Articles | Volume 28, issue 11
https://doi.org/10.5194/hess-28-2505-2024
© Author(s) 2024. 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-28-2505-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
13 Jun 2024
Research article |
| 13 Jun 2024
| 13 Jun 2024
Metamorphic testing of machine learning and conceptual hydrologic models
Peter Reichert
CORRESPONDING AUTHOR
Eawag: Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland
retired
Kai Ma
Institute of International Rivers and Eco-Security, Yunnan University, Kunming, China
Yunnan Key Laboratory of International Rivers and Transboundary Eco-security, Yunnan University, Kunming, China
Marvin Höge
Eawag: Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland
Fabrizio Fenicia
Eawag: Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland
Marco Baity-Jesi
Eawag: Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland
Dapeng Feng
Civil and Environmental Engineering, Pennsylvania State University, University Park, State College, PA, USA
Chaopeng Shen
Civil and Environmental Engineering, Pennsylvania State University, University Park, State College, PA, USA
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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., 29, 2361–2375, https://doi.org/10.5194/hess-29-2361-2025, https://doi.org/10.5194/hess-29-2361-2025, 2025
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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.
Yuan Yang, Ming Pan, Dapeng Feng, Mu Xiao, Taylor Dixon, Robert Hartman, Chaopeng Shen, Yalan Song, Agniv Sengupta, Luca Delle Monache, and F. Martin Ralph
EGUsphere, https://doi.org/10.5194/egusphere-2025-1708, https://doi.org/10.5194/egusphere-2025-1708, 2025
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We explore a machine learning-based data integration method that integrates streamflow (Q) and snow water equivalent (SWE) to improve streamflow estimates at various lag times (1–10 days, 1–6 months) and timescales (daily and monthly) over Western U.S. basins. Benefits rank as: integrating Q at the daily scale > Q at the monthly scale > SWE at the monthly scale > SWE at the daily scale. Results highlight the method’s potential for short- and long-term streamflow forecasting in the Western U.S.
Jiangtao Liu, Chaopeng Shen, Fearghal O'Donncha, Yalan Song, Wei Zhi, Hylke E. Beck, Tadd Bindas, Nicholas Kraabel, and Kathryn Lawson
EGUsphere, https://doi.org/10.5194/egusphere-2025-1706, https://doi.org/10.5194/egusphere-2025-1706, 2025
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Using global and regional datasets, we compared attention-based models and Long Short-Term Memory (LSTM) models to predict hydrologic variables. Our results show LSTM models perform better in simpler tasks, whereas attention-based models perform better in complex scenarios, offering insights for improved water resource management.
Mohammad Sina Jahangir, John Quilty, Chaopeng Shen, Andrea Scott, Scott Steinschneider, and Jan Adamowski
EGUsphere, https://doi.org/10.5194/egusphere-2025-846, https://doi.org/10.5194/egusphere-2025-846, 2025
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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This study presents a novel hybrid approach to streamflow prediction, significantly improving the efficiency and accuracy of fine-tuning deep learning models for hydrological prediction. Tested across numerous catchments in the U.S. and Europe, this method accelerates the fine-tuning process and improves prediction accuracy in locations beyond the training data. This innovative approach sets the stage for future hydrological models leveraging transfer learning.
Peijun Li, Yalan Song, Ming Pan, Kathryn Lawson, and Chaopeng Shen
EGUsphere, https://doi.org/10.5194/egusphere-2025-483, https://doi.org/10.5194/egusphere-2025-483, 2025
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This study explores how combining different model types improves streamflow predictions, especially in data-sparse scenarios. By integrating two highly accurate models with distinct mechanisms and leveraging multiple meteorological datasets, we highlight their unique strengths and set new accuracy benchmarks across spatiotemporal conditions. Our findings enhance the understanding of how diverse models and multi-source data can be effectively used to improve hydrological predictions.
Thiago Victor Medeiros do Nascimento, Julia Rudlang, Sebastian Gnann, Jan Seibert, Markus Hrachowitz, and Fabrizio Fenicia
EGUsphere, https://doi.org/10.5194/egusphere-2025-739, https://doi.org/10.5194/egusphere-2025-739, 2025
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Large-sample hydrological studies often overlook the importance of detailed landscape data in explaining river flow variability. Analyzing over 4,000 European catchments, we found that geology becomes a dominant factor—especially for baseflow—when using detailed regional maps. This highlights the need for high-resolution geological data to improve river flow regionalization, particularly in non-monitored areas.
