Articles | Volume 29, issue 21
https://doi.org/10.5194/hess-29-6115-2025
© 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-29-6115-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
11 Nov 2025
Research article |
| 11 Nov 2025
| 11 Nov 2025
Can discharge be used to inversely correct precipitation?
Chair of Hydrology, Institute of Water and Environment (IWU), Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
Ralf Loritz
Chair of Hydrology, Institute of Water and Environment (IWU), Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
Hoshin Gupta
Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson 85721, United States
Erwin Zehe
Chair of Hydrology, Institute of Water and Environment (IWU), Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
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Sanika Baste, Sebastian Lerch, Daniel Klotz, and Ralf Loritz
Hydrol. Earth Syst. Sci., 30, 6339–6358, https://doi.org/10.5194/hess-30-6339-2026, https://doi.org/10.5194/hess-30-6339-2026, 2026
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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.
Mohammad Farmani, Hoshin V. Gupta, Ali Behrangi, Muhammad Jawad, Sadaf Moghisi, and Guo-Yue Niu
EGUsphere, https://doi.org/10.48550/arXiv.2603.25093, https://doi.org/10.48550/arXiv.2603.25093, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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Machine learning can predict streamflow accurately but often lacks physical interpretability. We develop a mass-conserving hybrid AI model that progressively adds hydrological processes, including soil storage, infiltration, ponding, and deep drainage. Tests across 15 U.S. basins show that added process structure can improve streamflow prediction, with drainage benefiting arid and snow-dominated basins but reducing skill in humid regions.
Pau Wiersma, Ralf Loritz, Sanika Baste, Katharina Hafner, and Grégoire Mariéthoz
EGUsphere, https://doi.org/10.5194/egusphere-2026-5373, https://doi.org/10.5194/egusphere-2026-5373, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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Despite their long record length and information on catchment-wide snowmelt, streamflow observations have not previously been used to constrain snow reanalyses. We show that a bidirectional LSTM can learn the snowmelt-streamflow relationship and subsequently reconstruct snowmelt from streamflow in unseen years and catchments. Combining streamflow and meteorology as inputs yields the best performance, while a streamflow-only model already widely outperforms the ERA5-Land snowmelt benchmark.
Doğa Yahşi, Samuel Schroers, Ulrike Scherer, Núria Martínez-Carreras, and Erwin Zehe
EGUsphere, https://doi.org/10.5194/egusphere-2026-4957, https://doi.org/10.5194/egusphere-2026-4957, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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Heavy storms and soil erosion threaten ecosystems and water quality. To understand what drives these events, we analyzed and simulated rainfall-runoff experiments and their energy dynamics. We found that initial soil wetness and ground texture control runoff more than slope or rain intensity. We showed that ground texture limits flow speed and rougher surfaces channel water into pathways that efficiently transport water and soil, which helps us improve land management and soil conservation.
Eduardo Jose Acuna Espinoza, Manuel Álvarez Chaves, Frederik Kratzert, Daniel Klotz, Martin Gauch, Robert Lang, Dominik Elfgang, Alexander Dolich, Ralf Loritz, and Uwe Ehret
EGUsphere, https://doi.org/10.5194/egusphere-2026-4885, https://doi.org/10.5194/egusphere-2026-4885, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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We present the Multi-Frequency Masked-Forecasting LSTM (MF2LSTM), a pipeline unifying multi-frequency modeling, missing-data handling, and real-time data assimilation for hourly streamflow forecasting. Forced with ICON-D2 weather data, MF2LSTM yields higher performance than LARSIM, the operational model used in Baden-Württemberg, Germany. Using a single-cell baseline, this work proves that simple deep learning models can deliver high-level operational performance without extra complexity.
Mohammad A. Farmani, Andrew Bennet, Sadaf Moghisi, Hoshin Gupta, Muhammad Jawad, Ali Behrangi, Ahmad A. Tavakoly, and Guo-Yue Niu
EGUsphere, https://doi.org/10.5194/egusphere-2026-4157, https://doi.org/10.5194/egusphere-2026-4157, 2026
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This study presents RiverGraphNet, an artificial intelligence framework for predicting how runoff moves through connected river networks. Applied to Arizona’s Salt–Verde watershed, the method improved daily streamflow prediction relative to a standard physics-based routing model, especially for event timing and flow distributions. The results show that combining river-network structure with artificial intelligence can support better flood, reservoir, and water-resource prediction.
Jean-Paul Brede, Pia Ebeling, Jens Kiesel, and Ralf Loritz
EGUsphere, https://doi.org/10.5194/egusphere-2026-3604, https://doi.org/10.5194/egusphere-2026-3604, 2026
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Predicting river water quality is challenging because measurements are sparse and irregular. We trained artificial-intelligence models on 408 German rivers to forecast river flow and six water-quality variables together. A more flexible training approach lets one model predict different variables from whatever data are available, pointing toward unified environmental models.
