Articles | Volume 29, issue 6
https://doi.org/10.5194/hess-29-1749-2025
© 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-29-1749-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical note
| 
26 Mar 2025
Technical note |
| 26 Mar 2025
| 26 Mar 2025
Technical note: An approach for handling multiple temporal frequencies with different input dimensions using a single LSTM cell
Eduardo Acuña Espinoza
CORRESPONDING AUTHOR
Institute of Water and Environment, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Frederik Kratzert
Google Research, Vienna, Austria
Daniel Klotz
Google Research, Vienna, Austria
Machine Learning in Earth Science, Interdisciplinary Transformation University Austria, Linz, Austria
Martin Gauch
Google Research, Zurich, Switzerland
Manuel Álvarez Chaves
Stuttgart Center for Simulation Science, Statistical Model-Data Integration, University of Stuttgart, Stuttgart, Germany
Ralf Loritz
Institute of Water and Environment, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Uwe Ehret
Institute of Water and Environment, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
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Manuel Álvarez Chaves, Eduardo Acuña Espinoza, Uwe Ehret, and Anneli Guthke
EGUsphere, https://doi.org/10.5194/egusphere-2025-1699, https://doi.org/10.5194/egusphere-2025-1699, 2025
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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This study evaluates hybrid hydrological models that combine physics-based and data-driven components, using Information Theory to measure their relative contributions. When testing conceptual models with LSTMs 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.
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.
Sanika Baste, Daniel Klotz, Eduardo Acuña Espinoza, Andras Bardossy, and Ralf Loritz
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This study evaluates the extrapolation performance of Long Short-Term Memory (LSTM) networks in rainfall-runoff modeling, specifically under extreme conditions. The findings reveal that the LSTM cannot predict discharge values beyond a theoretical limit, which is well below the extremity of its training data. This behavior results from the LSTM's gating structures rather than saturation of cell states alone.
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
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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.
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.
Manuel Álvarez Chaves, Eduardo Acuña Espinoza, Uwe Ehret, and Anneli Guthke
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This study evaluates hybrid hydrological models that combine physics-based and data-driven components, using Information Theory to measure their relative contributions. When testing conceptual models with LSTMs 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
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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.
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
EGUsphere, https://doi.org/10.5194/egusphere-2025-1076, https://doi.org/10.5194/egusphere-2025-1076, 2025
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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Four process-based and four data-driven hydrological models are compared using different training data. We found process-based models to perform better with small data sets 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.
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.
Sanika Baste, Daniel Klotz, Eduardo Acuña Espinoza, Andras Bardossy, and Ralf Loritz
EGUsphere, https://doi.org/10.5194/egusphere-2025-425, https://doi.org/10.5194/egusphere-2025-425, 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 conditions. The findings reveal that the LSTM cannot predict discharge values beyond a theoretical limit, which is well below the extremity of its training data. This behavior results from the LSTM's gating structures rather than saturation of cell states alone.
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
Preprint 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.
Ashish Manoj J, Ralf Loritz, Hoshin Gupta, and Erwin Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-375, https://doi.org/10.5194/hess-2024-375, 2024
Revised manuscript under review for HESS
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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.
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
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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.
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Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-427, https://doi.org/10.5194/essd-2024-427, 2024
Revised manuscript under review for ESSD
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Large-sample datasets are essential in hydrological science to support modelling studies and advance process understanding. Caravan is a community initiative to create a large-sample hydrology dataset of meteorological forcing data, catchment attributes, and discharge data for catchments around the world. This dataset is a subset of hydrological discharge data and station-based watersheds from the Global Runoff Data Centre (GRDC), which are covered by an open data policy.
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.
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.
Andrea L. Campoverde, Uwe Ehret, Patrick Ludwig, and Joaquim G. Pinto
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-134, https://doi.org/10.5194/gmd-2024-134, 2024
Revised manuscript not accepted
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We looked at how well the model WRF-Hydro performed during the 2018 drought event in the River Rhine basin, even though it is typically used for floods. We used the meteorological ERA5 reanalysis dataset to simulate River Rhine’s streamflow and adjusted the model using parameters and actual discharge measurements. We focused on Lake Constance, a key part of the basin, but found issues with the model’s lake outflow simulation. By removing the lake module, we obtained more accurate results.
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.
Sarah Quỳnh Giang Ho and Uwe Ehret
EGUsphere, https://doi.org/10.5194/egusphere-2024-2167, https://doi.org/10.5194/egusphere-2024-2167, 2024
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In this paper, we use models to demonstrate that even small flood reservoirs – which capture water to avoid floods downstream – can be repurposed to release water in drier conditions without affecting their ability to protect against floods. By capturing water and releasing once water levels are low, we show that reservoirs can greatly increase water available in drought. Having more water coming in, however, is not necessarily better for drought protection.
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.
Uwe Ehret and Pankaj Dey
Hydrol. Earth Syst. Sci., 27, 2591–2605, https://doi.org/10.5194/hess-27-2591-2023, https://doi.org/10.5194/hess-27-2591-2023, 2023
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We propose the
c-u-curvemethod to characterize dynamical (time-variable) systems of all kinds.
Uis for uncertainty and expresses how well a system can be predicted in a given period of time.
Cis for complexity and expresses how predictability differs between different periods, i.e. how well predictability itself can be predicted. The method helps to better classify and compare dynamical systems across a wide range of disciplines, thus facilitating scientific collaboration.
Patrick Ludwig, Florian Ehmele, Mário J. Franca, Susanna Mohr, Alberto Caldas-Alvarez, James E. Daniell, Uwe Ehret, Hendrik Feldmann, Marie Hundhausen, Peter Knippertz, Katharina Küpfer, Michael Kunz, Bernhard Mühr, Joaquim G. Pinto, Julian Quinting, Andreas M. Schäfer, Frank Seidel, and Christina Wisotzky
Nat. Hazards Earth Syst. Sci., 23, 1287–1311, https://doi.org/10.5194/nhess-23-1287-2023, https://doi.org/10.5194/nhess-23-1287-2023, 2023
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Heavy precipitation in July 2021 led to widespread floods in western Germany and neighboring countries. The event was among the five heaviest precipitation events of the past 70 years in Germany, and the river discharges exceeded by far the statistical 100-year return values. Simulations of the event under future climate conditions revealed a strong and non-linear effect on flood peaks: for +2 K global warming, an 18 % increase in rainfall led to a 39 % increase of the flood peak in the Ahr river.
Susanna Mohr, Uwe Ehret, Michael Kunz, Patrick Ludwig, Alberto Caldas-Alvarez, James E. Daniell, Florian Ehmele, Hendrik Feldmann, Mário J. Franca, Christian Gattke, Marie Hundhausen, Peter Knippertz, Katharina Küpfer, Bernhard Mühr, Joaquim G. Pinto, Julian Quinting, Andreas M. Schäfer, Marc Scheibel, Frank Seidel, and Christina Wisotzky
Nat. Hazards Earth Syst. Sci., 23, 525–551, https://doi.org/10.5194/nhess-23-525-2023, https://doi.org/10.5194/nhess-23-525-2023, 2023
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The flood event in July 2021 was one of the most severe disasters in Europe in the last half century. The objective of this two-part study is a multi-disciplinary assessment that examines the complex process interactions in different compartments, from meteorology to hydrological conditions to hydro-morphological processes to impacts on assets and environment. In addition, we address the question of what measures are possible to generate added value to early response management.
