Articles | Volume 29, issue 21
https://doi.org/10.5194/hess-29-6115-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-29-6115-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
11 Nov 2025
Research article |
| 11 Nov 2025
| 11 Nov 2025
Can discharge be used to inversely correct precipitation?
Chair of Hydrology, Institute of Water and Environment (IWU), Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
Ralf Loritz
Chair of Hydrology, Institute of Water and Environment (IWU), Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
Hoshin Gupta
Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson 85721, United States
Erwin Zehe
Chair of Hydrology, Institute of Water and Environment (IWU), Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
Related authors
No articles found.
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
Short summary
Short summary
This study evaluates the extrapolation performance of long short-term memory (LSTM) networks in rainfall–runoff modeling, specifically under extreme precipitation conditions. The findings reveal that the LSTM cannot predict discharge values beyond a theoretical limit and that this limit is well below the extremity of its training data. This behavior results from the LSTM's gating structures rather than saturation of the cell states alone.
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
Short summary
Short summary
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
Short summary
Short summary
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
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
Short summary
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.
Dan Elhanati, Erwin Zehe, Ishai Dror, and Brian Berkowitz
EGUsphere, https://doi.org/10.5194/egusphere-2025-3365, https://doi.org/10.5194/egusphere-2025-3365, 2025
Short summary
Short summary
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.
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
Short summary
Short summary
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
Preprint under review for ESSD
Short summary
Short summary
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.
Svenja Hoffmeister, Sibylle Kathrin Hassler, Friederike Lang, Rebekka Maier, Betserai Isaac Nyoka, and Erwin Zehe
EGUsphere, https://doi.org/10.5194/egusphere-2025-1719, https://doi.org/10.5194/egusphere-2025-1719, 2025
Short summary
Short summary
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.
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
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
The CAMELS-DE dataset features data from 1582 streamflow gauges across Germany, with records spanning from 1951 to 2020. This comprehensive dataset, which includes time series of up to 70 years (median 46 years), enables advanced research on water flow and environmental trends and supports the development of hydrological models.
Svenja Hoffmeister, Rafael Bohn Reckziegel, Ben du Toit, Sibylle K. Hassler, Florian Kestel, Rebekka Maier, Jonathan P. Sheppard, and Erwin Zehe
Hydrol. Earth Syst. Sci., 28, 3963–3982, https://doi.org/10.5194/hess-28-3963-2024, https://doi.org/10.5194/hess-28-3963-2024, 2024
Short summary
Short summary
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
Short summary
Short summary
Hydrological hybrid models promise to merge the performance of deep learning methods with the interpretability of process-based models. One hybrid approach is the dynamic parameterization of conceptual models using long short-term memory (LSTM) networks. We explored this method to evaluate the effect of the flexibility given by LSTMs on the process-based part.
Luis Andres De la Fuente, Mohammad Reza Ehsani, Hoshin Vijai Gupta, and Laura Elizabeth Condon
Hydrol. Earth Syst. Sci., 28, 945–971, https://doi.org/10.5194/hess-28-945-2024, https://doi.org/10.5194/hess-28-945-2024, 2024
Short summary
Short summary
Long short-term memory (LSTM) is a widely used machine-learning model in hydrology, but it is difficult to extract knowledge from it. We propose HydroLSTM, which represents processes like a hydrological reservoir. Models based on HydroLSTM perform similarly to LSTM while requiring fewer cell states. The learned parameters are informative about the dominant hydrology of a catchment. Our results show how parsimony and hydrological knowledge extraction can be achieved by using the new structure.
Samuel Schroers, Ulrike Scherer, and Erwin Zehe
Hydrol. Earth Syst. Sci., 27, 2535–2557, https://doi.org/10.5194/hess-27-2535-2023, https://doi.org/10.5194/hess-27-2535-2023, 2023
Short summary
Short summary
The hydrological cycle shapes our landscape. With an accelerating change of the world's climate and hydrological dynamics, concepts of evolution of natural systems become more important. In this study, we elaborated a thermodynamic framework for runoff and sediment transport and show from model results as well as from measurements during extreme events that the developed concept is useful for understanding the evolution of the system's mass, energy, and entropy fluxes.