Ather Abbas, Yuan Yang, Ming Pan, Yves Tramblay, Chaopeng Shen, Haoyu Ji, Solomon H. Gebrechorkos, Florian Pappenberger, Jong Cheol Pyo, Dapeng Feng, George Huffman, Phu Nguyen, Christian Massari, Luca Brocca, Tan Jackson, and Hylke E. Beck
EGUsphere, https://doi.org/10.5194/egusphere-2024-4194, https://doi.org/10.5194/egusphere-2024-4194, 2025
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Our study evaluated 23 precipitation datasets using a hydrological model at global scale to assess their suitability and accuracy. We found that MSWEP V2.8 excels due to its ability to integrate data from multiple sources, while others, such as IMERG and JRA-3Q, demonstrated strong regional performances. This research assists in selecting the appropriate dataset for applications in water resource management, hazard assessment, agriculture, and environmental monitoring.
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.
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.
Hongkai Gao, Markus Hrachowitz, Lan Wang-Erlandsson, Fabrizio Fenicia, Qiaojuan Xi, Jianyang Xia, Wei Shao, Ge Sun, and Hubert H. G. Savenije
Hydrol. Earth Syst. Sci., 28, 4477–4499, https://doi.org/10.5194/hess-28-4477-2024, https://doi.org/10.5194/hess-28-4477-2024, 2024
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The concept of the root zone is widely used but lacks a precise definition. Its importance in Earth system science is not well elaborated upon. Here, we clarified its definition with several similar terms to bridge the multi-disciplinary gap. We underscore the key role of the root zone in the Earth system, which links the biosphere, hydrosphere, lithosphere, atmosphere, and anthroposphere. To better represent the root zone, we advocate for a paradigm shift towards ecosystem-centred modelling.
Dapeng Feng, Hylke Beck, Jens de Bruijn, Reetik Kumar Sahu, Yusuke Satoh, Yoshihide Wada, Jiangtao Liu, Ming Pan, Kathryn Lawson, and Chaopeng Shen
Geosci. Model Dev., 17, 7181–7198, https://doi.org/10.5194/gmd-17-7181-2024, https://doi.org/10.5194/gmd-17-7181-2024, 2024
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Accurate hydrologic modeling is vital to characterizing water cycle responses to climate change. For the first time at this scale, we use differentiable physics-informed machine learning hydrologic models to simulate rainfall–runoff processes for 3753 basins around the world and compare them with purely data-driven and traditional modeling approaches. This sets a benchmark for hydrologic estimates around the world and builds foundations for improving global hydrologic simulations.
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.
Jiaxing Liang, Hongkai Gao, Fabrizio Fenicia, Qiaojuan Xi, Yahui Wang, and Hubert H. G. Savenije
EGUsphere, https://doi.org/10.5194/egusphere-2024-550, https://doi.org/10.5194/egusphere-2024-550, 2024
Preprint archived
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The root zone storage capacity (Sumax) is a key element in hydrology and land-atmospheric interaction. In this study, we utilized a hydrological model and a dynamic parameter identification method, to quantify the temporal trends of Sumax for 497 catchments in the USA. We found that 423 catchments (85 %) showed increasing Sumax, which averagely increased from 178 to 235 mm between 1980 and 2014. The increasing trend was also validated by multi-sources data and independent methods.
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.
Hongkai Gao, Fabrizio Fenicia, and Hubert H. G. Savenije
Hydrol. Earth Syst. Sci., 27, 2607–2620, https://doi.org/10.5194/hess-27-2607-2023, https://doi.org/10.5194/hess-27-2607-2023, 2023
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It is a deeply rooted perception that soil is key in hydrology. In this paper, we argue that it is the ecosystem, not the soil, that is in control of hydrology. Firstly, in nature, the dominant flow mechanism is preferential, which is not particularly related to soil properties. Secondly, the ecosystem, not the soil, determines the land–surface water balance and hydrological processes. Moving from a soil- to ecosystem-centred perspective allows more realistic and simpler hydrological models.
