Blöschl, G., Bierkens, M. F. P., Chambel, A., et al.: Twenty-three unsolved problems in hydrology (UPH) – a community perspective, Hydrol. Sci. J., 64, 1141–1158, https://doi.org/10.1080/02626667.2019.1620507, 2019.
Brêda, J. P. L. F., Melsen, L. A., Athanasiadis, I., Van Dijk, A., Siqueira, V. A., Verhoef, A., Zeng, Y., and van der Ploeg, M.: Predictor Importance for Hydrological Fluxes of Global Hydrological and Land Surface Models, Water Resour. Res., 60, https://doi.org/10.1029/2023WR036418, 2024.
Brinkerhoff, C. B., Gleason, C. J., Kotchen, M. J., Kysar, D. A., and Raymond, P. A.: Ephemeral stream water contributions to United States drainage networks, Science, 384, 1476–1482, https://doi.org/10.1126/science.adg9430, 2024.
Brunner, M. I., Slater, L., Tallaksen, L. M., and Clark, M.: Challenges in modeling and predicting floods and droughts: A review, Wiley Interdiscip. Rev. Water, 8, 1–32, https://doi.org/10.1002/wat2.1520, 2021.
Clark, M. P., Vogel, R. M., Lamontagne, J. R., Mizukami, N., Knoben, W. J. M., Tang, G., Gharari, S., Freer, J. E., Whitfield, P. H., Shook, K. R., and Papalexiou, S. M.: The Abuse of Popular Performance Metrics in Hydrologic Modeling, Water Resour. Res., 57, 1–16, https://doi.org/10.1029/2020WR029001, 2021.
Costigan, K. H. and Daniels, M. D.: Damming the prairie: Human alteration of Great Plains river regimes, J. Hydrol., 444–445, 90–99, https://doi.org/10.1016/j.jhydrol.2012.04.008, 2012.
De Meester, J. and Willems, P.: Analysing spatial variability in drought sensitivity of rivers using explainable artificial intelligence, Sci. Total Environ., 931, 172685, https://doi.org/10.1016/j.scitotenv.2024.172685, 2024.
Elnashar, A., Wang, L., Wu, B., Zhu, W., and Zeng, H.: Synthesis of global actual evapotranspiration from 1982 to 2019, Earth Syst. Sci. Data, 13, 447–480, https://doi.org/10.5194/essd-13-447-2021, 2021.
Fox, E. W., Hill, R. A., Leibowitz, S. G., Olsen, A. R., Thornbrugh, D. J., and Weber, M. H.: Assessing the accuracy and stability of variable selection methods for random forest modeling in ecology, Environ. Monit. Assess., 189, https://doi.org/10.1007/s10661-017-6025-0, 2017.
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. Assoc., 57, 885–905, https://doi.org/10.1111/1752-1688.12964, 2021.
Frame, J. M., Araki, R., Bhuiyan, S. A., Bindas, T., Rapp, J., Bolotin, L., Deardorff, E., Liu, Q., Haces-Garcia, F., Liao, M., Frazier, N., and Ogden, F. L.: Machine Learning for a Heterogeneous Water Modeling Framework, J. Am. Water Resour. Assoc., 61, 1–10, https://doi.org/10.1111/1752-1688.70000, 2025.
Friedman, J.: Greedy Function Approximation: A Gradient Boosting Machine, Ann. Stat., 29, 1189–1232, 2001.
Golden, H. E., Christensen, J. R., McMillan, H. K., Kelleher, C. A., Lane, C. R., Husic, A., Li, L., Ward, A. S., Hammond, J., Seybold, E. C., Jaeger, K. L., Zimmer, M., Sando, R., Jones, C. N., Segura, C., Mahoney, D. T., Price, A. N., and Cheng, F.: Advancing the science of headwater streamflow for global water protection, Nat. Water, 3, 16–26, https://doi.org/10.1038/s44221-024-00351-1, 2025.
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.
