Articles | Volume 26, issue 19
https://doi.org/10.5194/hess-26-5085-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-26-5085-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| Highlight paper
| 
11 Oct 2022
Research article | Highlight paper |
| 11 Oct 2022
| 11 Oct 2022
Improving hydrologic models for predictions and process understanding using neural ODEs
Department of Systems Analysis, Integrated Assessment and Modelling, Eawag, Dübendorf, Switzerland
Andreas Scheidegger
Department of Systems Analysis, Integrated Assessment and Modelling, Eawag, Dübendorf, Switzerland
Marco Baity-Jesi
Department of Systems Analysis, Integrated Assessment and Modelling, Eawag, Dübendorf, Switzerland
Carlo Albert
Department of Systems Analysis, Integrated Assessment and Modelling, Eawag, Dübendorf, Switzerland
Fabrizio Fenicia
Department of Systems Analysis, Integrated Assessment and Modelling, Eawag, Dübendorf, Switzerland
Related authors
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
Short summary
Short summary
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.
Peter Reichert, Kai Ma, Marvin Höge, Fabrizio Fenicia, Marco Baity-Jesi, Dapeng Feng, and Chaopeng Shen
Hydrol. Earth Syst. Sci., 28, 2505–2529, https://doi.org/10.5194/hess-28-2505-2024, https://doi.org/10.5194/hess-28-2505-2024, 2024
Short summary
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.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
Peter Reichert, Kai Ma, Marvin Höge, Fabrizio Fenicia, Marco Baity-Jesi, Dapeng Feng, and Chaopeng Shen
Hydrol. Earth Syst. Sci., 28, 2505–2529, https://doi.org/10.5194/hess-28-2505-2024, https://doi.org/10.5194/hess-28-2505-2024, 2024
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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.
Simone Ulzega and Carlo Albert
Hydrol. Earth Syst. Sci., 27, 2935–2950, https://doi.org/10.5194/hess-27-2935-2023, https://doi.org/10.5194/hess-27-2935-2023, 2023
Short summary
Short summary
Embedding input uncertainties in hydrological modelling naturally leads to stochastic models, which render parameter calibration an often computationally intractable problem. We use a case study from urban hydrology based on a stochastic rain model, and we employ a highly efficient Hamiltonian Monte Carlo inference algorithm with a timescale separation to demonstrate that fully fledged Bayesian inference with stochastic models is no longer off-limits for hydrological applications.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Abbott, M., Bathurst, J., Cunge, J., O'Connell, P., and Rasmussen, J.:
An introduction to the European Hydrological System – Systeme Hydrologique Europeen, “SHE”, 1: History and philosophy of a physically-based, distributed modelling system, J Hydrol., 87, 45–59, https://doi.org/10.1016/0022-1694(86)90114-9, 1986. a
Addor, N., Newman, A. J., Mizukami, N., and Clark, M. P.:
The CAMELS data set: catchment attributes and meteorology for large-sample studies, Hydrol. Earth Syst. Sci., 21, 5293–5313, https://doi.org/10.5194/hess-21-5293-2017, 2017. a, b
Bennett, A. and Nijssen, B.: Deep learned process parameterizations provide better representations of turbulent heat fluxes in hydrologic models, Water Resour. Res., 57, e2020WR029328, https://doi.org/10.1029/2020WR029328, 2021. a, b
Bezanson, J., Edelman, A., Karpinski, S., and Shah, V. B.:
Julia: A fresh approach to numerical computing, SIAM Rev., 59, 65–98, 2017. a
Chen, R. T., Rubanova, Y., Bettencourt, J., and Duvenaud, D.:
Neural ordinary differential equations, arXiv [preprint], arXiv:1806.07366, 2018. a, b
Clark, M. P., Slater, A. G., Rupp, D. E., Woods, R. A., Vrugt, J. A., Gupta, H. V., Wagener, T., and Hay, L. E.: Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models, Water Resour. Res., 44, W00B02, https://doi.org/10.1029/2007WR006735, 2008. a