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.
Sella Nevo, Efrat Morin, Adi Gerzi Rosenthal, Asher Metzger, Chen Barshai, Dana Weitzner, Dafi Voloshin, Frederik Kratzert, Gal Elidan, Gideon Dror, Gregory Begelman, Grey Nearing, Guy Shalev, Hila Noga, Ira Shavitt, Liora Yuklea, Moriah Royz, Niv Giladi, Nofar Peled Levi, Ofir Reich, Oren Gilon, Ronnie Maor, Shahar Timnat, Tal Shechter, Vladimir Anisimov, Yotam Gigi, Yuval Levin, Zach Moshe, Zvika Ben-Haim, Avinatan Hassidim, and Yossi Matias
Hydrol. Earth Syst. Sci., 26, 4013–4032, https://doi.org/10.5194/hess-26-4013-2022, https://doi.org/10.5194/hess-26-4013-2022, 2022
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Early flood warnings are one of the most effective tools to save lives and goods. Machine learning (ML) models can improve flood prediction accuracy but their use in operational frameworks is limited. The paper presents a flood warning system, operational in India and Bangladesh, that uses ML models for forecasting river stage and flood inundation maps and discusses the models' performances. In 2021, more than 100 million flood alerts were sent to people near rivers over an area of 470 000 km2.
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.
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.
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.
Elnaz Azmi, Uwe Ehret, Steven V. Weijs, Benjamin L. Ruddell, and Rui A. P. Perdigão
Hydrol. Earth Syst. Sci., 25, 1103–1115, https://doi.org/10.5194/hess-25-1103-2021, https://doi.org/10.5194/hess-25-1103-2021, 2021
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Computer models should be as simple as possible but not simpler. Simplicity refers to the length of the model and the effort it takes the model to generate its output. Here we present a practical technique for measuring the latter by the number of memory visits during model execution by
Strace, a troubleshooting and monitoring program. The advantage of this approach is that it can be applied to any computer-based model, which facilitates model intercomparison.
Ralf Loritz, Markus Hrachowitz, Malte Neuper, and Erwin Zehe
Hydrol. Earth Syst. Sci., 25, 147–167, https://doi.org/10.5194/hess-25-147-2021, https://doi.org/10.5194/hess-25-147-2021, 2021
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This study investigates the role and value of distributed rainfall in the runoff generation of a mesoscale catchment. We compare the performance of different hydrological models at different periods and show that a distributed model driven by distributed rainfall yields improved performances only during certain periods. We then step beyond this finding and develop a spatially adaptive model that is capable of dynamically adjusting its spatial model structure in time.
Stephanie Thiesen, Diego M. Vieira, Mirko Mälicke, Ralf Loritz, J. Florian Wellmann, and Uwe Ehret
Hydrol. Earth Syst. Sci., 24, 4523–4540, https://doi.org/10.5194/hess-24-4523-2020, https://doi.org/10.5194/hess-24-4523-2020, 2020
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A spatial interpolator has been proposed for exploring the information content of the data in the light of geostatistics and information theory. It showed comparable results to traditional interpolators, with the advantage of presenting generalization properties. We discussed three different ways of combining distributions and their implications for the probabilistic results. By its construction, the method provides a suitable and flexible framework for uncertainty analysis and decision-making.
Uwe Ehret, Rik van Pruijssen, Marina Bortoli, Ralf Loritz, Elnaz Azmi, and Erwin Zehe
Hydrol. Earth Syst. Sci., 24, 4389–4411, https://doi.org/10.5194/hess-24-4389-2020, https://doi.org/10.5194/hess-24-4389-2020, 2020
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In this paper we propose adaptive clustering as a new method for reducing the computational efforts of distributed modelling. It consists of identifying similar-acting model elements during the runtime, clustering them, running the model for just a few representatives per cluster, and mapping their results to the remaining model elements in the cluster. With the example of a hydrological model, we show that this saves considerable computation time, while largely maintaining the output quality.
Frederik Kratzert, Daniel Klotz, Guy Shalev, Günter Klambauer, Sepp Hochreiter, and Grey Nearing
Hydrol. Earth Syst. Sci., 23, 5089–5110, https://doi.org/10.5194/hess-23-5089-2019, https://doi.org/10.5194/hess-23-5089-2019, 2019
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A new approach for regional rainfall–runoff modeling using long short-term memory (LSTM)-based models is presented and benchmarked against a range of well-known hydrological models. The approach significantly outperforms regionally calibrated hydrological models but also basin-wise calibrated models. Furthermore, we propose an adaption of the LSTM that allows us to extract the learned catchment understanding of the model and show that it matches our hydrology expert knowledge.
Alexander Sternagel, Ralf Loritz, Wolfgang Wilcke, and Erwin Zehe
Hydrol. Earth Syst. Sci., 23, 4249–4267, https://doi.org/10.5194/hess-23-4249-2019, https://doi.org/10.5194/hess-23-4249-2019, 2019
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We present our hydrological LAST-Model to simulate preferential soil water flow and tracer transport in macroporous soils. It relies on a Lagrangian perspective of the movement of discrete water particles carrying tracer masses through the subsoil and is hence an alternative approach to common models. Sensitivity analyses reveal the physical validity of the model concept and evaluation tests show that LAST can depict well observed tracer mass profiles with fingerprints of preferential flow.
Axel Kleidon, Erwin Zehe, and Ralf Loritz
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2019-52, https://doi.org/10.5194/esd-2019-52, 2019
Manuscript not accepted for further review
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Many fluxes in Earth systems are not homogeneously distributed across space, but occur highly concentrated in structures, such as turbulent eddies, river networks, vascular networks of plants, or human-made infrastructures. Yet, the highly-organized nature of these fluxes is typically only described at a rudimentary level, if at all. We propose that it requires a novel approach to describe these structures that focuses on the work done to build and maintain these structures, and the feedbacks.
Ralf Loritz, Axel Kleidon, Conrad Jackisch, Martijn Westhoff, Uwe Ehret, Hoshin Gupta, and Erwin Zehe
Hydrol. Earth Syst. Sci., 23, 3807–3821, https://doi.org/10.5194/hess-23-3807-2019, https://doi.org/10.5194/hess-23-3807-2019, 2019
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In this study, we develop a topographic index explaining hydrological similarity within a energy-centered framework, with the observation that the majority of potential energy is dissipated when rainfall becomes runoff.
Malte Neuper and Uwe Ehret
Hydrol. Earth Syst. Sci., 23, 3711–3733, https://doi.org/10.5194/hess-23-3711-2019, https://doi.org/10.5194/hess-23-3711-2019, 2019
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In this study, we apply a data-driven approach to quantitatively estimate precipitation using weather radar data. The method is based on information theory concepts. It uses predictive relations expressed by empirical discrete probability distributions, which are directly derived from data rather than the standard deterministic functions.
Stephanie Thiesen, Paul Darscheid, and Uwe Ehret
Hydrol. Earth Syst. Sci., 23, 1015–1034, https://doi.org/10.5194/hess-23-1015-2019, https://doi.org/10.5194/hess-23-1015-2019, 2019
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We present a data-driven approach created to explore the full information of data sets, avoiding parametric assumptions. The evaluations are based on Information Theory concepts, introducing an objective measure of information and uncertainty. The approach was applied to automatically identify rainfall-runoff events in discharge time series, however it is generic enough to be adapted to other practical applications.