Doaa Aboelyazeed, Chonggang Xu, Forrest M. Hoffman, Jiangtao Liu, Alex W. Jones, Chris Rackauckas, Kathryn Lawson, and Chaopeng Shen
Biogeosciences, 20, 2671–2692, https://doi.org/10.5194/bg-20-2671-2023, https://doi.org/10.5194/bg-20-2671-2023, 2023
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Photosynthesis is critical for life and has been affected by the changing climate. Many parameters come into play while modeling, but traditional calibration approaches face many issues. Our framework trains coupled neural networks to provide parameters to a photosynthesis model. Using big data, we independently found parameter values that were correlated with those in the literature while giving higher correlation and reduced biases in photosynthesis rates.
Dapeng Feng, Hylke Beck, Kathryn Lawson, and Chaopeng Shen
Hydrol. Earth Syst. Sci., 27, 2357–2373, https://doi.org/10.5194/hess-27-2357-2023, https://doi.org/10.5194/hess-27-2357-2023, 2023
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Powerful hybrid models (called δ or delta models) embrace the fundamental learning capability of AI and can also explain the physical processes. Here we test their performance when applied to regions not in the training data. δ models rivaled the accuracy of state-of-the-art AI models under the data-dense scenario and even surpassed them for the data-sparse one. They generalize well due to the physical structure included. δ models could be ideal candidates for global hydrologic assessment.
Louise J. Slater, Louise Arnal, Marie-Amélie Boucher, Annie Y.-Y. Chang, Simon Moulds, Conor Murphy, Grey Nearing, Guy Shalev, Chaopeng Shen, Linda Speight, Gabriele Villarini, Robert L. Wilby, Andrew Wood, and Massimiliano Zappa
Hydrol. Earth Syst. Sci., 27, 1865–1889, https://doi.org/10.5194/hess-27-1865-2023, https://doi.org/10.5194/hess-27-1865-2023, 2023
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Hybrid forecasting systems combine data-driven methods with physics-based weather and climate models to improve the accuracy of predictions for meteorological and hydroclimatic events such as rainfall, temperature, streamflow, floods, droughts, tropical cyclones, or atmospheric rivers. We review recent developments in hybrid forecasting and outline key challenges and opportunities in the field.
Jiangtao Liu, David Hughes, Farshid Rahmani, Kathryn Lawson, and Chaopeng Shen
Geosci. Model Dev., 16, 1553–1567, https://doi.org/10.5194/gmd-16-1553-2023, https://doi.org/10.5194/gmd-16-1553-2023, 2023
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Under-monitored regions like Africa need high-quality soil moisture predictions to help with food production, but it is not clear if soil moisture processes are similar enough around the world for data-driven models to maintain accuracy. We present a deep-learning-based soil moisture model that learns from both in situ data and satellite data and performs better than satellite products at the global scale. These results help us apply our model globally while better understanding its limitations.
Marvin Höge, Andreas Scheidegger, Marco Baity-Jesi, Carlo Albert, and Fabrizio Fenicia
Hydrol. Earth Syst. Sci., 26, 5085–5102, https://doi.org/10.5194/hess-26-5085-2022, https://doi.org/10.5194/hess-26-5085-2022, 2022
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Neural ODEs fuse physics-based models with deep learning: neural networks substitute terms in differential equations that represent the mechanistic structure of the system. The approach combines the flexibility of machine learning with physical constraints for inter- and extrapolation. We demonstrate that neural ODE models achieve state-of-the-art predictive performance while keeping full interpretability of model states and processes in hydrologic modelling over multiple catchments.
Hongkai Gao, Chuntan Han, Rensheng Chen, Zijing Feng, Kang Wang, Fabrizio Fenicia, and Hubert Savenije
Hydrol. Earth Syst. Sci., 26, 4187–4208, https://doi.org/10.5194/hess-26-4187-2022, https://doi.org/10.5194/hess-26-4187-2022, 2022
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Frozen soil hydrology is one of the 23 unsolved problems in hydrology (UPH). In this study, we developed a novel conceptual frozen soil hydrological model, FLEX-Topo-FS. The model successfully reproduced the soil freeze–thaw process, and its impacts on hydrologic connectivity, runoff generation, and groundwater. We believe this study is a breakthrough for the 23 UPH, giving us new insights on frozen soil hydrology, with broad implications for predicting cold region hydrology in future.
