Articles | Volume 29, issue 21
https://doi.org/10.5194/hess-29-5871-2025
© Author(s) 2025. 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-29-5871-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
03 Nov 2025
Research article |
| 03 Nov 2025
| 03 Nov 2025
Unveiling the limits of deep learning models in hydrological extrapolation tasks
Institute of Water and Environment, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Daniel Klotz
Interdisciplinary Transformation University Austria, Linz, Austria
Google Research, Vienna, Austria
Eduardo Acuña Espinoza
Institute of Water and Environment, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Andras Bardossy
Institut für Wasser- und Umweltsystemmodellierung, Universität Stuttgart, Stuttgart, Germany
Ralf Loritz
Institute of Water and Environment, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
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Sanika Baste, Sebastian Lerch, Daniel Klotz, and Ralf Loritz
EGUsphere, https://doi.org/10.5194/egusphere-2026-469, https://doi.org/10.5194/egusphere-2026-469, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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Probabilistic runoff predictions are capable of providing information about the possibility of occurrence of rare and high-stake events, which are largely underestimated by deterministic predictions, as they predict an expectation of the conditional runoff predictions. This additional information can be leveraged to aid flood warning communication by learning reward-based rules for selecting quantiles from the predictive distributions based on hydrological and societal contexts.
Sanika Baste, Sebastian Lerch, Daniel Klotz, and Ralf Loritz
EGUsphere, https://doi.org/10.5194/egusphere-2026-469, https://doi.org/10.5194/egusphere-2026-469, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
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Probabilistic runoff predictions are capable of providing information about the possibility of occurrence of rare and high-stake events, which are largely underestimated by deterministic predictions, as they predict an expectation of the conditional runoff predictions. This additional information can be leveraged to aid flood warning communication by learning reward-based rules for selecting quantiles from the predictive distributions based on hydrological and societal contexts.
Manuel Álvarez Chaves, Eduardo Acuña Espinoza, Uwe Ehret, and Anneli Guthke
Hydrol. Earth Syst. Sci., 30, 629–658, https://doi.org/10.5194/hess-30-629-2026, https://doi.org/10.5194/hess-30-629-2026, 2026
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This study evaluates hybrid hydrological models combining physics-based and data-driven components, using Information Theory to measure their relative contributions. When testing conceptual models with Long Short-Term Memory (LSTM) networks that adjust parameters over time, we found performance primarily comes from the data-driven component, with physics constraints adding minimal value. We propose a quantitative tool to analyse this behaviour and suggest a workflow for diagnosing hybrid models.
Martin Gauch, Frederik Kratzert, Daniel Klotz, Grey Nearing, Deborah Cohen, and Oren Gilon
Hydrol. Earth Syst. Sci., 29, 6221–6235, https://doi.org/10.5194/hess-29-6221-2025, https://doi.org/10.5194/hess-29-6221-2025, 2025
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Missing input data are one of the most common challenges when building deep learning hydrological models. We present and analyze different methods that can produce predictions when certain inputs are missing during training or inference. Our proposed strategies provide high accuracy while allowing for more flexible data handling and being robust to outages in operational scenarios.
Ashish Manoj J, Ralf Loritz, Hoshin Gupta, and Erwin Zehe
Hydrol. Earth Syst. Sci., 29, 6115–6135, https://doi.org/10.5194/hess-29-6115-2025, https://doi.org/10.5194/hess-29-6115-2025, 2025
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Traditional hydrological models typically operate in a forward mode, simulating streamflow and other catchment fluxes based on precipitation input. In this study, we explored the possibility of reversing this process, inferring precipitation from streamflow data, to improve flood event modelling. We then used the generated precipitation series to run hydrological models, resulting in more accurate estimates of streamflow and soil moisture.
Maria Staudinger, Anna Herzog, Ralf Loritz, Tobias Houska, Sandra Pool, Diana Spieler, Paul D. Wagner, Juliane Mai, Jens Kiesel, Stephan Thober, Björn Guse, and Uwe Ehret
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.
Judith Nijzink, Ralf Loritz, Laurent Gourdol, Davide Zoccatelli, Jean François Iffly, and Laurent Pfister
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-482, https://doi.org/10.5194/essd-2024-482, 2025
Revised manuscript under review for ESSD
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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.
