ADVANCING GROUNDWATER MODELLING USING DEEP LEARNING METHODS

Advances in groundwater level modelling and time series deep learning (DL) techniques have progressed separately with limited integrations. Against the backdrop of the successful advancements in Artificial Intelligence (AI) over the past few decades, we are currently witnessing the accelerated adoption of cutting-edge intelligent technologies in the field of hydrology. However, the application of deep learning in groundwater research continues to face numerous challenges. For instance, despite its powerful nonlinear fitting capabilities, deep learning models are often criticized and questioned due to their black-box nature, which limits their ability to advance the development of science. This is especially apparent in groundwater level studies, where the intricate dynamics and unique environmental variables create a need for more tailored deep learning applications in groundwater level simulation, which prompts researchers to hold new expectations for the development of deep learning in groundwater level simulation. Within these expectations, there are two crucial issues that need to be addressed: 1) How to integrate deep learning algorithms with the specific physical processes involved in groundwater modelling? 2) How to illuminate the black box of deep learning models and enhance human understanding of groundwater dynamics? This thesis contributes to addressing these challenges by undertaking three research works that explore the application of two novel intelligent technologies in catchment-scale groundwater level simulation. These research works provide new insights and avenues for resolving the aforementioned challenges. Specifically, this thesis consists of three main topics: (1) Examining the impacts of region-averaged hydrometeorological and hydrogeological characteristics on improving the accuracy of groundwater level prediction using machine learning. (2) Embedding groundwater-related water balance mechanisms into recurrent deep learning methods for groundwater level simulation. (3) Introducing a new perspective from the decision-making procedure of deep learning models by state-of-the-art interpretable techniques to explain and understand extreme groundwater dynamics. The first topic of this thesis introduces a well-designed deep learning model for groundwater level simulation, and explore the statistical relationship between the model's performance, catchment characteristics, and groundwater dynamics, supported by an ample amount of data. This research summarizes the common characteristics of basins suitable for simulating groundwater level dynamics using deep learning, thereby deepening the understanding of the features associated with using deep learning to simulate groundwater levels. The focus of the second topic is to explore deep learning models constrained by physics laws for simulating groundwater dynamics. Formulas related to groundwater-related water balances are incorporated as additional algorithmic bases and constraints within deep learning models for groundwater level simulation. In this hybrid model, the combination of physical constraints and deep learning techniques enhances the model’s ability to comprehend the hydrogeological and hydrometeorological properties of the catchments, thereby improving the accuracy and generalization capability for predicting groundwater level. The focus of the third topic is to investigate hydrological insights related to groundwater from the perspective of deep learning models. Two state-of-the-art interpretability techniques for deep learning models are employed to analyse the underlying causes of groundwater drought events at different scales and seasons. This study integrated cutting-edge explainable DL methods into groundwater drought studies, thereby providing a new perspective for analysing the cause of drought events. It underscores the ability of explainable DL to deepen the understanding of hydrological phenomena, highlighting the imperative of synthesizing knowledge from various disciplines. While I carefully acknowledge the existing limitations of current algorithms, this study also reveals prospects for their future development. Overall, this thesis demonstrates the tremendous potential of utilizing deep learning techniques based on artificial neural networks to drive advancements in groundwater simulation. With thoughtful and innovative utilization of more intelligent technologies, it can be anticipated that significant strides in addressing the urgent groundwater challenges we are currently facing. By applying deep learning techniques, This thesis offers fresh insights and practical solutions for better understanding and managing groundwater resources, contributing to incremental advancements in the field.

[Abhishek, and T. Kinouchi (2022), Multidecadal Land Water and Groundwater Drought Evaluation in Peninsular India, Remote Sensing, 14(6), doi:10.3390/rs14061486.Addor, N., Newman, A.J., Mizukami, N., Clark, M.P. (2017), The CAMELS data set: catchment attributes and meteorology for large-sample studies. Hydrology and Earth System Sciences, 21(10): 5293-5313. DOI:10.5194/hess-21-5293-2017.Afan, H. A., A. Ibrahem Ahmed Osman, Y. Essam, A. N. Ahmed, Y. F. Huang, O. Kisi, M. Sherif, A. Sefelnasr, K.-w. Chau, and A. El-Shafie (2021), Modeling the fluctuations of groundwater level by employing ensemble deep learning techniques, Engineering Applications of Computational Fluid Mechanics, 15(1), 1420-1439, doi:10.1080/19942060.2021.1974093.Ahmmed, B., and V. V. Vesselinov (2022), Machine learning and shallow groundwater chemistry to identify geothermal prospects in the Great Basin, USA, Renewable Energy, 197, 1034-1048, doi:10.1016/j.renene.2022.08.024.Al-Fugara, A. k., H. R. Pourghasemi, A. R. Al-Shabeeb, M. Habib, R. Al-Adamat, H. Al-Amoush, and A. L. Collins (2020), A comparison of machine learning models for the mapping of groundwater spring potential, Environmental Earth Sciences, 79(10), doi:10.1007/s12665-020-08944-1.Amaranto, A., F. Munoz‐Arriola, D. P. Solomatine, and G. Corzo (2019), A Spatially Enhanced Data‐Driven Multimodel to Improve Semiseasonal Groundwater Forecasts in the High Plains Aquifer, USA, Water Resources Research, 55(7), 5941-5961, doi:10.1029/2018wr024301.Amaranto, A., F. Pianosi, D. Solomatine, G. Corzo, and F. Muñoz-Arriola (2020), Sensitivity analysis of data-driven groundwater forecasts to hydroclimatic controls in irrigated croplands, Journal of Hydrology, 587, doi:10.1016/j.jhydrol.2020.124957.Appenzeller, T. (2017), The AI revolution in science, Science, doi:10.1126/science. aan7064.Arabameri, A., S. C. Pal, F. Rezaie, O. A. Nalivan, I. Chowdhuri, A. Saha, S. Lee, and H. Moayedi (2021), Modeling groundwater potential using novel GIS-based machine-learning ensemble techniques, Journal of Hydrology: Regional Studies, 36, doi:10.1016/j.ejrh.2021.100848.Arras, L., Osman, A., Müller, K.