Articles | Volume 29, issue 21
https://doi.org/10.5194/hess-29-6257-2025
© 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-29-6257-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Fully differentiable, fully distributed rainfall-runoff modeling
Fedor Scholz
CORRESPONDING AUTHOR
Neuro-Cognitive Modeling Group, University of Tübingen, Tübingen, Germany
Manuel Traub
Neuro-Cognitive Modeling Group, University of Tübingen, Tübingen, Germany
Christiane Zarfl
Environmental Systems Analysis, University of Tübingen, Tübingen, Germany
Thomas Scholten
Soil Science and Geomorphology, University of Tübingen, Tübingen, Germany
Martin V. Butz
Neuro-Cognitive Modeling Group, University of Tübingen, Tübingen, Germany
Related authors
No articles found.
Kerstin Rau, Katharina Eggensperger, Frank Schneider, Michael Blaschek, Philipp Hennig, and Thomas Scholten
SOIL, 11, 833–847, https://doi.org/10.5194/soil-11-833-2025, https://doi.org/10.5194/soil-11-833-2025, 2025
Short summary
Short summary
We developed an uncertainty method to show where machine learning (ML) models predicting soil units are most reliable, especially for transfer tasks. The model was able to correctly predict soil patterns, especially along rivers, in a new but similar region without retraining. It was too confident about common soil types, showing the need for balanced data. This helps improve soil maps and guides better planning for future data collection, saving time and resources while showing uncertainty.
Mathias Bellat, Mjahid Zebari, Benjamin Glissman, Tobias Rentschler, Paola Sconzo, Nafiseh Kakhani, Ruhollah Taghizadeh-Mehrjardi, Pegah Kohsravani, Bekas Brifany, Peter Pfälzner, and Thomas Scholten
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2025-418, https://doi.org/10.5194/essd-2025-418, 2025
Preprint under review for ESSD
Short summary
Short summary
This dataset presents the first soil maps for the region produced using digital mapping techniques. It includes predictions for ten major physical and chemical soil properties at various depths, plus a map of total soil depth. For each property, we selected the most accurate models and key environmental drivers. In Southwestern Asia and many arid or semi-arid regions, detailed soil data are often missing. This dataset fills that gap, supporting agriculture, research, planning, and local policy.
Kay D. Seufferheld, Pedro V. G. Batista, Hadi Shokati, Thomas Scholten, and Peter Fiener
EGUsphere, https://doi.org/10.5194/egusphere-2025-3391, https://doi.org/10.5194/egusphere-2025-3391, 2025
This preprint is open for discussion and under review for SOIL (SOIL).
Short summary
Short summary
Soil erosion by water threatens food security, but soil conservation practices can help protect arable land. We tested a soil erosion model that simulates sediment yields in micro-scale watersheds with soil conservation in place. The model captured the very low sediment yields but showed limited accuracy on an annual time scale. However, it performed well when applied to larger areas over longer timeframes, demonstrating its suitability for strategic long-term soil conservation planning.
Hadi Shokati, Kay D. Seufferheld, Peter Fiener, and Thomas Scholten
EGUsphere, https://doi.org/10.5194/egusphere-2025-3146, https://doi.org/10.5194/egusphere-2025-3146, 2025
Short summary
Short summary
Floods threaten lives and property and require rapid mapping. We compared two artificial intelligence approaches on aerial imagery: a fine‑tuned Segment Anything Model (SAM) guided by point or bounding box prompts, and a U‑Net network with ResNet‑50 and ResNet‑101 backbones. The point‑based SAM was the most accurate with precise boundaries. Faster and more reliable flood maps help rescue teams, insurers, and planners to act quickly.
