Articles | Volume 28, issue 13
https://doi.org/10.5194/hess-28-2871-2024
© 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-28-2871-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A national-scale hybrid model for enhanced streamflow estimation – consolidating a physically based hydrological model with long short-term memory (LSTM) networks
Department of Hydrology, Geological Survey of Denmark and Greenland, Copenhagen 1350, Denmark
Julian Koch
Department of Hydrology, Geological Survey of Denmark and Greenland, Copenhagen 1350, Denmark
Simon Stisen
Department of Hydrology, Geological Survey of Denmark and Greenland, Copenhagen 1350, Denmark
Lars Troldborg
Department of Hydrology, Geological Survey of Denmark and Greenland, Copenhagen 1350, Denmark
Raphael J. M. Schneider
Department of Hydrology, Geological Survey of Denmark and Greenland, Copenhagen 1350, Denmark
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We developed a CAMELS-style dataset in Denmark, which contains hydrometeorological time series and landscape attributes for 3330 catchments (304 gauged). Many catchments in CAMELS-DK are small and at low elevations. The dataset provides information on groundwater characteristics and dynamics, as well as quantities related to the human impact on the hydrological system in Denmark. The dataset is especially relevant for developing data-driven and hybrid physically informed modeling frameworks.
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The amount and spatio-temporal distribution of soil moisture, the water in the upper soil, is of great relevance for agriculture and water management. Here, we investigate whether the established downscaling algorithm combining different satellite products to estimate medium-scale soil moisture is applicable to higher resolutions and whether results can be improved by accounting for land cover types. Original satellite data and downscaled soil moisture are compared with ground observations.
Cited articles
Abbott, M. B., Bathurst, J. C., Cunge, J. A., O'Connell, P. E., 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.
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.
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.
Amendola, M., Arcucci, R., Mottet, L., Casas, C. Q., Fan, S., Pain, C., Linden, P., and Guo, Y.-K.: Data Assimilation in the Latent Space of a Neural Network, arXiv [preprint], https://doi.org/10.48550/arXiv.2012.12056, 2020.
Arsenault, R., Martel, J.-L., Brunet, F., Brissette, F., and Mai, J.: Continuous streamflow prediction in ungauged basins: long short-term memory neural networks clearly outperform traditional hydrological models, Hydrol. Earth Syst. Sci., 27, 139–157, https://doi.org/10.5194/hess-27-139-2023, 2023.
Baroni, G., Schalge, B., Rakovec, O., Kumar, R., Schüler, L., Samaniego, L., Simmer, C., and Attinger, S.: A Comprehensive Distributed Hydrological Modeling Intercomparison to Support Process Representation and Data Collection Strategies, Water Resour. Res., 55, 990–1010, https://doi.org/10.1029/2018WR023941, 2019.
Beven, K.: How to make advances in hydrological modelling, Hydrol. Adv. Theory Pract., 1969, 19–32, https://doi.org/10.2166/nh.2019.134, 2020.
Beven, K. J.: A discussion of distributed hydrological modelling, in: Distributed hydrological modelling, Springer, 255–278, https://doi.org/10.1007/978-94-009-0257-2_13, 1996.
Cai, Z. and Peng, C.: A study on training fine-tuning of convolutional neural networks, in: 2021 13th International Conference on Knowledge and Smart Technology (KST), 21–24 January 2021, Bangsaen, Chonburi, Thailand, 84–89, https://doi.org/10.1109/KST51265.2021.9415793, 2021.
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.
Cheng, M., Fang, F., Kinouchi, T., Navon, I. M., and Pain, C. C.: Long lead-time daily and monthly streamflow forecasting using machine learning methods, J. Hydrol., 590, 125376, https://doi.org/10.1016/j.jhydrol.2020.125376, 2020.
Cho, K. and Kim, Y.: Improving streamflow prediction in the WRF-Hydro model with LSTM networks, J. Hydrol., 605, 127297, https://doi.org/10.1016/j.jhydrol.2021.127297, 2022.
Coxon, G., Addor, N., Bloomfield, J. P., Freer, J., Fry, M., Hannaford, J., Howden, N. J. K., Lane, R., Lewis, M., Robinson, E. L., Wagener, T., and Woods, R.: CAMELS-GB: hydrometeorological time series and landscape attributes for 671 catchments in Great Britain, Earth Syst. Sci. Data, 12, 2459–2483, https://doi.org/10.5194/essd-12-2459-2020, 2020.