-R., & Samek, W. (2019). Evaluating Recurrent Neural Network Explanations. https://doi.org/10.48550/arXiv.1904.11829Arrieta, A. B., Díaz-Rodríguez, N., Del Ser, J., Bennetot, A., Tabik, S., Barbado, A., et al. (2020), Explainable Artificial Intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI. Information Fusion, 58, 82–115. https://doi.org/10.1016/j.inffus.2019.12.012Ayzel, G., Heistermann, M. (2021), The effect of calibration data length on the performance of a conceptual hydrological model versus LSTM and GRU: A case study for six basins from the CAMELS dataset. Computers & Geosciences, 149. DOI:10.1016/j.cageo.2021.104708.Babovic, V. (2005), Data mining in hydrology, Hydrological Processes, 19(7), 1511– 1515, doi:10.1002/hyp.5862. Babovic, V., and M. B. Abbott (1997a), The evolution of equations from hydraulic data part I: Theory, Journal of Hydraulic Research, 35(3), 397–410, doi:10.1080/ 00221689709498420. Babovic, V., and M. B. Abbott (1997b), The evolution of equations from hydraulic data part II: Applications, Journal of Hydraulic Research, 35(3), 411–430, doi:10.1080/ 00221689709498421Babovic, V., and M. Keijzer (2000), Genetic programming as a model induction engine, Journal of Hydroinformatics, 2(1), 35–60, doi:10.2166/hydro.2000.0004.Babovic, V. (2009), Introducing knowledge into learning based on genetic programming, Journal of Hydroinformatics, 11(3-4), 181-193.Babovic, V., and M. Keijzer (2002), Rainfall runoff modelling based on genetic programming, Nordic Hydrology, 33(5), 331-346.Baghel, S., M. P. Tripathi, D. Khalkho, N. Al-Ansari, A. Kumar, and A. Elbeltagi (2023), Delineation of suitable sites for groundwater recharge based on groundwater potential with RS, GIS, and AHP approach for Mand catchment of Mahanadi Basin, Sci Rep, 13(1), 9860, doi:10.1038/s41598-023-36897-5.Bai, T., and P. Tahmasebi (2022), Characterization of groundwater contamination: A transformer-based deep learning model, Advances in Water Resources, 164, doi:10.1016/j.advwatres.2022.104217.Banerjee, A., M. Kemter, B. Goswami, B. Merz, J. Kurths, and N. Marwan (2023), Spatial coherence patterns of extreme winter precipitation in the U.S, Theoretical and Applied Climatology, 152(1-2), 385-395, doi:10.1007/s00704-023-04393-5.Banwart, S. A., N. P. Nikolaidis, Y.-G. Zhu, C. L. Peacock, and D. L. Sparks (2019), Soil Functions: Connecting Earth's Critical Zone, Annual Review of Earth and Planetary Sciences, 47(1), 333-359.Bao, J., L. Li, and F. Redoloza (2020), Coupling ensemble smoother and deep learning with generative adversarial networks to deal with non-Gaussianity in flow and transport data assimilation, Journal of Hydrology, 590, doi:10.1016/j.jhydrol.2020.125443.Barredo Arrieta, A. et al. (2020), Explainable Artificial Intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI. Information Fusion, 58: 82-115.Barzegar, R., A. Asghari Moghaddam, J. Adamowski, and E. Fijani (2016), Comparison of machine learning models for predicting fluoride contamination in groundwater, Stochastic Environmental Research and Risk Assessment, 31(10), 2705-2718, doi:10.1007/s00477-016-1338-z.Bedi, S., A. Samal, C. Ray, and D. Snow (2020), Comparative evaluation of machine learning models for groundwater quality assessment, Environ Monit Assess, 192(12), 776, doi:10.1007/s10661-020-08695-3.Benahmed, L., Houichi, L. (2018), The effect of simple imputations based on four variants of PCA methods on the quantiles of annual rainfall data. Environ Monit Assess, 190(10): 569. DOI:10.1007/s10661-018-6913-y.Best, K. B., M. E. Miro, R. M. Kirpes, N. Kaynar, and A. Najera Chesler (2021), Data-driven decision support tools for assessing the vulnerability of community water systems to groundwater contamination in Los Angeles County, Environmental Science & Policy, 124, 393-400, doi:10.1016/j.envsci.2021.07.015.Beven, K.J., Cloke, H.L. (2012), Comment on “Hyperresolution global land surface modeling: Meeting a grand challenge for monitoring Earth's terrestrial water” by Eric F. Wood et al. Water Resources Research, 48(1). DOI:10.1029/2011wr010982.Binder, A., Montavon, G., Bach, S., Müller, K.-R., & Samek, W. (2016). Layer-wise Relevance Propagation for Neural Networks with Local Renormalization Layers. https://doi.org/10.48550/arXiv.1604.00825Bloomfield, J. P., B. P. Marchant, S. H. Bricker, and R. B. Morgan (2015), Regional analysis of groundwater droughts using hydrograph classification, Hydrology and Earth System Sciences, 19(10), 4327-4344, doi:10.5194/hess-19-4327-2015.Bloomfield, J. P., and B. P. Marchant (2013), Analysis of groundwater drought building on the standardised precipitation index approach, Hydrology and Earth System Sciences, 17(12), 4769-4787, doi:10.5194/hess-17-4769-2013.Bloomfield, J. P., B. P. Marchant, and A. A. McKenzie (2019), Changes in groundwater drought associated with anthropogenic warming, Hydrology and Earth System Sciences, 23(3), 1393-1408, doi:10.5194/hess-23-1393-2019.Boumis, G., M. Kumar, J. R. Nimmo, and T. P. Clement (2022), Influence of Shallow Groundwater Evapotranspiration on Recharge Estimation Using the Water Table Fluctuation Method, Water Resources Research, 58(10), doi:10.1029/2022wr032073.Brodrick, P.G., Davies, A.B., Asner, G.P. (2019), Uncovering Ecological Patterns with Convolutional Neural Networks. Trends Ecol Evol, 34(8): 734-745. DOI:10.1016/j.tree.2019.03.006.Broxton, P. D., W. J. D. Leeuwen, and J. A. Biederman (2019), Improving Snow Water Equivalent Maps With Machine Learning of Snow Survey and Lidar Measurements, Water Resources Research, 55(5), 3739-3757.Brunner, P., Therrien, R., Renard, P., Simmons, C.T., Franssen, H.-J.H. (2017), Advances in understanding river-groundwater interactions. Reviews of Geophysics, 55(3): 818-854. DOI:10.1002/2017rg000556Butcher, J. C. (2000), Numerical methods for ordinary differential equations in the 20th century. Journal of Computational and Applied Mathematics, 125(1-2), 1-29.Carroll, R.W.H. et al. (2018), Factors controlling seasonal groundwater and solute flux from snow-dominated basins. Hydrological Processes, 32(14): 2187-2202. DOI:10.1002/hyp.13151Cai, H., H. Shi, S. Liu, and V. Babovic (2021), Impacts of regional characteristics on improving the accuracy of groundwater level prediction using machine learning: The case of central eastern continental United States, Journal of Hydrology: Regional Studies, 37.Cai, H., S. Liu, H. Shi, Z. Zhou, S. Jiang, and V. Babovic (2022), Toward improved lumped groundwater level predictions at catchment scale: Mutual integration of water balance mechanism and deep learning method, Journal of Hydrology, 613, doi:10.1016/j.jhydrol.2022.128495.Chadalawada, J., and V. Babovic (2019), Review and comparison of performance indices for automatic model induction, Journal of Hydroinformatics, 21(1), 13-31, doi:10.2166/hydro.2017.078.Chadalawada, J., Havlicek, V., Babovic, V. (2017), A Genetic Programming Approach to System Identification of Rainfall-Runoff Models. Water Resources Management, 31(12): 3975-3992. DOI:10.1007/s11269-017-1719-1Chadalawada, J., H. M. V. V. Herath, and V. Babovic (2020), Hydrologically Informed Machine Learning for Rainfall‐Runoff Modeling: A Genetic Programming‐Based Toolkit for Automatic Model Induction, Water Resources Research, 56(4).Chen, W., P. Tsangaratos, I. Ilia, Z. Duan, and X. Chen (2019), Groundwater spring potential mapping using population-based evolutionary algorithms and data mining methods, Sci Total Environ, 684, 31-49, doi:10.1016/j.scitotenv.2019.05.312.Chen, C. et al. (2019), Effects of agricultural activities on the temporal variations of streamflow: trends and long memory. Stochastic Environmental Research and Risk Assessment, 33(8-9): 1553-1564. DOI:10.1007/s00477-019-01714-x.Chen, C., W. He, H. Zhou, Y. Xue, and M. Zhu (2020), A comparative study among machine learning and numerical models for simulating groundwater dynamics in the Heihe River Basin, northwestern China, Sci Rep, 10(1), 3904.Chen, Y., and D. Zhang (2020a), Well Log Generation via Ensemble Long Short‐Term Memory (EnLSTM) Network, Geophys Res Lett, 47(23), doi:10.1029/2020gl087685.Chen, Y., and Zhang, D. (2020b), Physics-Constrained Deep Learning of Geomechanical Logs. IEEE Transactions on Geoscience and Remote Sensing, 58(8): 5932-5943. DOI:10.1109/tgrs.2020.2973171Chen, Y. et al. (2021). Theory-guided hard constraint projection (HCP): a knowledge-based data-driven scientific machine learning method, Journal of Computational PhysicCheng, W.