Luis Andres De la Fuente, Mohammad Reza Ehsani, Hoshin Vijai Gupta, and Laura E. Condon
EGUsphere, https://doi.org/10.5194/egusphere-2023-666, https://doi.org/10.5194/egusphere-2023-666, 2023
Preprint archived
Short summary
Short summary
Long Short-Term Memory (LSTM) is a widely-used machine learning (ML) model in hydrology. However, it is difficult to extract knowledge from it. We propose HydroLSTM which represents processes analogous to a hydrological reservoir. Models using HydroLSTM perform similarly to LSTM but require fewer cell states. The learned parameters are informative about the dominant hydroclimatic characteristics of a catchment. Our results demonstrate how hydrological knowledge is encoded in the new structure.
Judith Meyer, Malte Neuper, Luca Mathias, Erwin Zehe, and Laurent Pfister
Hydrol. Earth Syst. Sci., 26, 6163–6183, https://doi.org/10.5194/hess-26-6163-2022, https://doi.org/10.5194/hess-26-6163-2022, 2022
Short summary
Short summary
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
Short summary
Short summary
In this study, we combine a deep-learning approach that predicts sap flow with a hydrological model to improve soil moisture and transpiration estimates at the catchment scale. Our results highlight that hybrid-model approaches, combining machine learning with physically based models, are a promising way to improve our ability to make hydrological predictions.
Jonathan M. Frame, Frederik Kratzert, Daniel Klotz, Martin Gauch, Guy Shalev, Oren Gilon, Logan M. Qualls, Hoshin V. Gupta, and Grey S. Nearing
Hydrol. Earth Syst. Sci., 26, 3377–3392, https://doi.org/10.5194/hess-26-3377-2022, https://doi.org/10.5194/hess-26-3377-2022, 2022
Short summary
Short summary
The most accurate rainfall–runoff predictions are currently based on deep learning. There is a concern among hydrologists that deep learning models may not be reliable in extrapolation or for predicting extreme events. This study tests that hypothesis. The deep learning models remained relatively accurate in predicting extreme events compared with traditional models, even when extreme events were not included in the training set.
Samuel Schroers, Olivier Eiff, Axel Kleidon, Ulrike Scherer, Jan Wienhöfer, and Erwin Zehe
Hydrol. Earth Syst. Sci., 26, 3125–3150, https://doi.org/10.5194/hess-26-3125-2022, https://doi.org/10.5194/hess-26-3125-2022, 2022
Short summary
Short summary
In hydrology the formation of landform patterns is of special interest as changing forcings of the natural systems, such as climate or land use, will change these structures. In our study we developed a thermodynamic framework for surface runoff on hillslopes and highlight the differences of energy conversion patterns on two related spatial and temporal scales. The results indicate that surface runoff on hillslopes approaches a maximum power state.
Alexander Sternagel, Ralf Loritz, Brian Berkowitz, and Erwin Zehe
Hydrol. Earth Syst. Sci., 26, 1615–1629, https://doi.org/10.5194/hess-26-1615-2022, https://doi.org/10.5194/hess-26-1615-2022, 2022
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
Samuel Schroers, Olivier Eiff, Axel Kleidon, Jan Wienhöfer, and Erwin Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2021-79, https://doi.org/10.5194/hess-2021-79, 2021
Manuscript not accepted for further review
Short summary
Short summary
In this study we ask the basic question why surface runoff forms drainage networks and confluences at all and how structural macro form and micro topography is a result of thermodynamic laws. We find that on a macro level hillslopes should tend from negative exponential towards exponential forms and that on a micro level the formation of rills goes hand in hand with drainage network formation of river basins. We hypothesize that we can learn more about erosion processes if we extend this theory.
Nicolas Björn Rodriguez, Laurent Pfister, Erwin Zehe, and Julian Klaus
Hydrol. Earth Syst. Sci., 25, 401–428, https://doi.org/10.5194/hess-25-401-2021, https://doi.org/10.5194/hess-25-401-2021, 2021
Short summary
Short summary
Different parts of water have often been used as tracers to determine the age of water in streams. The stable tracers, such as deuterium, are thought to be unable to reveal old water compared to the radioactive tracer called tritium. We used both tracers, measured in precipitation and in a stream in Luxembourg, to show that this is not necessarily true. It is, in fact, advantageous to use the two tracers together, and we recommend systematically using tritium in future studies.
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
Short summary
Short summary
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.
Conrad Jackisch, Samuel Knoblauch, Theresa Blume, Erwin Zehe, and Sibylle K. Hassler
Biogeosciences, 17, 5787–5808, https://doi.org/10.5194/bg-17-5787-2020, https://doi.org/10.5194/bg-17-5787-2020, 2020
Short summary
Short summary
We developed software to calculate the root water uptake (RWU) of beech tree roots from soil moisture dynamics. We present our approach and compare RWU to measured sap flow in the tree stem. The study relates to two sites that are similar in topography and weather but with contrasting soils. While sap flow is very similar between the two sites, the RWU is different. This suggests that soil characteristics have substantial influence. Our easy-to-implement RWU estimate may help further studies.
