Articles | Volume 28, issue 4
https://doi.org/10.5194/hess-28-945-2024
© 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-28-945-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
27 Feb 2024
Research article |
| 27 Feb 2024
| 27 Feb 2024
Toward interpretable LSTM-based modeling of hydrological systems
Luis Andres De la Fuente
CORRESPONDING AUTHOR
Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson 85721, United States
Mohammad Reza Ehsani
Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson 85721, United States
Hoshin Vijai Gupta
Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson 85721, United States
Laura Elizabeth Condon
Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson 85721, United States
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Cited articles
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.
Addor, N., Nearing, G., Prieto, C., Newman, A. J., Le Vine, N., and Clark, M. P.: A Ranking of Hydrological Signatures Based on Their Predictability in Space, Water Resour. Res., 54, 8792–8812, https://doi.org/10.1029/2018WR022606, 2018.
Ali, G., Tetzlaff, D., Soulsby, C., McDonnell, J. J., and Capell, R.: A comparison of similarity indices for catchment classification using a cross-regional dataset, Adv. Water Resour., 40, 11–22, https://doi.org/10.1016/j.advwatres.2012.01.008, 2012.
Breiman, L.: Random Forest, Mach. Learn., 45, 5–32, https://doi.org/10.1023/A:1010933404324, 2001.
Burnash, R., Ferral, L., and McGuire, R.: A Generalized Streamflow Simulation System: Conceptual Modeling for Digital Computers, U.S. Department of Commerce, National Weather Service, and State of California, Department of Water Resources, 204 pp., https://www.google.com/books/edition/A_Generalized_Streamflow_Simulation_Syst/aQJDAAAAIAAJ?hl=en (last access: January 2023), 1973.
Carvalho, D. V., Pereira, E. M., and Cardoso, J. S.: Machine Learning Interpretability: A Survey on Methods and Metrics, Electronics, 8, 832, https://doi.org/10.3390/electronics8080832, 2019.
Chen, J., Zheng, F., May, R., Guo, D., Gupta, H., and Maier, H. R.: Improved data splitting methods for data-driven hydrological model development based on a large number of catchment samples, J. Hydrol., 613, 128340, https://doi.org/10.1016/j.jhydrol.2022.128340, 2022.
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.
Cui, Z., Zhou, Y., Guo, S., Wang, J., Ba, H., and He, S.: A novel hybrid XAJ-LSTM model for multi-step-ahead flood forecasting, Hydrol. Res., 52, 1436–1454, https://doi.org/10.2166/nh.2021.016, 2021.
De la Fuente, L.: Using Big-Data to Develop Catchment-Scale Hydrological Models for Chile, University of Arizona, 123 pp., http://hdl.handle.net/10150/656824 (last access: January 2023), 2021.
De la Fuente, L. A. and Bennett, A.: ldelafue/Hydro-LSTM: HydroLSTM (v1.0.0), Zenodo [code], https://doi.org/10.5281/zenodo.10694927, 2024.
De la Fuente, L. A., Gupta, H. V., and Condon, L. E.: Toward a Multi-Representational Approach to Prediction and Understanding, in Support of Discovery in Hydrology, Water Resour. Res., 59, e2021WR031548, https://doi.org/10.1029/2021WR031548, 2023.
de Lavenne, A., Andréassian, V., Crochemore, L., Lindström, G., and Arheimer, B.: Quantifying multi-year hydrological memory with Catchment Forgetting Curves, Hydrol. Earth Syst. Sci., 26, 2715–2732, https://doi.org/10.5194/hess-26-2715-2022, 2022.
Erion, G., Janizek, J. D., Sturmfels, P., Lundberg, S. M., and Lee, S.-I.: Improving performance of deep learning models with axiomatic attribution priors and expected gradients, Nat. Mach. Intell., 3, 620–631, https://doi.org/10.1038/s42256-021-00343-w, 2021.
Fan, F., Xiong, J., Li, M., and Wang, G.: On Interpretability of Artificial Neural Networks: A Survey, arXiv [preprint], https://doi.org/10.48550/arXiv.2001.02522, 2020.
Friedman, J. H.: Greedy Function Approximation: A Gradient Boosting Machine, Ann. Stat., 29, 1189–1232, 2001.
Gauch, M., Mai, J., and Lin, J.: The proper care and feeding of CAMELS: How limited training data affects streamflow prediction, Environ. Modell. Softw., 135, 104926, https://doi.org/10.1016/j.envsoft.2020.104926, 2021.