Clark, M. P., Nijssen, B., Lundquist, J. D., Kavetski, D., Rupp, D. E., Woods, R. A., Freer, J. E., Gutmann, E. D., Wood, A. W., Brekke, L. D., Arnold, J. R., Gochis, D. J., and Rasmussen, R. M.: A unified approach for process-based hydrologic modeling: 1. Modeling concept, Water Resour. Res., 51, 2498–2514, 2015. 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
Fenicia, F., Savenije, H. H., Matgen, P., and Pfister, L.: Understanding catchment behavior through stepwise model concept improvement, Water Resour. Res., 44, W01402, https://doi.org/10.1029/2006WR005563, 2008. a
Fenicia, F., Kavetski, D., and Savenije, H. H.: Elements of a flexible approach for conceptual hydrological modeling: 1. Motivation and theoretical development, Water Resour. Res., 47, W11510, https://doi.org/10.1029/2010WR010174, 2011. a, b
Fenicia, F., Kavetski, D., Savenije, H. H., Clark, M. P., Schoups, G., Pfister, L., and Freer, J.:
Catchment properties, function, and conceptual model representation: is there a correspondence?, Hydrol. Process., 28, 2451–2467, 2014. a
Fenicia, F., Kavetski, D., Savenije, H. H., and Pfister, L.:
From spatially variable streamflow to distributed hydrological models: Analysis of key modeling decisions, Water Resour. Res., 52, 954–989, 2016. a
Frame, J. M., Kratzert, F., Klotz, D., Gauch, M., Shalev, G., Gilon, O., Qualls, L. M., Gupta, H. V., and Nearing, G. S.: Deep learning rainfall–runoff predictions of extreme events, Hydrol. Earth Syst. Sci., 26, 3377–3392, https://doi.org/10.5194/hess-26-3377-2022, 2022. a, b
Gauch, M., Kratzert, F., Klotz, D., Nearing, G., Lin, J., and Hochreiter, S.:
Rainfall–runoff prediction at multiple timescales with a single Long Short-Term Memory network, Hydrol. Earth Syst. Sci., 25, 2045–2062, https://doi.org/10.5194/hess-25-2045-2021, 2021. a
Gharari, S. and Razavi, S.:
A review and synthesis of hysteresis in hydrology and hydrological modeling: Memory, path-dependency, or missing physics?, J. Hydrol., 566, 500–519, 2018. a
Gharari, S., Gupta, H. V., Clark, M. P., Hrachowitz, M., Fenicia, F., Matgen, P., and Savenije, H. H. G.:
Understanding the Information Content in the Hierarchy of Model Development Decisions: Learning From Data, Water Resour. Res., 57, e2020WR027948, https://doi.org/10.1029/2020WR027948, 2021. a, b, c
Gnann, S. J., McMillan, H. K., Woods, R. A., and Howden, N. J.: Including regional knowledge improves baseflow signature predictions in large sample hydrology, Water Resour. Res., 57, e2020WR028354, https://doi.org/10.1029/2020WR028354, 2021. a
Hoedt, P.-J., Kratzert, F., Klotz, D., Halmich, C., Holzleitner, M., Nearing, G., Hochreiter, S., and Klambauer, G.:
MC-LSTM: Mass-Conserving LSTM, arXiv [preprint], arXiv:2101.05186, 2021. a
Höge, M.: HydroNODE, GitHub [code], https://github.com/marv-in/HydroNODE (last access: 21 August 2022), 2022a. a
Höge, M.: HydroNODE-v1.0.0, Zenodo [code], https://doi.org/10.5281/zenodo.7085028, 2022b. a
Höge, M., Wöhling, T., and Nowak, W.:
A primer for model selection: The decisive role of model complexity, Water Resour. Res., 54, 1688–1715, 2018. a
Holzinger, A.:
Interactive machine learning for health informatics: when do we need the human-in-the-loop?, Brain Informatics, 3, 119–131, 2016. a
Innes, M., Edelman, A., Fischer, K., Rackauckas, C., Saba, E., Shah, V. B., and Tebbutt, W.:
A differentiable programming system to bridge machine learning and scientific computing, arXiv [preprint], arXiv:1907.07587, 2019. a
Julia: The Julia Programming Language, https://julialang.org/, last access: 11 October 2022. a
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., and Yang, L.:
Physics-informed machine learning, Nature Reviews Physics, 3, 422–440, 2021. a
Karpatne, A., Atluri, G., Faghmous, J. H., Steinbach, M., Banerjee, A., Ganguly, A., Shekhar, S., Samatova, N., and Kumar, V.:
Theory-guided data science: A new paradigm for scientific discovery from data, IEEE T Knowl. Data En., 29, 2318–2331, 2017. a
Kirchner, J. W.: Getting the right answers for the right reasons: Linking measurements, analyses, and models to advance the science of hydrology, Water Resour. Res., 42, W03S04, https://doi.org/10.1029/2005WR004362, 2006. a