Curceac, S., Atkinson, P. M., Milne, A., Wu, L., and Harris, P.: Adjusting for Conditional Bias in Process Model Simulations of Hydrological Extremes: An Experiment Using the North Wyke Farm Platform, Front. Artif. Intell., 3, 1–16, https://doi.org/10.3389/frai.2020.565859, 2020.
Danapour, M., Højberg, A. L., Jensen, K. H., and Stisen, S.: Assessment of regional inter-basin groundwater flow using both simple and highly parameterized optimization schemes, Hydrogeol. J., 27, 1929–1947, https://doi.org/10.1007/s10040-019-01984-3, 2019.
De la Fuente, L. A., Ehsani, M. R., Gupta, H. V., and Condon, L. E.: Towards Interpretable LSTM-based Modelling of Hydrological Systems, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2023-666, 2023.
Dembélé, M., Hrachowitz, M., Savenije, H. H. G., Mariéthoz, G., and Schaefli, B.: Improving the Predictive Skill of a Distributed Hydrological Model by Calibration on Spatial Patterns With Multiple Satellite Data Sets, Water Resour. Res., 56, 1–26, https://doi.org/10.1029/2019WR026085, 2020.
Devia, G. K., Ganasri, B. P., and Dwarakish, G. S.: A Review on Hydrological Models, Aquat. Pr., 4, 1001–1007, https://doi.org/10.1016/j.aqpro.2015.02.126, 2015.
Devitt, L., Neal, J., Coxon, G., Savage, J., and Wagener, T.: Flood hazard potential reveals global floodplain settlement patterns, Nat. Commun., 14, 2801, https://doi.org/10.1038/s41467-023-38297-9, 2023.
DHI: MIKE SHE User Guide and Reference Manual, https://manuals.mikepoweredbydhi.help/latest/Water_Resources/MIKE_SHE_Print.pdf (last access: 1 November 2022), 2020.
Duque, C., Nilsson, B., and Engesgaard, P.: Groundwater–surface water interaction in Denmark, WIRes Water, 10, 1–23, https://doi.org/10.1002/wat2.1664, 2023.
Fatichi, S., Vivoni, E. R., Ogden, F. L., Ivanov, V. Y., Mirus, B., Gochis, D., Downer, C. W., Camporese, M., Davison, J. H., and Ebel, B.: An overview of current applications, challenges, and future trends in distributed process-based models in hydrology, J. Hydrol., 537, 45–60, 2016.
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, 1–24, https://doi.org/10.1029/2019WR026793, 2020.
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.
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.
Frame, J. M., Kratzert, F., Raney, A., Rahman, M., Salas, F. R., and Nearing, G. S.: Post-Processing the National Water Model with Long Short-Term Memory Networks for Streamflow Predictions and Model Diagnostics, J. Am. Water Resour. As., 57, 885–905, https://doi.org/10.1111/1752-1688.12964, 2021.
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.
Gers, F. A., Schmidhuber, J., and Cummins, F.: Learning to forget: Continual prediction with LSTM, Neural Comput., 12, 2451–2471, 2000.
Ghorbani, A. and Zou, J.: Data shapley: Equitable valuation of data for machine learning, in: 36th Int. Conf. Mach. Learn. ICML 2019, 10–15 June 2019, Long Beach Convention Center, Long Beach, USA, 4053–4065, ISBN 9781510886988, 2019.
Goldstein, A., Kapelner, A., Bleich, J., and Pitkin, E.: Peeking Inside the Black Box: Visualizing Statistical Learning With Plots of Individual Conditional Expectation, J. Comput. Graph. Stat., 24, 44–65, https://doi.org/10.1080/10618600.2014.907095, 2015.
Greff, K., Srivastava, R. K., Koutnik, J., Steunebrink, B. R., and Schmidhuber, J.: LSTM: A Search Space Odyssey, IEEE T. Neur. Net. Lear., 28, 2222–2232, https://doi.org/10.1109/TNNLS.2016.2582924, 2017.
Gupta, H. V. and Kling, H.: On typical range, sensitivity, and normalization of Mean Squared Error and Nash-Sutcliffe Efficiency type metrics, Water Resour. Res., 47, 2–4, https://doi.org/10.1029/2011WR010962, 2011.
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, J. Hydrol., 377, 80–91, 2009.