-C., M. Putti, D. R. Kendall, and W. W. G. Yeh (2011), A real-time groundwater management model using data assimilation, Water Resources Research, 47(6), doi:10.1029/2010wr009770.Clark, M.P. et al. (2015a), Improving the representation of hydrologic processes in Earth System Models. Water Resources Research, 51(8): 5929-5956. DOI:10.1002/2015wr017096Clark, M. P., et al. (2015b), A unified approach for process‐based hydrologic modeling: 2. Model implementation and case studies, Water Resources Research, 51(4), 2515-2542.Collenteur, R. A., M. Bakker, G. Klammler, and S. Birk (2021), Estimation of groundwater recharge from groundwater levels using nonlinear transfer function noise models and comparison to lysimeter data, Hydrol. Earth Syst. Sci., 25(5), 2931-2949, doi:10.5194/hess-25-2931-2021.Condon, L.E., Maxwell, R.M. (2015), Evaluating the relationship between topography and groundwater using outputs from a continental-scale integrated hydrology model. Water Resources Research, 51(8): 6602-6621. DOI:10.1002/2014wr016774.Cuthbert, M. O., T. Gleeson, N. Moosdorf, K. M. Befus, A. Schneider, J. Hartmann, and B. Lehner (2019), Global patterns and dynamics of climate–groundwater interactions, Nature Climate Change, 9(2), 137-141, doi:10.1038/s41558-018-0386-4.Dai, X. et al. (2021), Understanding topography-driven groundwater flow using fully-coupled surface-water and groundwater modeling. Journal of Hydrology, 594. DOI:10.1016/j.jhydrol.2020.125950.Dawson, C. W., Abrahart, R. J. & See, L. M. (2007), Hydrotest: a web based toolbox of evaluation metrics for the standardised assessment of hydrological forecasts. Environmental Modelling and Software 22, 1034–1052.de Graaf, I. E. M., T. Gleeson, L. P. H. Rens van Beek, E. H. Sutanudjaja, and M. F. P. Bierkens (2019), Environmental flow limits to global groundwater pumping, Nature, 574(7776), 90-94, doi:10.1038/s41586-019-1594-4.Di Nunno, F., Granata, F. (2020), Groundwater level prediction in Apulia region (Southern Italy) using NARX neural network. Environ Res, 190: 110062. DOI:10.1016/j.envres.2020.110062.Ding, Y. K., Zhu, Y. L., Feng, J., Zhang, P. C., & Cheng, Z. R. (2020), Interpretable spatio-temporal attention LSTM model for flood forecasting. Neurocomputing, 403, 348–359. https://doi.org/10.1016/j.neucom.2020.04.110.Du, M., Liu, N., Yang, F., Ji, S., & Hu, X. (2019), On attribution of recurrent neural network predictions via additive decomposition. Paper presented at the The World Wide Web Conference, San Francisco, CA, USA. https://doi.org/10.1145/3308558.3313545.Dunkerley, D. L., and T. L. Booth (1999), Plant canopy interception of rainfall and its significance in a banded landscape, arid western New South Wales, Australia, Water Resources Research, 35(5), 1581-1586.Eltahir, E. A. B., and Yeh, P. J.-F. (1999), On the asymmetric response of aquifer water level to floods and droughts in Illinois, Water Resour. Res., 35( 4), 1199– 1217, doi:10.1029/1998WR900071.Epting, J. et al. (2018), Spatiotemporal scales of river-groundwater interaction – The role of local interaction processes and regional groundwater regimes. Science of The Total Environment, 618: 1224-1243. DOI:10.1016/j.scitotenv.2017.09.219.Erion, G., Janizek, J. D., Sturmfels, P., Lundberg, S. M., & Lee, S. I. (2021), Improving performance of deep learning models with axiomatic attribution priors and expected gradients. Nature Machine Intelligence, 3(7), 620–631.Evans, S., Williams, G.P., Jones, N.L., Ames, D.P., Nelson, E.J. (2020), Exploiting Earth Observation Data to Impute Groundwater Level Measurements with an Extreme Learning Machine. Remote Sensing, 12(12). DOI:10.3390/rs12122044.Fallah-Mehdipour, E., O. Bozorg Haddad, and M. A. Mariño (2013), Prediction and simulation of monthly groundwater levels by genetic programming, Journal of Hydro-environment Research, 7(4), 253-260, doi:https://doi.org/10.1016/j.jher.2013.03.005.Fan, Y., H. Li, and G. Miguez-Macho (2013), Global patterns of groundwater table depth, Science, 339(6122), 940-943, doi:10.1126/science.1229881.Fatichi, S., D. Or, R. Walko, H. Vereecken, M. H. Young, T. A. Ghezzehei, T. Hengl, S. Kollet, N. Agam, and R. Avissar (2020), Soil structure is an important omission in Earth System Models, Nat Commun, 11(1), 522.Fatichi, S. et al. (2016), An overview of current applications, challenges, and future trends in distributed process-based models in hydrology. Journal of Hydrology, 537: 45-60. DOI:10.1016/j.jhydrol.2016.03.026.Feng, D., J. Liu, K. Lawson, and C. Shen (2022), Differentiable, Learnable, Regionalized Process‐Based Models With Multiphysical Outputs can Approach State‐Of‐The‐Art Hydrologic Prediction Accuracy, Water Resources Research, 58(10), doi: 10.1029/2022wr032404.Feng, D., K. Fang, and C. Shen (2020), Enhancing Streamflow Forecast and Extracting Insights Using Long‐Short Term Memory Networks With Data Integration at Continental Scales, Water Resources Research, 56(9).Fienen, M. N., J. P. Masterson, N. G. Plant, B. T. Gutierrez, and E. R. Thieler (2013), Bridging groundwater models and decision support with a Bayesian network, Water Resources Research, 49(10), 6459-6473, doi:10.1002/wrcr.20496.Frame, J, Ulrich, P, Nearing, G, Gupta, H, Kratzert, F. (2022), On strictly enforced mass conservation constraints for modeling the rainfall-runoff process, EarthArXiv, doi: https://doi.org/10.31223/X5BH0P.Gao, S., Y. Huang, S. Zhang, J. Han, G. Wang, M. Zhang, and Q. Lin (2020), Short-term runoff prediction with GRU and LSTM networks without requiring time step optimization during sample generation, Journal of Hydrology, 589.Ghassemi, M., L. Oakden-Rayner, and A. L. Beam (2021), The false hope of current approaches to explainable artificial intelligence in health care, The Lancet Digital Health, 3(11), e745-e750.Ghojogh, B., & Ghodsi, A. (2023). Recurrent Neural Networks and Long Short-Term Memory Networks: Tutorial and Survey. https://doi.org/10.48550/arXiv.2304.11461Gleeson, T., Moosdorf, N., Hartmann, J., and van Beek, L. P. H. (2014), A glimpse beneath earth’s surface: GLobal HYdrogeology MaPS (GLHYMPS) of permeability and porosity, Geophys. Res. Lett., 41, 3891–3898, https://doi.org/10.1002/2014GL059856.Gleeson, T., Marklund, L., Smith, L., Manning, A.H. (2011), Classifying the water table at regional to continental scales. Geophys Res Lett, 38(5): n/a-n/a. DOI:10.1029/2010gl046427.Graves, Alex; Wayne, Greg; Danihelka, Ivo (2014). "Neural Turing Machines". arXiv:1410.5401Gullacher, A., D. M. Allen, and J. D. Goetz (2023), Early Warning Indicators of Groundwater Drought in Mountainous Regions, Water Resources Research, 59(8), doi:10.1029/2022wr033399.Gunning, D., & Aha, D. W. (2019), DARPA’s explainable artificial intelligence (XAI) program. AI Magazine, 40(2), 44–58. https://doi. org/10.1609/aimag.v40i2.2850.Guo, H. (2017), Big earth data: A new frontier in earth and information sciences, Big Earth Data, 1(1-2), 4–20, doi:10.1080/20964471.2017.1403062Guo, M., W. Yue, T. Wang, N. Zheng, and L. Wu (2021), Assessing the use of standardized groundwater index for quantifying groundwater drought over the conterminous US, Journal of Hydrology, 