Cited articles
Acuña Espinoza, E., Loritz, R., Álvarez Chaves, M., Bäuerle, N., and Ehret, U.: To bucket or not to bucket? Analyzing the performance and interpretability of hybrid hydrological models with dynamic parameterization, Hydrol. Earth Syst. Sci., 28, 2705–2719, https://doi.org/10.5194/hess-28-2705-2024, 2024.
Adam, J. C., Clark, E. A., Lettenmaier, D. P. and Wood, E. F.: Correction of global precipitation products for orographic effects, J. Climate, 19, 15–38, https://doi.org/10.1175/JCLI3604.1, 2006.
Agarwal, A., Marwan, N., Maheswaran, R., Ozturk, U., Kurths, J., and Merz, B.: Optimal design of hydrometric station networks based on complex network analysis, Hydrol. Earth Syst. Sci., 24, 2235–2251, https://doi.org/10.5194/hess-24-2235-2020, 2020.
Alexopoulos, M. J., Müller-Thomy, H., Nistahl, P., Šraj, M., and Bezak, N.: Validation of precipitation reanalysis products for rainfall-runoff modelling in Slovenia, Hydrol. Earth Syst. Sci., 27, 2559–2578, https://doi.org/10.5194/hess-27-2559-2023, 2023.
Bandhauer, M., Isotta, F., Lakatos, M., Lussana, C., Båserud, L., Izsák, B., Szentes, O., Tveito, O. E., and Frei, C.: Evaluation of daily precipitation analyses in E-OBS (v19.0e) and ERA5 by comparison to regional high-resolution datasets in European regions, Int. J. Climatol., 42, 727–747, https://doi.org/10.1002/joc.7269, 2022.
Bárdossy, A., Anwar, F., and Seidel, J.: Hydrological Modelling in Data Sparse Environment: Inverse Modelling of a Historical Flood Event, Water (Switzerland), 12, https://doi.org/10.3390/w12113242, 2020.
Bárdossy, A., Kilsby, C., Birkinshaw, S., Wang, N., and Anwar, F.: Is Precipitation Responsible for the Most Hydrological Model Uncertainty?, Front. Water, 4, 1–17, https://doi.org/10.3389/frwa.2022.836554, 2022.
Baste, S., Klotz, D., Espinoza, E. A., Bardossy, A., and Loritz, R.: Unveiling the Limits of Deep Learning Models in Hydrological Extrapolation Tasks, Hydrol. Earth Syst. Sci., 29, 5871–5891, https://doi.org/10.5194/hess-29-5871-2025, 2025.
Beauchamp, J., Leconte, R., Trudel, M., and Brissette, F.: Estimation of the summer-fall PMP and PMF of a northern watershed under a changed climate, Water Resour. Res., 49, 3852–3862, https://doi.org/10.1002/wrcr.20336, 2013.
Berghuijs, W. R., Harrigan, S., Molnar, P., Slater, L. J., and Kirchner, J. W.: The Relative Importance of Different Flood-Generating Mechanisms Across Europe, Water Resour. Res., 55, 4582–4593, https://doi.org/10.1029/2019WR024841, 2019.
Bergström, S. and Forsman, A.: Development of a Conceptual Deterministic Rainfall–Runoff Model., Nord. Hydrol., 4, 147–170, https://doi.org/10.2166/nh.1973.0012, 1973.
Bishop, C. M.: Pattern recognition and machine learning, Springer, New York, ISBN 978-0-387-31073-2, 2006.
Borga, M., Gaume, E., Creutin, J. D., and Marchi, L.: Surveying flash floods: gauging the ungauged extremes, Hydrol. Process., 22, 3883–3885, https://doi.org/10.1002/hyp.7111, 2008.1.
Brocca, L., Moramarco, T., Melone, F., and Wagner, W.: A new method for rainfall estimation through soil moisture observations, Geophys. Res. Lett., 40, 853–858, https://doi.org/10.1002/grl.50173, 2013.