Qutbudin Ishanch, Kanchan Mishra, Christiane Zarfl, and Kathryn Fitzsimmons
EGUsphere, https://doi.org/10.5194/egusphere-2025-1426, https://doi.org/10.5194/egusphere-2025-1426, 2025
Preprint archived
Short summary
Short summary
This study assesses flood risk in Afghanistan using an integrated hydro-morphological approach with remote sensing and GIS techniques. Unlike traditional models, it incorporates physical, social, and economic factors from open-source data, offering an adaptable solution for data-scarce regions. Findings show high flood hazards in the Amu and Kabul River basins due to precipitation, topography, and drainage. This framework supports disaster management and enhanced flood resilience.
Corinna Gall, Silvana Oldenburg, Martin Nebel, Thomas Scholten, and Steffen Seitz
SOIL, 11, 199–212, https://doi.org/10.5194/soil-11-199-2025, https://doi.org/10.5194/soil-11-199-2025, 2025
Short summary
Short summary
Soil erosion is a major issue in vineyards due to often steep slopes and fallow interlines. While cover crops are typically used for erosion control, moss restoration has not yet been explored. In this study, moss restoration reduced surface runoff by 71.4 % and sediment discharge by 75.8 % compared with bare soil, similar to cover crops. Mosses could serve as ground cover where mowing is impractical, potentially reducing herbicide use in viticulture, although further research is needed.
Wanjun Zhang, Thomas Scholten, Steffen Seitz, Qianmei Zhang, Guowei Chu, Linhua Wang, Xin Xiong, and Juxiu Liu
Hydrol. Earth Syst. Sci., 28, 3837–3854, https://doi.org/10.5194/hess-28-3837-2024, https://doi.org/10.5194/hess-28-3837-2024, 2024
Short summary
Short summary
Rainfall input generally controls soil water and plant growth. We focus on rainfall redistribution in succession sequence forests over 22 years. Some changes in rainwater volume and chemistry in the throughfall and stemflow and drivers were investigated. Results show that shifted open rainfall over time and forest factors induced remarkable variability in throughfall and stemflow, which potentially makes forecasting future changes in water resources in the forest ecosystems more difficult.
Jonas Leon Schaper, Olaf A. Cirpka, Joerg Lewandowski, and Christiane Zarfl
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2023-141, https://doi.org/10.5194/hess-2023-141, 2023
Manuscript not accepted for further review
Short summary
Short summary
In this study, we present a model approach to quantify river water to riverbed sediment travel times as a continuous function of time using natural electrical conductivity fluctuations as a tracer. We show that apparent water travel times from surface waters through riverbed sediments can be highly dynamic, which may be caused by actual variations of porewater velocity following diurnal variations of head gradients or by a shift of the spatial arrangement of flow paths and their lengths.
Nicolás Riveras-Muñoz, Steffen Seitz, Kristina Witzgall, Victoria Rodríguez, Peter Kühn, Carsten W. Mueller, Rómulo Oses, Oscar Seguel, Dirk Wagner, and Thomas Scholten
SOIL, 8, 717–731, https://doi.org/10.5194/soil-8-717-2022, https://doi.org/10.5194/soil-8-717-2022, 2022
Short summary
Short summary
Biological soil crusts (biocrusts) stabilize the soil surface mainly in arid regions but are also present in Mediterranean and humid climates. We studied this stabilizing effect through wet and dry sieving along a large climatic gradient in Chile and found that the stabilization of soil aggregates persists in all climates, but their role is masked and reserved for a limited number of size fractions under humid conditions by higher vegetation and organic matter contents in the topsoil.
Corinna Gall, Martin Nebel, Dietmar Quandt, Thomas Scholten, and Steffen Seitz
Biogeosciences, 19, 3225–3245, https://doi.org/10.5194/bg-19-3225-2022, https://doi.org/10.5194/bg-19-3225-2022, 2022
Short summary
Short summary
Soil erosion is one of the most serious environmental challenges of our time, which also applies to forests when forest soil is disturbed. Biological soil crusts (biocrusts) can play a key role as erosion control. In this study, we combined soil erosion measurements with vegetation surveys in disturbed forest areas. We found that soil erosion was reduced primarily by pioneer bryophyte-dominated biocrusts and that bryophytes contributed more to soil erosion mitigation than vascular plants.