Gers, F. A. and Schmidhuber, E.: LSTM recurrent networks learn simple context-free and context-sensitive languages, IEEE T. Neural Networ., 12, 1333–1340, https://doi.org/10.1109/72.963769, 2001.
Glorot, X. and Bengio, Y.: Understanding the difficulty of training deep feedforward neural networks, Proc. Mach. Learn. Res., 9, 249–256, 2010.
Graves, A., Eck, D., Beringer, N., and Schmidhuber, J.: Biologically Plausible Speech Recognition with LSTM Neural Nets, in: Biologically Inspired Approaches to Advanced Information Technology, vol. 3141, edited by: Ijspeert, A. J., Murata, M., and Wakamiya, N., Springer Berlin Heidelberg, Berlin, Heidelberg, 127–136, https://doi.org/10.1007/978-3-540-27835-1_10, 2004.
Guo, D., Zheng, F., Gupta, H., and Maier, H. R.: On the Robustness of Conceptual Rainfall-Runoff Models to Calibration and Evaluation Data Set Splits Selection: A Large Sample Investigation, Water Resour. Res., 56, e2019WR026752, https://doi.org/10.1029/2019WR026752, 2020.
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, https://doi.org/10.1016/j.jhydrol.2009.08.003, 2009.
Hargreaves, G. and Samani, Z.: Reference Crop Evapotranspiration from Temperature, Appl. Eng. Agric., 1, 96–99, https://doi.org/10.13031/2013.26773, 1985.
Hey, T., Butler, K., Jackson, S., and Thiyagalingam, J.: Machine learning and big scientific data, Philos. T. Roy. Soc. A, 378, 20190054, https://doi.org/10.1098/rsta.2019.0054, 2020.
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.
Hoedt, P.-J., Kratzert, F., Klotz, D., Halmich, C., Holzleitner, M., Nearing, G., Hochreiter, S., and Klambauer, G.: MC-LSTM: Mass-Conserving LSTM, in: Volume 139: International Conference on Machine Learning, 18–24 July 2021, virtual, 4275–4286, https://proceedings.mlr.press/v139/hoedt21a.html (last access: January 2023), 2021.
Huber, P. J.: Robust Estimation of a Location Parameter, Ann. Math. Stat., 35, 73–101, https://doi.org/10.1214/aoms/1177703732, 1964.
Jiang, S., Zheng, Y., Wang, C., and Babovic, V.: Uncovering Flooding Mechanisms Across the Contiguous United States Through Interpretive Deep Learning on Representative Catchments, Water Resour. Res., 58, e2021WR030185, https://doi.org/10.1029/2021WR030185, 2022.
Khandelwal, A., Xu, S., Li, X., Jia, X., Stienbach, M., Duffy, C., Nieber, J., and Kumar, V.: Physics Guided Machine Learning Methods for Hydrology, arXiv [preprint], https://doi.org/10.48550/arXiv.2012.02854, 2020.
Kingma, D. P. and Ba, J.: Adam: A Method for Stochastic Optimization, arXiv [preprint], https://doi.org/10.48550/arXiv.1412.6980, 29 January 2017.
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., 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.
Kratzert, F., Gauch, M., Nearing, G., and Klotz, D.: NeuralHydrology – A Python library for Deep Learningresearch in hydrology, J. Open Sour. Softw., 7, 4050, https://doi.org/10.21105/joss.04050, 2022.
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.
Lienhard, J. H.: A statistical mechanical prediction of the dimensionless unit hydrograph, J. Geophys. Res., 69, 5231–5238, https://doi.org/10.1029/JZ069i024p05231, 1964.
Linardatos, P., Papastefanopoulos, V., and Kotsiantis, S.: Explainable AI: A Review of Machine Learning Interpretability Methods, Entropy, 23, 18, https://doi.org/10.3390/e23010018, 2020.
Ma, Y., Montzka, C., Bayat, B., and Kollet, S.: Using Long Short-Term Memory networks to connect water table depth anomalies to precipitation anomalies over Europe, Hydrol. Earth Syst. Sci., 25, 3555–3575, https://doi.org/10.5194/hess-25-3555-2021, 2021.
Miller, T.: Explanation in artificial intelligence: Insights from the social sciences, Artif. Intell., 267, 1–38, https://doi.org/10.1016/j.artint.2018.07.007, 2019.