Bronstert, A., Agarwal, A., Boessenkool, B., Crisologo, I., Fischer, M., Heistermann, M., Köhn-Reich, L., López-Tarazón, J. A., Moran, T., Ozturk, U., Reinhardt-Imjela, C., and Wendi, D.: Forensic hydro-meteorological analysis of an extreme flash flood: The 2016-05-29 event in Braunsbach, SW Germany, Sci. Total Environ., 630, 977–991, https://doi.org/10.1016/j.scitotenv.2018.02.241, 2018.
Casado Rodríguez, J.: CAMELS-ES: Catchment Attributes and Meteorology for Large-Sample Studies – Spain, Zenodo [code], https://doi.org/10.5281/zenodo.8428374, 2023.
Chen, C. T. and Chang, W. Der: A feedforward neural network with function shape autotuning, Neural Networks, 9, 627–641, https://doi.org/10.1016/0893-6080(96)00006-8, 1996.
Clerc-Schwarzenbach, F. M., Selleri, G., Neri, M., Toth, E., van Meerveld, I., and Seibert, J.: Large-sample hydrology: a few camels or a whole caravan?, Hydrology and Earth System Sciences, 28, 4219–4237, https://doi.org/10.5194/hess-28-4219-2024, 2024.
Cornes, R. C., van der Schrier, G., van den Besselaar, E. J. M., and Jones, P. D.: An Ensemble Version of the E-OBS Temperature and Precipitation Data Sets, J. Geophys. Res. Atmos., 123, 9391–9409, https://doi.org/10.1029/2017JD028200, 2018.
Coxon, G., Addor, N., Bloomfield, J. P., Freer, J., Fry, M., Hannaford, J., Howden, N. J. K., Lane, R., Lewis, M., Robinson, E. L., Wagener, T., and Woods, R.: CAMELS-GB: hydrometeorological time series and landscape attributes for 671 catchments in Great Britain, Earth Syst. Sci. Data, 12, 2459–2483, https://doi.org/10.5194/essd-12-2459-2020, 2020.
Dolich, A., Maharjan, A., Mälicke, M., Manoj J, A., and Loritz, R.: Caravan-DE: Caravan extension Germany – German dataset for large-sample hydrology, Zenodo [code], https://doi.org/10.5281/zenodo.14755229, 2025.
Dunne, T.: Field studies of hillslope flow processes, in: Hillslope Hydrology, edited by: Kirkby, M. J., John Wiley & Sons, 227–293, ISBN 978-0-471-99510-4, 1978.
Essou, G. R. C., Sabarly, F., Lucas-Picher, P., Brissette, F., and Poulin, A.: Can precipitation and temperature from meteorological reanalyses be used for hydrological modeling?, J. Hydrometeorol., 17, 1929–1950, https://doi.org/10.1175/JHM-D-15-0138.1, 2016.
Färber, C., Plessow, H., Kratzert, F., Addor, N., Shalev, G., and Looser, U.: GRDC-Caravan: extending the original dataset with data from the Global Runoff Data Centre, Zenodo [code], https://doi.org/10.5281/zenodo.10074416, 2023.
Fujihara, Y., Simonovic, S. P., Topaloglu, F., Tanaka, K., and Watanabe, T.: An inverse-modelling approach to assess the impacts of climate change in the Seyhan River basin, Turkey, Hydrol. Sci. J., 53, 1121–1136, https://doi.org/10.1623/hysj.53.6.1121, 2008.
Gelaro, R., McCarty, W., Suárez, M. J., Todling, R., Molod, A., Takacs, L., Randles, C. A., Darmenov, A., Bosilovich, M. G., Reichle, R., Wargan, K., Coy, L., Cullather, R., Draper, C., Akella, S., Buchard, V., Conaty, A., da Silva, A. M., Gu, W., Kim, G.-K., Koster, R., Lucchesi, R., Merkova, D., Nielsen, J. E., Partyka, G., Pawson, S., Putman, W., Rienecker, M., Schubert, S. D., Sienkiewicz, M., and Zhao, B.: The Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2), J. Clim., 30, 5419–5454, https://doi.org/10.1175/JCLI-D-16-0758.1, 2017.
Global Modeling And Assimilation Office: MERRA-2 tavg1_2d_lnd_Nx: 2d, 1-Hourly, Time-Averaged, Single-Level, Assimilation, Land Surface Diagnostics V5.12.4, https://doi.org/10.5067/RKPHT8KC1Y1T, 2015.
Goteti, G. and Famiglietti, J.: Extent of gross underestimation of precipitation in India, Hydrol. Earth Syst. Sci., 28, 3435–3455, https://doi.org/10.5194/hess-28-3435-2024, 2024.