Alexander Dolich, Eduardo Acuña Espinoza, Uwe Ehret, Michael Kraft, Jan Bondy, Johannes Meuer, and Ralf Loritz
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2026-289, https://doi.org/10.5194/essd-2026-289, 2026
Preprint under review for ESSD
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CAMELS-DE-1h provides a unified collection of hourly river flow and weather time series for 1,611 German catchments from 2001 to 2024, alongside operational weather forecasts. Benchmark simulation results serve as a baseline for future model development. This dataset allows researchers to investigate small and medium-sized catchments that react quickly to heavy rainfall and to test models under operational conditions, improving future flood forecasting and early warning systems.
Benedikt Heudorfer, Hoshin Gupta, Alexander Dolich, and Ralf Loritz
EGUsphere, https://doi.org/10.5194/egusphere-2026-1965, https://doi.org/10.5194/egusphere-2026-1965, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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For most rivers, water level is not measured, making flood prediction difficult. But it's still possible with certain models. We want to improve these models and test if better models or better data help when predicting floods with these models in the United States. Results show that better data (measured by satellites) improves predictions more than better model designs. Actually, simple models often worked best. And we show that we need better measurement of landscape information.
Erwin Zehe, Laurent Pfister, Dan Elhanati, and Brian Berkowitz
Hydrol. Earth Syst. Sci., 30, 2093–2106, https://doi.org/10.5194/hess-30-2093-2026, https://doi.org/10.5194/hess-30-2093-2026, 2026
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Travel or transit time distributions play a key role in contaminant leaching from the partially saturated zone into groundwater. Here we show that average travel times are of different water isotopes may differ by 5 %–10 %. These difference arise in case of imperfect mixing due to trapping of isotope molecules in bottle necks of very small hydraulic conductivity. Molecules with smaller diffusion coefficient stay there for a longer time.
Svenja Hoffmeister, Sibylle Kathrin Hassler, Rebekka Maier, Friederike Lang, Betserai Isaac Nyoka, and Erwin Zehe
Biogeosciences, 23, 1545–1567, https://doi.org/10.5194/bg-23-1545-2026, https://doi.org/10.5194/bg-23-1545-2026, 2026
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Combining trees and crops in agroforestry systems can potentially be a sustainable option for agriculture facing climate change impacts. We used methods from soil science and hydrology to assess the effect of adding gliricidia trees to maize fields, on carbon content, soil properties and water availability. Our results show a clear increase in carbon contents and effects on physical soil characteristics and water uptake and retention as a consequence of the agroforestry treatment.
Dan Elhanati, Erwin Zehe, Ishai Dror, and Brian Berkowitz
Hydrol. Earth Syst. Sci., 29, 6577–6587, https://doi.org/10.5194/hess-29-6577-2025, https://doi.org/10.5194/hess-29-6577-2025, 2025
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Measurements of water isotopes are often used to estimate water transit time distributions and aquifer storage thickness in catchments. However, laboratory-scale measurements show that water isotopes exhibit transport behavior identical to that of inert chemical tracers rather than of pure water. The measured mean tracer and apparent mean water velocities are not necessarily equal; recognition of this inequality is critical when estimating catchment properties such as aquifer storage thickness.
Sanika Baste, Daniel Klotz, Eduardo Acuña Espinoza, Andras Bardossy, and Ralf Loritz
Hydrol. Earth Syst. Sci., 29, 5871–5891, https://doi.org/10.5194/hess-29-5871-2025, https://doi.org/10.5194/hess-29-5871-2025, 2025
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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.
Evgeny Shavelzon, Erwin Zehe, and Yaniv Edery
Hydrol. Earth Syst. Sci., 29, 5625–5644, https://doi.org/10.5194/hess-29-5625-2025, https://doi.org/10.5194/hess-29-5625-2025, 2025
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We analyze how chemical reactions and fluid movement in porous materials interact, focusing on how water channels form in underground environments. Using a thermodynamic approach, we track energy dissipation due to fluid friction and chemical reaction, and correlate it with the intensity of the emerged water channels to understand this process. Over time, water channels become more defined, reducing energy dissipation due to mixing, reaction and fluid friction.
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.
Karl Nicolaus van Zweel, Laurent Gourdol, Jean François Iffly, Loïc Léonard, François Barnich, Laurent Pfister, Erwin Zehe, and Christophe Hissler
Earth Syst. Sci. Data, 17, 2217–2229, https://doi.org/10.5194/essd-17-2217-2025, https://doi.org/10.5194/essd-17-2217-2025, 2025
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Our study monitored groundwater in a Luxembourg forest over a year to understand water and chemical changes. We found seasonal variations in water chemistry, influenced by rainfall and soil interactions. These data help predict environmental responses and manage water resources better. By measuring key parameters like pH and dissolved oxygen, our research provides valuable insights into groundwater behaviour and serves as a resource for future environmental studies.
