 4099–4126, https://doi.org/10.5194/hess-28-4099-2024, https://doi.org/10.5194/hess-28-4099-2024, 2024
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This work examines the impact of temporal and spatial information on the uncertainty estimation of streamflow forecasts. The study emphasizes the importance of data updates and global information for precise uncertainty estimates. We use conformal prediction to show that recent data enhance the estimates, even if only available infrequently. Local data yield reasonable average estimations but fall short for peak-flow events. The use of global data significantly improves these predictions.
Frederik Kratzert, Martin Gauch, Daniel Klotz, and Grey Nearing
Hydrol. Earth Syst. Sci., 28, 4187–4201, https://doi.org/10.5194/hess-28-4187-2024, https://doi.org/10.5194/hess-28-4187-2024, 2024
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Recently, a special type of neural-network architecture became increasingly popular in hydrology literature. However, in most applications, this model was applied as a one-to-one replacement for hydrology models without adapting or rethinking the experimental setup. In this opinion paper, we show how this is almost always a bad decision and how using these kinds of models requires the use of large-sample hydrology data sets.
Daniel Klotz, Martin Gauch, Frederik Kratzert, Grey Nearing, and Jakob Zscheischler
Hydrol. Earth Syst. Sci., 28, 3665–3673, https://doi.org/10.5194/hess-28-3665-2024, https://doi.org/10.5194/hess-28-3665-2024, 2024
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The evaluation of model performance is essential for hydrological modeling. Using performance criteria requires a deep understanding of their properties. We focus on a counterintuitive aspect of the Nash–Sutcliffe efficiency (NSE) and show that if we divide the data into multiple parts, the overall performance can be higher than all the evaluations of the subsets. Although this follows from the definition of the NSE, the resulting behavior can have unintended consequences in practice.
Eduardo Acuña Espinoza, Ralf Loritz, Manuel Álvarez Chaves, Nicole Bäuerle, and Uwe Ehret
Hydrol. Earth Syst. Sci., 28, 2705–2719, https://doi.org/10.5194/hess-28-2705-2024, https://doi.org/10.5194/hess-28-2705-2024, 2024
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Hydrological hybrid models promise to merge the performance of deep learning methods with the interpretability of process-based models. One hybrid approach is the dynamic parameterization of conceptual models using long short-term memory (LSTM) networks. We explored this method to evaluate the effect of the flexibility given by LSTMs on the process-based part.
Jonathan Demaeyer, Jonas Bhend, Sebastian Lerch, Cristina Primo, Bert Van Schaeybroeck, Aitor Atencia, Zied Ben Bouallègue, Jieyu Chen, Markus Dabernig, Gavin Evans, Jana Faganeli Pucer, Ben Hooper, Nina Horat, David Jobst, Janko Merše, Peter Mlakar, Annette Möller, Olivier Mestre, Maxime Taillardat, and Stéphane Vannitsem
Earth Syst. Sci. Data, 15, 2635–2653, https://doi.org/10.5194/essd-15-2635-2023, https://doi.org/10.5194/essd-15-2635-2023, 2023
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A benchmark dataset is proposed to compare different statistical postprocessing methods used in forecasting centers to properly calibrate ensemble weather forecasts. This dataset is based on ensemble forecasts covering a portion of central Europe and includes the corresponding observations. Examples on how to download and use the data are provided, a set of evaluation methods is proposed, and a first benchmark of several methods for the correction of 2 m temperature forecasts is performed.
Grey S. Nearing, Daniel Klotz, Jonathan M. Frame, Martin Gauch, Oren Gilon, Frederik Kratzert, Alden Keefe Sampson, Guy Shalev, and Sella Nevo
Hydrol. Earth Syst. Sci., 26, 5493–5513, https://doi.org/10.5194/hess-26-5493-2022, https://doi.org/10.5194/hess-26-5493-2022, 2022
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When designing flood forecasting models, it is necessary to use all available data to achieve the most accurate predictions possible. This manuscript explores two basic ways of ingesting near-real-time streamflow data into machine learning streamflow models. The point we want to make is that when working in the context of machine learning (instead of traditional hydrology models that are based on
bio-geophysics), it is not necessary to use complex statistical methods for injecting sparse data.
Ralf Loritz, Maoya Bassiouni, Anke Hildebrandt, Sibylle K. Hassler, and Erwin Zehe
Hydrol. Earth Syst. Sci., 26, 4757–4771, https://doi.org/10.5194/hess-26-4757-2022, https://doi.org/10.5194/hess-26-4757-2022, 2022
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In this study, we combine a deep-learning approach that predicts sap flow with a hydrological model to improve soil moisture and transpiration estimates at the catchment scale. Our results highlight that hybrid-model approaches, combining machine learning with physically based models, are a promising way to improve our ability to make hydrological predictions.