Gu, L., Yin, J., Wang, S., Chen, J., Qin, H., Yan, X., He, S., and Zhao, T.: How well do the multi-satellite and atmospheric reanalysis products perform in hydrological modelling, J. Hydrol., 617, 128920, https://doi.org/10.1016/j.jhydrol.2022.128920, 2023.
Gupta, H. V., Kling, H., Yilmaz, K. K., and Martinez, G. F.: Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling, J. Hydrol., 377, 80–91, https://doi.org/10.1016/j.jhydrol.2009.08.003, 2009.
Hochreiter, S.: The Vanishing Gradient Problem During Learning Recurrent Neural Nets and Problem Solutions, Int. J. Uncertainty, Fuzziness Knowledge-Based Syst., 06, 107–116, https://doi.org/10.1142/S0218488598000094, 1998.
Höge, M., Kauzlaric, M., Siber, R., Schönenberger, U., Horton, P., Schwanbeck, J., Floriancic, M. G., Viviroli, D., Wilhelm, S., Sikorska-Senoner, A. E., Addor, N., Brunner, M., Pool, S., Zappa, M., and Fenicia, F.: Catchment attributes and hydro-meteorological time series for large-sample studies across hydrologic Switzerland, Earth Syst. Sci. Data, 15, 5755–5784, https://doi.org/10.5194/essd-15-5755-2023, 2023.
Horton, R. E.: The role of infiltration in the hydrology cycle, Eos Trans, AGU, 14, 446–460, https://doi.org/10.1029/TR014i001p00446, 1932.
Hrachowitz, M., Savenije, H. H. G., Blöschl, G., McDonnell, J. J., Sivapalan, M., Pomeroy, J. W., Arheimer, B., Blume, T., Clark, M. P., Ehret, U., Fenicia, F., Freer, J. E., Gelfan, A., Gupta, H. V., Hughes, D. A., Hut, R. W., Montanari, A., Pande, S., Tetzlaff, D., Troch, P. A., Uhlenbrook, S., Wagener, T., Winsemius, H. C., Woods, R. A., Zehe, E., and Cudennec, C.: A decade of Predictions in Ungauged Basins (PUB)-a review, Hydrol. Sci. J., 58, 1198–1255, https://doi.org/10.1080/02626667.2013.803183, 2013.
Kirchner, J. W.: Catchments as simple dynamical systems: Catchment characterization, rainfall–runoff modeling, and doing hydrology backward, Water Resour. Res., 45, 1–34, https://doi.org/10.1029/2008WR006912, 2009.
Klotz, D., Kratzert, F., Gauch, M., Keefe Sampson, A., Brandstetter, J., Klambauer, G., Hochreiter, S., and Nearing, G.: Uncertainty estimation with deep learning for rainfall–runoff modeling, Hydrol. Earth Syst. Sci., 26, 1673–1693, https://doi.org/10.5194/hess-26-1673-2022, 2022.
Kratzert, F., Klotz, D., Brenner, C., Schulz, K., and Herrnegger, M.: Rainfall–runoff modelling using Long Short-Term Memory (LSTM) networks, Hydrol. Earth Syst. Sci., 22, 6005–6022, https://doi.org/10.5194/hess-22-6005-2018, 2018.
Kratzert, F., Nearing, G., Addor, N., Erickson, T., Gauch, M., Gilon, O., Gudmundsson, L., Hassidim, A., Klotz, D., Nevo, S., Shalev, G., and Matias, Y.: Caravan – A global community dataset for large-sample hydrology, Sci. Data, 10, 61, https://doi.org/10.1038/s41597-023-01975-w, 2023.
Kretzschmar, A., Tych, W., and Chappell, N. A.: Reversing hydrology: Estimation of sub-hourly rainfall time-series from streamflow, Environ. Model. Softw., 60, 290–301, https://doi.org/10.1016/j.envsoft.2014.06.017, 2014.
Krier, R., Matgen, P., Goergen, K., Pfister, L., Hoffmann, L., Kirchner, J. W., Uhlenbrook, S., and Savenije, H. H. G.: Inferring catchment precipitation by doing hydrology backward: A test in 24 small and mesoscale catchments in Luxembourg, Water Resour. Res., 48, 1–15, https://doi.org/10.1029/2011WR010657, 2012.
