Abstract
The quantitative analyses of karst spring discharge typically rely on physical-based models, which are inherently uncertain. To improve the understanding of the mechanism of spring discharge fluctuation and the relationship between precipitation and spring discharge, three machine learning methods were developed to reduce the predictive errors of physical-based groundwater models, simulate the discharge of Longzici spring’s karst area, and predict changes in the spring on the basis of long time series precipitation monitoring and spring water flow data from 1987 to 2018. The three machine learning methods included two artificial neural networks (ANNs), namely multilayer perceptron (MLP) and long short-term memory–recurrent neural network (LSTM–RNN), and support vector regression (SVR). A normalization method was introduced for data preprocessing to make the three methods robust and computationally efficient. To compare and evaluate the capability of the three machine learning methods, the mean squared error (MSE), mean absolute error (MAE), and root-mean-square error (RMSE) were selected as the performance metrics for these methods. Simulations showed that MLP reduced MSE, MAE, and RMSE to 0.0010, 0.0254, and 0.0318, respectively. Meanwhile, LSTM–RNN reduced MSE to 0.0010, MAE to 0.0272, and RMSE to 0.0329. Moreover, the decrease in MSE, MAE, and RMSE was 0.0397, 0.1694, and 0.1991, respectively, for SVR. Results indicated that MLP performed slightly better than LSTM–RNN, and MLP and LSTM–RNN performed considerably better than SVR. Furthermore, ANNs were demonstrated to be prior machine learning methods for simulating and predicting karst spring discharge.
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The data are collected by the grassroots units of the Chinese government.
References
Amaranto A, Munoz-Arriola F, Solomatine D, Corzo G (2019) A spatially enhanced data-driven multimodel to improve semiseasonal groundwater forecasts in the high plains aquifer, USA. Water Resour Res 55(7):5941–5961. https://doi.org/10.1029/2018WR024301
Avanzi F, Johnson R, Oroza C, Hirashima H, Maurer T, Yamaguchi S (2019) Insights into preferential flow snowpack runoff using random forest. Water Resour Res 55(12):10727–10746. https://doi.org/10.1029/2019WR024828
Barthel R, Banzhaf S (2016) Groundwater and surface water interaction at the regional-scale—a review with focus on regional integrated models. Water Resour Manag 30(1):1–32. https://doi.org/10.1007/s11269-015-1163-z
Barzegar R, Asghari Moghaddam A, Deo R, Fijani E, Tziritis E (2018) Mapping groundwater contamination risk of multiple aquifers using multi-model ensemble of machine learning algorithms. Sci Total Environ 621C:697–712. https://doi.org/10.1016/j.scitotenv.2017.11.185
Bengio Y, LeCun Y et al (2007) Scaling learning algorithms towards AI. Large-Scale Kernel Mach 34(5):1–41
Degu A, Birk S, Dietzel M, Leis A, Winkler G, Mogessie A, Kebede S (2016) Groundwater flow dynamics in the complex aquifer system of Gidabo river basin (Ethiopian rift): a multi-proxy approach. Hydrogeol J 25(2):519–538. https://doi.org/10.1007/s10040-016-1489-5
Diodato N, Guerriero L, Fiorillo F, Esposito L, Revellino P, Grelle G, Guadagno F (2014) Predicting monthly spring discharges using a simple statistical model. Water Resour Manag 28(4):969–978. https://doi.org/10.1007/s11269-014-0527-0
Fiorillo F, Doglioni A (2010) The relation between karst spring discharge and rainfall by the cross-correlation analysis. Hydrogeol J 18(8):1881–1895. https://doi.org/10.1007/s10040-010-0666-1
Glorot X, Bengio Y (2010) Understanding the difficulty of training deep feedforward neural networks. J Mach Learn Res Proc Track 9:249–256
Granata F, Saroli M, De Marinis G, Gargano R (2018) Machine learning models for spring discharge forecasting. Geofluids 1:1–13. https://doi.org/10.1155/2018/8328167
Hadi S, Tombul M (2018) Monthly streamflow forecasting using continuous wavelet and multi-gene genetic programming combination. J Hydrol 561:674–687. https://doi.org/10.1016/j.jhydrol.2018.04.036
He K, Zhang X, Ren S, Sun J (2015) Delving deep into rectifiers: surpassing human-level performance on ImageNet classification. IEEE Int Conf Comput Vis ICCV 2015 1502:1026–1034. https://doi.org/10.1109/ICCV.2015.123
Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735
Hu C, Hao Y, Yeh TC, Pang B, Wu Z (2008) Simulation of spring flows from a karst aquifer with an artificial neural network. Hydrol Process 22(5):596–604. https://doi.org/10.1002/hyp.6625
Kenda K, Senozetnik M, Klemen K, Mladenić D (2018) Groundwater modeling with machine learning techniques: Ljubljana polje aquifer. Multidiscip Dig Publ Inst Proc 2(11):697. https://doi.org/10.3390/proceedings2110697
Kingma D, Ba J (2014) Adam: a method for stochastic optimization. In: International conference on learning representations
Kratzert F, Klotz D, Brenner C, Karsten S, Herrnegger M (2018) Rainfall-runoff modelling using long short-term memory (LSTM) networks. Hydrol Earth Syst Sci 22(11):6005–6022. https://doi.org/10.5194/hess-22-6005-2018