Kirchner, J. W.: Catchments as simple dynamical systems: Catchment characterization, rainfall-runoff modeling, and doing hydrology backward, Water Resour. Res., 45, W02429, https://doi.org/10.1029/2008WR006912, 2009. a
Knoben, W. J., Freer, J. E., Peel, M., Fowler, K., and Woods, R. A.: A brief analysis of conceptual model structure uncertainty using 36 models and 559 catchments, Water Resour. Res., 56, e2019WR025975, https://doi.org/10.1029/2019WR025975, 2020. a, b
Kraft, B., Jung, M., Körner, M., Koirala, S., and Reichstein, M.:
Towards hybrid modeling of the global hydrological cycle, Hydrol. Earth Syst. Sci., 26, 1579–1614, https://doi.org/10.5194/hess-26-1579-2022, 2022. 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
Kratzert, F., Herrnegger, M., Klotz, D., Hochreiter, S., and Klambauer, G.:
NeuralHydrology–interpreting LSTMs in hydrology, in: Explainable AI: Interpreting, explaining and visualizing deep learning, edited by: Samek, W., Montavon, G., Vedaldi, A., Hansen, L., and Müller, K. R., Springer, 347–362, https://doi.org/10.1007/978-3-030-28954-6_19, 2019a. a
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, 2019c. a, b, c
Kratzert, F., Klotz, D., Hochreiter, S., and Nearing, G. S.:
A note on leveraging synergy in multiple meteorological data sets with deep learning for rainfall–runoff modeling, Hydrol. Earth Syst. Sci., 25, 2685–2703, https://doi.org/10.5194/hess-25-2685-2021, 2021. a
Lechner, M. and Hasani, R.:
Learning long-term dependencies in irregularly-sampled time series, arXiv [preprint], arXiv:2006.04418, 2020. a
Lees, T., Buechel, M., Anderson, B., Slater, L., Reece, S., Coxon, G., and Dadson, S. J.:
Benchmarking data-driven rainfall–runoff models in Great Britain: a comparison of long short-term memory (LSTM)-based models with four lumped conceptual models, Hydrol. Earth Syst. Sci., 25, 5517–5534, https://doi.org/10.5194/hess-25-5517-2021, 2021. a
Lees, T., Reece, S., Kratzert, F., Klotz, D., Gauch, M., De Bruijn, J., Kumar Sahu, R., Greve, P., Slater, L., and Dadson, S. J.:
Hydrological concept formation inside long short-term memory (LSTM) networks, Hydrol. Earth Syst. Sci., 26, 3079–3101, https://doi.org/10.5194/hess-26-3079-2022, 2022. a, b
Li, L., Sullivan, P. L., Benettin, P., Cirpka, O. A., Bishop, K., Brantley, S. L., Knapp, J. L., van Meerveld, I., Rinaldo, A., Seibert, J., Wen, H., and Kirchner, J. W.: Toward catchment hydro-biogeochemical theories, Wiley Interdisciplinary Reviews: Water, 8, e1495, https://doi.org/10.1002/wat2.1495, 2021. a
Loritz, R., Gupta, H., Jackisch, C., Westhoff, M., Kleidon, A., Ehret, U., and Zehe, E.:
On the dynamic nature of hydrological similarity, Hydrol. Earth Syst. Sci., 22, 3663–3684, https://doi.org/10.5194/hess-22-3663-2018, 2018. 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
Molnar, C.:
Interpretable Machine Learning, 2nd edn., https://christophm.github.io/interpretable-ml-book (last access: 21 August 2022), 2022. a
Molnar, C., Casalicchio, G., and Bischl, B.: Interpretable machine learning–a brief history, state-of-the-art and challenges, in: Joint European Conference on Machine Learning and Knowledge Discovery in Databases, Springer, 417–431, https://doi.org/10.1007/978-3-030-65965-3_28, 2020. a
Montavon, G., Samek, W., and Müller, K.-R.:
Methods for interpreting and understanding deep neural networks, Digit. Signal Process., 73, 1–15, https://doi.org/10.1016/j.dsp.2017.10.011, 2018. a
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, T. ASABE, 50, 885–900, 2007. a
Nearing, G. S., Pelissier, C. S., Kratzert, F., Klotz, D., Gupta, H. V., Frame, J. M., and Sampson, A. K.: Physically Informed Machine Learning for Hydrological Modeling Under Climate Nonstationarity, in: 44th NOAA Annual Climate Diagnostics and Prediction Workshop, UMBC Faculty Collection, https://www.nws.noaa.gov/ost/climate/STIP/44CDPW/44cdpw-GNearing.pdf (last access: 21 August 2022), 2019. 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