Li, B., Rodell, M., Kumar, S., Beaudoing, H. K., Getirana, A., Zaitchik, B. F., de Goncalves, L. G., Cossetin, C., Bhanja, S., Mukherjee, A., Tian, S., Tangdamrongsub, N., Long, D., Nanteza, J., Lee, J., Policelli, F., Goni, I. B., Daira, D., Bila, M., de Lannoy, G., Mocko, D., Steele-Dunne, S. C., Save, H., and Bettadpur, S.: Global GRACE Data Assimilation for Groundwater and Drought Monitoring: Advances and Challenges, Water Resour. Res., 55, 7564–7586, https://doi.org/10.1029/2018WR024618, 2019.
Linke, S., Lehner, B., Ouellet Dallaire, C., Ariwi, J., Grill, G., Anand, M., Beames, P., Burchard-Levine, V., Maxwell, S., Moidu, H., Tan, F., and Thieme, M.: Global hydro-environmental sub-basin and river reach characteristics at high spatial resolution, Sci. Data, 6, 283, https://doi.org/10.1038/s41597-019-0300-6, 2019.
Loritz, R., Hassler, S. K., Jackisch, C., Allroggen, N., van Schaik, L., Wienhöfer, J., and Zehe, E.: Picturing and modeling catchments by representative hillslopes, Hydrol. Earth Syst. Sci., 21, 1225–1249, https://doi.org/10.5194/hess-21-1225-2017, 2017.
Loritz, R., Dolich, A., Acuña Espinoza, E., Ebeling, P., Guse, B., Götte, J., Hassler, S. K., Hauffe, C., Heidbüchel, I., Kiesel, J., Mälicke, M., Müller-Thomy, H., Stölzle, M., and Tarasova, L.: CAMELS-DE: hydro-meteorological time series and attributes for 1582 catchments in Germany, Earth Syst. Sci. Data, 16, 5625–5642, https://doi.org/10.5194/essd-16-5625-2024, 2024a.
Loritz, R., Wu, C. H., Klotz, D., Gauch, M., Kratzert, F., and Bassiouni, M.: Generalizing Tree–Level Sap Flow Across the European Continent, Geophys. Res. Lett., 51, https://doi.org/10.1029/2023GL107350, 2024b.
Manoj J, A.: Simulation results of Manoj J et al. (2023), Zenodo [code], https://doi.org/10.5281/zenodo.10958813, 2024.
Manoj J, A.: Ash-Manoj/Hy2DL_Caravan: Conceptual models for Manoj J et al. (2024), Zenodo [code], https://doi.org/10.5281/zenodo.15051966, 2025a.
Manoj J, A.: Ash-Manoj/lstm_backward: LSTM models for Manoj J et al. (2024), Zenodo [code], https://doi.org/10.5281/zenodo.14161027, 2025b.
Manoj J, A., Pérez Ciria, T., Chiogna, G., Salzmann, N., and Agarwal, A.: Characterising the coincidence of soil moisture – precipitation extremes as a possible precursor to European floods, J. Hydrol., 620, 129445, https://doi.org/10.1016/j.jhydrol.2023.129445, 2023.
Manoj J, A., Loritz, R., Villinger, F., Mälicke, M., Koopaeidar, M., Göppert, H., and Zehe, E.: Toward Flash Flood Modeling Using Gradient Resolving Representative Hillslopes, Water Resour. Res., 60, https://doi.org/10.1029/2023WR036420, 2024.
Merz, B., Blöschl, G., Vorogushyn, S., Dottori, F., Aerts, J. C. J. H., Bates, P., Bertola, M., Kemter, M., Kreibich, H., Lall, U., and Macdonald, E.: Causes, impacts and patterns of disastrous river floods, Nat. Rev. Earth Environ., 2, 592–609, https://doi.org/10.1038/s43017-021-00195-3, 2021.
Meyer, J., Neuper, M., Mathias, L., Zehe, E., and Pfister, L.: Atmospheric conditions favouring extreme precipitation and flash floods in temperate regions of Europe, Hydrol. Earth Syst. Sci., 26, 6163–6183, https://doi.org/10.5194/hess-26-6163-2022, 2022.
Milly, P. C. D., Betancourt, J., Falkenmark, M., Hirsch, R. M., Kundzewicz, Z. W., Lettenmaier, D. P., and Stouffer, R. J.: Climate change: Stationarity is dead: Whither water management?, Science, 319, 573–574, https://doi.org/10.1126/science.1151915, 2008.