Erwin Zehe, Ralf Loritz, Conrad Jackisch, Martijn Westhoff, Axel Kleidon, Theresa Blume, Sibylle K. Hassler, and Hubert H. Savenije
Hydrol. Earth Syst. Sci., 23, 971–987, https://doi.org/10.5194/hess-23-971-2019, https://doi.org/10.5194/hess-23-971-2019, 2019
Frederik Kratzert, Daniel Klotz, Claire Brenner, Karsten Schulz, and Mathew Herrnegger
Hydrol. Earth Syst. Sci., 22, 6005–6022, https://doi.org/10.5194/hess-22-6005-2018, https://doi.org/10.5194/hess-22-6005-2018, 2018
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In this paper, we propose a novel data-driven approach for
rainfall–runoff modelling, using the long short-term memory (LSTM) network, a special type of recurrent neural network. We show in three different experiments that this network is able to learn to predict the discharge purely from meteorological input parameters (such as precipitation or temperature) as accurately as (or better than) the well-established Sacramento Soil Moisture Accounting model, coupled with the Snow-17 snow model.
Ralf Loritz, Hoshin Gupta, Conrad Jackisch, Martijn Westhoff, Axel Kleidon, Uwe Ehret, and Erwin Zehe
Hydrol. Earth Syst. Sci., 22, 3663–3684, https://doi.org/10.5194/hess-22-3663-2018, https://doi.org/10.5194/hess-22-3663-2018, 2018
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In this study we explore the role of spatially distributed information on hydrological modeling. For that, we develop and test an approach which draws upon information theory and thermodynamic reasoning. We show that the proposed set of methods provide a powerful framework for understanding and diagnosing how and when process organization and functional similarity of hydrological systems emerge in time and, hence, when which landscape characteristic is important in a model application.
Karsten Schulz, Reinhard Burgholzer, Daniel Klotz, Johannes Wesemann, and Mathew Herrnegger
Hydrol. Earth Syst. Sci., 22, 2607–2613, https://doi.org/10.5194/hess-22-2607-2018, https://doi.org/10.5194/hess-22-2607-2018, 2018
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The unit hydrograph has been one of the most widely employed modelling techniques to predict rainfall-runoff behaviour of hydrological catchments. We developed a lecture theatre experiment including some student involvement to illustrate the principles behind this modelling technique. The experiment only uses very simple and cheap material including a set of plastic balls (representing rainfall), magnetic stripes (tacking the balls to the white board) and sieves (for ball/water gauging).
Simon Paul Seibert, Conrad Jackisch, Uwe Ehret, Laurent Pfister, and Erwin Zehe
Hydrol. Earth Syst. Sci., 21, 2817–2841, https://doi.org/10.5194/hess-21-2817-2017, https://doi.org/10.5194/hess-21-2817-2017, 2017
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Runoff production mechanisms and their corresponding physiographic controls continue to pose major research challenges in catchment hydrology. We propose innovative data-driven diagnostic signatures for overcoming the prevailing status quo in inter-comparison studies. Specifically, we present dimensionless double mass curves which allow us to infer information on runoff generation at the seasonal and annual timescales. The method is based on commonly available data.
Ralf Loritz, Sibylle K. Hassler, Conrad Jackisch, Niklas Allroggen, Loes van Schaik, Jan Wienhöfer, and Erwin Zehe
Hydrol. Earth Syst. Sci., 21, 1225–1249, https://doi.org/10.5194/hess-21-1225-2017, https://doi.org/10.5194/hess-21-1225-2017, 2017
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In this study we examine whether we can step beyond the qualitative character of perceptual models by using them as a blueprint for setting up representative hillslope models. Thereby we test the hypothesis of whether a single hillslope can represent the functioning of an entire lower mesoscale catchment in a spatially aggregated way.
Simon Paul Seibert, Uwe Ehret, and Erwin Zehe
Hydrol. Earth Syst. Sci., 20, 3745–3763, https://doi.org/10.5194/hess-20-3745-2016, https://doi.org/10.5194/hess-20-3745-2016, 2016
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While the assessment of "vertical" (magnitude) errors of streamflow simulations is standard practice, "horizontal" (timing) errors are rarely considered. To assess their role, we propose a method to quantify both errors simultaneously which closely resembles visual hydrograph comparison. Our results reveal differences in time–magnitude error statistics for different flow conditions. The proposed method thus offers novel perspectives for model diagnostics and evaluation.
E. Zehe, U. Ehret, L. Pfister, T. Blume, B. Schröder, M. Westhoff, C. Jackisch, S. J. Schymanski, M. Weiler, K. Schulz, N. Allroggen, J. Tronicke, L. van Schaik, P. Dietrich, U. Scherer, J. Eccard, V. Wulfmeyer, and A. Kleidon
Hydrol. Earth Syst. Sci., 18, 4635–4655, https://doi.org/10.5194/hess-18-4635-2014, https://doi.org/10.5194/hess-18-4635-2014, 2014
U. Ehret, H. V. Gupta, M. Sivapalan, S. V. Weijs, S. J. Schymanski, G. Blöschl, A. N. Gelfan, C. Harman, A. Kleidon, T. A. Bogaard, D. Wang, T. Wagener, U. Scherer, E. Zehe, M. F. P. Bierkens, G. Di Baldassarre, J. Parajka, L. P. H. van Beek, A. van Griensven, M. C. Westhoff, and H. C. Winsemius
Hydrol. Earth Syst. Sci., 18, 649–671, https://doi.org/10.5194/hess-18-649-2014, https://doi.org/10.5194/hess-18-649-2014, 2014
E. Zehe, U. Ehret, T. Blume, A. Kleidon, U. Scherer, and M. Westhoff
Hydrol. Earth Syst. Sci., 17, 4297–4322, https://doi.org/10.5194/hess-17-4297-2013, https://doi.org/10.5194/hess-17-4297-2013, 2013
A. Kleidon, E. Zehe, U. Ehret, and U. Scherer
Hydrol. Earth Syst. Sci., 17, 225–251, https://doi.org/10.5194/hess-17-225-2013, https://doi.org/10.5194/hess-17-225-2013, 2013
Related subject area
Subject: Catchment hydrology | Techniques and Approaches: Modelling approaches
Evaluating the effects of topography and land use change on hydrological signatures: a comparative study of two adjacent watersheds
Technical note: What does the Standardized Streamflow Index actually reflect? Insights and implications for hydrological drought analysis
Long short-term memory networks for enhancing real-time flood forecasts: a case study for an underperforming hydrologic model
Assessing the value of high-resolution rainfall and streamflow data for hydrological modeling: an analysis based on 63 catchments in southeast China
Catchments do not strictly follow Budyko curves over multiple decades, but deviations are minor and predictable
Scale dependency in modeling nivo-glacial hydrological systems: the case of the Arolla basin, Switzerland
Extended-range forecasting of stream water temperature with deep-learning models
Projections of streamflow intermittence under climate change in European drying river networks
Economic valuation of subsurface water contributions to watershed ecosystem services using a fully integrated groundwater–surface-water model
Analyzing the generalization capabilities of a hybrid hydrological model for extrapolation to extreme events
CH-RUN: a deep-learning-based spatially contiguous runoff reconstruction for Switzerland
Runoff component quantification and future streamflow projection in a large mountainous basin based on a multidata-constrained cryospheric–hydrological model
Exploring the potential processes controlling changes in precipitation–runoff relationships in non-stationary environments
A diversity-centric strategy for the selection of spatio-temporal training data for LSTM-based streamflow forecasting
Simulating the Tone River eastward diversion project in Japan carried out 4 centuries ago
Lack of robustness of hydrological models: a large-sample diagnosis and an attempt to identify hydrological and climatic drivers
Achieving water budget closure through physical hydrological process modelling: insights from a large-sample study
Heavy-tailed flood peak distributions: what is the effect of the spatial variability of rainfall and runoff generation?