Nevo, S., Morin, E., Gerzi Rosenthal, A., Metzger, A., Barshai, C., Weitzner, D., Voloshin, D., Kratzert, F., Elidan, G., Dror, G., Begelman, G., Nearing, G., Shalev, G., Noga, H., Shavitt, I., Yuklea, L., Royz, M., Giladi, N., Peled Levi, N., Reich, O., Gilon, O., Maor, R., Timnat, S., Shechter, T., Anisimov, V., Gigi, Y., Levin, Y., Moshe, Z., Ben-Haim, Z., Hassidim, A., and Matias, Y.: Flood forecasting with machine learning models in an operational framework, Hydrol. Earth Syst. Sci., 26, 4013–4032, https://doi.org/10.5194/hess-26-4013-2022, 2022. a
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, e, f
Prieto, C., Le Vine, N., Kavetski, D., García, E., and Medina, R.:
Flow prediction in ungauged catchments using probabilistic random forests regionalization and new statistical adequacy tests, Water Resour. Res., 55, 4364–4392, 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
Raissi, M., Perdikaris, P., and Karniadakis, G. E.:
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, J. Comput. Phys., 378, 686–707, 2019. a
Reichert, P., Ammann, L., and Fenicia, F.: Potential and Challenges of Investigating Intrinsic Uncertainty of Hydrological Models with Stochastic, Time-Dependent Parameters, Water Resour. Res., 57, e2020WR028400, https://doi.org/10.1029/2020WR028400, 2021. a
Samek, W., Montavon, G., Vedaldi, A., Hansen, L. K., and Müller, K.-R.:
Explainable AI: interpreting, explaining and visualizing deep learning, Springer Nature, in: vol. 11700, Springer Nature,
https://doi.org/10.1007/978-3-030-28954-6, 2019. a, b
Savenije, H. H. G.:
HESS Opinions “The art of hydrology”*, Hydrol. Earth Syst. Sci., 13, 157–161, https://doi.org/10.5194/hess-13-157-2009, 2009. a
Schaefli, B. and Gupta, H. V.:
Do Nash values have value?, Hydrol. Process., 21, 2075–2080, 2007. a
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., Laloy, E., Elshorbagy, A., Albert, A., Bales, J., Chang, F.-J., Ganguly, S., Hsu, K.-L., Kifer, D., Fang, Z., Fang, K., Li, D., Li, X., and Tsai, W.-P.:
HESS Opinions: Incubating deep-learning-powered hydrologic science advances as a community, Hydrol. Earth Syst. Sci., 22, 5639–5656, https://doi.org/10.5194/hess-22-5639-2018, 2018. a
Sivapalan, M., Blöschl, G., Zhang, L., and Vertessy, R.:
Downward approach to hydrological prediction, Hydrol. Process., 17, 2101–2111, 2003. a
Steffen, M.: A simple method for monotonic interpolation in one dimension, Astron. Astrophys., 239, 443–450, 1990. a
Tartakovsky, A. M., Marrero, C. O., Perdikaris, P., Tartakovsky, G. D., and Barajas-Solano, D.: Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems, Water Resour. Res., 56, e2019WR026731, https://doi.org/10.1029/2019WR026731, 2020. a
Yilmaz, K. K., Gupta, H. V., and Wagener, T.:
A process-based diagnostic approach to model evaluation: Application to the NWS distributed hydrologic model, Water Resour. Res., 44, W09417, https://doi.org/10.1029/2007WR006716, 2008. a, b
Young, P.:
Top-down and data-based mechanistic modelling of rainfall–flow dynamics at the catchment scale, Hydrol. Process., 17, 2195–2217, 2003. a
Zhao, W. L., Gentine, P., Reichstein, M., Zhang, Y., Zhou, S., Wen, Y., Lin, C., Li, X., and Qiu, G. Y.:
Physics-constrained machine learning of evapotranspiration, Geophys. Res. Lett., 46, 14496–14507, 2019. a
Executive editor
This is a paper demonstrating the added value of hybrid modeling approaches for modeling hydrological features (flow and internal states). The paper is well written and will be sent out for a detailed scientific review. The combination of ANN with ODE-based hydrological models is a good way forward to construct hybrid modeling approaches. It is a significant step forward compared to the current state of the art.
This is a paper demonstrating the added value of hybrid modeling approaches for modeling...
Short summary
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.
Neural ODEs fuse physics-based models with deep learning: neural networks substitute terms in...