Hammond, J. C., Zimmer, M., Shanafield, M., Kaiser, K., Godsey, S. E., Mims, M. C., Zipper, S. C., Burrows, R. M., Kampf, S. K., Dodds, W., Jones, C. N., Krabbenhoft, C. A., Boersma, K. S., Datry, T., Olden, J. D., Allen, G. H., Price, A. N., Costigan, K., Hale, R., Ward, A. S., and Allen, D. C.: Spatial Patterns and Drivers of Nonperennial Flow Regimes in the Contiguous United States, Geophys. Res. Lett., 48, 1–11, https://doi.org/10.1029/2020GL090794, 2021.
Hay, L., Norton, P., Viger, R., Markstrom, S., Steven Regan, R., and Vanderhoof, M.: Modelling surface-water depression storage in a Prairie Pothole Region, Hydrol. Process., 32, 462–479, https://doi.org/10.1002/hyp.11416, 2018.
Heskes, T., Sijben, E., Bucur, I. G., and Claassen, T.: Causal shapley values: Exploiting causal knowledge to explain individual predictions of complex models, Adv. Neural Inf. Process. Syst., https://doi.org/10.48550/arXiv.2011.01625, 2020.
Ho, T. K.: The random subspace method for constructing decision forests, IEEE Trans. Pattern Anal. Mach. Intell., 20, 832–844, https://doi.org/10.1109/34.709601, 1998.
Hodgkins, G. A., Over, T. M., Dudley, R. W., Russell, A. M., and LaFontaine, J. H.: The consequences of neglecting reservoir storage in national-scale hydrologic models: An appraisal of key streamflow statistics, J. Am. Water Resour. Assoc., 60, 110–131, https://doi.org/10.1111/1752-1688.13161, 2024.
Hopkins, K. G., Fanelli, R. M., Bhaskar, A. S., and Woznicki, S. A.: Changes in event-based streamflow magnitude and timing after suburban development with infiltration-based stormwater management, Hydrol. Process., https://doi.org/10.1002/hyp.13593, 2019.
Huang, F., Shangguan, W., Li, Q., Li, L., and Zhang, Y.: Beyond prediction: An integrated post-hoc approach to interpret complex model in hydrometeorology, Environ. Model. Softw., 167, https://doi.org/10.1016/j.envsoft.2023.105762, 2023.
Hughes, M., Jackson, D. L., Unruh, D., Wang, H., Hobbins, M., Ogden, F. L., Cifelli, R., Cosgrove, B., DeWitt, D., Dugger, A., Ford, T. W., Fuchs, B., Glaudemans, M., Gochis, D., Quiring, S. M., RafieeiNasab, A., Webb, R. S., Xia, Y., and Xu, L.: Evaluation of Retrospective National Water Model Soil Moisture and Streamflow for Drought-Monitoring Applications, J. Geophys. Res.-Atmos., 129, 1–25, https://doi.org/10.1029/2023JD038522, 2024.
Husic, A.: Interrogating Process Deficiencies in Large-Scale Hydrologic Models with Interpretable Machine Learning, OSF [data set], https://doi.org/10.17605/OSF.IO/MNQCZ, 2025.
Jachens, E. R., Hutcheson, H., Thomas, M. B., and Steward, D. R.: Effects of Groundwater-Surface Water Exchange Mechanism in the National Water Model over the Northern High Plains Aquifer, USA, J. Am. Water Resour. Assoc., 57, 241–255, https://doi.org/10.1111/1752-1688.12869, 2021.
Johnson, J. M., Fang, S., Sankarasubramanian, A., Rad, A. M., Kindl da Cunha, L., Jennings, K. S., Clarke, K. C., Mazrooei, A., and Yeghiazarian, L.: Comprehensive Analysis of the NOAA National Water Model: A Call for Heterogeneous Formulations and Diagnostic Model Selection, J. Geophys. Res.-Atmos., 128, 1–21, https://doi.org/10.1029/2023JD038534, 2023a.
Johnson, J. M., Blodgett, D. L., Clarke, K. C., and Pollak, J.: Restructuring and serving web-accessible streamflow data from the NOAA National Water Model historic simulations, Sci. Data, 10, 1–10, https://doi.org/10.1038/s41597-023-02316-7, 2023b.
Lahmers, T. M., Hazenberg, P., Gupta, H., Castro, C., Gochis, D., Dugger, A., Yates, D., Read, L., Karsten, L., and Wang, Y. H.: Evaluation of NOAA National Water Model Parameter Calibration in Semiarid Environments Prone to Channel Infiltration, J. Hydrometeorol., 22, 2939–2969, https://doi.org/10.1175/JHM-D-20-0198.1, 2021.