State updating of the Xin'anjiang model: joint assimilating streamflow and multi-source soil moisture data via the asynchronous ensemble Kalman filter with enhanced error models
Improving the hydrological consistency of a process-based solute-transport model by simultaneous calibration of streamflow and stream concentrations
Leveraging a time-series event separation method to disentangle time-varying hydrologic controls on streamflow – application to wildfire-affected catchments
The significance of the leaf area index for evapotranspiration estimation in SWAT-T for characteristic land cover types of West Africa
Improved representation of soil moisture processes through incorporation of cosmic-ray neutron count measurements in a large-scale hydrologic model
Spatio-temporal patterns and trends of streamflow in water-scarce Mediterranean basins
A large-sample modelling approach towards integrating streamflow and evaporation data for the Spanish catchments
Seasonal variation in land cover estimates reveals sensitivities and opportunities for environmental models
Estimating response times, flow velocities, and roughness coefficients of Canadian Prairie basins
Learning landscape features from streamflow with autoencoders
Hydrological regime index for non-perennial rivers
On the use of streamflow transformations for hydrological model calibration
Simulation-based inference for parameter estimation of complex watershed simulators
Multi-scale soil moisture data and process-based modeling reveal the importance of lateral groundwater flow in a subarctic catchment
CONCN: A high-resolution, integrated surface water-groundwater ParFlow modeling platform of continental China
Catchment response to climatic variability: implications for root zone storage and streamflow predictions
Assesing the Value of High-Resolution Data and Parameters Transferability Across Temporal Scales in Hydrological Modeling: A Case Study in Northern China
Hybrid hydrological modeling for large alpine basins: a semi-distributed approach
Technical note: How many models do we need to simulate hydrologic processes across large geographical domains?
Karst aquifer discharge response to rainfall interpreted as anomalous transport
HESS Opinions: Never train a Long Short-Term Memory (LSTM) network on a single basin
Large-sample hydrology – a few camels or a whole caravan?
Comment on “Are soils overrated in hydrology?” by Gao et al. (2023)
Multi-decadal fluctuations in root zone storage capacity through vegetation adaptation to hydro-climatic variability have minor effects on the hydrological response in the Neckar River basin, Germany
Projected future changes in the cryosphere and hydrology of a mountainous catchment in the upper Heihe River, China
On the importance of plant phenology in the evaporative process of a semi-arid woodland: could it be why satellite-based evaporation estimates in the miombo differ?
Assessing the adequacy of traditional hydrological models for climate change impact studies: A case for long-short-term memory (LSTM) neural networks
Regionalization of GR4J model parameters for river flow prediction in Paraná, Brazil
Evolution of river regimes in the Mekong River basin over 8 decades and the role of dams in recent hydrological extremes
Skill of seasonal flow forecasts at catchment scale: an assessment across South Korea
To what extent do flood-inducing storm events change future flood hazards?
When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling
Haifan Liu, Haochen Yan, and Mingfu Guan
Hydrol. Earth Syst. Sci., 29, 2109–2132, https://doi.org/10.5194/hess-29-2109-2025, https://doi.org/10.5194/hess-29-2109-2025, 2025
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Land changes and landscape features critically impact water systems. Studying two watersheds in China’s Greater Bay Area, we found slope strongly influences water processes in mountainous areas. However, this relationship is weak in the lower regions of steeper watersheds. Urbanization leads to an increase in annual surface runoff, while flatter watersheds exhibit a buffering capacity against this effect. However, this buffering capacity diminishes with increasing annual rainfall intensity.
Fabián Lema, Pablo A. Mendoza, Nicolás A. Vásquez, Naoki Mizukami, Mauricio Zambrano-Bigiarini, and Ximena Vargas
Hydrol. Earth Syst. Sci., 29, 1981–2002, https://doi.org/10.5194/hess-29-1981-2025, https://doi.org/10.5194/hess-29-1981-2025, 2025
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Hydrological droughts affect ecosystems and socioeconomic activities worldwide. Despite the fact that they are commonly described with the Standardized Streamflow Index (SSI), there is limited understanding of what they truly reflect in terms of water cycle processes. Here, we used state-of-the-art hydrological models in Andean basins to examine drivers of SSI fluctuations. The results highlight the importance of careful selection of indices and timescales for accurate drought characterization and monitoring.
Sebastian Gegenleithner, Manuel Pirker, Clemens Dorfmann, Roman Kern, and Josef Schneider
Hydrol. Earth Syst. Sci., 29, 1939–1962, https://doi.org/10.5194/hess-29-1939-2025, https://doi.org/10.5194/hess-29-1939-2025, 2025
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Accurate early-warning systems are crucial for reducing the damage caused by flooding events. In this study, we explored the potential of long short-term memory networks for enhancing the forecast accuracy of hydrologic models employed in operational flood forecasting. The presented approach elevated the investigated hydrologic model’s forecast accuracy for further ahead predictions and at flood event runoff.
Mahmut Tudaji, Yi Nan, and Fuqiang Tian
Hydrol. Earth Syst. Sci., 29, 1919–1937, https://doi.org/10.5194/hess-29-1919-2025, https://doi.org/10.5194/hess-29-1919-2025, 2025
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Common intuition holds that higher input data resolution leads to better results. To assess the benefits of high-resolution data, we conduct simulation experiments using data with various temporal resolutions across multiple catchments and find that higher-resolution data do not always improve model performance, challenging the necessity of pursuing such data. In catchments with small areas or significant flow variability, high-resolution data is more valuable.
Muhammad Ibrahim, Miriam Coenders-Gerrits, Ruud van der Ent, and Markus Hrachowitz
Hydrol. Earth Syst. Sci., 29, 1703–1723, https://doi.org/10.5194/hess-29-1703-2025, https://doi.org/10.5194/hess-29-1703-2025, 2025
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The quantification of precipitation into evaporation and runoff is vital for water resources management. The Budyko framework, based on aridity and evaporative indices of a catchment, can be an ideal tool for that. However, recent research highlights deviations of catchments from the expected evaporative index, casting doubt on its reliability. This study quantifies deviations of 2387 catchments, finding them minor and predictable. Integrating these into predictions upholds the framework's efficacy.
