A physics-informed geospatial machine-learning downscaling framework for improving extreme rainfall

Abstract

Reliable high-resolution precipitation is essential for monitoring hydrologic extremes and informing climate-risk decisions, yet satellite precipitation products often show biases and remain too coarse (5–25 km) to resolve localized processes. Conventional downscaling also tends to overlook dynamic moisture–cloud mechanisms that drive precipitation variability. We develop a Physics-Informed Geospatial Machine-Learning Downscaling rainfall model (PIGMLD) to produce 1-km daily precipitation over China (2000–2020) by combining the 10-km Global Precipitation Measurement (GPM) Integrated Multi-satellitE Retrievals for GPM (IMERG) (GPM IMERG) product with rare ground observations, ERA5-Land precipitation, and physically traceable covariates describing moisture, clouds, and land–atmosphere coupling. Evaluation against independent gauges across China and nine major river basins shows broad skill gains: 84.1 % of stations achieve KGE > 0.60, with improved event detection and reduced systematic bias. Gains are constrained by complex topography and sparse in-situ stations in the Northwest and Southwest basins (median RMSE = 1.18 mm; KGE = 0.45). For heavy and torrential rainfall, RMSE decreases by 36.1 % and 28.3 %, respectively. Relative threshold assessments indicate robust corrections under dry and wet extremes: for events below the 10th percentile, BIAS is reduced by ∼66.7 % at > 90 % of stations; for events ≥ 90th percentile, underestimation is substantially alleviated, with BIAS typically reduced by ∼50.1 %. XGBoost–SHAP attribution reveals scale-dependent controls: 10-km estimates are dominated by cloud and column moisture, whereas 1-km estimates are more sensitive to near-surface humidity and land-surface states, and heavy rainfall reflects coupled moisture–dynamics–thermodynamics interactions. Overall, PIGMLD provides a mechanism-aware pathway for producing and interpreting 1-km precipitation fields and clarifies when finer-scale information improves extreme-event characterization.

Keywords

Rainfall / Physics-informed geospatial machine-learning downscaling / Data fusion / Extremes / Governing factors

References

[1] Abdelmoaty, H.M., Papalexiou, S.M., Mamalakis, A., Singh, S., Coia, V., Hairabedian, M., Szeftel, P., Grover, P., 2025. Generative adversarial networks for downscaling hourly precipitation in the Canadian prairies. J. Geophys. Res.: Mach. Learn. Comput. 2 (4), e2025JH000678. doi: 10.1029/2025jh000678.

[2] Acuña Espinoza, E., Loritz, R., Kratzert, F., Klotz, D., Gauch, M., Álvarez Chaves, M., Ehret, U., 2025. Analyzing the generalization capabilities of a hybrid hydrological model for extrapolation to extreme events. Hydrol. Earth Syst. Sci. 29 (5), 1277-1294. doi: 10.5194/hess-29-1277-2025.

[3] AghaKouchak, A., Huning, L.S., Sadegh, M., Qin, Y., Markonis, Y., Vahedifard, F., Love, C.A., Mishra, A., Mehran, A., Obringer, R., Hjelmstad, A., Pallickara, S., Jiwa, S., Hanel, M., Zhao, Y.X., Pendergrass, A.G., Arabi, M., Davis, S.J., Ward, P.J., Svoboda, M., Pulwarty, R., Kreibich, H., 2023. Toward impact-based monitoring of drought and its cascading hazards. Nat. Rev. Earth Environ. 4 (8), 582-595. doi: 10.1038/s43017-023-00457-2.

[4] Ali, H., Fowler, H.J., Turner, A.G., 2025. High-resolution climate models improve simulation of monsoon rainfall changes in the Ganga-Brahmaputra-Meghna basin. Clim. Dyn. 63 (6), 246. doi: 10.1007/s00382-025-07716-6.

[5] Azad, R., Aghdam, E.K., Rauland, A., Jia, Y.W., Avval, A.H., Bozorgpour, A., Karimijafarbigloo, S., Cohen, J.P., Adeli, E., Merhof, D., 2024. Medical image segmentation review: the success of U-Net. IEEE Trans. Pattern Anal. Mach. Intell. 46 (12), 10076-10095. doi: 10.1109/TPAMI.2024.3435571.

[6] Barnhart, T.B., Putman, A.L., Heldmyer, A.J., Rey, D.M., Hammond, J.C., Driscoll, J.M., Sexstone, G.A., 2024. Evaluating distributed snow model resolution and meteorology parameterizations against streamflow observations: finer is not always better. Water Resour. Res. 60 (7), e2023WR035982. doi: 10.1029/2023wr035982.

[7] Bellier, J., Scheuerer, M., Hamill, T.M., 2020. Precipitation downscaling with gibbs sampling: an improved method for producing realistic, weather-dependent, and anisotropic fields. J. Hydrometeorol. 21 (11), 2487-2505. doi: 10.1175/Jhm-D-20-0069.1.