Abbas El Hachem, Jochen Seidel, and András Bárdossy
Hydrol. Earth Syst. Sci., 29, 1335–1357, https://doi.org/10.5194/hess-29-1335-2025, https://doi.org/10.5194/hess-29-1335-2025, 2025
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The influence of climate change on areal precipitation extremes is examined. After an upscaling of reference observations, the climate model data are corrected, and a downscaling to a finer spatial scale is done. For different temporal durations and spatial scales, areal precipitation extremes are derived. The final result indicates an increase in the expected rainfall depth compared to reference values. However, the increase varied with the duration and area size.
Eduardo Acuña Espinoza, Ralf Loritz, Frederik Kratzert, Daniel Klotz, Martin Gauch, Manuel Álvarez Chaves, and Uwe Ehret
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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Data-driven techniques have shown the potential to outperform process-based models in rainfall–runoff simulations. Hybrid models, combining both approaches, aim to enhance accuracy and maintain interpretability. Expanding the set of test cases to evaluate hybrid models under different conditions, we test their generalization capabilities for extreme hydrological events.
Daniel Klotz, Peter Miersch, Thiago V. M. do Nascimento, Fabrizio Fenicia, Martin Gauch, and Jakob Zscheischler
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-450, https://doi.org/10.5194/essd-2024-450, 2025
Revised manuscript under review for ESSD
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Data availability is central to hydrological science. It is the basis for advancing our understanding of hydrological processes, building prediction models, and anticipatory water management. We present a data-driven daily runoff reconstruction product for natural streamflow. We name it EARLS: European aggregated reconstruction for large-sample studies. The reconstructions represent daily simulations of natural streamflow across Europe and cover the period from 1953 to 2020.
Ralf Loritz, Alexander Dolich, Eduardo Acuña Espinoza, Pia Ebeling, Björn Guse, Jonas Götte, Sibylle K. Hassler, Corina Hauffe, Ingo Heidbüchel, Jens Kiesel, Mirko Mälicke, Hannes Müller-Thomy, Michael Stölzle, and Larisa Tarasova
Earth Syst. Sci. Data, 16, 5625–5642, https://doi.org/10.5194/essd-16-5625-2024, https://doi.org/10.5194/essd-16-5625-2024, 2024
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The CAMELS-DE dataset features data from 1582 streamflow gauges across Germany, with records spanning from 1951 to 2020. This comprehensive dataset, which includes time series of up to 70 years (median 46 years), enables advanced research on water flow and environmental trends and supports the development of hydrological models.
Abbas El Hachem, Jochen Seidel, Tess O'Hara, Roberto Villalobos Herrera, Aart Overeem, Remko Uijlenhoet, András Bárdossy, and Lotte de Vos
Hydrol. Earth Syst. Sci., 28, 4715–4731, https://doi.org/10.5194/hess-28-4715-2024, https://doi.org/10.5194/hess-28-4715-2024, 2024
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Amy C. Green, Chris Kilsby, and András Bárdossy
Hydrol. Earth Syst. Sci., 28, 4539–4558, https://doi.org/10.5194/hess-28-4539-2024, https://doi.org/10.5194/hess-28-4539-2024, 2024
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Weather radar is a crucial tool in rainfall estimation, but radar rainfall estimates are subject to many error sources, with the true rainfall field unknown. A flexible model for simulating errors relating to the radar rainfall estimation process is implemented, inverting standard processing methods. This flexible and efficient model performs well in generating realistic weather radar images visually for a large range of event types.
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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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.
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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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.
András Bárdossy and Faizan Anwar
Hydrol. Earth Syst. Sci., 27, 1987–2000, https://doi.org/10.5194/hess-27-1987-2023, https://doi.org/10.5194/hess-27-1987-2023, 2023
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This study demonstrates the fact that the large river flows forecasted by the models show an underestimation that is inversely related to the number of locations where precipitation is recorded, which is independent of the model. The higher the number of points where the amount of precipitation is recorded, the better the estimate of the river flows.
Abbas El Hachem, Jochen Seidel, Florian Imbery, Thomas Junghänel, and András Bárdossy
Hydrol. Earth Syst. Sci., 26, 6137–6146, https://doi.org/10.5194/hess-26-6137-2022, https://doi.org/10.5194/hess-26-6137-2022, 2022
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Through this work, a methodology to identify outliers in intense precipitation data was presented. The results show the presence of several suspicious observations that strongly differ from their surroundings. Many identified outliers did not have unusually high values but disagreed with their neighboring values at the corresponding time steps. Weather radar and discharge data were used to distinguish between single events and false observations.