Legates, D. R. and McCabe, G. J.: Evaluating the use of “goodness-of-fit” Measures in hydrologic and hydroclimatic model validation, Water Resour. Res., 35, 233–241, https://doi.org/10.1029/1998WR900018, 1999.
Li, C., Yu, G., Wang, J., and Horton, D. E.: Toward Improved Regional Hydrological Model Performance Using State-Of-The-Science Data-Informed Soil Parameters, Water Resour. Res., 59, 1–23, https://doi.org/10.1029/2023WR034431, 2023.
Linke, S., Lehner, B., Ouellet Dallaire, C., Ariwi, J., Grill, G., Anand, M., Beames, P., Burchard-Levine, V., Maxwell, S., Moidu, H., Tan, F., and Thieme, M.: Global hydro-environmental sub-basin and river reach characteristics at high spatial resolution, Sci. Data, 6, 1–16, https://doi.org/10.1038/s41597-019-0300-6, 2019.
Liu, D., Guo, S., Wang, Z., Liu, P., Yu, X., Zhai, Q., and Zou, H.: Statistics for sample splitting for the calibration and validation of hydrological models, Stoch. Environ. Res. Risk Assess., 1–18, https://doi.org/10.1007/s00477-018-1539-8, 2018.
Lundberg, S. M., Erion, G., Chen, H., DeGrave, A., Prutkin, J. M., Nair, B., Katz, R., Himmelfarb, J., Bansal, N., and Lee, S. I.: From local explanations to global understanding with explainable AI for trees, Nat. Mach. Intell., 2, 56–67, https://doi.org/10.1038/s42256-019-0138-9, 2020.
Ma, Y., Leonarduzzi, E., Defnet, A., Melchior, P., Condon, L. E., and Maxwell, R. M.: Water Table Depth Estimates over the Contiguous United States Using a Random Forest Model, Groundwater, 62, 34–43, https://doi.org/10.1111/gwat.13362, 2024.
Mai, J.: Ten strategies towards successful calibration of environmental models, J. Hydrol., 620, 129414, https://doi.org/10.1016/j.jhydrol.2023.129414, 2023.
Mai, J., Craig, J. R., Tolson, B. A., and Arsenault, R.: The sensitivity of simulated streamflow to individual hydrologic processes across North America, Nat. Commun., 13, 455, https://doi.org/10.1038/s41467-022-28010-7, 2022.
Maier, H., Taghikhah, F., Nabavi, E., Razavi, S., Gupta, H., Wu, W., Radford, D. A. G., and Huang, J.: How much X is in XAI: Responsible use of “Explainable” artificial intelligence in hydrology and water resources, J. Hydrol. X, 25, 100185, https://doi.org/10.1016/j.hydroa.2024.100185, 2024.
McMillan, S. K., Wilson, H. F., Tague, C. L., Hanes, D. M., Inamdar, S., Karwan, D. L., Loecke, T., Morrison, J., Murphy, S. F., and Vidon, P.: Before the storm: antecedent conditions as regulators of hydrologic and biogeochemical response to extreme climate events, Biogeochemistry, 141, 487–501, https://doi.org/10.1007/s10533-018-0482-6, 2018.
Michalek, A. T., Villarini, G., and Husic, A.: Climate change projected to impact structural hillslope connectivity at the global scale, Nat. Commun., 14, 6788, https://doi.org/10.1038/s41467-023-42384-2, 2023.
Morris, M. D.: Factorial sampling plans for preliminary computational experiments, Technometrics, 33, 161–174, https://doi.org/10.1080/00401706.1991.10484804, 1991.
National Forest Climate Change Maps: Your Guide to the Future, Forest Service, U.S. Department of Agriculture,
https://www.fs.usda.gov/rm/boise/AWAE/projects/national-forest-climate-change-maps.html, last access: 1 December 2024.