[8] Bellprat, O., Guemas, V., Doblas-Reyes, F., Donat, M.G., 2019. Towards reliable extreme weather and climate event attribution. Nat. Commun. 10, 1732. doi: 10.1038/s41467-019-09729-2.

[9] Bjarke, N.R., Livneh, B., Barsugli, J.J., Pendergrass, A.G., Small, E.E., 2024. Evaluating large-storm dominance in high-resolution GCMs and observations across the western contiguous United States. Earths Future 12 (6), e2023EF004289. doi: 10.1029/2023EF004289.

[10] Brempong, E.A., Hassen, M.A., MohamedKhair, M., Dube, V., Potes, S.H., Graham, O., Brik, A., McGovern, A., Huffman, G.J., Hickey, J., 2025. Oya: deep learning for accurate global precipitation estimation. arXiv: 2511.10562. https://arxiv.org/abs/2511.10562.

[11] Brocca, L., Barbetta, S., Camici, S., Ciabatta, L., Dari, J., Filippucci, P., Massari, C., Modanesi, S., Tarpanelli, A., Bonaccorsi, B., Mosaffa, H., Wagner, W., Vreugdenhil, M., Quast, R., Alfieri, L., Gabellani, S., Avanzi, F., Rains, D., Miralles, D.G., Mantovani, S., Briese, C., Domeneghetti, A., Jacob, A., Castelli, M., Camps-Valls, G., Volden, E., Fernandez, D., 2024. A digital twin of the terrestrial water cycle: a glimpse into the future through high-resolution Earth observations. Front. Sci. 1, 1190191. doi: 10.3389/fsci.2023.1190191.

[12] Chang, P., Fu, D., Liu, X., Castruccio, F.S., Prein, A.F., Danabasoglu, G., Wang, X.Q., Bacmeister, J., Zhang, Q.Y., Rosenbloom, N., King, T., Bates, S.C., 2026. Future extreme precipitation amplified by intensified mesoscale moisture convergence. Nat. Geosci. 19 (1), 33-41. doi: 10.1038/s41561-025-01859-1.

[13] Chen, T.Q., Guestrin, C., 2016. XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, pp. 785-794. doi: 10.1145/2939672.2939785.

[14] Deng, C., Jiang, X.H., Jiang, C.T., Nie, T., Lei, Y.X., Yang, A.L., 2025. Insights into teleconnection mechanism of extreme precipitation events based on the SHAP-XGBoost model: evidence from Hekou-Longmen section in China. Nat. Hazards 121 (6), 7447-7468. doi: 10.1007/s11069-024-07054-6.

[15] Du, Y., Wang, D.G., Zhu, J.X., Lin, Z.Q., Zhong, Y.X., 2022. Intercomparison of multiple high-resolution precipitation products over China: climatology and extremes. Atmos. Res. 278, 106342. doi: 10.1016/j.atmosres.2022.106342.

[16] Emmanuel, I., Andrieu, H., Leblois, E., Flahaut, B., 2012. Temporal and spatial variability of rainfall at the urban hydrological scale. J. Hydrol. 430-431, 162-172. doi: 10.1016/j.jhydrol.2012.02.013.

[17] Eyring, V., Collins, W.D., Gentine, P., Barnes, E.A., Barreiro, M., Beucler, T., Bocquet, M., Bretherton, C.S., Christensen, H.M., Dagon, K., Gagne, D.J., Hall, D., Hammerling, D., Hoyer, S., Iglesias-Suarez, F., Lopez-Gomez, I., McGraw, M.C., Meehl, G.A., Molina, M.J., Monteleoni, C., Mueller, J., Pritchard, M.S., Rolnick, D., Runge, J., Stier, P., Watt-Meyer, O., Weigel, K., Yu, R., Zanna, L., 2024. Pushing the frontiers in climate modelling and analysis with machine learning. Nat. Clim. Chang. 14 (9), 916-928. doi: 10.1038/s41558-024-02095-y.

[18] Fowler, H.J., Lenderink, G., Prein, A.F., Westra, S., Allan, R.P., Ban, N., Barbero, R., Berg, P., Blenkinsop, S., Do, H.X., Guerreiro, S., Haerter, J.O., Kendon, E.J., Lewis, E., Schaer, C., Sharma, A., Villarini, G., Wasko, C., Zhang, X.B., 2021. Anthropogenic intensification of short-duration rainfall extremes. Nat. Rev. Earth Environ. 2 (2), 107-122. doi: 10.1038/s43017-020-00128-6.

[19] Fraehr, N., Wang, Q.J., Wu, W.Y., Nathan, R., 2023. Supercharging hydrodynamic inundation models for instant flood insight. Nat. Water 1 (10), 835-843. doi: 10.1038/s44221-023-00132-2.