Sascha Scherer, Benjamin Höpfer, Katleen Deckers, Elske Fischer, Markus Fuchs, Ellen Kandeler, Jutta Lechterbeck, Eva Lehndorff, Johanna Lomax, Sven Marhan, Elena Marinova, Julia Meister, Christian Poll, Humay Rahimova, Manfred Rösch, Kristen Wroth, Julia Zastrow, Thomas Knopf, Thomas Scholten, and Peter Kühn
SOIL, 7, 269–304, https://doi.org/10.5194/soil-7-269-2021, https://doi.org/10.5194/soil-7-269-2021, 2021
Short summary
Short summary
This paper aims to reconstruct Middle Bronze Age (MBA) land use practices in the northwestern Alpine foreland (SW Germany, Hegau). We used a multi-proxy approach including biogeochemical proxies from colluvial deposits in the surroundings of a MBA settlement, on-site archaeobotanical and zooarchaeological data and off-site pollen data. From our data we infer land use practices such as plowing, cereal growth, forest farming and use of fire that marked the beginning of major colluvial deposition.
Cited articles
Al Hossain, B. M. T., Ahmed, T., Aktar, M. N., Fida, M., Khan, A., Islam, A., Yazdan, M. M. S., Noor, F., and Rahaman, A. Z.: Climate Change Impacts on Water Availability in the Meghna Basin, in: Proceedings of the 5th International Conference on Water and Flood Management (ICWFM-2015), Dhaka, Bangladesh, 6–8, ISBN 9789843388018, 2015. a
AWGN: Amtliches Digitales Wasserwirtschaftliches Gewässernetz (AWGN), https://www.lubw.baden-wuerttemberg.de/wasser/awgn (last access: 23 July 2024), 2023. a
Bharati, L., Lacombe, G., Gurung, P., Jayakody, P., Hoanh, C. T., and Smakhtin, V.: The Impacts of Water Infrastructure and Climate Change on the Hydrology of the Upper Ganges River Basin, International Water Management Institute (Research Report 142), https://doi.org/10.5337/2011.210, 2011. 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 Resources Research, 60, e2023WR035337, https://doi.org/10.1029/2023WR035337, 2024. a
Börgel, F., Karsten, S., Rummel, K., and Gräwe, U.: From weather data to river runoff: using spatiotemporal convolutional networks for discharge forecasting, Geosci. Model Dev., 18, 2005–2019, https://doi.org/10.5194/gmd-18-2005-2025, 2025. a
Brutsaert, W.: Hydrology: An Introduction (2nd ed.), Cambridge University Press, Cambridge, UK, ISBN 9781107135277, 2023. a
Butz, M. V., Bilkey, D., Humaidan, D., Knott, A., and Otte, S.: Learning, planning, and control in a monolithic neural event inference architecture, Neural Networks, 117, 135–144, https://doi.org/10.1016/j.neunet.2019.05.001, 2019. a
Butz, M. V., Mittenbühler, M., Schwöbel, S., Achimova, A., Gumbsch, C., Otte, S., and Kiebel, S.: Contextualizing predictive minds, Neuroscience & Biobehavioral Reviews, 168, 105948, https://doi.org/10.1016/j.neubiorev.2024.105948, 2025. a
Camporese, M. and Girotto, M.: Recent advances and opportunities in data assimilation for physics-based hydrological modeling, Frontiers in Water, 4, 948832, https://doi.org/10.3389/frwa.2022.948832, 2022. a
Chen, S., Zwart, J. A., and Jia, X.: Physics-Guided Graph Meta Learning for Predicting Water Temperature and Streamflow in Stream Networks, in: KDD 22: The 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD, 22, 2752–2761, ISBN 9781450393850, https://doi.org/10.1145/3534678.3539115, 2022. a
Cho, K., van Merrienboer, B., Bahdanau, D., and Bengio, Y.: On the Properties of Neural Machine Translation: Encoder–Decoder Approaches, in: Proceedings of SSST-8, Eighth Workshop on Syntax, Semantics and Structure in Statistical Translation, https://doi.org/10.3115/v1/w14-4012, 2014. a