Riccardo Silini, Sebastian Lerch, Nikolaos Mastrantonas, Holger Kantz, Marcelo Barreiro, and Cristina Masoller
Earth Syst. Dynam., 13, 1157–1165, https://doi.org/10.5194/esd-13-1157-2022, https://doi.org/10.5194/esd-13-1157-2022, 2022
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The Madden–Julian Oscillation (MJO) has important socioeconomic impacts due to its influence on both tropical and extratropical weather extremes. In this study, we use machine learning (ML) to correct the predictions of the weather model holding the best performance, developed by the European Centre for Medium-Range Weather Forecasts (ECMWF). We show that the ML post-processing leads to an improved prediction of the MJO geographical location and intensity.
Juliane Mai, Hongren Shen, Bryan A. Tolson, Étienne Gaborit, Richard Arsenault, James R. Craig, Vincent Fortin, Lauren M. Fry, Martin Gauch, Daniel Klotz, Frederik Kratzert, Nicole O'Brien, Daniel G. Princz, Sinan Rasiya Koya, Tirthankar Roy, Frank Seglenieks, Narayan K. Shrestha, André G. T. Temgoua, Vincent Vionnet, and Jonathan W. Waddell
Hydrol. Earth Syst. Sci., 26, 3537–3572, https://doi.org/10.5194/hess-26-3537-2022, https://doi.org/10.5194/hess-26-3537-2022, 2022
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Model intercomparison studies are carried out to test various models and compare the quality of their outputs over the same domain. In this study, 13 diverse model setups using the same input data are evaluated over the Great Lakes region. Various model outputs – such as streamflow, evaporation, soil moisture, and amount of snow on the ground – are compared using standardized methods and metrics. The basin-wise model outputs and observations are made available through an interactive website.
Jonathan M. Frame, Frederik Kratzert, Daniel Klotz, Martin Gauch, Guy Shalev, Oren Gilon, Logan M. Qualls, Hoshin V. Gupta, and Grey S. Nearing
Hydrol. Earth Syst. Sci., 26, 3377–3392, https://doi.org/10.5194/hess-26-3377-2022, https://doi.org/10.5194/hess-26-3377-2022, 2022
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The most accurate rainfall–runoff predictions are currently based on deep learning. There is a concern among hydrologists that deep learning models may not be reliable in extrapolation or for predicting extreme events. This study tests that hypothesis. The deep learning models remained relatively accurate in predicting extreme events compared with traditional models, even when extreme events were not included in the training set.
Thomas Lees, Steven Reece, Frederik Kratzert, Daniel Klotz, Martin Gauch, Jens De Bruijn, Reetik Kumar Sahu, Peter Greve, Louise Slater, and Simon J. Dadson
Hydrol. Earth Syst. Sci., 26, 3079–3101, https://doi.org/10.5194/hess-26-3079-2022, https://doi.org/10.5194/hess-26-3079-2022, 2022
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Despite the accuracy of deep learning rainfall-runoff models, we are currently uncertain of what these models have learned. In this study we explore the internals of one deep learning architecture and demonstrate that the model learns about intermediate hydrological stores of soil moisture and snow water, despite never having seen data about these processes during training. Therefore, we find evidence that the deep learning approach learns a physically realistic mapping from inputs to outputs.
Daniel Klotz, Frederik Kratzert, Martin Gauch, Alden Keefe Sampson, Johannes Brandstetter, Günter Klambauer, Sepp Hochreiter, and Grey Nearing
Hydrol. Earth Syst. Sci., 26, 1673–1693, https://doi.org/10.5194/hess-26-1673-2022, https://doi.org/10.5194/hess-26-1673-2022, 2022
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This contribution evaluates distributional runoff predictions from deep-learning-based approaches. We propose a benchmarking setup and establish four strong baselines. The results show that accurate, precise, and reliable uncertainty estimation can be achieved with deep learning.
Alexander Sternagel, Ralf Loritz, Brian Berkowitz, and Erwin Zehe
Hydrol. Earth Syst. Sci., 26, 1615–1629, https://doi.org/10.5194/hess-26-1615-2022, https://doi.org/10.5194/hess-26-1615-2022, 2022
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We present a (physically based) Lagrangian approach to simulate diffusive mixing processes on the pore scale beyond perfectly mixed conditions. Results show the feasibility of the approach for reproducing measured mixing times and concentrations of isotopes over pore sizes and that typical shapes of breakthrough curves (normally associated with non-uniform transport in heterogeneous soils) may also occur as a result of imperfect subscale mixing in a macroscopically homogeneous soil matrix.
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Short summary
Probabilistic runoff predictions capture the likelihood of rare, high-stakes events that deterministic models – which predict only the conditional expectation – tend to underestimate. This added information can improve flood warning communication by learning reward-based rules for selecting predictive quantiles suited to specific hydrological and societal contexts.
Probabilistic runoff predictions capture the likelihood of rare, high-stakes events that...