[20] García-García, A., Stradiotti, P., Di Paolo, F., Filippucci, P., Fischer, M., Orság, M., Brocca, L., Peng, J., Dorigo, W., Gruber, A., Droppers, B., Wanders, N., Haag, A., Weerts, A., Modiri, E., Rakovec, O., Francés, F., Dall’Amico, M., Anderson, M., Hain, C., Samaniego, L., 2026. Intercomparison of Earth Observation products for hyper-resolution hydrological modelling over Europe. Remote Sens. Environ. 333, 115131. doi: 10.1016/j.rse.2025.115131.

[21] Gavahi, K., Foroumandi, E., Moradkhani, H., 2023. A deep learning-based framework for multi-source precipitation fusion. Remote Sens. Environ. 295, 113723. doi: 10.1016/j.rse.2023.113723.

[22] Gou, J.Y., Soja, B., 2024. Global high-resolution total water storage anomalies from self-supervised data assimilation using deep learning algorithms. Nat. Water 2 (2), 139-150. doi: 10.1038/s44221-024-00194-w.

[23] Han, J.Y., Miao, C.Y., Gou, J.J., Zheng, H.Y., Zhang, Q., Guo, X.Y., 2023. A new daily gridded precipitation dataset for the Chinese mainland based on gauge observations. Earth Syst. Sci. Data 15 (7), 3147-3161. doi: 10.5194/essd-15-3147-2023.

[24] Hartke, S.H., Wright, D.B., Li, Z., Maggioni, V., Kirschbaum, D.B., Khan, S., 2022. Ensemble representation of satellite precipitation uncertainty using a nonstationary, anisotropic autocorrelation model. Water Resour. Res. 58 (8), e2021WR031650. doi: 10.1029/2021WR031650.

[25] He, J., Yang, K., Tang, W.J., Lu, H., Qin, J., Chen, Y.Y., Li, X., 2020. The first high-resolution meteorological forcing dataset for land process studies over China. Sci. Data 7, 25. doi: 10.1038/s41597-020-0369-y.

[26] He, J., Zhang, L.M., Xiao, T., Wang, H.J., Luo, H.Y., 2023c. Deep learning enables super-resolution hydrodynamic flooding process modeling under spatiotemporally varying rainstorms. Water Res. 239, 120057. doi: 10.1016/j.watres.2023.120057.

[27] He, K.L., Chen, X.H., Liu, J., Zhao, D.M., 2023b. A multiple-step scheme for the improvement of satellite precipitation products over the Tibetan Plateau from multi-source information. Sci. Total Environ. 873, 162378. doi: 10.1016/j.scitotenv.2023.162378.

[28] He, K.L., Zhao, W., Brocca, L., Quintana-Seguí, P., 2023a. SMPD: a soil moisture-based precipitation downscaling method for high-resolution daily satellite precipitation estimation. Hydrol. Earth Syst. Sci. 27 (1), 169-190. doi: 10.5194/hess-27-169-2023.

[29] He, K.L., Zhao, W., Brocca, L., Quintana-Seguí, P., Chen, X.H., 2025b. SMPD-MERG: a hybrid downscaling model for high-resolution daily precipitation estimation via merging surface soil moisture and multisource precipitation data. IEEE Trans. Geosci. Remote Sens. 63, 4104616. doi: 10.1109/TGRS.2025.3561253.

[30] He, K.L., Chen, X.H., Xu, C.Y., Zhao, D.M., Dong, C.Y., Yu, X., AghaKouchak, A., 2025a. Intensifying risk of tropical cyclone-induced cascading geohazards in China’s highly urbanized coastal regions. J. Hydrol. 663, 134132. doi: 10.1016/j.jhydrol.2025.134132.

[31] Hinojos, S., McPhillips, L., Stempel, P., Grady, C., 2023. Social and environmental vulnerability to flooding: investigating cross-scale hypotheses. Appl. Geogr. 157, 103017. doi: 10.1016/j.apgeog.2023.103017.

[32] Hong, Y., Adler, R.F., Huffman, G.J., Pierce, H., 2010. Applications of TRMM-based multi-satellite precipitation estimation for global runoff prediction: prototyping a global flood modeling system. In: Satellite Rainfall Applications For Surface Hydrology. Springer, Dordrecht, pp. 245-265. doi: 10.1007/978-90-481-2915-7_15.

[33] Hu, Q., Li, Z., Wang, L., Huang, Y., Wang, Y., Li, L., 2019. Rainfall spatial estimations: a review from spatial interpolation to multi-source data merging. Water 11 (3), 579. doi: 10.3390/w11030579.