Copernicus Climate Change Service, Climate Data Store: ERA5 hourly data on single levels from 1940 to present, Copernicus Climate Change Service (C3S) Climate Data Store (CDS), https://doi.org/10.24381/cds.adbb2d47, 2023. a
EU-DEM: EU-DEM v1.1, Dataset, https://land.copernicus.eu/imagery-in-situ/eu-dem/eu-dem-v1.1 (last access: 6 September 2023), 2016. a
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
Gigi, Y., Elidan, G., Hassidim, A., Matias, Y., Moshe, Z., Nevo, S., Shalev, G., and Wiesel, A.: Towards global remote discharge estimation: Using the few to estimate the many, arXiv [preprint], https://doi.org/10.48550/arXiv.1901.00786, 2019. a
Gillies, S. and others: Rasterio: geospatial raster I/O for Python programmers, GitHub, https://github.com/rasterio/rasterio (last access: 21 June 2024), 2013. a
GRDC: Global Runoff Data Centre, https://grdc.bafg.de/ (last access: 22 October 2024), 2024. a
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, Journal of Hydrology, 377, 80–91, https://doi.org/10.1016/j.jhydrol.2009.08.003, 2009. a, b
Hendrycks, D. and Gimpel, K.: Gaussian Error Linear Units (GELUs), arXiv [preprint], https://doi.org/10.48550/arXiv.1606.08415, 2016. a
Hochreiter, S. and Schmidhuber, J.: Long Short-Term Memory, Neural Computation, 9, 1735–1780, https://doi.org/10.1162/neco.1997.9.8.1735, 1997. a
Hoedt, P.-J., Kratzert, F., Klotz, D., Halmich, C., Holzleitner, M., Nearing, G., Hochreiter, S., and Klambauer, G.: MC-LSTM: Mass-Conserving LSTM, Proceedings of Machine Learning Research, arXiv [preprint], https://doi.org/10.48550/arXiv.2101.05186, 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
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, Hydrological Sciences Journal, 58, 1198–1255, https://doi.org/10.1080/02626667.2013.803183, 2013. a, b
Hunter, N. M., Bates, P. D., Horritt, M. S., and Wilson, M. D.: Simple spatially-distributed models for predicting flood inundation: A review, Geomorphology, 90, 208–225, 2007. a
Imhoff, R., Van Verseveld, W., Van Osnabrugge, B., and Weerts, A.: Scaling point-scale (pedo) transfer functions to seamless large-domain parameter estimates for high-resolution distributed hydrologic modeling: An example for the Rhine River, Water Resources Research, 56, e2019WR026807, https://doi.org/10.1029/2019WR026807, 2020. a
Imhoff, R. O., Brauer, C. C., van Heeringen, K.-J., Uijlenhoet, R., and Weerts, A. H.: Large-sample evaluation of radar rainfall nowcasting for flood early warning, Water Resources Research, 58, e2021WR031591, https://doi.org/10.1029/2021WR031591, 2022. a
Karlbauer, M., Otte, S., Lensch, H., Scholten, T., Wulfmeyer, V., and Butz, M. V.: A distributed neural network architecture for robust non-linear spatio-temporal prediction, arXiv [preprint], https://doi.org/10.48550/arXiv.1912.11141, 2019. a
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. 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
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, 2019. a, b
Kratzert, F., Klotz, D., Gauch, M., Klingler, C., Nearing, G., and Hochreiter, S.: Large-scale river network modeling using Graph Neural Networks, in: EGU General Assembly Conference Abstracts, EGU21–13375, https://doi.org/10.5194/egusphere-egu21-13375, 2021. a