Nicolle, P., Andréassian, V., Royer-Gaspard, P., Perrin, C., Thirel, G., Coron, L., and Santos, L.: Technical note: RAT – a robustness assessment test for calibrated and uncalibrated hydrological models, Hydrol. Earth Syst. Sci., 25, 5013–5027, https://doi.org/10.5194/hess-25-5013-2021, 2021.
Ogden, F., Avant, B., Bartel, R., Blodgett, D., Clark, E., Coon, E., Cosgrove, B., Cui, S., Kindl da Cunha, L., Farthing, M., Flowers, T., Frame, J., Frazier, N., Graziano, T., Gutenson, J., Johnson, D., McDaniel, R., Moulton, J., Loney, D., Peckham, S., Mattern, D., Jennings, K., Williamson, M., Savant, G., Tubbs, C., Garrett, J., Wood, A., and Johnson, J.: The Next Generation Water Resources Modeling Framework: Open Source, Standards Based, Community Accessible, Model Interoperability for Large Scale Water Prediction, in: AGU Fall Meeting Abstracts, New Orleans, LA, 13–17 December 2021,
https://ui.adsabs.harvard.edu/abs/2021AGUFM.H43D..01O/abstract, 2021.
Omernik, J. M.: Ecoregions of the Conterminous United, Ann. Assoc. Am. Geogr., 77, 118–125, 1987.
Pandit, A., Hogan, S., Mahoney, D. T., Ford, W. I., Fox, J. F., Wellen, C., and Husic, A.: Establishing performance criteria for evaluating watershed-scale sediment and nutrient models at fine temporal scales, Water Res., 274, 123156, https://doi.org/10.1016/j.watres.2025.123156, 2025.
Pasquier, U., Vahmani, P., and Jones, A. D.: Quantifying the City-Scale Impacts of Impervious Surfaces on Groundwater Recharge Potential: An Urban Application of WRF–Hydro, Water, 14, https://doi.org/10.3390/w14193143, 2022.
Pearson, K.: On lines and planes of closest fit to systems of points in space, London, Edinburgh, Dublin Philos. Mag. J. Sci., 2, 559–572, https://doi.org/10.1080/14786440109462720, 1901.
Pianosi, F., Beven, K., Freer, J., Hall, J. W., Rougier, J., Stephenson, D. B., and Wagener, T.: Sensitivity analysis of environmental models: A systematic review with practical workflow, Environ. Model. Softw., 79, 214–232, https://doi.org/10.1016/j.envsoft.2016.02.008, 2016.
Price, A. N., Jones, C. N., Hammond, J. C., Zimmer, M. A., and Zipper, S. C.: The Drying Regimes of Non-Perennial Rivers and Streams, Geophys. Res. Lett., 48, 1–12, https://doi.org/10.1029/2021GL093298, 2021.
Putman, A. L., Longley, P. C., McDonnell, M. C., Reddy, J., Katoski, M., Miller, O. L., and Brooks, J. R.: Isotopic evaluation of the National Water Model reveals missing agricultural irrigation contributions to streamflow across the western United States, Hydrol. Earth Syst. Sci., 28, 2895–2918, https://doi.org/10.5194/hess-28-2895-2024, 2024.
Regan, R. S., Juracek, K. E., Hay, L. E., Markstrom, S. L., Viger, R. J., Driscoll, J. M., LaFontaine, J. H., and Norton, P. A.: The U. S. Geological Survey National Hydrologic Model infrastructure: Rationale, description, and application of a watershed-scale model for the conterminous United States, Environ. Model. Softw., 111, 192–203, https://doi.org/10.1016/j.envsoft.2018.09.023, 2019.
Reinecke, R., Stein, L., Gnann, S., Andersson, J. C. M., Arheimer, B., Bierkens, M., Bonetti, S., Güntner, A., Kollet, S., Mishra, S., Moosdorf, N., Nazari, S., Pokhrel, Y., Prudhomme, C., Schewe, J., Shen, C., and Wagener, T.: Uncertainties as a Guide for Global Water Model Advancement, Wiley Interdiscip. Rev. Water, 12, 1–25, https://doi.org/10.1002/wat2.70025, 2025.
Ribeiro, M. T., Singh, S., and Guestrin, C.: “Why should i trust you?” Explaining the predictions of any classifier, Proc. ACM SIGKDD Int. Conf. Knowl. Discov. Data Min., 1135–1144, https://doi.org/10.1145/2939672.2939778, 2016.