598, doi:10.1016/j.jhydrol.2021.126227.Guo, Y., S. Huang, Q. Huang, G. Leng, W. Fang, L. Wang, and H. Wang (2020), Propagation thresholds of meteorological drought for triggering hydrological drought at various levels, Sci Total Environ, 712, 136502, doi:10.1016/j.scitotenv.2020.136502.Haenlein, M., & Kaplan, A. (2019). A Brief History of Artificial Intelligence: On the Past, Present, and Future of Artificial Intelligence. California Management Review, 61(4), 5–14. https://doi.org/10.1177/0008125619864925Han, Z., S. Huang, Q. Huang, G. Leng, Y. Liu, Q. Bai, P. He, H. Liang, and W. Shi (2021), GRACE-based high-resolution propagation threshold from meteorological to groundwater drought, Agricultural and Forest Meteorology, 307, doi:10.1016/j.agrformet.2021.108476.Han, Z., Huang, S., Huang, Q., Leng, G., Wang, H., Bai, Q., et al. (2019). Propagation dynamics from meteorological to groundwater drought and their possible influence. Journal of Hydrology, 578, 124102.Han, Z., S. Huang, Q. Huang, Q. Bai, G. Leng, H. Wang, J. Zhao, X. Wei, and X. Zheng (2020), Effects of vegetation restoration on groundwater drought in the Loess Plateau, China, Journal of Hydrology, 591, doi:10.1016/j.jhydrol.2020.125566.Hare, D.K., Helton, A.M., Johnson, Z.C., Lane, J.W., Briggs, M.A. (2021), Continental-scale analysis of shallow and deep groundwater contributions to streams. Nat Commun, 12(1): 1450. DOI:10.1038/s41467-021-21651-0.Hartmann, J. and Moosdorf, N. (2012), The new global lithological map database GLiM: A representation of rock properties at the Earth surface, Geochem. Geophy. Geosy., 13, 1–37, https://doi.org/10.1029/2012GC004370.Hellwig, J., I. E. M. Graaf, M. Weiler, and K. Stahl (2020), Large‐Scale Assessment of Delayed Groundwater Responses to Drought, Water Resources Research, 56(2), doi:10.1029/2019wr025441.Herrmann, F., N. Baghdadi, M. Blaschek, R. Deidda, R. Duttmann, I. La Jeunesse, H. Sellami, H. Vereecken, and F. Wendland (2016), Simulation of future groundwater recharge using a climate model ensemble and SAR-image based soil parameter distributions - A case study in an intensively-used Mediterranean catchment, Sci Total Environ, 543(Pt B), 889-905.Hintze, S., Glauser, G., Hunkeler, D. (2020), Influence of surface water – groundwater interactions on the spatial distribution of pesticide metabolites in groundwater. Science of The Total Environment, 733. DOI:10.1016/j.scitotenv.2020.139109.Hochreiter, S., & Schmidhuber, J. (1997), Long short-term memory. Neural Computation, 9(8), 1735–1780. https://doi.org/10.1162/ neco.1997.9.8.1735.Hoedt, P.-J., F. Kratzert, D. Klotz, C. Halmich, M. Holzleitner, G. S. Nearing, S. Hochreiter, and G. Klambauer (2021), MC-LSTM: Mass-Conserving LSTM, in Proceedings of the 38th International Conference on Machine Learning, edited by M. Marina and Z. Tong, pp. 4275--4286, PMLR, Proceedings of Machine Learning Research.Hokanson, K.J., Mendoza, C.A., Devito, K.J. (2019), Interactions Between Regional Climate, Surficial Geology, and Topography: Characterizing Shallow Groundwater Systems in Subhumid, Low‐Relief Landscapes. Water Resources Research, 55(1): 284-297. DOI:10.1029/2018wr023934.Horton, R. E. (1933), The Rôle of infiltration in the hydrologic cycle, Eos Trans. AGU, 14( 1), 446– 460, doi:10.1029/TR014i001p00446.Hotelling, H. (1933), Analysis of a complex of statistical variables into principal components. J. Educ. Psychol, 24(6): 417–440. DOI: 10.1037/h0071325.Huang, X., L. Gao, R. S. Crosbie, N. Zhang, G. Fu, and R. Doble (2019), Groundwater Recharge Prediction Using Linear Regression, Multi-Layer Perception Network, and Deep Learning, Water, 11(9), doi:10.3390/w11091879.Huntington, J.L., Niswonger, R.G. (2012), Role of surface-water and groundwater interactions on projected summertime streamflow in snow dominated regions: An integrated modeling approach. Water Resources Research, 48(11). DOI:10.1029/2012wr012319.Hurst H E. (1951), Long-term storage capacity of reservoirs[J]. Transactions of the American Society of Civil Engineers, 116(1):770–799.Jaafarzadeh, M. S., N. Tahmasebipour, A. Haghizadeh, H. R. Pourghasemi, and H. Rouhani (2021), Groundwater recharge potential zonation using an ensemble of machine learning and bivariate statistical models, Sci Rep, 11(1), 5587, doi:10.1038/s41598-021-85205-6.Jeong, J. et al. (2020), Estimation of groundwater level based on the robust training of recurrent neural networks using corrupted data. Journal of Hydrology, 582. DOI:10.1016/j.jhydrol.2019.124512.Jiang, S., Zheng, Y., Solomatine, D. (2020), Improving AI System Awareness of Geoscience Knowledge: Symbiotic Integration of Physical Approaches and Deep Learning. Geophys Res Lett, 47(13). DOI:10.1029/2020gl088229.Jiang, S., Y. Zheng, C. Wang, and V. Babovic (2022), Uncovering Flooding Mechanisms Across the Contiguous United States Through Interpretive Deep Learning on Representative Catchments, Water Resources Research, 58(1), e2021WR030185.Jiang, S., Y. Zheng, V. Babovic, Y. Tian, and F. Han (2018), A computer vision-based approach to fusing spatiotemporal data for hydrological modeling, Journal of Hydrology, 567, 25-40.Jiang, S. J., V. Babovic, Y. Zheng, and J. Z. Xiong (2019), Advancing Opportunistic Sensing in Hydrology: A Novel Approach to Measuring Rainfall With Ordinary Surveillance Cameras, WATER RESOURCES RESEARCH, 55(4), 3004-3027.Jiang, Z.P., Shi, H.Y., Liu, S.N., Zhou, Z.Q., Wang, Y., Cai, H.J. (2021), Evolution characteristics of potential evapotranspiration over the Three-River Headwaters Region. Hydrological Sciences Journal, DOI: 10.1080/02626667.2021.1957105.Jiménez-Luna, J., F. Grisoni, and G. Schneider (2020), Drug discovery with explainable artificial intelligence, Nature Machine Intelligence, 2(10), 573-584.Joyce, D. W., A. Kormilitzin, K. A. Smith, and A. Cipriani (2023), Explainable artificial intelligence for mental health through transparency and interpretability for understandability, npj Digital Medicine, 6(1), 6.Kardan Moghaddam, H., S. Ghordoyee Milan, Z. Kayhomayoon, Z. Rahimzadeh Kivi, and N. Arya Azar (2021), The prediction of aquifer groundwater level based on spatial clustering approach using machine learning, Environ Monit Assess, 193(4), 173, doi:10.1007/s10661-021-08961-y.Karpatne, A., Atluri, G., Faghmous, J.H., Steinbach, M., Banerjee, A., Ganguly, A., et al., 2017. Theory-guided data science: a new paradigm for scientific discovery from data. IEEE Trans. Knowledge Data Eng. 29 (10), 2318–2331.Karpatne, A., Watkins, W., Read, J., Kumar, V., 2017. Physics-guided neural networks (pgnn): An application in lake temperature modeling. arXiv preprint arXiv: 1710.11431.Kattenborn, T., Eichel, J., Fassnacht, F.E. (2019), Convolutional Neural Networks enable efficient, accurate and fine-grained segmentation of plant species and communities from high-resolution UAV imagery. Sci Rep, 9(1): 17656. DOI:10.1038/s41598-019-53797-9.Kayhomayoon, Z., N. Arya Azar, S. Ghordoyee Milan, H. Kardan Moghaddam, and R. Berndtsson (2021), Novel approach for predicting groundwater storage loss using machine learning, J Environ Manage, 296, 113237, doi:10.1016/j.jenvman.2021.113237.Kebede, S., Charles, K., Godfrey, S., MacDonald, A., Taylor, R.G. (2021), Regional-scale interactions between groundwater and surface water under changing aridity: evidence from the River Awash Basin, Ethiopia. Hydrological Sciences Journal, 66(3): 450-463. DOI:10.1080/02626667.2021.1874613.Kidmose, J., Refsgaard, J.C., Troldborg, L., Seaby, L.P., Escrivà, M.M. (2013), Climate change impact on groundwater levels: ensemble modelling