Montanari, A., Young, G., Savenije, H. H. G., Hughes, D., Wagener, T., Ren, L. L., Koutsoyiannis, D., Cudennec, C., Toth, E., Grimaldi, S., Blöschl, G., Sivapalan, M., Beven, K., Gupta, H., Hipsey, M., Schaefli, B., Arheimer, B., Boegh, E., Schymanski, S. J., Di Baldassarre, G., Yu, B., Hubert, P., Huang, Y., Schumann, A., Post, D. A., Srinivasan, V., Harman, C., Thompson, S., Rogger, M., Viglione, A., McMillan, H., Characklis, G., Pang, Z., and Belyaev, V.: “Panta Rhei-Everything Flows”: Change in hydrology and society-The IAHS Scientific Decade 2013–2022, Hydrol. Sci. J., 58, 1256–1275, https://doi.org/10.1080/02626667.2013.809088, 2013.
Moriasi, D. N., Arnold, J. G., Van Liew, M. W., Bingner, R. L., Harmel, R. D., and Veith, T. L.: Model Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed Simulations, Trans. ASABE, 50, 885–900, https://doi.org/10.13031/2013.23153, 2007.
Muñoz-Sabater, J., Dutra, E., Agustí-Panareda, A., Albergel, C., Arduini, G., Balsamo, G., Boussetta, S., Choulga, M., Harrigan, S., Hersbach, H., Martens, B., Miralles, D. G., Piles, M., Rodríguez-Fernández, N. J., Zsoter, E., Buontempo, C., and Thépaut, J.-N.: ERA5-Land: a state-of-the-art global reanalysis dataset for land applications, Earth Syst. Sci. Data, 13, 4349–4383, https://doi.org/10.5194/essd-13-4349-2021, 2021.
Nash, J. E. and Sutcliffe, J. V: River flow forecasting through conceptual models, Part I – a discussion of principles, J. Hydrol., 27, 282–290, https://doi.org/10.1016/0022-1694(70)90255-6, 1970.
Nearing, G. S. and Gupta, H. V.: The quantity and quality of information in hydrologic models, Water Resour. Res., 51, 524–538, https://doi.org/10.1002/2014WR015895, 2015.
Nijzink, J., Loritz, R., Gourdol, L., Zoccatelli, D., Iffly, J. F., and Pfister, L.: CAMELS-LUX: Highly Resolved Hydro-Meteorological and Atmospheric Data for Physiographically Characterized Catchments around Luxembourg, Zenodo [code], https://doi.org/10.5281/zenodo.13846620, 2024.
Ongie, G., Jalal, A., Metzler, C. A., Baraniuk, R. G., Dimakis, A. G., and Willett, R.: Deep Learning Techniques for Inverse Problems in Imaging, IEEE J. Sel. Areas Inf. Theory, 1, 39–56, https://doi.org/10.1109/jsait.2020.2991563, 2020.
Onogi, K., Tsutsui, J., Koide, H., Sakamoto, M., Kobayashi, S., Hatsushika, H., Matsumoto, T., Yamazaki, N., Kamahori, H., Takahashi, K., Kadokura, S., Wada, K., Kato, K., Oyama, R., Ose, T., Mannoji, N., and Taira, R.: The JRA-25 Reanalysis, J. Meteorol. Soc. Japan. Ser. II, 85, 369–432, https://doi.org/10.2151/jmsj.85.369, 2007.
Rienecker, M. M., Suarez, M. J., Gelaro, R., Todling, R., Bacmeister, J., Liu, E., Bosilovich, M. G., Schubert, S. D., Takacs, L., Kim, G.-K., Bloom, S., Chen, J., Collins, D., Conaty, A., da Silva, A., Gu, W., Joiner, J., Koster, R. D., Lucchesi, R., Molod, A., Owens, T., Pawson, S., Pegion, P., Redder, C. R., Reichle, R., Robertson, F. R., Ruddick, A. G., Sienkiewicz, M., and Woollen, J.: MERRA: NASA's Modern-Era Retrospective Analysis for Research and Applications, J. Clim., 24, 3624–3648, https://doi.org/10.1175/JCLI-D-11-00015.1, 2011.
Seibert, J.: HBV light, HBV Light version 2 User's Man., https://www.geo.uzh.ch/dam/jcr:c8afa73c-ac90-478e-a8c7-929eed7b1b62/HBV_manual_2005.pdf (last access: 25 November 2024), 2005.
Seidel, J., Imbery, F., Dostal, P., Sudhaus, D., and Bürger, K.: Potential of historical meteorological and hydrological data for the reconstruction of historical flood events – the example of the 1882 flood in southwest Germany, Nat. Hazards Earth Syst. Sci., 9, 175–183, https://doi.org/10.5194/nhess-9-175-2009, 2009.
