Chadalawada, J., Herath, H. M. V. V., and Babovic, V.: Hydrologically Informed Machine Learning for Rainfall-Runoff Modeling: A Genetic Programming-Based Toolkit for Automatic Model Induction, Water Resour. Res., 56, e2019WR026933, https://doi.org/10.1029/2019WR026933, 2020.
Cranmer, M.: Interpretable machine learning for science with PySR and SymbolicRegression.jl, arXiv [preprint], https://doi.org/10.48550/arXiv.2305.01582, 2023.
Feigl, M., Herrnegger, M., Klotz, D., and Schulz, K.: Function Space Optimization: A Symbolic Regression Method for Estimating Parameter Transfer Functions for Hydrological Models, Water Resour. Res., 56, e2020WR027385, 10.1029/2020WR027385, 2020.
Feigl, M., Thober, S., Schweppe, R., Herrnegger, M., Samaniego, L., and Schulz, K.: Automatic Regionalization of Model Parameters for Hydrological Models, Water Resour. Res., 58, e2022WR031966, https://doi.org/10.1029/2022WR031966, 2022.
Feng, D., Fang, K., and Shen, C.: Enhancing Streamflow Forecast and Extracting Insights Using Long-Short Term Memory Networks With Data Integration at Continental Scales, Water Resour. Res., 56, e2019WR026793, https://doi.org/10.1029/2019wr026793, 2020.
Garzon, L. F. L., Johnson, M. F., Mount, N., and Gomez, H.: Exploring the effects of catchment morphometry on overland flow response to extreme rainfall using a 2D hydraulic-hydrological model (IBER), J. Hydrol., 627, 130405, https://doi.org/10.1016/j.jhydrol.2023.130405, 2023.
Gnann, S. J., McMillan, H. K., Woods, R. A., and Howden, N. J. K.: Including Regional Knowledge Improves Baseflow Signature Predictions in Large Sample Hydrology, Water Resour. Res., 57, e2020WR028354, https://doi.org/10.1029/2020WR028354, 2021.
Godsey, S. E., Kirchner, J. W., and Tague, C. L.: Effects of changes in winter snowpacks on summer low flows: case studies in the Sierra Nevada, California, USA, Hydrol. Process., 28, 5048–5064, https://doi.org/10.1002/hyp.9943, 2014.
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, 10.1016/j.jhydrol.2009.08.003, 2009.
Gustard, A., Bullock, A. D., and Dixon, J. M.: Low Flow Estimation in the United Kingdom, Institute of Hydrology, Wallingford, UK, ISBN 0948540451, 1992.
Häfner, D., Gemmrich, J., and Jochum, M.: Machine-guided discovery of a real-world rogue wave model, P. Natl. Acad. Sci. USA, 120, e2306275120, https://doi.org/10.1073/pnas.2306275120, 2023.
Hagedorn, B.: Hydrograph separation through multi objective optimization: Revealing the importance of a temporally and spatially constrained baseflow solute source, J. Hydrol., 590, 125349, https://doi.org/10.1016/j.jhydrol.2020.125349, 2020.
Hou, X., Xie, D., Feng, L., Shen, F., and Nienhuis, J. H.: Sustained increase in suspended sediments near global river deltas over the past two decades, Nat. Commun., 15, 3319, https://doi.org/10.1038/s41467-024-47598-6, 2024.
Humphrey, C. E., Solomon, D. K., Genereux, D. P., Gilmore, T. E., Mittelstet, A. R., Zlotnik, V. A., Zeyrek, C., Jensen, C. R., and MacNamara, M. R.: Using Automated Seepage Meters to Quantify the Spatial Variability and Net Flux of Groundwater to a Stream, Water Resour. Res., 58, e2021WR030711, https://doi.org/10.1029/2021WR030711, 2022.
Jenicek, M. and Ledvinka, O.: Importance of snowmelt contribution to seasonal runoff and summer low flows in Czechia, Hydrol. Earth Syst. Sci., 24, 3475–3491, https://doi.org/10.5194/hess-24-3475-2020, 2020.
Klotz, D., Herrnegger, M., and Schulz, K.: Symbolic Regression for the Estimation of Transfer Functions of Hydrological Models, Water Resour. Res., 53, 9402–9423, https://doi.org/10.1002/2017wr021253, 2017.
Koza, J. R.: Genetic programming as a means for programming computers by natural selection, Stat. Comput., 4, 87–112, https://doi.org/10.1007/BF00175355, 1994.
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.
Kronberger, G., de Franca, F. O., Burlacu, B., Haider, C., and Kommenda, M.: Shape-Constrained Symbolic Regression – Improving Extrapolation with Prior Knowledge, Evol. Comput., 30, 75–98, https://doi.org/10.1162/evco_a_00294, 2022.
