Articles | Volume 27, issue 12
https://doi.org/10.5194/hess-27-2357-2023
© Author(s) 2023. 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-27-2357-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
30 Jun 2023
Research article |
| 30 Jun 2023
| 30 Jun 2023
The suitability of differentiable, physics-informed machine learning hydrologic models for ungauged regions and climate change impact assessment
Dapeng Feng
Civil and Environmental Engineering, The Pennsylvania State
University, University Park, PA, USA
Hylke Beck
Physical Science and Engineering, King Abdullah University of
Science and Technology, Thuwal, Saudi Arabia
Kathryn Lawson
Civil and Environmental Engineering, The Pennsylvania State
University, University Park, PA, USA
Civil and Environmental Engineering, The Pennsylvania State
University, University Park, PA, USA
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Ather Abbas, Yuan Yang, Ming Pan, Yves Tramblay, Chaopeng Shen, Haoyu Ji, Solomon H. Gebrechorkos, Florian Pappenberger, JongCheol Pyo, Dapeng Feng, George Huffman, Phu Nguyen, Christian Massari, Luca Brocca, Jackson Tan, and Hylke E. Beck
Hydrol. Earth Syst. Sci., 30, 3399–3423, https://doi.org/10.5194/hess-30-3399-2026, https://doi.org/10.5194/hess-30-3399-2026, 2026
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Our study evaluated 24 precipitation datasets using a hydrological model at global scale to assess their suitability and accuracy. We found that MSWEP (Multi-Source Weighted-Ensemble Precipitation) V2.8 excels due to its ability to integrate data from multiple sources, while others, such as IMERG (Integrated Multi-satellitE Retrievals for Global Precipitation Mission) and GDAS (Global Data Assimilation System), demonstrated strong regional performances. This research assists in selecting the appropriate dataset for applications in water resource management, hazard assessment, agriculture, and environmental monitoring.
Kamlesh Sawadekar, Seth McGinnis, Peijun Li, Kathryn Lawson, and Chaopeng Shen
EGUsphere, https://doi.org/10.48550/arXiv.2604.23045, https://doi.org/10.48550/arXiv.2604.23045, 2026
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
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δCLIMBA can fix consistent errors with global circulation models so their precipitation is locally relevant. Instead of making corrections
directly, it predicts the coefficients of interpretable formulas to minimize bias. δCLIMBA learns to make interpretable corrections that,
once trained, can be easily applied on places without data. It accurately corrects both average rainfall and extreme storm events and
shows the promise to preserve future trends, and generalizes to new regions.
Abdolmehdi Behroozi, Kathryn Lawson, and Chaopeng Shen
EGUsphere, https://doi.org/10.5194/egusphere-2026-1982, https://doi.org/10.5194/egusphere-2026-1982, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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A hyper-efficient learnable model predicts flooding faster and more accurately than traditional methods. The two-part approach captures broad water movement then refines local flood details. Tested on rivers, dam breaks, and floodplains, it reproduced water depth, flooded areas, and flow timing. Water volume stays consistent and uncertain terrain data is handled well. The model delivers high-resolution predictions with far less computing effort, enabling faster, scalable flood risk assessment.
Cyril Thébault, Wouter J. M. Knoben, Nans Addor, Andrew J. Newman, Diana Spieler, Nicolás A. Vásquez, Yalan Song, Gaby J. Gründemann, Shaun Carney, Mukesh Kumar, Katie van Werkhoven, Chaopeng Shen, Andrew W. Wood, and Martyn P. Clark
EGUsphere, https://doi.org/10.5194/egusphere-2025-6083, https://doi.org/10.5194/egusphere-2025-6083, 2026
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Reliable river flow prediction guide water supply planning and flood protection. We tested whether selecting or combining many models improves accuracy compared with single model. 78 models were used and tested in 559 river basins across the United States. A carefully chosen single model nearly matched more complex multi-model approaches, while combining models gave slightly higher accuracy and lower uncertainty. However, no approach worked best everywhere.
Jiangtao Liu, Chaopeng Shen, Fearghal O'Donncha, Yalan Song, Wei Zhi, Hylke E. Beck, Tadd Bindas, Nicholas Kraabel, and Kathryn Lawson
Hydrol. Earth Syst. Sci., 29, 6811–6828, https://doi.org/10.5194/hess-29-6811-2025, https://doi.org/10.5194/hess-29-6811-2025, 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.
Peijun Li, Yalan Song, Ming Pan, Kathryn Lawson, and Chaopeng Shen
Hydrol. Earth Syst. Sci., 29, 6829–6861, https://doi.org/10.5194/hess-29-6829-2025, https://doi.org/10.5194/hess-29-6829-2025, 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.
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
Hydrol. Earth Syst. Sci., 29, 5453–5476, https://doi.org/10.5194/hess-29-5453-2025, https://doi.org/10.5194/hess-29-5453-2025, 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 d, 1–6 months) and timescales (daily and monthly) over Western US 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 US.
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.
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.
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.
