Articles | Volume 29, issue 19
https://doi.org/10.5194/hess-29-5005-2025
© 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-29-5005-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
08 Oct 2025
Research article |
| 08 Oct 2025
| 08 Oct 2025
How well do process-based and data-driven hydrological models learn from limited discharge data?
Maria Staudinger
CORRESPONDING AUTHOR
Department of Geography, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
Anna Herzog
Department of Hydrology and Climatology, Institute of Environmental Science and Geography, University of Potsdam, Potsdam, Germany
Ralf Loritz
Institute of Water and Environment, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Tobias Houska
Department of Landscape Ecology and Resources Management, University of Gießen, Gießen, Germany
Sandra Pool
Department Water Resources and Drinking Water, Eawag – Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland
Diana Spieler
Department of Hydrosciences, Institute of Hydrology and Meteorology, TUD Dresden University of Technology, Dresden, Germany
now at: Schulich School of Engineering, University of Calgary, Calgary, Canada
Paul D. Wagner
Department of Hydrology and Water Resources Management, Institute for Natural Resource Conservation, Kiel University, Kiel, Germany
Juliane Mai
Earth and Environmental Science, University of Waterloo, Waterloo, Ontario, Canada
Jens Kiesel
Department of Hydrology and Water Resources Management, Institute for Natural Resource Conservation, Kiel University, Kiel, Germany
Stone Environmental, 535 Stone Cutters Way, 05602 Montpelier, VT, USA
Stephan Thober
Computational Hydrosystems, Helmholtz Centre for Environmental Research – UFZ, Leipzig, Germany
Björn Guse
Department of Hydrology and Water Resources Management, Institute for Natural Resource Conservation, Kiel University, Kiel, Germany
German Research Centre for Geosciences, Section Hydrology, Potsdam, Germany
Uwe Ehret
Institute of Water and Environment, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
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Andrea L. Campoverde, Uwe Ehret, Patrick Ludwig, and Joaquim G. Pinto
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Revised manuscript not accepted
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Eduardo Acuña Espinoza, Ralf Loritz, Manuel Álvarez Chaves, Nicole Bäuerle, and Uwe Ehret
Hydrol. Earth Syst. Sci., 28, 2705–2719, https://doi.org/10.5194/hess-28-2705-2024, https://doi.org/10.5194/hess-28-2705-2024, 2024
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Qiutong Yu, Bryan A. Tolson, Hongren Shen, Ming Han, Juliane Mai, and Jimmy Lin
Hydrol. Earth Syst. Sci., 28, 2107–2122, https://doi.org/10.5194/hess-28-2107-2024, https://doi.org/10.5194/hess-28-2107-2024, 2024
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Ayenew D. Ayalew, Paul D. Wagner, Dejene Sahlu, and Nicola Fohrer
Hydrol. Earth Syst. Sci., 28, 1853–1872, https://doi.org/10.5194/hess-28-1853-2024, https://doi.org/10.5194/hess-28-1853-2024, 2024
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Elena Macdonald, Bruno Merz, Björn Guse, Viet Dung Nguyen, Xiaoxiang Guan, and Sergiy Vorogushyn
Hydrol. Earth Syst. Sci., 28, 833–850, https://doi.org/10.5194/hess-28-833-2024, https://doi.org/10.5194/hess-28-833-2024, 2024
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In some rivers, the occurrence of extreme flood events is more likely than in other rivers – they have heavy-tailed distributions. We find that threshold processes in the runoff generation lead to such a relatively high occurrence probability of extremes. Further, we find that beyond a certain return period, i.e. for rare events, rainfall is often the dominant control compared to runoff generation. Our results can help to improve the estimation of the occurrence probability of extreme floods.
Elizabeth Gachibu Wangari, Ricky Mwangada Mwanake, Tobias Houska, David Kraus, Gretchen Maria Gettel, Ralf Kiese, Lutz Breuer, and Klaus Butterbach-Bahl
Biogeosciences, 20, 5029–5067, https://doi.org/10.5194/bg-20-5029-2023, https://doi.org/10.5194/bg-20-5029-2023, 2023
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Agricultural landscapes act as sinks or sources of the greenhouse gases (GHGs) CO2, CH4, or N2O. Various physicochemical and biological processes control the fluxes of these GHGs between ecosystems and the atmosphere. Therefore, fluxes depend on environmental conditions such as soil moisture, soil temperature, or soil parameters, which result in large spatial and temporal variations of GHG fluxes. Here, we describe an example of how this variation may be studied and analyzed.