Li, P., Zhang, J., and Krebs, P.: Prediction of flow based on a CNN-LSTM combined deep learning approach, Water, 14, 993, 2022. a
Liu, Y. and Gupta, H. V.: Uncertainty in hydrologic modeling: Toward an integrated data assimilation framework, Water Resources Research, Volume 43, Issue 7, https://doi.org/10.1029/2006WR005756, 2007. a
Liu, Y., Weerts, A. H., Clark, M., Hendricks Franssen, H.-J., Kumar, S., Moradkhani, H., Seo, D.-J., Schwanenberg, D., Smith, P., van Dijk, A. I. J. M., van Velzen, N., He, M., Lee, H., Noh, S. J., Rakovec, O., and Restrepo, P.: Advancing data assimilation in operational hydrologic forecasting: progresses, challenges, and emerging opportunities, Hydrol. Earth Syst. Sci., 16, 3863–3887, https://doi.org/10.5194/hess-16-3863-2012, 2012. a, b
Liu, Z., Mao, H., Wu, C.-Y., Feichtenhofer, C., Darrell, T., and Xie, S.: A ConvNet for the 2020s, in: 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), https://doi.org/10.1109/cvpr52688.2022.01167, 2022. a
Longyang, Q., Choi, S., Tennant, H., Hill, D., Ashmead, N., Neilson, B. T., Newell, D. L., McNamara, J. P., and Xu, T.: Explainable Spatially Distributed Hydrologic Modeling of a Snow Dominated Mountainous Karst Watershed Using Attention, Authorea Preprints, https://doi.org/10.22541/essoar.171536019.93198716/v1, 2024. a
Marçais, J. and de Dreuzy, J.-R.: Prospective interest of deep learning for hydrological inference, Groundwater, 55, 688–692, 2017. a
Montzka, C., Pauwels, V. R., Franssen, H.-J. H., Han, X., and Vereecken, H.: Multivariate and multiscale data assimilation in terrestrial systems: A review, Sensors, 12, 16291–16333, 2012. a
Moradkhani, H., Hsu, K.-L., Gupta, H., and Sorooshian, S.: Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter, Water Resources Research, Volume 41, Issue 5, Article number W05012, https://doi.org/10.1029/2004WR003604, 2005. a
Moshe, Z., Metzger, A., Kratzert, F., Morin, E., Nevo, S., Elidan, G., and Elyaniv, R.: HydroNets: Leveraging River Network Structure and Deep Neural Networks for Hydrologic Modeling , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4135, https://doi.org/10.5194/egusphere-egu2020-4135, 2020. a
Muñoz-Carpena, R., Carmona-Cabrero, A., Yu, Z., Fox, G., and Batelaan, O.: Convergence of mechanistic modeling and artificial intelligence in hydrologic science and engineering, PLOS Water, 2, e0000059, https://doi.org/10.1371/journal.pwat.0000212, 2023. a
Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual models part I–A discussion of principles, Journal of Hydrology, 10, 282–290, 1970. a
Nearing, G., Kratzert, F., Sampson, A. K., Pelissier, C., Klotz, D., Frame, J., Prieto, C., and Gupta, H.: What Role Does Hydrological Science Play in the Age of Machine Learning?, Water Resources Research, 57, e2020WR028091, https://doi.org/10.31223/osf.io/3sx6g, 2020. a, b, c
Oddo, P. C., Bolten, J. D., Kumar, S. V., and Cleary, B.: Deep Convolutional LSTM for improved flash flood prediction, Frontiers in Water, 6, 1346104, https://doi.org/10.3389/frwa.2024.1346104, 2024. a
Otte, S., Karlbauer, M., and Butz, M. V.: Active Tuning, arXiv [preprint], https://doi.org/10.48550/arXiv.2010.03958, 2020. a
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, Advances in Neural Information Processing Systems, 12, https://doi.org/10.48550/arXiv.1912.01703, 2019. a
Pilon, P. J.: Guidelines for reducing flood losses, Tech. rep., United Nations International Strategy for Disaster Reduction (UNISDR), https://www.un.org/esa/sustdev/publications/flood_guidelines.pdf (last access: 11 November 2025), 2002. a