Harrigan, S., Zsoter, E., Cloke, H., Salamon, P., and Prudhomme, C.: Daily ensemble river discharge reforecasts and real-time forecasts from the operational Global Flood Awareness System, Hydrol. Earth Syst. Sci., 27, 1–19, https://doi.org/10.5194/hess-27-1-2023, 2023.
Hashemi, R., Brigode, P., Garambois, P.-A., and Javelle, P.: How can we benefit from regime information to make more effective use of long short-term memory (LSTM) runoff models?, Hydrol. Earth Syst. Sci., 26, 5793–5816, https://doi.org/10.5194/hess-26-5793-2022, 2022.
Hauswirth, S. M., Bierkens, M. F. P., Beijk, V., and Wanders, N.: The potential of data driven approaches for quantifying hydrological extremes, Adv. Water Resour., 155, 104017, https://doi.org/10.1016/j.advwatres.2021.104017, 2021.
Henriksen, H. J., Troldborg, L., Nyegaard, P., Sonnenborg, T. O., Refsgaard, J. C., and Madsen, B.: Methodology for construction, calibration and validation of a national hydrological model for Denmark, J. Hydrol., 280, 52–71, https://doi.org/10.1016/S0022-1694(03)00186-0, 2003.
Henriksen, H. J., Kragh, S. J., Gotfredsen, J., Ondracek, M., van Til, M., Jakobsen, A., Schneider, R. J. M., Koch, J., Troldborg, L., Rasmussen, P., Pasten-Zapata, E., and Stisen, S.: Udvikling af landsdækkende modelberegninger af terrænnære hydrologiske forhold i 100 m grid ved anvendelse af DK-modellen: Dokumentationsrapport vedr. modelleverancer til Hydrologisk Informations- og Prognosesystem. Udarbejdet som en del af Den Fællesoffen, GEUS, https://doi.org/10.22008/gpub/38113, 2021.
Henriksen, H. J., Schneider, R., Koch, J., Ondracek, M., Troldborg, L., Seidenfaden, I. K., Kragh, S. J., Bøgh, E., and Stisen, S.: A New Digital Twin for Climate Change Adaptation, Water Management, and Disaster Risk Reduction (HIP Digital Twin), Water-Sui, 15, 25, https://doi.org/10.3390/w15010025, 2023.
Herrera, P. A., Marazuela, M. A., and Hofmann, T.: Parameter estimation and uncertainty analysis in hydrological modeling, WIRes Water, 9, 1–23, https://doi.org/10.1002/wat2.1569, 2022.
Hochreiter, S. and Schmidhuber, J.: Long Short-Term Memory, Neural Comput., 9, 1735–1780, https://doi.org/10.1162/neco.1997.9.8.1735, 1997.
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.
Højberg, A. L., Troldborg, L., Nyegaard, P., Ondracek, M., and Stisen, S.: Handling and linking data and hydrological models – experiences from the Danish national water resources model (DK-model), Modelcare2010, 141–144, ISBN 9787562524175, 2009.
Højberg, A. L., Troldborg, L., Stisen, S., Christensen, B. B. S. S., and Henriksen, H. J.: Stakeholder driven update and improvement of a national water resources model, Environ. Modell. Softw., 40, 202–213, https://doi.org/10.1016/j.envsoft.2012.09.010, 2013.
Hoy, A. Q.: Protecting water resources calls for international efforts, Science, 356, 814–815, https://doi.org/10.1126/science.356.6340.814, 2017.
Hunt, K. M. R., Matthews, G. R., Pappenberger, F., and Prudhomme, C.: Using a long short-term memory (LSTM) neural network to boost river streamflow forecasts over the western United States, Hydrol. Earth Syst. Sci., 26, 5449–5472, https://doi.org/10.5194/hess-26-5449-2022, 2022.
Käding, C., Rodner, E., Freytag, A., and Denzler, J.: Fine-tuning deep neural networks in continuous learning scenarios, Lect. Notes Comput. Sc. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), 10118 LNCS, 588–605, https://doi.org/10.1007/978-3-319-54526-4_43, 2017.
Kawaguchi, K., Bengio, Y., and Kaelbling, L.: Generalization in Deep Learning, in: Mathmatical Aspects of Deep Learning, Cambridge University Press, 112–148, https://doi.org/10.1017/9781009025096.003, 2022.
