Articles | Volume 26, issue 6
https://doi.org/10.5194/hess-26-1615-2022
© Author(s) 2022. 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-26-1615-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
25 Mar 2022
Research article |
| 25 Mar 2022
| 25 Mar 2022
Stepping beyond perfectly mixed conditions in soil hydrological modelling using a Lagrangian approach
Alexander Sternagel
CORRESPONDING AUTHOR
Institute of Water Resources and River Basin Management – Hydrology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Ralf Loritz
Institute of Water Resources and River Basin Management – Hydrology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Brian Berkowitz
Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot, Israel
Erwin Zehe
Institute of Water Resources and River Basin Management – Hydrology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
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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.
Sanika Baste, Sebastian Lerch, Daniel Klotz, and Ralf Loritz
EGUsphere, https://doi.org/10.5194/egusphere-2026-469, https://doi.org/10.5194/egusphere-2026-469, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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Probabilistic runoff predictions are capable of providing information about the possibility of occurrence of rare and high-stake events, which are largely underestimated by deterministic predictions, as they predict an expectation of the conditional runoff predictions. This additional information can be leveraged to aid flood warning communication by learning reward-based rules for selecting quantiles from the predictive distributions based on hydrological and societal contexts.
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.
Ashish Manoj J, Ralf Loritz, Hoshin Gupta, and Erwin Zehe
Hydrol. Earth Syst. Sci., 29, 6115–6135, https://doi.org/10.5194/hess-29-6115-2025, https://doi.org/10.5194/hess-29-6115-2025, 2025
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Traditional hydrological models typically operate in a forward mode, simulating streamflow and other catchment fluxes based on precipitation input. In this study, we explored the possibility of reversing this process, inferring precipitation from streamflow data, to improve flood event modelling. We then used the generated precipitation series to run hydrological models, resulting in more accurate estimates of streamflow and soil moisture.
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.
Erwin Zehe, Laurent Pfister, Dan Elhanati, and Brian Berkowitz
EGUsphere, https://doi.org/10.5194/egusphere-2025-4656, https://doi.org/10.5194/egusphere-2025-4656, 2025
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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.
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.
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.
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.
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.
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.
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.
Brian Berkowitz
Hydrol. Earth Syst. Sci., 26, 2161–2180, https://doi.org/10.5194/hess-26-2161-2022, https://doi.org/10.5194/hess-26-2161-2022, 2022
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Extensive efforts have focused on quantifying conservative chemical transport in geological formations. We assert that an explicit accounting of temporal information, under uncertainty, in addition to spatial information, is fundamental to an effective modeling formulation. We further assert that efforts to apply chemical transport equations at large length scales, based on measurements and model parameter values relevant to significantly smaller length scales, are an unattainable
holy grail.
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.
Jan Bondy, Jan Wienhöfer, Laurent Pfister, and Erwin Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2021-174, https://doi.org/10.5194/hess-2021-174, 2021
Manuscript not accepted for further review
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The Budyko curve is a widely-used and simple framework to predict the mean water balance of river catchments. While many catchments are in close accordance with the Budyko curve, others show more or less significant deviations. Our study aims at better understanding the role of soil storage characteristics in the mean water balance and offsets from the Budyko curve. Soil storage proved to be a very sensitive property and potentially explains significant deviations from the curve.
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Short summary
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.
We present a (physically based) Lagrangian approach to simulate diffusive mixing processes on...