Anne-Laure Argentin, Pascal Horton, Bettina Schaefli, Jamal Shokory, Felix Pitscheider, Leona Repnik, Mattia Gianini, Simone Bizzi, Stuart N. Lane, and Francesco Comiti
Hydrol. Earth Syst. Sci., 29, 1725–1748, https://doi.org/10.5194/hess-29-1725-2025, https://doi.org/10.5194/hess-29-1725-2025, 2025
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In this article, we show that by taking the optimal parameters calibrated with a semi-lumped model for the discharge at a catchment's outlet, we can accurately simulate runoff at various points within the study area, including three nested and three neighboring catchments. In addition, we demonstrate that employing more intricate melt models, which better represent physical processes, enhances the transfer of parameters in the simulation, until we observe overparameterization.
Ryan S. Padrón, Massimiliano Zappa, Luzi Bernhard, and Konrad Bogner
Hydrol. Earth Syst. Sci., 29, 1685–1702, https://doi.org/10.5194/hess-29-1685-2025, https://doi.org/10.5194/hess-29-1685-2025, 2025
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We generate operational forecasts of daily maximum stream water temperature for 32 consecutive days at 54 stations in Switzerland with our best-performing data-driven model. The average forecast error is 0.38 °C for 1 d ahead and increases to 0.90 °C for 32 d ahead given the uncertainty in the meteorological variables influencing water temperature. Here we compare the skill of several models, how well they can forecast at new and ungauged stations, and the importance of different model inputs.
Louise Mimeau, Annika Künne, Alexandre Devers, Flora Branger, Sven Kralisch, Claire Lauvernet, Jean-Philippe Vidal, Núria Bonada, Zoltán Csabai, Heikki Mykrä, Petr Pařil, Luka Polović, and Thibault Datry
Hydrol. Earth Syst. Sci., 29, 1615–1636, https://doi.org/10.5194/hess-29-1615-2025, https://doi.org/10.5194/hess-29-1615-2025, 2025
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Our study projects how climate change will affect the drying of river segments and stream networks in Europe, using advanced modelling techniques to assess changes in six river networks across diverse ecoregions. We found that drying events will become more frequent and intense and will start earlier or last longer, potentially turning some river sections from perennial to intermittent. The results are valuable for river ecologists for evaluating the ecological health of river ecosystem.
Tariq Aziz, Steven K. Frey, David R. Lapen, Susan Preston, Hazen A. J. Russell, Omar Khader, Andre R. Erler, and Edward A. Sudicky
Hydrol. Earth Syst. Sci., 29, 1549–1568, https://doi.org/10.5194/hess-29-1549-2025, https://doi.org/10.5194/hess-29-1549-2025, 2025
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This study determines the value of subsurface water for ecosystem services' supply in an agricultural watershed in Ontario, Canada. Using a fully integrated water model and an economic valuation approach, the research highlights subsurface water's critical role in maintaining watershed ecosystem services. The study informs on the sustainable use of subsurface water and introduces a new method for managing watershed ecosystem services.
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.
Basil Kraft, Michael Schirmer, William H. Aeberhard, Massimiliano Zappa, Sonia I. Seneviratne, and Lukas Gudmundsson
Hydrol. Earth Syst. Sci., 29, 1061–1082, https://doi.org/10.5194/hess-29-1061-2025, https://doi.org/10.5194/hess-29-1061-2025, 2025
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This study reconstructs daily runoff in Switzerland (1962–2023) using a deep-learning model, providing a spatially contiguous dataset on a medium-sized catchment grid. The model outperforms traditional hydrological methods, revealing shifts in Swiss water resources, including more frequent dry years and declining summer runoff. The reconstruction is publicly available.
Mengjiao Zhang, Yi Nan, and Fuqiang Tian
Hydrol. Earth Syst. Sci., 29, 1033–1060, https://doi.org/10.5194/hess-29-1033-2025, https://doi.org/10.5194/hess-29-1033-2025, 2025
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Owing to differences in the existing published results, we conducted a detailed analysis of the runoff components and future trends in the Yarlung Tsangpo River basin and found that the contributions of snowmelt and glacier melt runoff to streamflow (both ~5 %) are limited and much lower than previous results. The streamflow in this area will continuously increase in the future, but the overestimated contribution of glacier melt could lead to an underestimation of this increasing trend.
Tian Lan, Tongfang Li, Hongbo Zhang, Jiefeng Wu, Yongqin David Chen, and Chong-Yu Xu
Hydrol. Earth Syst. Sci., 29, 903–924, https://doi.org/10.5194/hess-29-903-2025, https://doi.org/10.5194/hess-29-903-2025, 2025
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This study develops an integrated framework based on the novel Driving index for changes in Precipitation–Runoff Relationships (DPRR) to explore the controlling changes in precipitation–runoff relationships in non-stationary environments. According to the quantitative results of the candidate driving factors, the possible process explanations for changes in the precipitation–runoff relationships are deduced. The main contribution offers a comprehensive understanding of hydrological processes.
Everett Snieder and Usman T. Khan
Hydrol. Earth Syst. Sci., 29, 785–798, https://doi.org/10.5194/hess-29-785-2025, https://doi.org/10.5194/hess-29-785-2025, 2025
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Improving the accuracy of flood forecasts is paramount to minimising flood damage. Machine learning (ML) models are increasingly being applied for flood forecasting. Such models are typically trained on large historic hydrometeorological datasets. In this work, we evaluate methods for selecting training datasets that maximise the spatio-temporal diversity of the represented hydrological processes. Empirical results showcase the importance of hydrological diversity in training ML models.
Joško Trošelj and Naota Hanasaki
Hydrol. Earth Syst. Sci., 29, 753–766, https://doi.org/10.5194/hess-29-753-2025, https://doi.org/10.5194/hess-29-753-2025, 2025
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This study presents the first distributed hydrological simulation which confirms claims raised by historians that the eastward diversion project of the Tone River in Japan was conducted 4 centuries ago to increase low flows and subsequent travelling possibilities surrounding the capital, Edo (Tokyo), using inland navigation. We showed that great steps forward can be made for improving quality of life with small human engineering waterworks and small interventions in the regime of natural flows.
Léonard Santos, Vazken Andréassian, Torben O. Sonnenborg, Göran Lindström, Alban de Lavenne, Charles Perrin, Lila Collet, and Guillaume Thirel
Hydrol. Earth Syst. Sci., 29, 683–700, https://doi.org/10.5194/hess-29-683-2025, https://doi.org/10.5194/hess-29-683-2025, 2025
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This work investigates how hydrological models are transferred to a period in which climate conditions are different to the ones of the period in which they were set up. The robustness assessment test built to detect dependencies between model error and climatic drivers was applied to three hydrological models in 352 catchments in Denmark, France and Sweden. Potential issues are seen in a significant number of catchments for the models, even though the catchments differ for each model.
Xudong Zheng, Dengfeng Liu, Shengzhi Huang, Hao Wang, and Xianmeng Meng
Hydrol. Earth Syst. Sci., 29, 627–653, https://doi.org/10.5194/hess-29-627-2025, https://doi.org/10.5194/hess-29-627-2025, 2025
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Water budget non-closure is a widespread phenomenon among multisource datasets which undermines the robustness of hydrological inferences. This study proposes a Multisource Dataset Correction Framework grounded in Physical Hydrological Process Modelling to enhance water budget closure, termed PHPM-MDCF. We examined the efficiency and robustness of the framework using the CAMELS dataset and achieved an average reduction of 49 % in total water budget residuals across 475 CONUS basins.