Ke, G., Meng, Q., Finley, T., Wang, T., Chen, W., Ma, W., Ye, Q., and Liu, T. Y.: LightGBM: A highly efficient gradient boosting decision tree, Adv. Neur. In., 3147–3155, ISBN 9781510860964, 2017.
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.
Koch, J. and Schneider, R.: Long short-term memory networks enhance rainfall-runoff modelling at the national scale of Denmark, GEUS Bull., 49, 1–7, https://doi.org/10.34194/geusb.v49.8292, 2022.
Koch, J., Cornelissen, T., Fang, Z., Bogena, H., Diekkrüger, B., Kollet, S., and Stisen, S.: Inter-comparison of three distributed hydrological models with respect to seasonal variability of soil moisture patterns at a small forested catchment, J. Hydrol., 533, 234–249, 2016.
Koch, J., Gotfredsen, J., Schneider, R., Troldborg, L., Stisen, S., and Henriksen, H. J.: High Resolution Water Table Modeling of the Shallow Groundwater Using a Knowledge-Guided Gradient Boosting Decision Tree Model, Front. Water, 3, 1–14, https://doi.org/10.3389/frwa.2021.701726, 2021.
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.
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.
Kratzert, F., Herrnegger, M., Klotz, D., Hochreiter, S., and Klambauer, G.: NeuralHydrology – Interpreting LSTMs in Hydrology, Lect. Notes Comput. Sc. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), 11700 LNCS, 347–362, https://doi.org/10.1007/978-3-030-28954-6_19, 2019a.
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, 2019b.
Kratzert, F., Gauch, M., Nearing, G., Hochreiter, S., and Klotz, D.: Niederschlags-Abfluss-Modellierung mit Long Short-Term Memory (LSTM), Österreichische Wasser- und Abfallwirtschaft, 73, 270–280, https://doi.org/10.1007/s00506-021-00767-z, 2021a.
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, 2021b.
Kratzert, F., Gauch, M., Nearing, G., and Klotz, D.: NeuralHydrology – A Python library for Deep Learning research in hydrology, J. Open Source Softw., 7, 4050, https://doi.org/10.21105/joss.04050, 2022.
Kumari, N., Srivastava, A., Sahoo, B., Raghuwanshi, N. S., and Bretreger, D.: Identification of Suitable Hydrological Models for Streamflow Assessment in the Kangsabati River Basin, India, by Using Different Model Selection Scores, Nat. Resour. Res., 30, 4187–4205, https://doi.org/10.1007/s11053-021-09919-0, 2021.
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.
Li, D. and Zhang, H. R.: Improved Regularization and Robustness for Fine-tuning in Neural Networks, Adv. Neur. In., 33, 27249–27262, 2021.
Liu, S., Wang, J., Wang, H., and Wu, Y.: Post-processing of hydrological model simulations using the convolutional neural network and support vector regression, Hydrol. Res., 53, 605–621, https://doi.org/10.2166/nh.2022.004, 2022.
Ma, K., Feng, D., Lawson, K., Tsai, W., 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.
MacNeil, D. and Eliasmith, C.: Fine-tuning and the stability of recurrent neural networks, PLoS One, 6, e22885, https://doi.org/10.1371/journal.pone.0022885, 2011.
Moges, E., Demissie, Y., Larsen, L., and Yassin, F.: Review: Sources of hydrological model uncertainties and advances in their analysis, Water-Sui, 13, 1–23, https://doi.org/10.3390/w13010028, 2021.
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.
Nearing, G. S., Klotz, D., Frame, J. M., Gauch, M., Gilon, O., Kratzert, F., Sampson, A. K., Shalev, G., and Nevo, S.: Technical note: Data assimilation and autoregression for using near-real-time streamflow observations in long short-term memory networks, Hydrol. Earth Syst. Sci., 26, 5493–5513, https://doi.org/10.5194/hess-26-5493-2022, 2022.
Neural Hydrology: Using Neural Networks in Hydrology, GitHub, https://neuralhydrology.github.io (last access: 20 March 2023), 2024.
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.
Pakoksung, K. and Takagi, M.: Effect of DEM sources on distributed hydrological model to results of runoff and inundation area, Model. Earth Syst. Environ., 7, 1891–1905, https://doi.org/10.1007/s40808-020-00914-7, 2021.
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, Adv. Neural Info. Proc. Syst., 32, ISBN 9781713807933, 2019.
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, 2020.