of extreme values. Hydrology and Earth System Sciences, 17(4): 1619-1634. DOI:10.5194/hess-17-1619-2013.Kingma, D. P., & Ba, J. (2015), Adam: A method for stochastic optimization. Paper presented at the 3rd International Conference on Learning Representations, San Diego, CA, USA. Retrieved from https://arxiv.org/abs/1412.6980.Klotz, D., F. Kratzert, M. Gauch, A. Keefe Sampson, G. Klambauer, S. Hochreiter, and G. Nearing (2020), Uncertainty Estimation with Deep Learning for Rainfall-Runoff Modelling, arXiv e-prints, arXiv:2012.14295.Koscielny-Bunde, E., Kantelhardt, J.W., Braun, P., Bunde, A., Havlin, S. (2006), Long-term persistence and multifractality of river runoff records: Detrended fluctuation studies. Journal of Hydrology, 322(1-4): 120-137. DOI:10.1016/j.jhydrol.2005.03.004.Kouziokas, G. N., A. Chatzigeorgiou, and K. Perakis (2018), Multilayer Feed Forward Models in Groundwater Level Forecasting Using Meteorological Data in Public Management, Water Resources Management, 32(15), 5041-5052, doi:10.1007/s11269-018-2126-y.Kratzert, F. et al. (2019a), Toward Improved Predictions in Ungauged Basins: Exploiting the Power of Machine Learning. Water Resources Research, 55(12): 11344-11354. DOI:10.1029/2019wr026065.Kratzert, F. et al. (2019b), Towards learning universal, regional, and local hydrological behaviors via machine learning applied to large-sample datasets. Hydrology and Earth System Sciences, 23(12): 5089-5110. DOI:10.5194/hess-23-5089-2019.Kratzert, F., Klotz, D., Brenner, C., Schulz, K., & Herrnegger, M. (2018), Rainfall-runoff modelling using Long Short-Term Memory (LSTM) networks. Hydrology and Earth System Sciences, 22(11), 6005–6022. https://doi.org/10.5194/hess-22-6005-2018.Kirkby, M. (1975), Hydrograph modelling strategies, in: Processes in Human and Physical Geography, edited by: Peel, R., Chisholm, M., and Haggett, P., Heinemann, London, 69–90. Kumar, R., S. B. Dwivedi, and S. Gaur (2021), A comparative study of machine learning and Fuzzy-AHP technique to groundwater potential mapping in the data-scarce region, Computers & Geosciences, 155, doi:10.1016/j.cageo.2021.104855.Leavesley, G.H., Lichty, R.W., Troutman, B.M., Saindon, L.G. (1983), Precipitation-Runoff-Modeling-System, User’s Manual, Water Resource Investigations Report 83-4238, US Geological Survey.LeCun Y, Boser B, Denker J S, et al. (1989), Backpropagation applied to handwritten zip code recognition[J]. Neural computation, 1(4): 541-551.LeCun Y, Bottou L, Bengio Y, et al. (1998), Gradient-based learning applied to document recognition[J]. Proceedings of the IEEE, 86(11): 2278-2324.Lee, S., Y. Hyun, S. Lee, and M.-J. Lee (2020), Groundwater Potential Mapping Using Remote Sensing and GIS-Based Machine Learning Techniques, Remote Sensing, 12(7), doi:10.3390/rs12071200.Lever, J., Krzywinski, M., Altman, N. (2017), Principal component analysis. Nature Methods, 14(7): 641-642. DOI:10.1038/nmeth.4346.Li, B., and M. Rodell (2015a), Evaluation of a model-based groundwater drought indicator in the conterminous U.S, Journal of Hydrology, 526, 78-88, doi:10.1016/j.jhydrol.2014.09.027.Li, B., M. Rodell, and J. S. Famiglietti (2015b), Groundwater variability across temporal and spatial scales in the central and northeastern U.S, Journal of Hydrology, 525, 769-780, doi:10.1016/j.jhydrol.2015.04.033.Li, B., H. Beaudoing, and M. Rodell, NASA/GSFC/HSL (2018). GLDAS Catchment Land Surface Model L4 daily 0.25 x 0.25 degree V2.0, Greenbelt, Maryland, USA, Goddard Earth Sciences Data and Information Services Center (GES DISC) [Dataset]. https://disc.gsfc.nasa.gov/datasets/GLDAS_CLSM025_D_2.0/summaryLi, B., Rodell, M., Sheffield, J., Wood, E. and Sutanudjaja, E. (2019a). Long-term, non-anthropogenic groundwater storage changes simulated by three global-scale hydrological models, Scientific Reports, 9, 10746, doi: 10.1038/s41598-019-47219-z.Li, B., et al. (2019b). Global GRACE Data Assimilation for Groundwater and Drought Monitoring: Advances and Challenges, Water Resources Research, 55(9), 7564-7586.Li, L., C. Bao, P. L. Sullivan, S. Brantley, Y. Shi, and C. Duffy (2017), Understanding watershed hydrogeochemistry: 2. Synchronized hydrological and geochemical processes drive stream chemostatic behavior, Water Resources Research, 53(3), 2346-2367.Li, Z., Zhang, Y.-K. (2007), Quantifying fractal dynamics of groundwater systems with detrended fluctuation analysis. Journal of Hydrology, 336(1-2): 139-146. DOI:10.1016/j.jhydrol.2006.12.017.Li, J., D. Zhang, N. Wang, and H. Chang (2022), Deep Learning of Two-Phase Flow in Porous Media via Theory-Guided Neural Networks, SPE Journal, 27(02), 1176-1194, doi:10.2118/208602-pa.Li, J., Y. Zhou, W. Wang, S. Liu, Y. Li, and P. Wu (2022), Response of hydrogeological processes in a regional groundwater system to environmental changes: A modeling study of Yinchuan Basin, China, Journal of Hydrology, 615, 128619.Liang, X., Zhang, Y.-K. (2013), Temporal and spatial variation and scaling of groundwater levels in a bounded unconfined aquifer. Journal of Hydrology, 479: 139-145. DOI:10.1016/j.jhydrol.2012.11.044.Liang, X.Y., Zhang, Y.K. (2015), Analyses of uncertainties and scaling of groundwater level fluctuations. Hydrology and Earth System Sciences, 19(7): 2971-2979. DOI:10.5194/hess-19-2971-2015.Liang, X., H. Zhan, and Y.-K. Zhang (2018), Aquifer Recharge Using a Vadose Zone Infiltration Well, Water Resources Research, 54(11), 8847-8863.Liu, S.N., Shi, H.Y. (2019), A recursive approach to long-term prediction of monthly precipitation using genetic programming. Water Resources Management, 33(3): 1103-1121.Lundberg, S., & Lee, S.-I. (2017), A unified approach to interpreting model predictions. Paper presented at the Advances in Neural Information Processing Systems, Long Beach, CA, USA. Retrieved from http://papers.nips.cc/paper/7062-a-unified-approach-to-interpreting-model-prediction.Ma, Y., et al. (2022), On the Principles of Parsimony and Self-Consistency for the Emergence of Intelligence. https://doi.org/10.48550/arXiv.2207.04630.Ma, Y., C. Montzka, B. Bayat, and S. Kollet (2021a), Using Long Short-Term Memory networks to connect water table depth anomalies to precipitation anomalies over Europe, Hydrology and Earth System Sciences, 25(6), 3555-3575.Ma, Y., C. Montzka, B. Bayat, and S. Kollet (2021b), An Indirect Approach Based on Long Short-Term Memory Networks to Estimate Groundwater Table Depth Anomalies Across Europe With an Application for Drought Analysis, Frontiers in Water, 3.Machiwal, D., N. Rangi, and A. Sharma (2014), Integrated knowledge- and data-driven approaches for groundwater potential zoning using GIS and multi-criteria decision making techniques on hard-rock terrain of Ahar catchment, Rajasthan, India, Environmental Earth Sciences, 73(4), 1871-1892, doi:10.1007/s12665-014-3544-7.Malekzadeh, M., Kardar, S., Saeb, K., Shabanlou, S., Taghavi, L. (2019), A Novel Approach for Prediction of Monthly Ground Water Level Using a Hybrid Wavelet and Non-Tuned Self-Adaptive Machine Learning Model. Water Resources Management, 33(4): 1609-1628. DOI:10.1007/s11269-019-2193-8.Marchant, B. P., & Bloomfield, J. P. (2018), Spatio-temporal modelling of the status of groundwater droughts. Journal of Hydrology, 564, 397-413.Markstrom, S.L., Niswonger, R.G., Regan, R.S., Prudic, D.E., and Barlow, P.M. (2008), GSFLOW-Coupled Ground-water and Surface-water FLOW model based on the integration of the Precipitation-Runoff Modeling System (PRMS) and the Modular Ground-Water Flow Model (MODFLOW-2005): U.S. Geological Survey