Marco Dal Molin, Dmitri Kavetski, and Fabrizio Fenicia
Geosci. Model Dev., 14, 7047–7072, https://doi.org/10.5194/gmd-14-7047-2021, https://doi.org/10.5194/gmd-14-7047-2021, 2021
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This paper introduces SuperflexPy, an open-source Python framework for building flexible conceptual hydrological models. SuperflexPy is available as open-source code and can be used by the hydrological community to investigate improved process representations, for model comparison, and for operational work.
Hongkai Gao, Chuntan Han, Rensheng Chen, Zijing Feng, Kang Wang, Fabrizio Fenicia, and Hubert Savenije
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2021-264, https://doi.org/10.5194/hess-2021-264, 2021
Manuscript not accepted for further review
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Permafrost hydrology is one of the 23 major unsolved problems in hydrology. In this study, we used a stepwise modeling and dynamic parameter method to examine the impact of permafrost on streamflow in the Hulu catchment in western China. We found that: topography and landscape are dominant controls on catchment response; baseflow recession is slower than other regions; precipitation-runoff relationship is non-stationary; permafrost impacts on streamflow mostly at the beginning of melting season.
Laurène J. E. Bouaziz, Fabrizio Fenicia, Guillaume Thirel, Tanja de Boer-Euser, Joost Buitink, Claudia C. Brauer, Jan De Niel, Benjamin J. Dewals, Gilles Drogue, Benjamin Grelier, Lieke A. Melsen, Sotirios Moustakas, Jiri Nossent, Fernando Pereira, Eric Sprokkereef, Jasper Stam, Albrecht H. Weerts, Patrick Willems, Hubert H. G. Savenije, and Markus Hrachowitz
Hydrol. Earth Syst. Sci., 25, 1069–1095, https://doi.org/10.5194/hess-25-1069-2021, https://doi.org/10.5194/hess-25-1069-2021, 2021
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We quantify the differences in internal states and fluxes of 12 process-based models with similar streamflow performance and assess their plausibility using remotely sensed estimates of evaporation, snow cover, soil moisture and total storage anomalies. The dissimilarities in internal process representation imply that these models cannot all simultaneously be close to reality. Therefore, we invite modelers to evaluate their models using multiple variables and to rely on multi-model studies.
Renaud Hostache, Dominik Rains, Kaniska Mallick, Marco Chini, Ramona Pelich, Hans Lievens, Fabrizio Fenicia, Giovanni Corato, Niko E. C. Verhoest, and Patrick Matgen
Hydrol. Earth Syst. Sci., 24, 4793–4812, https://doi.org/10.5194/hess-24-4793-2020, https://doi.org/10.5194/hess-24-4793-2020, 2020
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Our objective is to investigate how satellite microwave sensors, particularly Soil Moisture and Ocean Salinity (SMOS), may help to reduce errors and uncertainties in soil moisture simulations with a large-scale conceptual hydro-meteorological model. We assimilated a long time series of SMOS observations into a hydro-meteorological model and showed that this helps to improve model predictions. This work therefore contributes to the development of faster and more accurate drought prediction tools.
Cited articles
Alvarez-Garreton, C., Mendoza, P. A., Boisier, J. P., Addor, N., Galleguillos, M., Zambrano-Bigiarini, M., Lara, A., Puelma, C., Cortes, G., Garreaud, R., McPhee, J., and Ayala, A.: The CAMELS-CL dataset: catchment attributes and meteorology for large sample studies – Chile dataset, Hydrol. Earth Syst. Sci., 22, 5817–5846, https://doi.org/10.5194/hess-22-5817-2018, 2018. a
Bai, P., Liu, X., and Xie, J.: Simulating runoff under changing climatic conditions: A comparison of the long short-term memory network with two conceptual hydrologic models, J. Hydrol., 592, 125779, https://doi.org/10.1016/j.jhydrol.2020.125779, 2021. a, b
Bezanson, J., Karpinski, S., Shah, V. B., and Edelman, A.: Julia: A fast dynamic language for technical computing, arXiv [preprint], https://doi.org/10.48550/arXiv.1209.5145, 2012. a