Refsgaard, J. C., Stisen, S., and Koch, J.: Hydrological process knowledge in catchment modelling – Lessons and perspectives from 60 years development, Hydrol. Process., 36, 1–20, https://doi.org/10.1002/hyp.14463, 2022.
Roy, A., Kasiviswanathan, K. S., Patidar, S., Adeloye, A. J., Soundharajan, B. S., and Ojha, C. S. P.: A Novel Physics-Aware Machine Learning-Based Dynamic Error Correction Model for Improving Streamflow Forecast Accuracy, Water Resour. Res., 59, e2022WR033318, https://doi.org/10.1029/2022WR033318, 2023.
Sahraei, S., Asadzadeh, M., and Unduche, F.: Signature-based multi-modelling and multi-objective calibration of hydrologic models: Application in flood forecasting for Canadian Prairies, J. Hydrol., 588, 125095, https://doi.org/10.1016/j.jhydrol.2020.125095, 2020.
Satoh, Y., Yoshimura, K., Pokhrel, Y., Kim, H., Shiogama, H., Yokohata, T., Hanasaki, N., Wada, Y., Burek, P., Byers, E., Schmied, H. M., Gerten, D., Ostberg, S., Gosling, S. N., Boulange, J. E. S., and Oki, T.: The timing of unprecedented hydrological drought under climate change, Nat. Commun., 13, 3287, https://doi.org/10.1038/s41467-022-30729-2, 2022.
Scharling, M.: Klimagrid Danmark – Nedbør, lufttemperatur og potentiel fordampning 20×20 & 40×40 km – Metodebeskrivelse, Danish Meteorol. Inst., https://www.dmi.dk/fileadmin/user_upload/Rapporter/TR/1999/tr99-12.pdf (last access: 2 July 2024), 1999a.
Scharling, M.: Klimagrid Danmark Nedbør 10×10 km (ver. 2) – Metodebeskrivelse, Danish Meteorol. Inst., 15–17, https://www.dmi.dk/fileadmin/user_upload/Rapporter/TR/1999/tr99-15.pdf (last access: 2 July 2024), 1999b.
Schneider, R., Henriksen, H. J., and Stisen, S.: A robust objective function for calibration of groundwater models in light of deficiencies of model structure and observations, J. Hydrol., 613, 128339, https://doi.org/10.1016/j.jhydrol.2022.128339, 2022a.
Schneider, R., Koch, J., Troldborg, L., Henriksen, H. J., and Stisen, S.: Machine-learning-based downscaling of modelled climate change impacts on groundwater table depth, Hydrol. Earth Syst. Sci., 26, 5859–5877, https://doi.org/10.5194/hess-26-5859-2022, 2022b.
Shen, Y., Ruijsch, J., Lu, M., Sutanudjaja, E. H., and Karssenberg, D.: Random forests-based error-correction of streamflow from a large-scale hydrological model: Using model state variables to estimate error terms, Comput. Geosci., 159, 105019, https://doi.org/10.1016/j.cageo.2021.105019, 2022.
Silvestro, F., Gabellani, S., Rudari, R., Delogu, F., Laiolo, P., and Boni, G.: Uncertainty reduction and parameter estimation of a distributed hydrological model with ground and remote-sensing data, Hydrol. Earth Syst. Sci., 19, 1727–1751, https://doi.org/10.5194/hess-19-1727-2015, 2015.
Slater, L. J., Arnal, L., Boucher, M.-A., Chang, A. Y.-Y., Moulds, S., Murphy, C., Nearing, G., Shalev, G., Shen, C., Speight, L., Villarini, G., Wilby, R. L., Wood, A., and Zappa, M.: Hybrid forecasting: blending climate predictions with AI models, Hydrol. Earth Syst. Sci., 27, 1865–1889, https://doi.org/10.5194/hess-27-1865-2023, 2023.
Soltani, M., Bjerre, E., Koch, J., and Stisen, S.: Integrating remote sensing data in optimization of a national water resources model to improve the spatial pattern performance of evapotranspiration, J. Hydrol., 603, 127026, https://doi.org/10.1016/j.jhydrol.2021.127026, 2021.
Stisen, S., Sonnenborg, T. O., Højberg, A. L., Troldborg, L., and Refsgaard, J. C.: Evaluation of Climate Input Biases and Water Balance Issues Using a Coupled Surface-Subsurface Model, Vadose Zone J., 10, 37–53, https://doi.org/10.2136/vzj2010.0001, 2011.