Elena Macdonald, Bruno Merz, Viet Dung Nguyen, and Sergiy Vorogushyn
Hydrol. Earth Syst. Sci., 29, 447–463, https://doi.org/10.5194/hess-29-447-2025, https://doi.org/10.5194/hess-29-447-2025, 2025
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Flood peak distributions indicate how likely the occurrence of an extreme flood is at a certain river. If the distribution has a so-called heavy tail, extreme floods are more likely than might be anticipated. We find heavier tails in small catchments compared to large catchments, and spatially variable rainfall leads to a lower occurrence probability of extreme floods. Spatially variable runoff does not show effects. The results can improve estimations of probabilities of extreme floods.
Junfu Gong, Xingwen Liu, Cheng Yao, Zhijia Li, Albrecht H. Weerts, Qiaoling Li, Satish Bastola, Yingchun Huang, and Junzeng Xu
Hydrol. Earth Syst. Sci., 29, 335–360, https://doi.org/10.5194/hess-29-335-2025, https://doi.org/10.5194/hess-29-335-2025, 2025
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Our study introduces a new method to improve flood forecasting by combining soil moisture and streamflow data using an advanced data assimilation technique. By integrating field and reanalysis soil moisture data and assimilating this with streamflow measurements, we aim to enhance the accuracy of flood predictions. This approach reduces the accumulation of past errors in the initial conditions at the start of the forecast, helping to better prepare for and respond to floods.
Jordy Salmon-Monviola, Ophélie Fovet, and Markus Hrachowitz
Hydrol. Earth Syst. Sci., 29, 127–158, https://doi.org/10.5194/hess-29-127-2025, https://doi.org/10.5194/hess-29-127-2025, 2025
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To increase the predictive power of hydrological models, it is necessary to improve their consistency, i.e. their physical realism, which is measured by the ability of the model to reproduce observed system dynamics. Using a model to represent the dynamics of water and nitrate and dissolved organic carbon concentrations in an agricultural catchment, we showed that using solute-concentration data for calibration is useful to improve the hydrological consistency of the model.
Haley A. Canham, Belize Lane, Colin B. Phillips, and Brendan P. Murphy
Hydrol. Earth Syst. Sci., 29, 27–43, https://doi.org/10.5194/hess-29-27-2025, https://doi.org/10.5194/hess-29-27-2025, 2025
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The influence of watershed disturbances has proved challenging to disentangle from natural streamflow variability. This study evaluates the influence of time-varying hydrologic controls on rainfall–runoff in undisturbed and wildfire-disturbed watersheds using a novel time-series event separation method. Across watersheds, water year type and season influenced rainfall–runoff patterns. Accounting for these controls enabled clearer isolation of wildfire effects.
Fabian Merk, Timo Schaffhauser, Faizan Anwar, Ye Tuo, Jean-Martial Cohard, and Markus Disse
Hydrol. Earth Syst. Sci., 28, 5511–5539, https://doi.org/10.5194/hess-28-5511-2024, https://doi.org/10.5194/hess-28-5511-2024, 2024
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Evapotranspiration (ET) is computed from the vegetation (plant transpiration) and soil (soil evaporation). In western Africa, plant transpiration correlates with vegetation growth. Vegetation is often represented using the leaf area index (LAI). In this study, we evaluate the importance of the LAI for ET calculation. We take a close look at this interaction and highlight its relevance. Our work contributes to the understanding of terrestrial water cycle processes .
Eshrat Fatima, Rohini Kumar, Sabine Attinger, Maren Kaluza, Oldrich Rakovec, Corinna Rebmann, Rafael Rosolem, Sascha E. Oswald, Luis Samaniego, Steffen Zacharias, and Martin Schrön
Hydrol. Earth Syst. Sci., 28, 5419–5441, https://doi.org/10.5194/hess-28-5419-2024, https://doi.org/10.5194/hess-28-5419-2024, 2024
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This study establishes a framework to incorporate cosmic-ray neutron measurements into the mesoscale Hydrological Model (mHM). We evaluate different approaches to estimate neutron counts within the mHM using the Desilets equation, with uniformly and non-uniformly weighted average soil moisture, and the physically based code COSMIC. The data improved not only soil moisture simulations but also the parameterisation of evapotranspiration in the model.
Laia Estrada, Xavier Garcia, Joan Saló-Grau, Rafael Marcé, Antoni Munné, and Vicenç Acuña
Hydrol. Earth Syst. Sci., 28, 5353–5373, https://doi.org/10.5194/hess-28-5353-2024, https://doi.org/10.5194/hess-28-5353-2024, 2024
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Hydrological modelling is a powerful tool to support decision-making. We assessed spatio-temporal patterns and trends of streamflow for 2001–2022 with a hydrological model, integrating stakeholder expert knowledge on management operations. The results provide insight into how climate change and anthropogenic pressures affect water resources availability in regions vulnerable to water scarcity, thus raising the need for sustainable management practices and integrated hydrological modelling.
Patricio Yeste, Matilde García-Valdecasas Ojeda, Sonia R. Gámiz-Fortis, Yolanda Castro-Díez, Axel Bronstert, and María Jesús Esteban-Parra
Hydrol. Earth Syst. Sci., 28, 5331–5352, https://doi.org/10.5194/hess-28-5331-2024, https://doi.org/10.5194/hess-28-5331-2024, 2024
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Integrating streamflow and evaporation data can help improve the physical realism of hydrologic models. We investigate the capabilities of the Variable Infiltration Capacity (VIC) to reproduce both hydrologic variables for 189 headwater located in Spain. Results from sensitivity analyses indicate that adding two vegetation parameters is enough to improve the representation of evaporation and that the performance of VIC exceeded that of the largest modelling effort currently available in Spain.
Daniel T. Myers, David Jones, Diana Oviedo-Vargas, John Paul Schmit, Darren L. Ficklin, and Xuesong Zhang
Hydrol. Earth Syst. Sci., 28, 5295–5310, https://doi.org/10.5194/hess-28-5295-2024, https://doi.org/10.5194/hess-28-5295-2024, 2024
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We studied how streamflow and water quality models respond to land cover data collected by satellites during the growing season versus the non-growing season. The land cover data showed more trees during the growing season and more built areas during the non-growing season. We next found that the use of non-growing season data resulted in a higher modeled nutrient export to streams. Knowledge of these sensitivities would be particularly important when models inform water resource management.
Kevin R. Shook, Paul H. Whitfield, Christopher Spence, and John W. Pomeroy
Hydrol. Earth Syst. Sci., 28, 5173–5192, https://doi.org/10.5194/hess-28-5173-2024, https://doi.org/10.5194/hess-28-5173-2024, 2024
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Recent studies suggest that the velocities of water running off landscapes in the Canadian Prairies may be much smaller than generally assumed. Analyses of historical flows for 23 basins in central Alberta show that many of the rivers responded more slowly and that the flows are much slower than would be estimated from equations developed elsewhere. The effects of slow flow velocities on the development of hydrological models of the region are discussed, as are the possible causes.
Alberto Bassi, Marvin Höge, Antonietta Mira, Fabrizio Fenicia, and Carlo Albert
Hydrol. Earth Syst. Sci., 28, 4971–4988, https://doi.org/10.5194/hess-28-4971-2024, https://doi.org/10.5194/hess-28-4971-2024, 2024
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The goal is to remove the impact of meteorological drivers in order to uncover the unique landscape fingerprints of a catchment from streamflow data. Our results reveal an optimal two-feature summary for most catchments, with a third feature associated with aridity and intermittent flow that is needed for challenging cases. Baseflow index, aridity, and soil or vegetation attributes strongly correlate with learnt features, indicating their importance for streamflow prediction.