Miao Q, Pan B, Wang H, Hsu K, Sorooshian S (2019) Improving monsoon precipitation prediction using combined convolutional and long short term memory neural network. Water 11(5):977. https://doi.org/10.3390/w11050977
Paleologos E, Skitzi I, Katsifarakis K, Darivianakis N (2013) Neural network simulation of spring flow in karst environments. Stoch Environ Res Risk Assess 27(8):1829–1837. https://doi.org/10.1007/s00477-013-0717-y
Rahmati O, Choubin B, Fathabadi A, Coulon F, Soltani E, Shahabi H, Mollaefar E, Tiefenbacher J, Cipullo S, Ahmad BB, Tien Bui D (2019) Predicting uncertainty of machine learning models for modelling nitrate pollution of groundwater using quantile regression and UNEEC methods. Sci Total Environ 688:855–866. https://doi.org/10.1016/j.scitotenv.2019.06.320
Rajaee T, Ebrahimi H, Nourani V (2019) A review of the artificial intelligence methods in groundwater level modeling. J Hydrol 572:336–351. https://doi.org/10.1016/j.jhydrol.2018.12.037
Ramachandran P, Zoph B, Le QV (2018) Searching for activation functions. arXiv preprint arXiv 572. https://doi.org/10.05941
Rumelhart D, Hinton G, Williams R (1986) Learning representations by back propagating errors. Nature 323(6088):533–536. https://doi.org/10.1038/323533a0
Sahoo B, Jha R, Singh A, Kumar D (2019) Long short-term memory (LSTM) recurrent neural network for low-flow hydrological time series forecasting. Acta Geophys 67(5):1471–1481. https://doi.org/10.1007/s11600-019-00330-1
Salerno F, Tartari G (2009) A coupled approach of surface hydrological modeling and wavelet analysis for understanding the baseflow components of river discharge in karst environments. J Hydrol 376(1–2):295–306. https://doi.org/10.1016/j.jhydrol.2009.07.042
Shen C (2017) A trans-disciplinary review of deep learning research for water resources scientists. Water Resour Res 54(11):8558–8593. https://doi.org/10.1029/2018WR022643
Shen H, Liang Y, Cheng Y, Huang C (2017) Study on the regional evapotranspiration over different surface conditions of the longzici spring drainage(in Chinese). Carsolog Sin 36(2):234–241
Tang G, Long D, Behrangi A, Wang C, Hong Y (2018) Exploring deep neural networks to retrieve rain and snow in high latitudes using multisensor and reanalysis data. Water Resour Res 54(10):8253–8278. https://doi.org/10.1029/2018WR023830
Taylor R, Scanlon B, Doell P, Rodell M, Beek R, Wada Y, Longuevergne L, Leblanc M, Famiglietti J, Edmunds M, Konikow L, Green T, Chen J, Taniguchi M, Bierkens M, Macdonald A, Fan Y, Maxwell R, Yechieli Y, Treidel H (2013) Ground water and climate change. Nat Clim Change 3(4):322–329. https://doi.org/10.1038/nclimate1744
Tongal H, Booij M (2018) Simulation and forecasting of streamflows using machine learning models coupled with base flow separation. J Hydrol 564:182–266. https://doi.org/10.1016/j.jhydrol.2018.07.004
Wang H, Zhang Z, Guo Q (2010) Research on dynamic characteristics and attenuation causes of the flow rate of longzici spring. Sci-Tech Inf Dev Econ 20:168–170
Wang X, Liu T, Zheng X, Peng H, Xin J, Zhang B (2018) Short-term prediction of groundwater level using improved random forest regression with a combination of random features. Appl Water Sci 8(5):125. https://doi.org/10.1007/s13201-018-0742-6
Yaseen Z, Jaafar O, Deo R, Kisi O, Adamowski J, Quilty J, El-Shafie A (2016) Boost stream-flow forecasting model with extreme learning machine data-driven: a case study in a semi-arid region in Iraq. J Hydrol 542:603–614. https://doi.org/10.1016/j.jhydrol.2016.09.035
Zhang J, Zhu Y, Zhang X, Ye M, Yang J (2018) Developing a long short-term memory (LSTM) based model for predicting water table depth in agricultural areas. J Hydrol 561:918–929. https://doi.org/10.1016/j.jhydrol.2018.04.065
Zhu S, Hrnjica B, Ptak M, Choiński A, Sivakumar B (2020) Forecasting of water level in multiple temperate lakes using machine learning models. J Hydrol 585:124819. https://doi.org/10.1016/j.jhydrol.2020.124819
Acknowledgements
The authors would like to acknowledge Fei He from Shanghai Jiao Tong University for his valuable comments and suggestions.
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This study was supported by Joint Funds of the National Natural Science Foundation of China (U1839207) and University of Chinese Academy of Sciences.
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The code can be downloaded from https://github.com/Sophiaaaaaaaaa/ML-for-Predicting-Spring-Discharge.
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Communicated by Michael Nones, Ph.D. (CO-EDITOR-IN-CHIEF)/Jaroslaw Napiórkowski (AE) (ASSOCIATE EDITOR).
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Cheng, S., Qiao, X., Shi, Y. et al. Machine learning for predicting discharge fluctuation of a karst spring in North China. Acta Geophys. 69, 257–270 (2021). https://doi.org/10.1007/s11600-020-00522-0
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DOI: https://doi.org/10.1007/s11600-020-00522-0