Margarita Choulga, Francesca Moschini, Cinzia Mazzetti, Stefania Grimaldi, Juliana Disperati, Hylke Beck, Peter Salamon, and Christel Prudhomme
Hydrol. Earth Syst. Sci., 28, 2991–3036, https://doi.org/10.5194/hess-28-2991-2024, https://doi.org/10.5194/hess-28-2991-2024, 2024
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CEMS_SurfaceFields_2022 dataset is a new set of high-resolution maps for land type (e.g. lake, forest), soil properties and population water needs at approximately 2 and 6 km at the Equator, covering Europe and the globe (excluding Antarctica). We describe what and how new high-resolution information can be used to create the dataset. The paper suggests that the dataset can be used as input for river, weather or other models, as well as for statistical descriptions of the region of interest.
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
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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.
Oscar M. Baez-Villanueva, Mauricio Zambrano-Bigiarini, Diego G. Miralles, Hylke E. Beck, Jonatan F. Siegmund, Camila Alvarez-Garreton, Koen Verbist, René Garreaud, Juan Pablo Boisier, and Mauricio Galleguillos
Hydrol. Earth Syst. Sci., 28, 1415–1439, https://doi.org/10.5194/hess-28-1415-2024, https://doi.org/10.5194/hess-28-1415-2024, 2024
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Various drought indices exist, but there is no consensus on which index to use to assess streamflow droughts. This study addresses meteorological, soil moisture, and snow indices along with their temporal scales to assess streamflow drought across hydrologically diverse catchments. Using data from 100 Chilean catchments, findings suggest that there is not a single drought index that can be used for all catchments and that snow-influenced areas require drought indices with larger temporal scales.
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.
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.
Sara Sadri, James S. Famiglietti, Ming Pan, Hylke E. Beck, Aaron Berg, and Eric F. Wood
Hydrol. Earth Syst. Sci., 26, 5373–5390, https://doi.org/10.5194/hess-26-5373-2022, https://doi.org/10.5194/hess-26-5373-2022, 2022
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A farm-scale hydroclimatic machine learning framework to advise farmers was developed. FarmCan uses remote sensing data and farmers' input to forecast crop water deficits. The 8 d composite variables are better than daily ones for forecasting water deficit. Evapotranspiration (ET) and potential ET are more effective than soil moisture at predicting crop water deficit. FarmCan uses a crop-specific schedule to use surface or root zone soil moisture.
Jiawei Hou, Albert I. J. M. van Dijk, Hylke E. Beck, Luigi J. Renzullo, and Yoshihide Wada
Hydrol. Earth Syst. Sci., 26, 3785–3803, https://doi.org/10.5194/hess-26-3785-2022, https://doi.org/10.5194/hess-26-3785-2022, 2022
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We used satellite imagery to measure monthly reservoir water volumes for 6695 reservoirs worldwide for 1984–2015. We investigated how changing precipitation, streamflow, evaporation, and human activity affected reservoir water storage. Almost half of the reservoirs showed significant increasing or decreasing trends over the past three decades. These changes are caused, first and foremost, by changes in precipitation rather than by changes in net evaporation or dam release patterns.
Oscar M. Baez-Villanueva, Mauricio Zambrano-Bigiarini, Pablo A. Mendoza, Ian McNamara, Hylke E. Beck, Joschka Thurner, Alexandra Nauditt, Lars Ribbe, and Nguyen Xuan Thinh
Hydrol. Earth Syst. Sci., 25, 5805–5837, https://doi.org/10.5194/hess-25-5805-2021, https://doi.org/10.5194/hess-25-5805-2021, 2021
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Most rivers worldwide are ungauged, which hinders the sustainable management of water resources. Regionalisation methods use information from gauged rivers to estimate streamflow over ungauged ones. Through hydrological modelling, we assessed how the selection of precipitation products affects the performance of three regionalisation methods. We found that a precipitation product that provides the best results in hydrological modelling does not necessarily perform the best for regionalisation.
Peter Uhe, Daniel Mitchell, Paul D. Bates, Nans Addor, Jeff Neal, and Hylke E. Beck
Geosci. Model Dev., 14, 4865–4890, https://doi.org/10.5194/gmd-14-4865-2021, https://doi.org/10.5194/gmd-14-4865-2021, 2021
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We present a cascade of models to compute high-resolution river flooding. This takes meteorological inputs, e.g., rainfall and temperature from observations or climate models, and takes them through a series of modeling steps. This is relevant to evaluating current day and future flood risk and impacts. The model framework uses global data sets, allowing it to be applied anywhere in the world.
Yuting Yang, Tim R. McVicar, Dawen Yang, Yongqiang Zhang, Shilong Piao, Shushi Peng, and Hylke E. Beck
Hydrol. Earth Syst. Sci., 25, 3411–3427, https://doi.org/10.5194/hess-25-3411-2021, https://doi.org/10.5194/hess-25-3411-2021, 2021
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This study developed an analytical ecohydrological model that considers three aspects of vegetation response to eCO2 (i.e., stomatal response, LAI response, and rooting depth response) to detect the impact of eCO2 on continental runoff over the past 3 decades globally. Our findings suggest a minor role of eCO2 on the global runoff changes, yet highlight the negative runoff–eCO2 response in semiarid and arid regions which may further threaten the limited water resource there.
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Short summary
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.
Powerful hybrid models (called δ or delta models) embrace the fundamental learning capability...