Molnar, C.: Interpretable Machine Learning, 2nd Edn., Independently, https://christophm.github.io/interpretable-ml-book/ (last access: January 2023), 2022.
Newman, A., Sampson, K., Clark, M., Bock, A., Viger, R., Blodgett, D., Addor, N., and MIzukami, M.: A large-sample watershed-scale hydrometeorological dataset for the contiguous USA, NCAR [data set], https://doi.org/10.5065/D6MW2F4D, 2014.
Parviainen, E.: Dimension Reduction for Regression with Bottleneck Neural Networks, in: Intelligent Data Engineering and Automated Learning – IDEAL 2010, vol. 6283, edited by: Fyfe, C., Tino, P., Charles, D., Garcia-Osorio, C., and Yin, H., Springer Berlin Heidelberg, Berlin, Heidelberg, 37–44, https://doi.org/10.1007/978-3-642-15381-5_5, 2010.
Perrin, C., Michel, C., and Andréassian, V.: Improvement of a parsimonious model for streamflow simulation, J. Hydrol., 279, 275–289, https://doi.org/10.1016/S0022-1694(03)00225-7, 2003.
Pilgrim, D. H., Chapman, T. G., and Doran, D. G.: Problems of rainfall-runoff modelling in arid and semiarid regions, Hydrolog. Sci. J., 33, 379–400, https://doi.org/10.1080/02626668809491261, 1988.
Pugliese, R., Regondi, S., and Marini, R.: Machine learning-based approach: global trends, research directions, and regulatory standpoints, Data Science and Management, 4, 19–29, https://doi.org/10.1016/j.dsm.2021.12.002, 2021.
Qiu, R., Wang, Y., Rhoads, B., Wang, D., Qiu, W., Tao, Y., and Wu, J.: River water temperature forecasting using a deep learning method, J. Hydrol., 595, 126016, https://doi.org/10.1016/j.jhydrol.2021.126016, 2021.
Rodríguez-Iturbe, I. and Valdés, J. B.: The geomorphologic structure of hydrologic response, Water Resour. Res., 15, 1409–1420, https://doi.org/10.1029/WR015i006p01409, 1979.
Sherman, L.: Stream Flow from Rainfall by the Unit Graph Method, Eng. News-Rec., 108, 501–505, 1932.
Singh, R., Archfield, S. A., and Wagener, T.: Identifying dominant controls on hydrologic parameter transfer from gauged to ungauged catchments – A comparative hydrology approach, J. Hydrol., 517, 985–996, https://doi.org/10.1016/j.jhydrol.2014.06.030, 2014.
Song, H., Kim, S., Kim, M., and Lee, J.-G.: Ada-boundary: accelerating DNN training via adaptive boundary batch selection, Mach. Learn., 109, 1837–1853, https://doi.org/10.1007/s10994-020-05903-6, 2020.
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., and Polosukhin, I.: Attention Is All You Need, arXiv [preprint], https://doi.org/10.48550/arXiv.1706.03762, 2017.
Wang, Y., Gupta, H. V., Zeng, X., and Niu, G.: 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.
Xu, T. and Liang, F.: Machine learning for hydrologic sciences: An introductory overview, WIREs Water, 8, e1533, https://doi.org/10.1002/wat2.1533, 2021.
Zheng, F., Maier, H. R., Wu, W., Dandy, G. C., Gupta, H. V., and Zhang, T.: On Lack of Robustness in Hydrological Model Development Due to Absence of Guidelines for Selecting Calibration and Evaluation Data: Demonstration for Data-Driven Models, Water Resour. Res., 54, 1013–1030, https://doi.org/10.1002/2017WR021470, 2018.
Zheng, F., Chen, J., Maier, H. R., and Gupta, H.: Achieving Robust and Transferable Performance for Conservation-Based Models of Dynamical Physical Systems, Water Resour. Res., 58, e2021WR031818, https://doi.org/10.1029/2021WR031818, 2022.
Short summary
Long short-term memory (LSTM) is a widely used machine-learning model in hydrology, but it is difficult to extract knowledge from it. We propose HydroLSTM, which represents processes like a hydrological reservoir. Models based on HydroLSTM perform similarly to LSTM while requiring fewer cell states. The learned parameters are informative about the dominant hydrology of a catchment. Our results show how parsimony and hydrological knowledge extraction can be achieved by using the new structure.
Long short-term memory (LSTM) is a widely used machine-learning model in hydrology, but it is...