Pablo Fernando Dornes and Rocío Noelia Comas
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-338, https://doi.org/10.5194/hess-2024-338, 2024
Revised manuscript accepted for HESS
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The Desaguadero-Salado-Chadiluevú-Curacó (DSCC) River is a semiarid river which is severely dammed in its tributaries which collect the snowmelt runoff. This runoff feeds mostly gravitational irrigation systems of very low efficiency. As a result, the DSCC River does not have natural runoff. The proposed Hydrological Regime Index (HRI) is able to discriminate and quantify regime alterations under permanent and non-permanent flow conditions and with low and high impoundment conditions.
Guillaume Thirel, Léonard Santos, Olivier Delaigue, and Charles Perrin
Hydrol. Earth Syst. Sci., 28, 4837–4860, https://doi.org/10.5194/hess-28-4837-2024, https://doi.org/10.5194/hess-28-4837-2024, 2024
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We discuss how mathematical transformations impact calibrated hydrological model simulations. We assess how 11 transformations behave over the complete range of streamflows. Extreme transformations lead to models that are specialized for extreme streamflows but show poor performance outside the range of targeted streamflows and are less robust. We show that no a priori assumption about transformations can be taken as warranted.
Robert Hull, Elena Leonarduzzi, Luis De La Fuente, Hoang Viet Tran, Andrew Bennett, Peter Melchior, Reed M. Maxwell, and Laura E. Condon
Hydrol. Earth Syst. Sci., 28, 4685–4713, https://doi.org/10.5194/hess-28-4685-2024, https://doi.org/10.5194/hess-28-4685-2024, 2024
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Large-scale hydrologic simulators are a needed tool to explore complex watershed processes and how they may evolve with a changing climate. However, calibrating them can be difficult because they are costly to run and have many unknown parameters. We implement a state-of-the-art approach to model calibration using neural networks with a set of experiments based on streamflow in the upper Colorado River basin.
Jari-Pekka Nousu, Kersti Leppä, Hannu Marttila, Pertti Ala-aho, Giulia Mazzotti, Terhikki Manninen, Mika Korkiakoski, Mika Aurela, Annalea Lohila, and Samuli Launiainen
Hydrol. Earth Syst. Sci., 28, 4643–4666, https://doi.org/10.5194/hess-28-4643-2024, https://doi.org/10.5194/hess-28-4643-2024, 2024
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We used hydrological models, field measurements, and satellite-based data to study the soil moisture dynamics in a subarctic catchment. The role of groundwater was studied with different ways to model the groundwater dynamics and via comparisons to the observational data. The choice of groundwater model was shown to have a strong impact, and representation of lateral flow was important to capture wet soil conditions. Our results provide insights for ecohydrological studies in boreal regions.
Chen Yang, Zitong Jia, Wenjie Xu, Zhongwang Wei, Xiaolang Zhang, Yiguang Zou, Jeffrey McDonnell, Laura Condon, Yongjiu Dai, and Reed Maxwell
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-292, https://doi.org/10.5194/hess-2024-292, 2024
Revised manuscript accepted for HESS
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We developed the first high-resolution, integrated surface water-groundwater hydrologic model of the entire continental China using ParFlow. The model shows good performance of streamflow and water table depth when compared to global data products and observations. It is essential for water resources management and decision making in China within a consistent framework in the changing world. It also has significant implications for similar modeling in other places in the world.
Nienke Tempel, Laurène Bouaziz, Riccardo Taormina, Ellis van Noppen, Jasper Stam, Eric Sprokkereef, and Markus Hrachowitz
Hydrol. Earth Syst. Sci., 28, 4577–4597, https://doi.org/10.5194/hess-28-4577-2024, https://doi.org/10.5194/hess-28-4577-2024, 2024
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This study explores the impact of climatic variability on root zone water storage capacities and, thus, on hydrological predictions. Analysing data from 286 areas in Europe and the US, we found that, despite some variations in root zone storage capacity due to changing climatic conditions over multiple decades, these changes are generally minor and have a limited effect on water storage and river flow predictions.
Mahmut Tudaji, Yi Nan, and Fuqiang Tian
EGUsphere, https://doi.org/10.5194/egusphere-2024-2966, https://doi.org/10.5194/egusphere-2024-2966, 2024
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We assessed the value of high-resolution data and parameters transferability across temporal scales based on 7 catchments in northern China. We found that higher resolution data does not always improve model performance, questioning the need for such data; Model parameters are transferable across different data resolutions, but not across computational time steps. It is recommended to utilize smaller computational time step when building hydrological models even without high-resolution data.
Bu Li, Ting Sun, Fuqiang Tian, Mahmut Tudaji, Li Qin, and Guangheng Ni
Hydrol. Earth Syst. Sci., 28, 4521–4538, https://doi.org/10.5194/hess-28-4521-2024, https://doi.org/10.5194/hess-28-4521-2024, 2024
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This paper developed hybrid semi-distributed hydrological models by employing a process-based model as the backbone and utilizing deep learning to parameterize and replace internal modules. The main contribution is to provide a high-performance tool enriched with explicit hydrological knowledge for hydrological prediction and to improve understanding about the hydrological sensitivities to climate change in large alpine basins.
Wouter J. M. Knoben, Ashwin Raman, Gaby J. Gründemann, Mukesh Kumar, Alain Pietroniro, Chaopeng Shen, Yalan Song, Cyril Thébault, Katie van Werkhoven, Andrew W. Wood, and Martyn P. Clark
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-279, https://doi.org/10.5194/hess-2024-279, 2024
Revised manuscript accepted for HESS
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Hydrologic models are needed to provide simulations of water availability, floods and droughts. The accuracy of these simulations is often quantified with so-called performance scores. A common thought is that different models are more or less applicable to different landscapes, depending on how the model works. We show that performance scores are not helpful in distinguishing between different models, and thus cannot easily be used to select an appropriate model for a specific place.
Dan Elhanati, Nadine Goeppert, and Brian Berkowitz
Hydrol. Earth Syst. Sci., 28, 4239–4249, https://doi.org/10.5194/hess-28-4239-2024, https://doi.org/10.5194/hess-28-4239-2024, 2024
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A continuous time random walk framework was developed to allow modeling of a karst aquifer discharge response to measured rainfall. The application of the numerical model yielded robust fits between modeled and measured discharge values, especially for the distinctive long tails found during recession times. The findings shed light on the interplay of slow and fast flow in the karst system and establish the application of the model for simulating flow and transport in such systems.
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.
Franziska Clerc-Schwarzenbach, Giovanni Selleri, Mattia Neri, Elena Toth, Ilja van Meerveld, and Jan Seibert
Hydrol. Earth Syst. Sci., 28, 4219–4237, https://doi.org/10.5194/hess-28-4219-2024, https://doi.org/10.5194/hess-28-4219-2024, 2024
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We show that the differences between the forcing data included in three CAMELS datasets (US, BR, GB) and the forcing data included for the same catchments in the Caravan dataset affect model calibration considerably. The model performance dropped when the data from the Caravan dataset were used instead of the original data. Most of the model performance drop could be attributed to the differences in precipitation data. However, differences were largest for the potential evapotranspiration data.