Bezanson, J., Edelman, A., Karpinski, S., and Shah, V. B.: Julia: A fresh approach to numerical computing, SIAM Rev., 59, 65–98, 2017. a
Bindas, T., Tsai, W.-P., Liu, J., Rahmani, F., Feng, D., Bian, Y., Lawson, K., and Shen, C.: Improving River Routing Using a Differentiable Muskingum-Cunge Model and Physics-Informed Machine Learning, Water Resour. Res., 60, e2023WR035337, https://doi.org/10.1029/2023WR035337, 2024. a
Blöschl, ü., Hall, J., Viglione, A., Perdigao, R. A. P., Parajka, J., Merz, B., Lun, D., Arheimer, B., Aronica, G. T., Bilibashi, A., Bohac, M., Bonacci, O., Borga, M., Canjevac, I., Castellarin, A., Chirico, G. B., Claps, P., Frolova, N., Ganora, D., Gorbachova, L., Gül, A., Hannaford, J., Harrigan, S., Kireeva, M., Kiss, A., Kjeldsen, T. R., Kohnova, S., Koskela, J. J., Ledvinka, O., Macdonald, N., Mavrova-Guirguinova, M., Mediero, L., Merz, R., Molnar, P., Montanari, A., Murphy, C., Osuch, M., Ovcharuk, V., Radevski, I., Salinas, J. L., Sauquet, E., Sraj, M., Szolgay, J., Volpi, E., Wilson, D., Zaimi, K., and Zivkovic, N.: Changing climate both increases and decreases European river floods, Nature, 573, 108–111, 2019. a
Chagas, V. B. P., Chaffe, P. L. B., Addor, N., Fan, F. M., Fleischmann, A. S., Paiva, R. C. D., and Siqueira, V. A.: CAMELS-BR: hydrometeorological time series and landscape attributes for 897 catchments in Brazil, Earth Syst. Sci. Data, 12, 2075–2096, https://doi.org/10.5194/essd-12-2075-2020, 2020. a
Coxon, G., Addor, N., Bloomfield, J., Freer, J., Fry, M., Hannaford, J., Howden, N., Lane, R., Lewis, M., Robinson, E., Wagener, T., and Woods, R.: Catchment attributes and hydro-meteorological timeseries for 671 catchments across Great Britain (CAMELS-GB), NERC Environmental Information Data Centre, https://doi.org/10.5285/8344e4f3-d2ea-44f5-8afa-86d2987543a9, 2020. a
Cui, G., Anderson, M., and Bales, R.: Mapping of snow water equivalent by a deep-learning model assimilating snow observations, J. Hydrol., 616, 128835, https://doi.org/10.1016/j.jhydrol.2022.128835, 2023. a
Fang, K., Shen, C., Kifer, D., and Yang, X.: Prolongation of SMAP to spatiotemporally seamless coverage of continental U.S. using a deep learning neural network, Geophys. Res. Lett., 44, 11030–11039, 2017. a
Fang, K., Shen, C., Ludwig, N., Godfrey, P., Mahjabin, T., and Doughty, C.: Combining a land surface model with groundwater model calibration to assess the impacts of groundwater pumping in a mountainous desert basin, Adv. Water Resour., 130, 12–28, 2019. a
Fang, K., Kifer, D., Lawson, K., and Shen, C.: Evaluating the potential and challenges of an uncertainty quantification method for long short-term memory models for soil moisture predictions, Water Resour. Res., 56, e2020WR028095, https://doi.org/10.1029/2020WR028095, 2020. a
Feng, D., Fang, K., and Shen, C.: Enhancing Streamflow Forecast and Extracting Insights Using Long‐Short Term Memory Networks With Data Integration at Continental Scales, Water Resour. Res., 56, e2019WR026793, https://doi.org/10.1029/2019WR026793, 2020. a, b, c, d
Feng, D., Lawson, K., and Shen, C.: Mitigating prediction error of deep learning streamflow models in large data-sparse regions with ensemble modeling and soft data, Geophys. Res. Lett., 48, e2021GL092999, https://doi.org/10.1029/2021GL092999, 2021. a, b
Feng, D., Liu, J., Lawson, K., and Shen, C.: Differentiable, learnable, regionalized process-based models with multiphysical outputs can approach state-of-the-art hydrologic prediction accuracy, Water Resour. Res., 58, e2022WR032404, https://doi.org/10.1029/2022WR032404, 2022. a
Fowler, K. J. A., Acharya, S. C., Addor, N., Chou, C., and Peel, M. C.: CAMELS-AUS: hydrometeorological time series and landscape attributes for 222 catchments in Australia, Earth Syst. Sci. Data, 13, 3847–3867, https://doi.org/10.5194/essd-13-3847-2021, 2021. a
Höge, M., Scheidegger, A., Baity-Jesi, M., Albert, C., and Fenicia, F.: Improving hydrologic models for predictions and process understanding using neural ODEs, Hydrol. Earth Syst. Sci., 26, 5085–5102, https://doi.org/10.5194/hess-26-5085-2022, 2022. a