Stisen, S., Ondracek, M., Troldborg, L., Schneider, R. J. M., and van Til, M. J.: National Vandressource Model. Modelopstilling og kalibrering af DK-model 2019, GEUS, Copenhagen, https://doi.org/10.22008/gpub/32631, 2020.
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.
Sutskever, I., Vinyals, O., and Le, Q. V.: Sequence to sequence learning with neural networks, Adv. Neur. In., 4, 3104–3112, 2014.
Tan, C., Sun, F., Kong, T., Zhang, W., Yang, C., and Liu, C.: A survey on deep transfer learning, Lect. Notes Comput. Sc. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), 11141 LNCS, 270–279, https://doi.org/10.1007/978-3-030-01424-7_27, 2018.
Tang, S., Sun, F., Liu, W., Wang, H., Feng, Y., and Li, Z.: Optimal Postprocessing Strategies With LSTM for Global Streamflow Prediction in Ungauged Basins, Water Resour. Res., 59, 1–16, https://doi.org/10.1029/2022WR034352, 2023.
Wang, Y., Liu, J., Li, C., Liu, Y., Xu, L., and Yu, F.: A data-driven approach for flood prediction using grid-based meteorological data, Hydrol. Process., 37, e14837, https://doi.org/10.1002/hyp.14837, 2023.
Wang, Y. H., Gupta, H. V., Zeng, X., and Niu, G. Y.: Exploring the Potential of Long Short-Term Memory Networks for Improving Understanding of Continental- and Regional-Scale Snowpack Dynamics, Water Resour. Res., 58, e2021WR031033, https://doi.org/10.1029/2021WR031033, 2022.
Wi, S. and Steinschneider, S.: On the need for physical constraints in deep learning rainfall–runoff projections under climate change: a sensitivity analysis to warming and shifts in potential evapotranspiration, Hydrol. Earth Syst. Sci., 28, 479–503, https://doi.org/10.5194/hess-28-479-2024, 2024.
Wilbrand, K., Taormina, R., ten Veldhuis, M., Visser, M., Hrachowitz, M., Nuttall, J., and Dahm, R.: Predicting streamflow with LSTM networks using global datasets, Front. Water, 5, 116612, https://doi.org/10.3389/frwa.2023.1166124, 2023.
Winsemius, H. C., Schaefli, B., Montanari, A., and Savenije, H. H. G.: On the calibration of hydrological models in ungauged basins: A framework for integrating hard and soft hydrological information, Water Resour. Res., 45, 1–15, https://doi.org/10.1029/2009WR007706, 2009.
Wu, H., Hu, T., Liu, Y., Zhou, H., Wang, J., and Long, M.: TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis, arXiv [preprint], https://doi.org/10.48550/arXiv.2210.02186, 2022.
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, 1–18, https://doi.org/10.1029/2007WR006716, 2008.
Yu, Q., Tolson, B. A., Shen, H., Han, M., Mai, J., and Lin, J.: Enhancing long short-term memory (LSTM)-based streamflow prediction with a spatially distributed approach, Hydrol. Earth Syst. Sci., 28, 2107–2122, https://doi.org/10.5194/hess-28-2107-2024, 2024.
Zhang, T., Liang, Z., Li, W., Wang, J., Hu, Y., and Li, B.: Statistical post-processing of precipitation forecasts using circulation classifications and spatiotemporal deep neural networks, Hydrol. Earth Syst. Sci., 27, 1945–1960, https://doi.org/10.5194/hess-27-1945-2023, 2023.
Zhang, Y., Ragettli, S., Molnar, P., Fink, O., and Peleg, N.: Generalization of an Encoder-Decoder LSTM model for flood prediction in ungauged catchments, J. Hydrol., 614, 128577, https://doi.org/10.1016/j.jhydrol.2022.128577, 2022.
Short summary
We developed hybrid schemes to enhance national-scale streamflow predictions, combining long short-term memory (LSTM) with a physically based hydrological model (PBM). A comprehensive evaluation of hybrid setups across Denmark indicates that LSTM models forced by climate data and catchment attributes perform well in many regions but face challenges in groundwater-dependent basins. The hybrid schemes supported by PBMs perform better in reproducing long-term streamflow behavior and extreme events.
We developed hybrid schemes to enhance national-scale streamflow predictions, combining long...