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.
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.
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.
Svenja Hoffmeister, Rafael Bohn Reckziegel, Ben du Toit, Sibylle K. Hassler, Florian Kestel, Rebekka Maier, Jonathan P. Sheppard, and Erwin Zehe
Hydrol. Earth Syst. Sci., 28, 3963–3982, https://doi.org/10.5194/hess-28-3963-2024, https://doi.org/10.5194/hess-28-3963-2024, 2024
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We studied a tree–crop ecosystem consisting of a blackberry field and an alder windbreak. In the water-scarce region, irrigation provides sufficient water for plant growth. The windbreak lowers the irrigation amount by reducing wind speed and therefore water transport into the atmosphere. These ecosystems could provide sustainable use of water-scarce landscapes, and we studied the complex interactions by observing several aspects (e.g. soil, nutrients, carbon assimilation, water).
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.
Luis Andres De la Fuente, Mohammad Reza Ehsani, Hoshin Vijai Gupta, and Laura Elizabeth Condon
Hydrol. Earth Syst. Sci., 28, 945–971, https://doi.org/10.5194/hess-28-945-2024, https://doi.org/10.5194/hess-28-945-2024, 2024
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Long short-term memory (LSTM) is a widely used machine-learning model in hydrology, but it is difficult to extract knowledge from it. We propose HydroLSTM, which represents processes like a hydrological reservoir. Models based on HydroLSTM perform similarly to LSTM while requiring fewer cell states. The learned parameters are informative about the dominant hydrology of a catchment. Our results show how parsimony and hydrological knowledge extraction can be achieved by using the new structure.
Samuel Schroers, Ulrike Scherer, and Erwin Zehe
Hydrol. Earth Syst. Sci., 27, 2535–2557, https://doi.org/10.5194/hess-27-2535-2023, https://doi.org/10.5194/hess-27-2535-2023, 2023
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The hydrological cycle shapes our landscape. With an accelerating change of the world's climate and hydrological dynamics, concepts of evolution of natural systems become more important. In this study, we elaborated a thermodynamic framework for runoff and sediment transport and show from model results as well as from measurements during extreme events that the developed concept is useful for understanding the evolution of the system's mass, energy, and entropy fluxes.
Luis Andres De la Fuente, Mohammad Reza Ehsani, Hoshin Vijai Gupta, and Laura E. Condon
EGUsphere, https://doi.org/10.5194/egusphere-2023-666, https://doi.org/10.5194/egusphere-2023-666, 2023
Preprint archived
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Long Short-Term Memory (LSTM) is a widely-used machine learning (ML) model in hydrology. However, it is difficult to extract knowledge from it. We propose HydroLSTM which represents processes analogous to a hydrological reservoir. Models using HydroLSTM perform similarly to LSTM but require fewer cell states. The learned parameters are informative about the dominant hydroclimatic characteristics of a catchment. Our results demonstrate how hydrological knowledge is encoded in the new structure.
Judith Meyer, Malte Neuper, Luca Mathias, Erwin Zehe, and Laurent Pfister
Hydrol. Earth Syst. Sci., 26, 6163–6183, https://doi.org/10.5194/hess-26-6163-2022, https://doi.org/10.5194/hess-26-6163-2022, 2022
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We identified and analysed the major atmospheric components of rain-intense thunderstorms that can eventually lead to flash floods: high atmospheric moisture, sufficient latent instability, and weak thunderstorm cell motion. Between 1981 and 2020, atmospheric conditions became likelier to support strong thunderstorms. However, the occurrence of extreme rainfall events as well as their rainfall intensity remained mostly unchanged.
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.
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.
Samuel Schroers, Olivier Eiff, Axel Kleidon, Ulrike Scherer, Jan Wienhöfer, and Erwin Zehe
Hydrol. Earth Syst. Sci., 26, 3125–3150, https://doi.org/10.5194/hess-26-3125-2022, https://doi.org/10.5194/hess-26-3125-2022, 2022
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In hydrology the formation of landform patterns is of special interest as changing forcings of the natural systems, such as climate or land use, will change these structures. In our study we developed a thermodynamic framework for surface runoff on hillslopes and highlight the differences of energy conversion patterns on two related spatial and temporal scales. The results indicate that surface runoff on hillslopes approaches a maximum power state.
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
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.
Traditional hydrological models typically operate in a forward mode, simulating streamflow and...