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.: CAMELS-CH: hydro-meteorological time series and landscape attributes for 331 catchments in hydrologic Switzerland, Earth Syst. Sci. Data, 15, 5755–5784, https://doi.org/10.5194/essd-15-5755-2023, 2023. a
Hrachowitz, M., Savenije, H., Blöschl, G., McDonnell, J., Sivapalan, M., Pomeroy, J., Arheimer, B., Blume, T., Clark, M., Ehret, U., Fenicia, F., Freer, J., Gelfan, A., Gupta, H., Hughes, D., Hut, R., Montanari, A., Pande, S., Tetzlaff, D., Troch, P., Uhlenbrook, S., Wagener, T., Winsemius, H., Woods, R., Zehe, E., and Cudennec, C.: A decade of Predictions in Ungauged Basins (PUB) – a review, Hydrolog. Sci. J., 58, 1198–1255, https://doi.org/10.1080/02626667.2013.803183, 2013. a
Jiang, S., Zheng, Y., and Solomatine, D.: Improving AI system awareness of geoscience knowledge: Symbiotic integration of physical approaches and deep learning, Geophys. Res. Lett., 46, e2020GL088229, https://doi.org/10.1029/2020GL088229, 2020. a, b, c
Kavetski, D., Kuczera, G., and Franks, S. W.: Calibration of conceptual hydrological models revisited: 1. Overcoming numerical artefacts, J. Hydrol., 320, 173–186, 2006. a
Konapala, G., Kao, S.-C., Painter, S. L., and Lu, D.: Machine learning assisted hybrid models can improve streamflow simulation in diverse catchments across the conterminous US, Environ. Res. Lett., 15, 104022, https://doi.org/10.1088/1748-9326/aba927, 2020. a
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. a, b, c, d
Kratzert, F., Klotz, D., Herrnegger, M., Sampson, A. K., Hochreiter, S., and Nearing, G. S.: Toward improved predictions in ungauged basins: Exploiting the power of machine learning, Water Resour. Res., 55, 11344–11354, https://doi.org/10.1029/2019WR026065, 2019a. a, b, c, d
Kratzert, F., Klotz, D., Shalev, G., Klambauer, G., Hochreiter, S., and Nearing, G.: Towards learning universal, regional, and local hydrological behaviors via machine learning applied to large-sample datasets, Hydrol. Earth Syst. Sci., 23, 5089–5110, https://doi.org/10.5194/hess-23-5089-2019, 2019b. a, b, c, d
Liu, D. C. and Nocedal, J.: On the limited memory BFGS method for large scale optimization, Math. Program., 45, 503–528, 1989. a
Ma, K., Feng, D., Lawson, K., Tsai, W.-P., Liang, C., Huang, X., Sharma, A., and Shen, C.: Transferring Hydrologic Data Across Continents – Leveraging Data-Rich Regions to Improve Hydrologic Prediction in Data-Sparse Regions, Water Resour. Res., 57, e2020WR028600, https://doi.org/10.1029/2020WR028600, 2021. a, b
Merz, R., Parajka, J., and Blöschl, G.: Time stability of catchment model parameters: Implications for climate impact analyses, Water Resour. Res., 47, W02531, https://doi.org/10.1029/2010WR009505, 2011. a
Mogensen, P. K. and Riseth, A. N.: Optim: A mathematical optimization package for Julia, Journal of Open Source Software, 3, 615, https://doi.org/10.21105/joss.00615, 2018. a
Natel de Moura, C., Seibert, J., and Detzel, H. M.: Evaluating the long short-term memory (LSTM) network for discharge prediction under changing climate conditions, Hydrol. Res., 53, 657–667, https://doi.org/10.2166/nh.2022.044, 2022. a, b
Nearing, G., Kratzert, F., Klotz, D., Hoedt, P.-J., Klambauer, G., Hochreiter, S., Gupta, H., Nevo, S., and Matias, Y.: A Deep Learning Architecture for Conservative Dynamical Systems: Application to Rainfall-Runoff Modeling, Virtual Workshop AI for Earth Sciences, NeurIPS, 12 December 2020, https://ai4earthscience.github.io/neurips-2020-workshop/papers/ai4earth_neurips_2020_51.pdf (last access: 1 November 2021), 2020. a
Nearing, G. S., Kratzert, F., Sampson, A. K., Pelissier, C. S., Klotz, D., Frame, J. M., Prieto, C., and Gupta, H. V.: What role does hydrological science play in the age of machine learning?, Water Resour. Res., 57, e2020WR028091, https://doi.org/10.1029/2020WR028091, 2021. a
Newman, A., Sampson, K., Clark, M. P., Bock, A., Viger, R. J., and Blodgett, D.: A large-sample watershed-scale hydrometeorological dataset for the contiguous USA, Boulder, CO, UCAR/NCAR [data set], https://doi.org/10.5065/D6MW2F4D, 2014.