Pokharel, S. and Roy, T.: A parsimonious setup for streamflow forecasting using CNN-LSTM, Journal of Hydroinformatics, jh2024114, https://doi.org/10.2166/hydro.2024.114, 2024. a, b
RADOLAN: RADOLAN/RADVOR, https://opendata.dwd.de/climate_environment/CDC/grids_germany/hourly/radolan/(last access: 6 September 2023), 2016. a
Rakovec, O., Weerts, A. H., Hazenberg, P., Torfs, P. J. J. F., and Uijlenhoet, R.: State updating of a distributed hydrological model with Ensemble Kalman Filtering: effects of updating frequency and observation network density on forecast accuracy, Hydrol. Earth Syst. Sci., 16, 3435–3449, https://doi.org/10.5194/hess-16-3435-2012, 2012. a
Samaniego, L., Kumar, R., and Attinger, S.: Multiscale parameter regionalization of a grid-based hydrologic model at the mesoscale, Water Resources Research, 46, W05523, https://doi.org/10.1029/2008WR007327, 2010. a
Scholz, F., Traub, M., Zarfl, C., Scholten, T., and Butz, M. V.: Fully differentiable, fully distributed River Discharge Prediction: data sets, Zenodo [data set], https://doi.org/10.5281/zenodo.13970575, 2024a. a
Scholz, F., Traub, M., Zarfl, C., Scholten, T., and Butz, M. V.: Fully differentiable, fully distributed River Discharge Prediction: code, Zenodo [code], https://doi.org/10.5281/zenodo.13992583, 2024b. a
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., Rahmani, F., Song, Y., Beck, H. E., Bindas, T., Dwivedi, D., Fang, K., Höge, M., Rackauckas, C., Mohanty, B., Roy, T., Xu, C., and Lawson, K.: Differentiable modelling to unify machine learning and physical models for geosciences, Nature Reviews Earth & Environment, 4, 552–567, https://doi.org/10.1038/s43017-023-00450-9, 2023. a
Shi, X., Chen, Z., Wang, H., Yeung, D.-Y., Wong, W.-k., and Woo, W.-c.: Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting, Advances in neural information processing systems, arXiv [preprint], https://doi.org/10.48550/arXiv.1506.04214, 2015. a
Simonyan, K., Vedaldi, A., and Zisserman, A.: Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps, arXiv [preprint], https://doi.org/10.48550/arXiv.1312.6034, 2013. a
Sit, M., Demiray, B., Xiang, Z., Ewing, G., Sermet, Y., and Demir, I.: A Comprehensive Review of Deep Learning Applications in Hydrology and Water Resources, https://doi.org/10.31223/osf.io/xs36g, 2020. a, b, c, d
Sit, M., Demiray, B., and Demir, I.: Short-term Hourly Streamflow Prediction with Graph Convolutional GRU Networks, arXiv [preprint], https://doi.org/10.48550/arXiv.2107.07039, 2021. a
Sun, A. Y., Jiang, P., Yang, Z.-L., Xie, Y., and Chen, X.: A graph neural network (GNN) approach to basin-scale river network learning: the role of physics-based connectivity and data fusion, Hydrol. Earth Syst. Sci., 26, 5163–5184, https://doi.org/10.5194/hess-26-5163-2022, 2022. a
Traub, M., Becker, F., Sauter, A., Otte, S., and Butz, M. V.: Loci-segmented: improving scene segmentation learning, in: International Conference on Artificial Neural Networks, 45–61, Springer, https://doi.org/10.1007/978-3-031-72338-4_4, 2024. a
Tyson, C., Longyang, Q., Neilson, B. T., Zeng, R., and Xu, T.: Effects of meteorological forcing uncertainty on high-resolution snow modeling and streamflow prediction in a mountainous karst watershed, Journal of Hydrology, 619, 129304, https://doi.org/10.1016/j.jhydrol.2023.129304, 2023. a