Seneviratne, S. I., Corti, T., Davin, E. L., Hirschi, M., Jaeger, E. B., Lehner, I., Orlowsky, B., and Teuling, A. J.: Investigating soil moisture–climate interactions in a changing climate: A review, Earth-Science Rev., 99, 125–161, https://doi.org/10.1016/j.earscirev.2010.02.004, 2010.
Sivapalan, M., Takeuchi, K., Franks, S. W., Gupta, V. K., Karambiri, H., Lakshmi, V., Liang, X., McDonnell, J. J., Mendiondo, E. M., O'Connell, P. E., Oki, T., Pomeroy, J. W., Schertzer, D., Uhlenbrook, S., and Zehe, E.: IAHS Decade on Predictions in Ungauged Basins (PUB), 2003–2012: Shaping an exciting future for the hydrological sciences, Hydrol. Sci. J., 48, 857–880, https://doi.org/10.1623/hysj.48.6.857.51421, 2003.
Sun, S. and Bertrand-Krajewski, J. L.: Separately accounting for uncertainties in rainfall and runoff: Calibration of event-based conceptual hydrological models in small urban catchments using Bayesian method, Water Resour. Res., 49, 5381–5394, https://doi.org/10.1002/wrcr.20444, 2013.
Tarek, M., Brissette, F. P., and Arsenault, R.: Evaluation of the ERA5 reanalysis as a potential reference dataset for hydrological modelling over North America, Hydrol. Earth Syst. Sci., 24, 2527–2544, https://doi.org/10.5194/hess-24-2527-2020, 2020.
Taszarek, M., Allen, J. T., Marchio, M., and Brooks, H. E.: Global climatology and trends in convective environments from ERA5 and rawinsonde data, npj Clim. Atmos. Sci., 4, 1–11, https://doi.org/10.1038/s41612-021-00190-x, 2021.
Tetzlaff, D., Carey, S. K., McNamara, J. P., Laudon, H., and Soulsby, C.: The essential value of long-term experimental data for hydrology and water management, Water Resour. Res., 53, 2598–2604, https://doi.org/10.1002/2017WR020838, 2017.
Teuling, A. J., Lehner, I., Kirchner, J. W., and Seneviratne, S. I.: Catchments as simple dynamical systems: Experience from a Swiss prealpine catchment, Water Resour. Res., 46, 1–15, https://doi.org/10.1029/2009WR008777, 2010.
Villinger, F., Loritz, R., and Zehe, E.: Torrents in small rural Catchments and the Potential of physics-based Models for their Simulation, Hydrol. und Wasserbewirtschaftung, 66, 284–285, https://doi.org/10.5675/HyWa_2022.6_1, 2022.
World Climate Research program (WCRP): Expert Team on Climate Change Detection and Indices (ETCCDI), https://www.wcrp-climate.org/etccdi (last access: 7 March 2025), 2021.
Xu, C., Wang, W., Hu, Y., and Liu, Y.: Evaluation of ERA5, ERA5-Land, GLDAS-2.1, and GLEAM potential evapotranspiration data over mainland China, J. Hydrol. Reg. Stud., 51, 101651, https://doi.org/10.1016/j.ejrh.2023.101651, 2024.
Yumnam, K., Kumar Guntu, R., Rathinasamy, M., and Agarwal, A.: Quantile-based Bayesian Model Averaging approach towards merging of precipitation products, J. Hydrol., 604, 127206, https://doi.org/10.1016/j.jhydrol.2021.127206, 2022.
Zehe, E. and Blöschl, G.: Predictability of hydrologic response at the plot and catchment scales: Role of initial conditions, Water Resour. Res., 40, https://doi.org/10.1029/2003WR002869, 2004.
Zehe, E., Maurer, T., Ihringer, J., and Plate, E.: Modelling water flow and mass transport in a Loess catchment, Phys. Chem. Earth, Part B, 26, 487–507, https://doi.org/10.1016/S0378-3774(99)00083-9, 2001.
Short summary
Traditional hydrological models typically operate in a forward mode, simulating streamflow and other catchment fluxes based on precipitation input. In this study, we explored the possibility of reversing this process, inferring precipitation from streamflow data, to improve flood event modelling. We then used the generated precipitation series to run hydrological models, resulting in more accurate estimates of streamflow and soil moisture.
Traditional hydrological models typically operate in a forward mode, simulating streamflow and...