Rojas, M., Quintero, F., and Krajewski, W. F.: Performance of the National Water Model in Iowa Using Independent Observations, J. Am. Water Resour. Assoc., 56, 568–585, https://doi.org/10.1111/1752-1688.12820, 2020.
Santos, L., Andréassian, V., Sonnenborg, T. O., Lindström, G., de Lavenne, A., Perrin, C., Collet, L., and Thirel, G.: Lack of robustness of hydrological models: a large-sample diagnosis and an attempt to identify hydrological and climatic drivers, Hydrol. Earth Syst. Sci., 29, 683–700, https://doi.org/10.5194/hess-29-683-2025, 2025.
Sarrazin, F., Pianosi, F., and Wagener, T.: Global Sensitivity Analysis of environmental models: Convergence and validation, Environ. Model. Softw., 79, 135–152, https://doi.org/10.1016/j.envsoft.2016.02.005, 2016.
Savenije, H. H. G.: HESS Opinions: Linking Darcy's equation to the linear reservoir, Hydrol. Earth Syst. Sci., 22, 1911–1916, https://doi.org/10.5194/hess-22-1911-2018, 2018.
Shapley, L. S.: A Value for n-Person Games, in: Contributions to the Theory of Games (AM-28), Volume II, edited by: Kuhn, H. W. and Tucker, A. W., Princeton University Press, 307–318, https://doi.org/10.1515/9781400881970-018, 1953.
Slater, L., Blougouras, G., Deng, L., Deng, Q., Ford, E., Hoek van Dijke, A., Huang, F., Jiang, S., Liu, Y., Moulds, S., Schepen, A., Yin, J., and Zhang, B: Challenges and opportunities of ML and explainable AI in large-sample hydrology, Phil. Trans. R. Soc., 383, 20240287, https://doi.org/10.1098/rsta.2024.0287, 2025.
Sobol', I.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simul., 55, 271–280, https://doi.org/10.1016/S0378-4754(00)00270-6, 2001.
Song, X., Zhang, J., Zhan, C., Xuan, Y., Ye, M., and Xu, C.: Global sensitivity analysis in hydrological modeling: Review of concepts, methods, theoretical framework, and applications, J. Hydrol., 523, 739–757, https://doi.org/10.1016/j.jhydrol.2015.02.013, 2015.
Tijerina, D., Condon, L., FitzGerald, K., Dugger, A., O'Neill, M. M., Sampson, K., Gochis, D., and Maxwell, R.: Continental Hydrologic Intercomparison Project, Phase 1: A Large-Scale Hydrologic Model Comparison Over the Continental United States, Water Resour. Res., 57, 1–27, https://doi.org/10.1029/2020WR028931, 2021.
Towler, E., Foks, S. S., Dugger, A. L., Dickinson, J. E., Essaid, H. I., Gochis, D., Viger, R. J., and Zhang, Y.: Benchmarking high-resolution hydrologic model performance of long-term retrospective streamflow simulations in the contiguous United States, Hydrol. Earth Syst. Sci., 27, 1809–1825, https://doi.org/10.5194/hess-27-1809-2023, 2023.
USGS water data for the Nation: U.S. Geological Survey National Water Information System database, U.S. Geological Survey, https://doi.org/10.5066/F7P55KJN, 2023.
Vrugt, J. A. and Beven, K. J.: Embracing equifinality with efficiency: Limits of Acceptability sampling using the DREAM(LOA)algorithm, J. Hydrol., 559, 954–971, https://doi.org/10.1016/j.jhydrol.2018.02.026, 2018.
Zarnaghsh, A. and Husic, A.: Degree of anthropogenic land disturbance controls fluvial sediment hysteresis, Environ. Sci. Technol., 55, 13737–13748, https://doi.org/10.1021/acs.est.1c00740, 2021.
Zehe, E. and Sivapalan, M.: Threshold behaviour in hydrological systems as (human) geo-ecosystems: manifestations, controls, implications, Hydrol. Earth Syst. Sci., 13, 1273–1297, https://doi.org/10.5194/hess-13-1273-2009, 2009.