Li, Q., Zhang, C., Wei, Z., Jin, X., Shangguan, W., Yuan, H., Zhu, J., Li, L., Liu, P., Chen, X., Yan, Y., and Dai, Y.: Advancing symbolic regression for earth science with a focus on evapotranspiration modeling, npj Climate and Atmospheric Science, 7, https://doi.org/10.1038/s41612-024-00861-5, 2024.
Li, X., Zhang, J., Li, D., Liu, X., Xu, J., and Yin, J.: UniSymNet: A Unified Symbolic Network Guided by Transformer, arXiv [preprint], https://doi.org/10.48550/arXiv.2505.06091, 2025.
Lin, Y., Mei, Y., and Wang, D.: Data and code archive for “Regionalization of Optimal Baseflow Separation using Catchment-scale Characteristics”, Zenodo [data set/code], https://doi.org/10.5281/zenodo.16924118, 2025.
Lin, Y., Mei, Y., Wang, D., Zhu, J., Wu, H., Wang, S., Yin, G., Gao, L., and N. Anagnostou, E.: Regionalization of Optimal Baseflow Separation using Catchment-scale Characteristics, Water Resour. Res., 62, https://doi.org/10.1029/2025WR040578, 2026.
Makke, N. and Chawla, S.: Interpretable scientific discovery with symbolic regression: a review, Artif. Intell. Rev., 57, https://doi.org/10.1007/s10462-023-10622-0, 2024.
McGlynn, B. L., McDonnell, J. J., Seibert, J., and Kendall, C.: Scale effects on headwater catchment runoff timing, flow sources, and groundwater-streamflow relations, Water Resour. Res., 40, https://doi.org/10.1029/2003WR002494, 2004.
McMillan, H.: Linking hydrologic signatures to hydrologic processes: A review, Hydrol. Process., 34, 1393–1409, https://doi.org/10.1002/hyp.13632, 2020.
McMillan, H. K., Gnann, S. J., and Araki, R.: Large Scale Evaluation of Relationships Between Hydrologic Signatures and Processes, Water Resour. Res., 58, e2021WR031751, https://doi.org/10.1029/2021WR031751, 2022.
Mei, Y. and Anagnostou, E. N.: A hydrograph separation method based on information from rainfall and runoff records, J. Hydrol., 523, 636–649, https://doi.org/10.1016/j.jhydrol.2015.01.083, 2015.
Mei, Y., Zhu, J., and Wang, D.: Data and Code Archive for “Optimal Baseflow Separation through Chemical Mass Balance: Comparing the Usages of Two Tracers, Two Concentration Estimation Methods, and Four Baseflow Filters”, Zenodo [data set/code], https://doi.org/10.5281/zenodo.8388365, 2024a.
Mei, Y., Wang, D., Zhu, J., Tang, G., Cai, C., Shen, X., Hong, Y., and Zhang, X.: Optimal Baseflow Separation Through Chemical Mass Balance: Comparing the Usages of Two Tracers, Tw
o Concentration Estimation Methods, and Four Baseflow Filters, Water Resour. Res., 60, https://doi.org/10.1029/2023wr036386, 2024b.
Nagy, E. D., Szilagyi, J., and Torma, P.: Calibrating the lyne-hollick filter for baseflow separation based on catchment response time, J. Hydrol., 638, https://doi.org/10.1016/j.jhydrol.2024.131483, 2024.
Noor, K., Marttila, H., Welker, J. M., Mustonen, K.-R., Kløve, B., and Ala-aho, P.: Snow sampling strategy can bias estimation of meltwater fractions in isotope hydrograph separation, J. Hydrol., 627, 130429, https://doi.org/10.1016/j.jhydrol.2023.130429, 2023.
Pelletier, A. and Andréassian, V.: Hydrograph separation: an impartial parametrisation for an imperfect method, Hydrol. Earth Syst. Sci., 24, 1171–1187, https://doi.org/10.5194/hess-24-1171-2020, 2020.
Piggott, A. R., Moin, S., and Southam, C.: A revised approach to the UKIH method for the calculation of baseflow [Une approche améliorée de la méthode de l'UKIH pour le calcul de l'écoulement de base], Hydrolog. Sci. J., 50, 920, https://doi.org/10.1623/hysj.2005.50.5.911, 2005.
Price, K.: Effects of watershed topography, soils, land use, and climate on baseflow hydrology in humid regions: A review, Prog. Phys. Geog., 35, 465–492, https://doi.org/10.1177/0309133311402714, 2011.
Rudin, C.: Stop Explaining Black Box Machine Learning Models for High Stakes Decisions and Use Interpretable Models Instead, Nat. Mach. Intell., 1, 206–215, https://doi.org/10.1038/s42256-019-0048-x, 2019.