Ueda, F., Tanouchi, H., Egusa, N., and Yoshihiro, T.: A Transfer Learning Approach Based on Radar Rainfall for River Water-Level Prediction, Water, 16, 607, https://doi.org/10.3390/w16040607, 2024. a
Ufrecht, W.: Hydrogeologische Modelle – ein Leitfaden mit Fallbeispielen, Schriftenreihe der Deutschen Geologischen Gesellschaft, 24, Schweizerbart Science Publishers, Stuttgart, Germany, http://www.schweizerbart.de//publications/detail/artno/171902400/Schriftenreihe_der_Dt_Ges_f_Geowissen (last access: 11 November 2025), 2002. a, b
Valeriano, O. C. S., Koike, T., Yang, K., and Yang, D.: Optimal dam operation during flood season using a distributed hydrological model and a heuristic algorithm, Journal of Hydrologic Engineering, 15, 580–586, 2010. a
Van Vliet, M. T., Franssen, W. H., Yearsley, J. R., Ludwig, F., Haddeland, I., Lettenmaier, D. P., and Kabat, P.: Global river discharge and water temperature under climate change, Global Environmental Change, 23, 450–464, 2013. a
Wang, C., Jiang, S., Zheng, Y., Han, F., Kumar, R., Rakovec, O., and Li, S.: Distributed Hydrological Modeling With Physics-Encoded Deep Learning: A General Framework and Its Application in the Amazon, Water Resources Research, 60, e2023WR036170, https://doi.org/10.1029/2023WR036170, 2024. a
Wright, L.: Ranger – a synergistic optimizer, GitHub, https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer (last access: 22 August 2024), 2019. a
Xiang, Z. and Demir, I.: Distributed long-term hourly streamflow predictions using deep learning – A case study for State of Iowa, Environmental Modelling & Software, 131, 104761, https://doi.org/10.1016/j.envsoft.2020.104761, 2020. a
Xiang, Z. and Demir, I.: Fully distributed rainfall-runoff modeling using spatial-temporal graph neural network, EarthArxiv, https://doi.org/https://doi.org/10.31223/X57P74, 2022. a
Xu, T., Longyang, Q., Tyson, C., Zeng, R., and Neilson, B. T.: Hybrid physically based and deep learning modeling of a snow dominated, mountainous, karst watershed, Water Resources Research, 58, e2021WR030993, https://doi.org/10.1029/2021WR030993, 2022. a
Yadan, O.: Hydra – A framework for elegantly configuring complex applications, Github, https://github.com/facebookresearch/hydra (last access: 28 October 2024), 2019. a
Zhong, L., Lei, H., Li, Z., and Jiang, S.: Advancing streamflow prediction in data-scarce regions through vegetation-constrained distributed hybrid ecohydrological models, Journal of Hydrology, 645, 132165, https://doi.org/10.1016/j.jhydrol.2024.132165, 2024. a
Zhu, S., Wei, J., Zhang, H., Xu, Y., and Qin, H.: Spatiotemporal deep learning rainfall-runoff forecasting combined with remote sensing precipitation products in large scale basins, Journal of Hydrology, 616, 128727, https://doi.org/10.1016/j.jhydrol.2022.128727, 2023. a
Short summary
We present a neural network model that estimates river discharge based on gridded elevation, precipitation, and solar radiation. Some instances of our model produce more accurate forecasts than the European Flood Awareness System (EFAS) when simulating discharge with lead times of 50 days on the Neckar river network in Germany. It consists of multiple components that are designed to model distinct sub-processes. We show that this makes the model behave in a more physically realistic way.
We present a neural network model that estimates river discharge based on gridded elevation,...