Marvin Höge, Martina Kauzlaric, Rosi Siber, Ursula Schönenberger, Pascal Horton, Jan Schwanbeck, Marius Günter Floriancic, Daniel Viviroli, Sibylle Wilhelm, Anna E. Sikorska-Senoner, Nans Addor, Manuela Brunner, Sandra Pool, Massimiliano Zappa, and Fabrizio Fenicia
Earth Syst. Sci. Data, 15, 5755–5784, https://doi.org/10.5194/essd-15-5755-2023, https://doi.org/10.5194/essd-15-5755-2023, 2023
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CAMELS-CH is an open large-sample hydro-meteorological data set that covers 331 catchments in hydrologic Switzerland from 1 January 1981 to 31 December 2020. It comprises (a) daily data of river discharge and water level as well as meteorologic variables like precipitation and temperature; (b) yearly glacier and land cover data; (c) static attributes of, e.g, topography or human impact; and (d) catchment delineations. CAMELS-CH enables water and climate research and modeling at catchment level.
Samah Larabi, Juliane Mai, Markus Schnorbus, Bryan A. Tolson, and Francis Zwiers
Hydrol. Earth Syst. Sci., 27, 3241–3263, https://doi.org/10.5194/hess-27-3241-2023, https://doi.org/10.5194/hess-27-3241-2023, 2023
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The computational cost of sensitivity analysis (SA) becomes prohibitive for large hydrologic modeling domains. Here, using a large-scale Variable Infiltration Capacity (VIC) deployment, we show that watershed classification helps identify the spatial pattern of parameter sensitivity within the domain at a reduced cost. Findings reveal the opportunity to leverage climate and land cover attributes to reduce the cost of SA and facilitate more rapid deployment of large-scale land surface models.
Ricky Mwangada Mwanake, Gretchen Maria Gettel, Elizabeth Gachibu Wangari, Clarissa Glaser, Tobias Houska, Lutz Breuer, Klaus Butterbach-Bahl, and Ralf Kiese
Biogeosciences, 20, 3395–3422, https://doi.org/10.5194/bg-20-3395-2023, https://doi.org/10.5194/bg-20-3395-2023, 2023
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Despite occupying <1 %; of the globe, streams are significant sources of greenhouse gas (GHG) emissions. In this study, we determined anthropogenic effects on GHG emissions from streams. We found that anthropogenic-influenced streams had up to 20 times more annual GHG emissions than natural ones and were also responsible for seasonal peaks. Anthropogenic influences also altered declining GHG flux trends with stream size, with potential impacts on stream-size-based spatial upscaling techniques.
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.
Robert Chlumsky, Juliane Mai, James R. Craig, and Bryan A. Tolson
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2023-69, https://doi.org/10.5194/hess-2023-69, 2023
Revised manuscript not accepted
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A blended model allows multiple hydrologic processes to be represented in a single model, which allows for a model to achieve high performance without the need to modify its structure for different catchments. Here, we improve upon the initial blended version by testing more than 30 blended models in twelve catchments to improve the overall model performance. We validate our proposed, updated blended model version with independent catchments, and make this version available for open use.
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.
Richard Arsenault, Jean-Luc Martel, Frédéric Brunet, François Brissette, and Juliane Mai
Hydrol. Earth Syst. Sci., 27, 139–157, https://doi.org/10.5194/hess-27-139-2023, https://doi.org/10.5194/hess-27-139-2023, 2023
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Predicting flow in rivers where no observation records are available is a daunting task. For decades, hydrological models were set up on these gauges, and their parameters were estimated based on the hydrological response of similar or nearby catchments where records exist. New developments in machine learning have now made it possible to estimate flows at ungauged locations more precisely than with hydrological models. This study confirms the performance superiority of machine learning models.