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.
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.
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.
Dhiraj Raj Gyawali and András Bárdossy
Hydrol. Earth Syst. Sci., 26, 3055–3077, https://doi.org/10.5194/hess-26-3055-2022, https://doi.org/10.5194/hess-26-3055-2022, 2022
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In this study, different extensions of the degree-day model were calibrated on snow-cover distribution against freely available satellite snow-cover images. The calibrated models simulated the distribution very well in Baden-Württemberg (Germany) and Switzerland. In addition to reliable identification of snow cover, the melt outputs from the calibrated models were able to improve the flow simulations in different catchments in the study region.
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.
Erwin Zehe, Ralf Loritz, Yaniv Edery, and Brian Berkowitz
Hydrol. Earth Syst. Sci., 25, 5337–5353, https://doi.org/10.5194/hess-25-5337-2021, https://doi.org/10.5194/hess-25-5337-2021, 2021
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This study uses the concepts of entropy and work to quantify and explain the emergence of preferential flow and transport in heterogeneous saturated porous media. We found that the downstream concentration of solutes in preferential pathways implies a downstream declining entropy in the transverse distribution of solute transport pathways. Preferential flow patterns with lower entropies emerged within media of higher heterogeneity – a stronger self-organization despite a higher randomness.
Jieru Yan, Fei Li, András Bárdossy, and Tao Tao
Hydrol. Earth Syst. Sci., 25, 3819–3835, https://doi.org/10.5194/hess-25-3819-2021, https://doi.org/10.5194/hess-25-3819-2021, 2021
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Accurate spatial precipitation estimates are important in various fields. An approach to simulate spatial rainfall fields conditioned on radar and rain gauge data is proposed. Unlike the commonly used Kriging methods, which provide a Kriged mean field, the output of the proposed approach is an ensemble of estimates that represents the estimation uncertainty. The approach is robust to nonlinear error in radar estimates and is shown to have some advantages, especially when estimating the extremes.
Frederik Kratzert, Daniel Klotz, Sepp Hochreiter, and Grey S. Nearing
Hydrol. Earth Syst. Sci., 25, 2685–2703, https://doi.org/10.5194/hess-25-2685-2021, https://doi.org/10.5194/hess-25-2685-2021, 2021
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We investigate how deep learning models use different meteorological data sets in the task of (regional) rainfall–runoff modeling. We show that performance can be significantly improved when using different data products as input and further show how the model learns to combine those meteorological input differently across time and space. The results are carefully benchmarked against classical approaches, showing the supremacy of the presented approach.
Martin Gauch, Frederik Kratzert, Daniel Klotz, Grey Nearing, Jimmy Lin, and Sepp Hochreiter
Hydrol. Earth Syst. Sci., 25, 2045–2062, https://doi.org/10.5194/hess-25-2045-2021, https://doi.org/10.5194/hess-25-2045-2021, 2021
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We present multi-timescale Short-Term Memory (MTS-LSTM), a machine learning approach that predicts discharge at multiple timescales within one model. MTS-LSTM is significantly more accurate than the US National Water Model and computationally more efficient than an individual LSTM model per timescale. Further, MTS-LSTM can process different input variables at different timescales, which is important as the lead time of meteorological forecasts often depends on their temporal resolution.
Alexander Sternagel, Ralf Loritz, Julian Klaus, Brian Berkowitz, and Erwin Zehe
Hydrol. Earth Syst. Sci., 25, 1483–1508, https://doi.org/10.5194/hess-25-1483-2021, https://doi.org/10.5194/hess-25-1483-2021, 2021
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The key innovation of the study is a method to simulate reactive solute transport in the vadose zone within a Lagrangian framework. We extend the LAST-Model with a method to account for non-linear sorption and first-order degradation processes during unsaturated transport of reactive substances in the matrix and macropores. Model evaluations using bromide and pesticide data from irrigation experiments under different flow conditions on various timescales show the feasibility of the method.
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Short summary
This study evaluates the extrapolation performance of long short-term memory (LSTM) networks in rainfall–runoff modeling, specifically under extreme precipitation conditions. The findings reveal that the LSTM cannot predict discharge values beyond a theoretical limit and that this limit is well below the extremity of its training data. This behavior results from the LSTM's gating structures rather than saturation of the cell states alone.
This study evaluates the extrapolation performance of long short-term memory (LSTM) networks in...