Sheta, A., Abdel-raouf, A., Fraihat, K., and Baareh, A. K.: Evolutionary Design of a PSO-Tuned Multigene Symbolic Regression Genetic Programming Model for River Flow Forecasting, International Journal of Advanced Computer Science and Applications, 14, 2023, 10.14569/IJACSA.2023.0140489, 2023.
Sólyom, P. B. and Tucker, G. E.: The importance of the catchment area–length relationship in governing non-steady state hydrology, optimal junction angles and drainage network pattern, Geomorphology, 88, 84–108, https://doi.org/10.1016/j.geomorph.2006.10.014, 2007.
Song, W., Jiang, S., Camps-Valls, G., Williams, M., Zhang, L., Reichstein, M., Vereecken, H., He, L., Hu, X., and Shi, L.: Towards data-driven discovery of governing equations in geosciences, Commun. Earth Environ., 5, 589, https://doi.org/10.1038/s43247-024-01760-6, 2024.
Stewart, M. K.: Promising new baseflow separation and recession analysis methods applied to streamflow at Glendhu Catchment, New Zealand, Hydrol. Earth Syst. Sci., 19, 2587–2603, https://doi.org/10.5194/hess-19-2587-2015, 2015.
Stoelzle, M., Schuetz, T., Weiler, M., Stahl, K., and Tallaksen, L. M.: Beyond binary baseflow separation: a delayed-flow index for multiple streamflow contributions, Hydrol. Earth Syst. Sci., 24, 849–867, https://doi.org/10.5194/hess-24-849-2020, 2020.
Sundararajan, M. and Najmi, A.: The Many Shapley Values for Model Explanation, Proceedings of the 37th International Conference on Machine Learning, Proceedings of Machine Learning Research (PMLR), 119,
https://proceedings.mlr.press/v119/sundararajan20b.html (last access: 29 May 2026), 2020.
Tan, X., Liu, B., and Tan, X.: Global Changes in Baseflow Under the Impacts of Changing Climate and Vegetation, Water Resour. Res., 56, e2020WR027349, https://doi.org/10.1029/2020WR027349, 2020.
Tarasova, L., Gnann, S., Yang, S., Hartmann, A., and Wagener, T.: Catchment characterization: Current descriptors, knowledge gaps and future opportunities, Earth-Sci. Rev., 252, https://doi.org/10.1016/j.earscirev.2024.104739, 2024.
Thorslund, J. and van Vliet, M. T. H.: A global dataset of surface water and groundwater salinity measurements from 1980–2019, Scientific Data, 7, 231, https://doi.org/10.1038/s41597-020-0562-z, 2020.
Wilstrup, C. and Kasak, J.: Symbolic regression outperforms other models for small data sets, arXiv [preprint], https://doi.org/10.48550/arXiv.2103.15147, 2021.
Wu, S., Zhao, J., Wang, H., and Sivapalan, M.: Regional Patterns and Physical Controls of Streamflow Generation Across the Conterminous United States, Water Resour. Res., 57, https://doi.org/10.1029/2020wr028086, 2021.
Xie, J., Liu, X., Tian, W., Wang, K., Bai, P., and Liu, C.: Estimating Gridded Monthly Baseflow From 1981 to 2020 for the Contiguous US Using Long Short-Term Memory (LSTM) Networks, Water Resour. Res., 58, https://doi.org/10.1029/2021wr031663, 2022.
Xie, J., Liu, X., Wang, K., Yang, T., Liang, K., and Liu, C.: Evaluation of typical methods for baseflow separation in the contiguous United States, J. Hydrol., 583, https://doi.org/10.1016/j.jhydrol.2020.124628, 2020.
Xie, J., Liu, X., Jasechko, S., Berghuijs, W. R., Wang, K., Liu, C., Reichstein, M., Jung, M., and Koirala, S.: Majority of global river flow sustained by groundwater, Nat. Geosci., https://doi.org/10.1038/s41561-024-01483-5, 2024.
Yan, X., Sun, J., Huang, Y., Xia, Y., Wang, Z., and Li, Z.: Detecting and attributing the changes in baseflow in China's Loess Plateau, J. Hydrol., 617, 128957, https://doi.org/10.1016/j.jhydrol.2022.128957, 2023.
Zhang, J., Zhang, Y., Song, J., and Cheng, L.: Evaluating relative merits of four baseflow separation methods in Eastern Australia, J. Hydrol., 549, 252–263, https://doi.org/10.1016/j.jhydrol.2017.04.004, 2017.
Zhang, J., Zhang, Y., Song, J., Cheng, L., Kumar Paul, P., Gan, R., Shi, X., Luo, Z., and Zhao, P.: Large-scale baseflow index prediction using hydrological modelling, linear and multilevel regression approaches, J. Hydrol., 585, 124780, https://doi.org/10.1016/j.jhydrol.2020.124780, 2020.