Friedrich Boeing, Oldrich Rakovec, Rohini Kumar, Luis Samaniego, Martin Schrön, Anke Hildebrandt, Corinna Rebmann, Stephan Thober, Sebastian Müller, Steffen Zacharias, Heye Bogena, Katrin Schneider, Ralf Kiese, Sabine Attinger, and Andreas Marx
Hydrol. Earth Syst. Sci., 26, 5137–5161, https://doi.org/10.5194/hess-26-5137-2022, https://doi.org/10.5194/hess-26-5137-2022, 2022
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In this paper, we deliver an evaluation of the second generation operational German drought monitor (https://www.ufz.de/duerremonitor) with a state-of-the-art compilation of observed soil moisture data from 40 locations and four different measurement methods in Germany. We show that the expressed stakeholder needs for higher resolution drought information at the one-kilometer scale can be met and that the agreement of simulated and observed soil moisture dynamics can be moderately improved.
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.
Bahar Bahrami, Anke Hildebrandt, Stephan Thober, Corinna Rebmann, Rico Fischer, Luis Samaniego, Oldrich Rakovec, and Rohini Kumar
Geosci. Model Dev., 15, 6957–6984, https://doi.org/10.5194/gmd-15-6957-2022, https://doi.org/10.5194/gmd-15-6957-2022, 2022
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Leaf area index (LAI) and gross primary productivity (GPP) are crucial components to carbon cycle, and are closely linked to water cycle in many ways. We develop a Parsimonious Canopy Model (PCM) to simulate GPP and LAI at stand scale, and show its applicability over a diverse range of deciduous broad-leaved forest biomes. With its modular structure, the PCM is able to adapt with existing data requirements, and run in either a stand-alone mode or as an interface linked to hydrologic models.
Daniel Viviroli, Anna E. Sikorska-Senoner, Guillaume Evin, Maria Staudinger, Martina Kauzlaric, Jérémy Chardon, Anne-Catherine Favre, Benoit Hingray, Gilles Nicolet, Damien Raynaud, Jan Seibert, Rolf Weingartner, and Calvin Whealton
Nat. Hazards Earth Syst. Sci., 22, 2891–2920, https://doi.org/10.5194/nhess-22-2891-2022, https://doi.org/10.5194/nhess-22-2891-2022, 2022
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Estimating the magnitude of rare to very rare floods is a challenging task due to a lack of sufficiently long observations. The challenge is even greater in large river basins, where precipitation patterns and amounts differ considerably between individual events and floods from different parts of the basin coincide. We show that a hydrometeorological model chain can provide plausible estimates in this setting and can thus inform flood risk and safety assessments for critical infrastructure.
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.
Wouter J. M. Knoben and Diana Spieler
Hydrol. Earth Syst. Sci., 26, 3299–3314, https://doi.org/10.5194/hess-26-3299-2022, https://doi.org/10.5194/hess-26-3299-2022, 2022
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This paper introduces educational materials that can be used to teach students about model structure uncertainty in hydrological modelling. There are many different hydrological models and differences between these models impact their usefulness in different places. Such models are often used to support decision making about water resources and to perform hydrological science, and it is thus important for students to understand that model choice matters.
Katrin M. Nissen, Stefan Rupp, Thomas M. Kreuzer, Björn Guse, Bodo Damm, and Uwe Ulbrich
Nat. Hazards Earth Syst. Sci., 22, 2117–2130, https://doi.org/10.5194/nhess-22-2117-2022, https://doi.org/10.5194/nhess-22-2117-2022, 2022
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A statistical model is introduced which quantifies the influence of individual potential triggering factors and their interactions on rockfall probability in central Europe. The most important factor is daily precipitation, which is most effective if sub-surface moisture levels are high. Freeze–thaw cycles in the preceding days can further increase the rockfall hazard. The model can be applied to climate simulations in order to investigate the effect of climate change on rockfall probability.