Newman, A. J., Clark, M. P., Sampson, K., Wood, A., Hay, L. E., Bock, A., Viger, R. J., Blodgett, D., Brekke, L., Arnold, J. R., Hopson, T., and Duan, Q.: Development of a large-sample watershed-scale hydrometeorological data set for the contiguous USA: data set characteristics and assessment of regional variability in hydrologic model performance, Hydrol. Earth Syst. Sci., 19, 209–223, https://doi.org/10.5194/hess-19-209-2015, 2015. a, b, c, d
Ng, K. W., Huang, Y. F., Koo, C. H., Chong, K. L., El-Shafie, A., and Ahmed, A. N.: A review of hybrid deep learning applications for streamflow forecasting, J. Hydrol., 625, 130141, https://doi.org/10.1016/j.jhydrol.2023.130141, 2023. a, b
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library, Curran Associates, Inc., Adv. Neur. In., 32, 8024–8035, http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf (last access: 6 June 2024), 2019. a
Rackauckas, C. and Nie, Q.: Differentialequations.jl–a performant and feature-rich ecosystem for solving differential equations in julia, Journal of Open Research Software, 5, 15, https://doi.org/10.5334/jors.151, 2017. a
Rahmani, F., Lawson, K., Ouyang, W., Appling, A., Oliver, S., and Shen, C.: Exploring the exceptional performance of a deep learning stream temperature model and the value of streamflow data, Environ. Res. Lett., 16, 024025, https://doi.org/10.1088/1748-9326/abd501, 2021. a
Razavi, S.: Deep Learning explained: Fundamentals, explainability, and bridgeability to process-based modelling, Environ. Modell. Softw., 144, 105159, https://doi.org/10.1016/j.envsoft.2021.105159, 2021. a, b, c
Read, J. S., Jia, X., Willard, J., Appling, A. P., Zwart, J. A., Oliver, S. K., Karpatne, A., Hansen, G. J. A., Hanson, P. C., Watkins, W., Stienbach, M., and Kumar, V.: Process-guided deep learning predictions of lake water temperature, Water Resour. Res., 55, 9173–9190, https://doi.org/10.1029/2019WR024922, 2019. a
Reichert, P., Ma, K., Hoge, M., Fenicia, F., Baity-Jesi, M., Feng, D., and Shen, C.: Data for: Metamorphic Testing of Machine Learning and Conceptual Hydrologic Models, Eawag: Swiss Federal Institute of Aquatic Science and Technology [code], https://doi.org/10.25678/000CQ0, 2024.
Revels, J., Lubin, M., and Papamarkou, T.: Forward-Mode Automatic Differentiation in Julia, arXiv [preprint], https://doi.org/10.48550/arXiv.1607.07892, 2016. a
Saha, G. K., Rahmani, F., Shen, C., Li, L., and Cibin, R.: A deep learning-based novel approach to generate continuous daily stream nitrate concentration for nitrate data-sparse watersheds, Sci. Total Environ., 878, 162930, https://doi.org/10.1016/j.scitotenv.2023.162930, 2023. a
Seibert, J. and Vis, M. J. P.: Teaching hydrological modeling with a user-friendly catchment-runoff-model software package, Hydrol. Earth Syst. Sci., 16, 3315–3325, https://doi.org/10.5194/hess-16-3315-2012, 2012. a, b
Shen, C.: A Transdisciplinary Review of Deep Learning Research and Its Relevance for Water Resources Scientists, Water Resour. Res., 54, 8558–8593, 2018. a
Shen, C.: MHPI-hydroDL, Zenodo [code], https://doi.org/10.5281/zenodo.3993880, 2020.