Ying Zhao, Mehdi Rahmati, Harry Vereecken, and Dani Or
Hydrol. Earth Syst. Sci., 28, 4059–4063, https://doi.org/10.5194/hess-28-4059-2024, https://doi.org/10.5194/hess-28-4059-2024, 2024
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Gao et al. (2023) question the importance of soil in hydrology, sparking debate. We acknowledge some valid points but critique their broad, unsubstantiated views on soil's role. Our response highlights three key areas: (1) the false divide between ecosystem-centric and soil-centric approaches, (2) the vital yet varied impact of soil properties, and (3) the call for a scale-aware framework. We aim to unify these perspectives, enhancing hydrology's comprehensive understanding.
Siyuan Wang, Markus Hrachowitz, and Gerrit Schoups
Hydrol. Earth Syst. Sci., 28, 4011–4033, https://doi.org/10.5194/hess-28-4011-2024, https://doi.org/10.5194/hess-28-4011-2024, 2024
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Root zone storage capacity (Sumax) changes significantly over multiple decades, reflecting vegetation adaptation to climatic variability. However, this temporal evolution of Sumax cannot explain long-term fluctuations in the partitioning of water fluxes as expressed by deviations ΔIE from the parametric Budyko curve over time with different climatic conditions, and it does not have any significant effects on shorter-term hydrological response characteristics of the upper Neckar catchment.
Zehua Chang, Hongkai Gao, Leilei Yong, Kang Wang, Rensheng Chen, Chuntan Han, Otgonbayar Demberel, Batsuren Dorjsuren, Shugui Hou, and Zheng Duan
Hydrol. Earth Syst. Sci., 28, 3897–3917, https://doi.org/10.5194/hess-28-3897-2024, https://doi.org/10.5194/hess-28-3897-2024, 2024
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An integrated cryospheric–hydrologic model, FLEX-Cryo, was developed that considers glaciers, snow cover, and frozen soil and their dynamic impacts on hydrology. We utilized it to simulate future changes in cryosphere and hydrology in the Hulu catchment. Our projections showed the two glaciers will melt completely around 2050, snow cover will reduce, and permafrost will degrade. For hydrology, runoff will decrease after the glacier has melted, and permafrost degradation will increase baseflow.
Henry M. Zimba, Miriam Coenders-Gerrits, Kawawa E. Banda, Petra Hulsman, Nick van de Giesen, Imasiku A. Nyambe, and Hubert H. G. Savenije
Hydrol. Earth Syst. Sci., 28, 3633–3663, https://doi.org/10.5194/hess-28-3633-2024, https://doi.org/10.5194/hess-28-3633-2024, 2024
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The fall and flushing of new leaves in the miombo woodlands co-occur in the dry season before the commencement of seasonal rainfall. The miombo species are also said to have access to soil moisture in deep soils, including groundwater in the dry season. Satellite-based evaporation estimates, temporal trends, and magnitudes differ the most in the dry season, most likely due to inadequate understanding and representation of the highlighted miombo species attributes in simulations.
Jean-Luc Martel, François Brissette, Richard Arsenault, Richard Turcotte, Mariana Castañeda-Gonzalez, William Armstrong, Edouard Mailhot, Jasmine Pelletier-Dumont, Gabriel Rondeau-Genesse, and Louis-Philippe Caron
EGUsphere, https://doi.org/10.5194/egusphere-2024-2133, https://doi.org/10.5194/egusphere-2024-2133, 2024
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This study compares Long Short-Term Memory (LSTM) neural networks with traditional hydrological models to predict future streamflow under climate change. Using data from 148 catchments, it finds that LSTM models, which learn from extensive data sequences, perform differently and often better than traditional hydrolgical models. The continental LSTM model, which includes data from diverse climate zones, is particularly effective for understanding climate impacts on water resources.
Louise Akemi Kuana, Arlan Scortegagna Almeida, Emílio Graciliano Ferreira Mercuri, and Steffen Manfred Noe
Hydrol. Earth Syst. Sci., 28, 3367–3390, https://doi.org/10.5194/hess-28-3367-2024, https://doi.org/10.5194/hess-28-3367-2024, 2024
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The authors compared regionalization methods for river flow prediction in 126 catchments from the south of Brazil, a region with humid subtropical and hot temperate climate. The regionalization method based on physiographic–climatic similarity had the best performance for predicting daily and Q95 reference flow. We showed that basins without flow monitoring can have a good approximation of streamflow using machine learning and physiographic–climatic information as inputs.
Huy Dang and Yadu Pokhrel
Hydrol. Earth Syst. Sci., 28, 3347–3365, https://doi.org/10.5194/hess-28-3347-2024, https://doi.org/10.5194/hess-28-3347-2024, 2024
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By examining basin-wide simulations of a river regime over 83 years with and without dams, we present evidence that climate variation was a key driver of hydrologic variabilities in the Mekong River basin (MRB) over the long term; however, dams have largely altered the seasonality of the Mekong’s flow regime and annual flooding patterns in major downstream areas in recent years. These findings could help us rethink the planning of future dams and water resource management in the MRB.
Yongshin Lee, Francesca Pianosi, Andres Peñuela, and Miguel Angel Rico-Ramirez
Hydrol. Earth Syst. Sci., 28, 3261–3279, https://doi.org/10.5194/hess-28-3261-2024, https://doi.org/10.5194/hess-28-3261-2024, 2024
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Following recent advancements in weather prediction technology, we explored how seasonal weather forecasts (1 or more months ahead) could benefit practical water management in South Korea. Our findings highlight that using seasonal weather forecasts for predicting flow patterns 1 to 3 months ahead is effective, especially during dry years. This suggest that seasonal weather forecasts can be helpful in improving the management of water resources.
Mariam Khanam, Giulia Sofia, and Emmanouil N. Anagnostou
Hydrol. Earth Syst. Sci., 28, 3161–3190, https://doi.org/10.5194/hess-28-3161-2024, https://doi.org/10.5194/hess-28-3161-2024, 2024
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Flooding worsens due to climate change, with river dynamics being a key in local flood control. Predicting post-storm geomorphic changes is challenging. Using self-organizing maps and machine learning, this study forecasts post-storm alterations in stage–discharge relationships across 3101 US stream gages. The provided framework can aid in updating hazard assessments by identifying rivers prone to change, integrating channel adjustments into flood hazard assessment.
Yalan Song, Wouter J. M. Knoben, Martyn P. Clark, Dapeng Feng, Kathryn Lawson, Kamlesh Sawadekar, and Chaopeng Shen
Hydrol. Earth Syst. Sci., 28, 3051–3077, https://doi.org/10.5194/hess-28-3051-2024, https://doi.org/10.5194/hess-28-3051-2024, 2024
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Differentiable models (DMs) integrate neural networks and physical equations for accuracy, interpretability, and knowledge discovery. We developed an adjoint-based DM for ordinary differential equations (ODEs) for hydrological modeling, reducing distorted fluxes and physical parameters from errors in models that use explicit and operation-splitting schemes. With a better numerical scheme and improved structure, the adjoint-based DM matches or surpasses long short-term memory (LSTM) performance.
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Short summary
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.
Long short-term memory (LSTM) networks have demonstrated state-of-the-art performance for...