Chaogui Lei, Paul D. Wagner, and Nicola Fohrer
Hydrol. Earth Syst. Sci., 26, 2561–2582, https://doi.org/10.5194/hess-26-2561-2022, https://doi.org/10.5194/hess-26-2561-2022, 2022
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We presented an integrated approach to hydrologic modeling and partial least squares regression quantifying land use change impacts on water and nutrient balance over 3 decades. Results highlight that most variations (70 %–80 %) in water quantity and quality variables are explained by changes in land use class-specific areas and landscape metrics. Arable land influences water quantity and quality the most. The study provides insights on water resources management in rural lowland catchments.
Michelle Viswanathan, Tobias K. D. Weber, Sebastian Gayler, Juliane Mai, and Thilo Streck
Biogeosciences, 19, 2187–2209, https://doi.org/10.5194/bg-19-2187-2022, https://doi.org/10.5194/bg-19-2187-2022, 2022
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We analysed the evolution of model parameter uncertainty and prediction error as we updated parameters of a maize phenology model based on yearly observations, by sequentially applying Bayesian calibration. Although parameter uncertainty was reduced, prediction quality deteriorated when calibration and prediction data were from different maize ripening groups or temperature conditions. The study highlights that Bayesian methods should account for model limitations and inherent data structures.
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.
Robert Schweppe, Stephan Thober, Sebastian Müller, Matthias Kelbling, Rohini Kumar, Sabine Attinger, and Luis Samaniego
Geosci. Model Dev., 15, 859–882, https://doi.org/10.5194/gmd-15-859-2022, https://doi.org/10.5194/gmd-15-859-2022, 2022
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The recently released multiscale parameter regionalization (MPR) tool enables
environmental modelers to efficiently use extensive datasets for model setups.
It flexibly ingests the datasets using user-defined data–parameter relationships
and rescales parameter fields to given model resolutions. Modern
land surface models especially benefit from MPR through increased transparency and
flexibility in modeling decisions. Thus, MPR empowers more sound and robust
simulations of the Earth system.
Michael Peichl, Stephan Thober, Luis Samaniego, Bernd Hansjürgens, and Andreas Marx
Hydrol. Earth Syst. Sci., 25, 6523–6545, https://doi.org/10.5194/hess-25-6523-2021, https://doi.org/10.5194/hess-25-6523-2021, 2021
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Using a statistical model that can also take complex systems into account, the most important factors affecting wheat yield in Germany are determined. Different spatial damage potentials are taken into account. In many parts of Germany, yield losses are caused by too much soil water in spring. Negative heat effects as well as damaging soil drought are identified especially for north-eastern Germany. The model is able to explain years with exceptionally high yields (2014) and losses (2003, 2018).
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.
Nariman Mahmoodi, Jens Kiesel, Paul D. Wagner, and Nicola Fohrer
Hydrol. Earth Syst. Sci., 25, 5065–5081, https://doi.org/10.5194/hess-25-5065-2021, https://doi.org/10.5194/hess-25-5065-2021, 2021
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In this study, we assessed the sustainability of water resources in a wadi region with the help of a hydrologic model. Our assessment showed that the increases in groundwater demand and consumption exacerbate the negative impact of climate change on groundwater sustainability and hydrologic regime alteration. These alterations have severe consequences for a downstream wetland and its ecosystem. The approach may be applicable in other wadi regions with different climate and water use systems.
Nicolas Gasset, Vincent Fortin, Milena Dimitrijevic, Marco Carrera, Bernard Bilodeau, Ryan Muncaster, Étienne Gaborit, Guy Roy, Nedka Pentcheva, Maxim Bulat, Xihong Wang, Radenko Pavlovic, Franck Lespinas, Dikra Khedhaouiria, and Juliane Mai
Hydrol. Earth Syst. Sci., 25, 4917–4945, https://doi.org/10.5194/hess-25-4917-2021, https://doi.org/10.5194/hess-25-4917-2021, 2021
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In this paper, we highlight the importance of including land-data assimilation as well as offline precipitation analysis components in a regional reanalysis system. We also document the performance of the first multidecadal 10 km reanalysis performed with the GEM atmospheric model that can be used for seamless land-surface and hydrological modelling in North America. It is of particular interest for transboundary basins, as existing datasets often show discontinuities at the border.
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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.
Three process-based and four data-driven hydrological models are compared using different...