Techniques and Methods 6-D1, 240 p.Meyers, Z. P., Frisbee, M. D., Rademacher, L. K., & Stewart-Maddox, N. S. (2021). Old groundwater buffers the effects of a major drought in groundwater-dependent ecosystems of the eastern Sierra Nevada (CA). Environmental Research Letters, 16(4), 044044. Mirzavand Borujeni, S., L. Arras, V. Srinivasan, and W. Samek (2023), Explainable sequence-to-sequence GRU neural network for pollution forecasting, Scientific Reports, 13(1), 9940.Miller, D. A. and White, R. A. (1998), A Conterminous United States Multilayer Soil Characteristics Dataset for Regional Climate and Hydrology Modeling, Earth Interact., 2, 1–26, https://doi.org/10.1175/10873562(1998)002<0001:ACUSMS>2.3.CO;2.Mishra, A. K., and V. P. Singh (2010), A review of drought concepts, Journal of Hydrology, 391(1-2), 202-216, doi:10.1016/j.jhydrol.2010.07.012.Mo, S. et al. (2017), A Taylor Expansion-Based Adaptive Design Strategy for Global Surrogate Modeling With Applications in Groundwater Modeling. Water Resources Research, 53(12): 10802-10823. DOI:10.1002/2017wr021622.Mo, S., Zhu, Y., Zabaras, N., Shi, X., Wu, J. (2019), Deep Convolutional Encoder‐Decoder Networks for Uncertainty Quantification of Dynamic Multiphase Flow in Heterogeneous Media. Water Resources Research, 55(1): 703-728. DOI:10.1029/2018wr023528.Moghaddam, D. D., O. Rahmati, M. Panahi, J. Tiefenbacher, H. Darabi, A. Haghizadeh, A. T. Haghighi, O. A. Nalivan, and D. Tien Bui (2020), The effect of sample size on different machine learning models for groundwater potential mapping in mountain bedrock aquifers, Catena, 187, doi:10.1016/j.catena.2019.104421.Mohan, C., A. W. Western, Y. Wei, and M. Saft (2018), Predicting groundwater recharge for varying land cover and climate conditions – a global meta-study, Hydrology and Earth System Sciences, 22(5), 2689-2703.Murdoch, W. J., Singh, C., Kumbier, K., Abbasi-Asl, R., & Yu, B. (2019), Definitions, methods, and applications in interpretable machine learning. Proceedings of the National Academy of Sciences of the United States of America, 116(44), 22071–22080. https://doi.org/10.1073/ pnas.1900654116.Nampak, H., B. Pradhan, and M. A. Manap (2014), Application of GIS based data driven evidential belief function model to predict groundwater potential zonation, Journal of Hydrology, 513, 283-300, doi:10.1016/j.jhydrol.2014.02.053.Nash, J. E., & Sutcliffe, J. V. (1970), River flow forecasting through conceptual models. Part I—A discussion of principles. Journal of Hydrology, 10(3), 282–290.Newman, A. J., et al. (2015), Development of a large-sample watershed-scale hydrometeorological data set for the contiguous USA: data set characteristics and assessment of regional variability in hydrologic model performance, Hydrology and Earth System Sciences, 19(1), 209-223.Newman, C.P. (2019), Variation in groundwater recharge and surface-water quality due to climatic extremes in semi-arid mountainous watersheds. Hydrogeol J, 27(5): 1627-1643. DOI:10.1007/s10040-019-01967-4.Niu, M., Horesh, L., & Chuang, I. (2019), Recurrent neural networks in the eye of differential equations. arXiv e‐prints, arXiv:1904.12933. Retrieved from https://arxiv.org/abs/1904.12933.Ossai, I. C., A. Ahmed, A. Hassan, and F. S. Hamid (2020), Remediation of soil and water contaminated with petroleum hydrocarbon: A review, ENVIRONMENTAL TECHNOLOGY & INNOVATION, 17.Páez, A. (2019), The Pragmatic Turn in Explainable Artificial Intelligence (XAI), Minds and Machines, 29(3), 441-459, doi:10.1007/s11023-019-09502-w.Patil, S., and M. Stieglitz (2014), Modelling daily streamflow at ungauged catchments: what information is necessary?, Hydrological Processes, 28(3), 1159-1169.Pearson, K. (1901), On lines and planes of closest fit to systems of points in space, Philosophical Magazine, 2(11): 559–572. DOI: 10.1080/14786440109462720.Pei, T., T. Qiu, and C. Shen (2023), Applying Knowledge-Guided Machine Learning to Slope Stability Prediction, Journal of Geotechnical and Geoenvironmental Engineering, 149(10), 04023089, doi:doi:10.1061/JGGEFK.GTENG-11053.Peng, C.K. et al. (1994), Mosaic organization of DNA nucleotides. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, 49(2): 1685-9. DOI:10.1103/physreve.49.1685.Perrone, D., et al. (2023), Stakeholder integration predicts better outcomes from groundwater sustainability policy, Nat Commun, 14(1), 3793, doi:10.1038/s41467-023-39363-y.Peters, N.E., Meybeck, M. and Chapman, D.V. (2006), Effects of Human Activities on Water Quality. In Encyclopedia of Hydrological Sciences (eds M.G. Anderson and J.J. McDonnell). https://doi.org/10.1002/0470848944.hsa096.Peters, E., Torfs, P.J.J.F., van Lanen, H.A.J. and Bier, G. (2003), Propagation of drought through groundwater—a new approach using linear reservoir theory. Hydrol. Process., 17: 3023-3040. https://doi.org/10.1002/hyp.1274.Pham, Q. B., M. Kumar, F. Di Nunno, A. Elbeltagi, F. Granata, A. R. M. T. Islam, S. Talukdar, X. C. Nguyen, A. N. Ahmed, and D. T. Anh (2022), Groundwater level prediction using machine learning algorithms in a drought-prone area, Neural Computing and Applications, 34(13), 10751-10773, doi:10.1007/s00521-022-07009-7.Portmann, R. W., S. Solomon, and G. C. Hegerl (2009), Spatial and seasonal patterns in climate change, temperatures, and precipitation across the United States, Proc Natl Acad Sci U S A, 106(18), 7324-7329, doi:10.1073/pnas.0808533106.Pourghasemi, H. R., N. Sadhasivam, S. Yousefi, S. Tavangar, H. Ghaffari Nazarlou, and M. Santosh (2020), Using machine learning algorithms to map the groundwater recharge potential zones, J Environ Manage, 265, 110525, doi:10.1016/j.jenvman.2020.110525.Poursaeid, M., Mastouri, R., Shabanlou, S., Najarchi, M. (2020), Estimation of total dissolved solids, electrical conductivity, salinity and groundwater levels using novel learning machines. Environmental Earth Sciences, 79(19). DOI:10.1007/s12665-020-09190-1.Rahmati, O., H. R. Pourghasemi, and A. M. Melesse (2016), Application of GIS-based data driven random forest and maximum entropy models for groundwater potential mapping: A case study at Mehran Region, Iran, Catena, 137, 360-372, doi:10.1016/j.catena.2015.10.010.Raissi, M., Perdikaris, P., Karniadakis, G.E. (2019), Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707.Rangelova, E., van der Wal, W., Braun, A., Sideris, M.G., Wu, P. (2007), Analysis of Gravity Recovery and Climate Experiment time-variable mass redistribution signals over North America by means of principal component analysis. Journal of Geophysical Research, 112(F3). DOI:10.1029/2006jf000615.Rasool, U., X. Yin, Z. Xu, M. A. Rasool, V. Senapathi, M. Hussain, J. Siddique, and J. C. Trabucco (2022), Mapping of groundwater productivity potential with machine learning algorithms: A case study in the provincial capital of Baluchistan, Pakistan, Chemosphere, 303(Pt 3), 135265, doi:10.1016/j.chemosphere.2022.135265.Reichstein, M., G. Camps-Valls, B. Stevens, M. Jung, J. Denzler, N. Carvalhais, and Prabhat (2019), Deep learning and process understanding for data-driven Earth system science, Nature, 566(7743), 195-204.Reinecke, R., et al. (2021), Uncertainty of simulated groundwater recharge at different global warming levels: a global-scale multi-model ensemble study, Hydrol. Earth Syst. Sci., 25(2), 787-810.Rudin, C. (2019), Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence, 1(5), 206–215. https://doi.org/10.1038/s42256-019-0048-x.Ruff, S. E., et al. (2023), Hydrogen and dark oxygen drive microbial productivity in diverse groundwater ecosystems, Nat Commun, 14(1), 3194, doi:10.1038/s41467-023-38523-4.Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986), Learning representations by back‐propagating errors. Nature, 323(6088), 533–536.Rust, W., I. Holman, J. Bloomfield, M. Cuthbert, and R. Corstanje (2019), Understanding the potential of climate teleconnections to project future groundwater drought, Hydrology and Earth System Sciences, 23(8), 3233-3245, doi:10.5194/hess-23-3233-2019.R. Collobert, J. Weston, L. Bottou, M. Karlen, K. Kavukcuglu, P. Kuksa. (2011), Natural Language Processing (Almost) from Scratch. Journal of Machine Learning Research 12:2493–2537.Sadat-Noori, M., Glamore, W., Khojasteh, D. (2019), Groundwater level prediction using genetic programming: the importance of precipitation data and weather station location on model accuracy. Environmental Earth Sciences, 79(1). DOI:10.1007/s12665-019-8776-0.Sadeghfam, S., A. Ehsanitabar, R. Khatibi, and R. Daneshfaraz (2018), Investigating ‘risk’ of groundwater drought occurrences by using reliability analysis, Ecological Indicators, 94, 170-184.Sagarika, S., Kalra, A., Ahmad, S. (2014), Evaluating the effect of persistence on long-term trends and analyzing step changes in streamflows of the continental United States. Journal of Hydrology, 517: 36-53. DOI:10.1016/j.jhydrol.2014.05.002.Sahoo, S., Russo, T.A., Elliott, J., Foster, I. (2017), Machine learning algorithms for modeling groundwater level changes in agricultural regions of the U.S. Water Resources Research, 53(5): 3878-3895. DOI:10.1002/2016wr019933.Sajedi-Hosseini, F., A. Malekian, B. Choubin, O. Rahmati, S. Cipullo, F. Coulon, and B. Pradhan (2018), A novel machine learning-based approach for the risk assessment of nitrate groundwater contamination, Sci Total Environ, 644, 954-962, doi:10.1016/j.scitotenv.2018.07.054.Sakoe, H., & Chiba, S. (1978). Dynamic-programming algorithm optimization for spoken word recognition. IEEE Transactions on Acoustics, Speech, & Signal Processing, 26(1), 43–49.Salem, G.S.A., Kazama, S., Shahid, S., Dey, N.C. (2017), Impact of temperature changes on groundwater levels and irrigation costs in a groundwater-dependent agricultural region in Northwest Bangladesh. Hydrological Research Letters, 11(1): 85-91. DOI:10.3178/hrl.11.85.Sarma, R., and S. K. Singh (2022), A Comparative Study of Data-driven Models for Groundwater Level Forecasting, Water Resources Management, 36(8), 2741-2756, doi:10.1007/s11269-022-03173-6.Schilling, K.E., Zhang, Y.K. (2012), Temporal scaling of groundwater level fluctuations near a stream. Ground Water, 50(1): 59-67. DOI:10.1111/j.1745-6584.2011.00804.x.Schreiner-McGraw, A. P., and H. Ajami (2021), Delayed response of groundwater to multi-year meteorological droughts in the absence of anthropogenic management, Journal of Hydrology, 603, doi:10.1016/j.jhydrol.2021.126917.Schuler, P., Campanyà, J., Moe, H., Doherty, D., Hunter Williams, N., & McCormackm, T. (2022). Mapping the groundwater memory across Ireland: A step towards a groundwater drought susceptibility assessment. Journal of Hydrology, 612, 128277.Schwalbe, G., and B. Finzel (2023), A comprehensive taxonomy for explainable artificial intelligence: a systematic survey of surveys on methods and concepts, Data Mining and Knowledge Discovery, doi:10.1007/s10618-022-00867-8.Seyoum, W., Kwon, D., Milewski, A. (2019), Downscaling GRACE TWSA Data into High-Resolution Groundwater Level Anomaly Using Machine Learning-Based Models in a Glacial Aquifer System. Remote Sensing, 11(7). DOI:10.3390/rs11070824.Shen, C., et al. (2018), HESS opinions: Incubating deep-learning-powered hydrologic science advances as a community, Hydrology and Earth System Sciences, 22(11), 5639–5656, doi:10.5194/hess-22-5639-2018.Shen, C., et al. (2023), Differentiable modelling to unify machine learning and physical models for geosciences, Nature Reviews Earth & Environment, 4(8), 552-567.Sherstinsky, A. (2020), Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) network, Physica D: Nonlinear Phenomena, 404, 132306.Shi, H.Y., Chen, J., Wang, K.Y., and Niu J. (2018), A new method and a new index for identifying socioeconomic drought events under climate change: a case study of the East River basin in China. Science of the Total Environment, 616-617, 363-375.Shrikumar, A., Greenside, P., Shcherbina, A., & Kundaje, A. (2017), Not Just a Black Box: Learning Important Features Through Propagating Activation Differences. Doi: 10.48550/arXiv.1605.01713Simonyan, K., Vedaldi, A., & Zisserman, A. (2014), Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps. Doi: 10.48550/arXiv.1312.6034.Singha, S., S. Pasupuleti, S. S. Singha, and S. Kumar (2020), Effectiveness of groundwater heavy metal pollution indices studies by deep-learning, J Contam Hydrol, 235, 103718, doi:10.1016/j.jconhyd.2020.103718.Song, T. Y., Ding, W., Wu, J., Liu, H. X., Zhou, H. C., & Chu, J. G. (2020), Flash flood forecasting based on long short-term memory networks. Water, 12(1). https://doi.org/10.3390/w12010109.Sorichetta, A., C. Ballabio, M. Masetti, G. R. Robinson, Jr., and S. Sterlacchini (2013), A comparison of data-driven groundwater vulnerability assessment methods, Ground Water, 51(6), 866-879, doi:10.1111/gwat.12012.Staff, S. (2017), AI is changing how we do science. get a glimpse, Science, doi:10.1126/ science.aan7049Stoelzle, M., Stahl, K., Morhard, A., & Weiler, M. (2014). Streamflow sensitivity to drought scenarios in catchments with different geology. Geophysical Research Letters, 41(17), 6174–6183.Sturmfels, P., Lundberg, S., & Lee, S.-I. (2020), Visualizing the impact of feature attribution baselines. Distill, 5(1). https://doi.org/10.23915/ distill.00022.Su, D., H. Zhang, H. Chen, J. Yi, P.-Y. Chen, and Y. Gao (2018), Is Robustness the Cost of Accuracy? – A Comprehensive Study on the Robustness of 18 Deep Image Classification Models, Springer International Publishing, Cham.Sun, J., L. Hu, D. Li, K. Sun, and Z. Yang (2022), Data-driven models for accurate groundwater level prediction and their practical significance in groundwater management, Journal of Hydrology, 608, doi:10.1016/j.jhydrol.2022.127630.Sun, J., L. Di, Z. Sun, Y. Shen, and Z. Lai (2019), County-Level Soybean Yield Prediction Using Deep CNN-LSTM Model, Sensors (Basel), 19(20), doi:10.3390/s19204363.Šútor, J., Štekauerová, V., Nagy, V. (2010), Comparison of the monitored and modeled soil water storage of the upper soil layer: the influence of soil properties and groundwater table level. Journal of Hydrology and Hydromechanics, 58(4): 279-283. DOI:10.2478/v10098-010-0026-9.Sundararajan, M., Taly, A. & Yan, Q. Axiomatic attribution for deep networks. In Proc. 34th International Conference on Machine Learning Vol. 70, 3319–3328 (Journal of Machine Learning Research, 2017).Tague, C., Grant, G.E. (2009), Groundwater dynamics mediate low-flow response to global warming in snow-dominated alpine regions. Water Resources Research, 45(7). DOI:10.1029/2008wr007179.Tan, L. S., Z. Zainuddin, and P. Ong (2018), Solving ordinary differential equations using neural networks, edited.Tan, Z., Q. Yang, and Y. Zheng (2020), Machine Learning Models of Groundwater Arsenic Spatial Distribution in Bangladesh: Influence of Holocene Sediment Depositional History, Environ Sci Technol, 54(15), 9454-9463, doi:10.1021/acs.est.0c03617.Tao, W., Q. Wang, L. Guo, H. Lin, X. Chen, Y. Sun, and S. Ning (2020), An enhanced rainfall–runoff model with coupled canopy interception, Hydrological Processes, 34(8), 1837-1853.Taormina, R., K.