Shen, C., Appling, A. P., Gentine, P., Bandai, T., Gupta, H., Tartakovsky, A., Baity-Jesi, M., Fenicia, F., Kifer, D., Li, L., Liu, X., Ren, W., Zheng, Y., Harman, C. J., Clark, M., Farthing, M., Feng, D., Kumar, P., Aboelyazeed, D., RahmaniHylke, F., Beck, E., Bindas, T., Dwivedi, D., Fang, K., Höge, M., Rackauckas, C., Roy. T., Xu, C., and Lawson, K.: Differentiable modelling to unify machine learning and physical models for geosciences, Nat. Rev. Earth Environ., 4, 552–567, 2023. a, b
Song, Y., Tsai, W.-P., Gluck, J., Rhoades, A., Zarzycki, C., McCrary, R., Lawson, K., and Shen, C.: LSTM-based data integration to improve snow water equivalent prediction and diagnose error sources, J. Hydrometeorol., 25, 223–237, 2024. a
Tsai, W.-P., Feng, D., Pan, M., Beck, H., Lawson, K., Yang, Y., Liu, J., and Shen, C.: From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling, Nat. Commun., 12, 5988, https://doi.org/10.1038/s41467-021-26107-z, 2021. a, b
Ukkola, A. M. and Prentice, I. C.: A worldwide analysis of trends in water-balance evapotranspiration, Hydrol. Earth Syst. Sci., 17, 4177–4187, https://doi.org/10.5194/hess-17-4177-2013, 2013. a, b, c, d
Van Rossum, G. and Drake, F. L.: Python 3 Reference Manual, CreateSpace, Scotts Valley, CA, ISBN 1441412697, 2009. a
Wang, J., Lan, C., Liu, C., Ouyang, Y., Qin, T., Lu, W., Chen, Y., Zeng, W., and Yu, P.: Generalizing to unseen domains: A survey on domain generalization, IEEE T. Knowl. Data En., 35, 8052–8072, https://doi.org/10.1109/TKDE.2022.3178128, 2022. a
Wi, S. and Steinschneider, S.: Correcting the mathematical structure of a hydrological model via Bayesian data assimilation, Water Resour. Res., 58, e2022WR032123, https://doi.org/10.1029/2022WR032123, 2022. a, b, c, d
Xie, K., Liu, P., Zhang, J., Han, D., Wang, G., and Shen, C.: Physics-guided deep learning for rainfall-runoff modeling by considering extreme events and monotonic relationships, J. Hydrol., 603, 127043, https://doi.org/10.1016/j.jhydrol.2021.127043, 2021. a
Yang, Y. and Chui, T. F. M.: Reliability assessment of machine learning models in hydrological predictions through metamorphic testing, Water Resour. Res., 57, e2020WR029471, https://doi.org/10.1029/2020WR029471, 2021. a, b, c
Zeiler, M. D.: ADADELTA: An Adaptive Learning Rate Method, arXiv [preprint], https://doi.org/10.48550/arXiv.1212.5701, 2012. a
Zhi, W., Ouyang, W., Shen, C., and Li, L.: Temperature outweighs light and flow as the predominant driver of dissolved oxygen in US rivers, Nature Water, 1, 249–260, 2023. a
Zhong, L., Lei, H., and Gao, B.: Developing a physics-informed deep learning model to simulate runoff response to climate change in Alpine catchments, Water Resour. Res., 59, e2022WR034118, https://doi.org/10.1029/2022WR034118, 2023. a
Short summary
We compared the predicted change in catchment outlet discharge to precipitation and temperature change for conceptual and machine learning hydrological models. We found that machine learning models, despite providing excellent fit and prediction capabilities, can be unreliable regarding the prediction of the effect of temperature change for low-elevation catchments. This indicates the need for caution when applying them for the prediction of the effect of climate change.
We compared the predicted change in catchment outlet discharge to precipitation and temperature...