-w. Chau, and R. Sethi (2012), Artificial neural network simulation of hourly groundwater levels in a coastal aquifer system of the Venice lagoon, Engineering Applications of Artificial Intelligence, 25(8), 1670-1676, doi:10.1016/j.engappai.2012.02.009.Tarbiyati, H., Nemati Saray, B. Weight initialization algorithm for physics-informed neural networks using finite differences. Engineering with Computers (2023). https://doi.org/10.1007/s00366-023-01883-yTavenard, R., Faouzi, J., Vandewiele, G., Divo, F., Androz, G., Holtz, C., et al. (2020). Tslearn, a machine learning toolkit for time series data. Journal of Machine Learning Research, 21, 1–6. Retrieved from http://jmlr.org/papers/v21/20-091.html.Tian, Y., Y. Zheng, B. Wu, X. Wu, J. Liu, and C. Zheng (2015), Modeling surface water-groundwater interaction in arid and semi-arid regions with intensive agriculture, Environ Modell Softw, 63, 170-184.Tran, H., E. Leonarduzzi, L. De la Fuente, R. B. Hull, V. Bansal, C. Chennault, P. Gentine, P. Melchior, L. E. Condon, and R. M. Maxwell (2021), Development of a Deep Learning Emulator for a Distributed Groundwater–Surface Water Model: ParFlow-ML, Water, 13(23).Trinh, D. H., and T. F. M. Chui (2013), An empirical method for approximating canopy throughfall, Hydrological Processes, 27(12), 1764-1772.Tsai, W.-P., D. Feng, M. Pan, H. Beck, K. Lawson, Y. Yang, J. Liu, and C. Shen (2021), From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling, Nature Communications, 12(1), 5988, doi:10.1038/s41467-021-26107-z.U.S. Geological Survey (2016). National Water Information System data available on the World Wide Web (USGS Water Data for the Nation) [Dataset], https://waterdata.usgs.gov/nwis/gw.Van Lanen, H. A. J., & Peters, E. (2000), Definition, Effects and Assessment of Groundwater Droughts. In J. V. Vogt, & F. Somna (Eds.), Drought and Drought Mitigation in Europe. Advances in Natural and Technological Hazards Research (pp. 49-61). Kluwer Academic Publisher.Van Loon, A. F., and H. A. J. van Lanen (2012), A process-based typology of hydrological drought, Hydrol. Earth Syst. Sci., 16, 1915-1946.Van Loon, A.F. (2015), Hydrological drought explained. WIREs Water, 2: 359-392. https://doi.org/10.1002/wat2.1085.Varadharajan, C., et al. (2022), Can machine learning accelerate process understanding and decision-relevant predictions of river water quality? Hydrological Processes, 36(4), e14565.Viana, F. A. C., R. G. Nascimento, A. Dourado, and Y. A. Yucesan (2021), Estimating model inadequacy in ordinary differential equations with physics-informed neural networks, Computers & Structures, 245.Wade, J., C. Kelleher, and D. M. Hannah (2023), Machine learning unravels controls on river water temperature regime dynamics, Journal of Hydrology, 623, 129821.Wang, N., Zhang, D., Chang, H., & Li, H. (2020), Deep learning of subsurface flow via theory-guided neural network. Journal of Hydrology, 584, 124700.Wang, N., H. Chang, and D. Zhang (2021a), Theory-guided Auto-Encoder for surrogate construction and inverse modeling, Computer Methods in Applied Mechanics and Engineering, 385, doi:10.1016/j.cma.2021.114037.Wang, N., H. Chang, and D. Zhang (2021b), Deep‐Learning‐Based Inverse Modeling Approaches: A Subsurface Flow Example, Journal of Geophysical Research: Solid Earth, 126(2).Wang, N., Chang, H., & Zhang, D. (2021c). Efficient uncertainty quantification for dynamic subsurface flow with surrogate by Theory-guided Neural Network. Computer Methods in Applied Mechanics and Engineering, 373, 113492. https://doi.org/10.1016/j.cma.2020.113492Wang, Y., L. Shi, X. Hu, W. Song, and L. Wang (2023), Multiphysics‐Informed Neural Networks for Coupled Soil Hydrothermal Modeling, Water Resources Research, 59(1), doi:10.1029/2022wr031960.Weider, K., & Boutt, D. F. (2010). Heterogeneous water table response to climate revealed by 60 years of ground water data. Geophysical Research Letters, 37(24), L24405.Xiong, R., Y. Zheng, N. Chen, Q. Tian, W. Liu, F. Han, S. Jiang, M. Lu, and Y. Zheng (2022), Predicting Dynamic Riverine Nitrogen Export in Unmonitored Watersheds: Leveraging Insights of AI from Data-Rich Regions, Environ Sci Technol, 56(14), 10530-10542, doi:10.1021/acs.est.2c02232.Yang, C., Zhang, Y.-K., Liang, X. (2017), Analysis of temporal variation and scaling of hydrological variables based on a numerical model of the Sagehen Creek watershed. Stochastic Environmental Research and Risk Assessment, 32(2): 357-368. DOI:10.1007/s00477-017-1421-0.Yang, G., Bowling, L.C. (2014), Detection of changes in hydrologic system memory associated with urbanization in the Great Lakes region. Water Resources Research, 50(5): 3750-3763. DOI:10.1002/2014wr015339.Yang, Y., V. Tresp, M. Wunderle, and P. A. Fasching (2018), Explaining Therapy Predictions with Layer-Wise Relevance Propagation in Neural Networks, paper presented at 2018 IEEE International Conference on Healthcare Informatics (ICHI), 4-7 June 2018.Yoon, H., S.-C. Jun, Y. Hyun, G.-O. Bae, and K.-K. Lee (2011), A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer, Journal of Hydrology, 396(1-2), 128-138.Young, P. C., & Ratto, M. (2011). Statistical emulation of large linear dynamic models. Technometrics, 53(1), 29-43.Yu, X., T. Cui, J. Sreekanth, S. Mangeon, R. Doble, P. Xin, D. Rassam, and M. Gilfedder (2020), Deep learning emulators for groundwater contaminant transport modelling, Journal of Hydrology, 590, doi:10.1016/j.jhydrol.2020.125351.Zeiler, M. D., and R. Fergus (2014), Visualizing and Understanding Convolutional Networks, paper presented at Computer Vision – ECCV 2014, Springer International Publishing, Cham.Zhang, J., X. Chen, A. Khan, Y.-k. Zhang, X. Kuang, X. Liang, M. L. Taccari, and J. Nuttall (2021), Daily runoff forecasting by deep recursive neural network, Journal of Hydrology, 596.Zhang, J. et al. (2021), Daily runoff forecasting by deep recursive neural network. Journal of Hydrology, 596. DOI:10.1016/j.jhydrol.2021.126067.Zhang, Y.-K., Li, Z. (2005), Temporal scaling of hydraulic head fluctuations: Nonstationary spectral analyses and numerical simulations. Water Resources Research, 41(7). DOI:10.1029/2004wr003797.Zhang, Y.-K., Schilling, K. (2004), Temporal scaling of hydraulic head and river base flow and its implication for groundwater recharge. Water Resources Research, 40(3). DOI:10.1029/2003wr002094.Zhang, J., Y. Zhu, X. Zhang, M. Ye, and J. Yang (2018), Developing a Long Short-Term Memory (LSTM) based model for predicting water table depth in agricultural areas, Journal of Hydrology, 561, 918-929.Zhao, W.L. et al. (2019), Physics-Constrained Machine Learning of Evapotranspiration. Geophys Res Lett, 46(24): 14496-14507. DOI:10.1029/2019gl085291.Zhou, Z., Shi, H., Fu, Q., Ding, Y., Li, T., & Liu, S. (2021), Investigating the propagation from meteorological to hydrological drought by introducing the nonlinear dependence with directed information transfer index. Water Resources Research, 57, e2021WR030028.Zhou, Z. et al. (2020), Is the cold region in Northeast China still getting warmer under climate change impact? Atmospheric Research, 237. DOI:10.1016/j.atmosres.2020.104864.Zhu, Y., Shi, L., Lin, L., Yang, J., Ye, M. (2012), A fully coupled numerical modeling for regional unsaturated–saturated water flow. Journal of Hydrology, 475: 188-203. DOI:10.1016/j.jhydrol.2012.09.048.Zipper, S. C., T. Dallemagne, T. Gleeson, T. C. Boerman, and A. Hartmann (2018), Groundwater Pumping Impacts on Real Stream Networks: Testing the Performance of Simple Management Tools, Water Resources Research, 54(8), 5471-5486.