[34] Hu, Z.W., Chu, Y.Q., Zhang, Y.H., Zheng, X.Y., Wang, J.Z., Xu, W.M., Wang, J., Wu, G.F., 2024. Scale matters: how spatial resolution impacts remote sensing based urban green space mapping? Int. J. Appl. Earth Obs. Geoinf. 134, 104178. doi: 10.1016/j.jag.2024.104178.

[35] Huang, X.Y., Swain, D.L., Hall, A.D., 2020. Future precipitation increase from very high resolution ensemble downscaling of extreme atmospheric river storms in California. Sci. Adv. 6 (29), eaba1323. doi: 10.1126/sciadv.aba1323.

[36] Huffman, G.J., Bolvin, D.T., Braithwaite, D., Hsu, K., Joyce, R., Kidd, C., Nelkin, E., Xie, P., 2023. Nasa global precipitation measurement (GPM) integrated multi-satellite retrievals for GPM (IMERG) version 07. Algorithm theoretical basis document (ATBD) version 47.

[37] Hundhausen, M., Fowler, H.J., Feldmann, H., Pinto, J.G ., 2025. Sub-hourly precipitation and rainstorm event profiles in a convection-permitting multi-GCM ensemble. Weather Clim. Extrem. 48, 100764. doi: 10.1016/j.wace.2025.100764.

[38] Karger, D.N., Conrad, O., Böhner, J., Kawohl, T., Kreft, H., Soria-Auza, R.W., Zimmermann, N.E., Linder, H.P., Kessler, M., 2017. Climatologies at high resolution for the Earth’s land surface areas. Sci. Data 4, 170122. doi: 10.1038/sdata.2017.122.

[39] Kling, H., Fuchs, M., Paulin, M., 2012. Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios. J. Hydrol. 424-425, 264-277. doi: 10.1016/j.jhydrol.2012.01.011.

[40] Kofidou, M., Stathopoulos, S., Gemitzi, A., 2023. Review on spatial downscaling of satellite derived precipitation estimates. Environ. Earth Sci. 82 (18), 424. doi: 10.1007/s12665-023-11115-7.

[41] Konapala, G., Mishra, A., 2020. Quantifying climate and catchment control on hydrological drought in the continental United States. Water Resour. Res. 56 (1), e2018WR024620. doi: 10.1029/2018WR024620.

[42] Krishnan, S., Pradhan, A., Indu, J., 2022. Estimation of high-resolution precipitation using downscaled satellite soil moisture and SM2RAIN approach. J. Hydrol. 610, 127926. doi: 10.1016/j.jhydrol.2022.127926.

[43] Kumar, A., Scaife, A.A., Merryfield, W.J., Coelho, C.A.S., Kolli, R.K., Fröhlich, K., Lim, E., He, Y.H., Honda, Y., Silva, J.A.M.P.A., Diouf, S., Okia, W.M., Hovsepyan, A., 2024. World Meteorological Organization (WMO)-accredited infrastructure to support operational climate prediction. Bull. Am. Meteor. Soc. 105 (11), E2126-E2143. doi: 10.1175/Bams-D-23-0284.1.

[44] Lee, J., Perera, D., Glickman, T., Taing, L., 2020. Water-related disasters and their health impacts: a global review. Prog. Disaster Sci. 8, 100123. doi: 10.1016/j.pdisas.2020.100123.

[45] Li, G., Zhao, C., Xu, M.Y., Feng, J.W., Zhong, L., Li, R., Fu, Y.F., 2024. Simulating moisture transport over the Tibetan Plateau in summer of 2015 across scales with a global variable-resolution model (MPAS-A). J. Geophys. Res. Atmos. 129 (14), e2023JD040205. doi: 10.1029/2023JD040205.

[46] Li, Q.L., Shi, G.S., Shangguan, W., Nourani, V., Li, J.D., Li, L., Huang, F.N., Zhang, Y., Wang, C.Y., Wang, D.G., Qiu, J.X., Lu, X.J., Dai, Y.J., 2022. A 1 km daily soil moisture dataset over China using in situ measurement and machine learning. Earth Syst. Sci. Data 14 (12), 5267-5286. doi: 10.5194/essd-14-5267-2022.

[47] Lopez-Gomez, I., Wan, Z.Y., Zepeda-Núñez, L., Schneider, T., Anderson, J., Sha, F., 2025. Dynamical-generative downscaling of climate model ensembles. Proc. Natl. Acad. Sci. U.S.A. 122 (17), e2420288122. doi: 10.1073/pnas.2420288122.

[48] Lu, J.Y., Wang, K.C., Wu, G.C., Mao, Y.N., 2024. Evaluation of multisource datasets in characterizing spatiotemporal characteristics of extreme precipitation from 2001 to 2019 in China. J. Hydrometeorol. 25 (3), 515-539. doi: 10.1175/Jhm-D-23-0162.1.

[49] Lundberg, S.M., Erion, G., Chen, H., DeGrave, A., Prutkin, J.M., Nair, B., Katz, R., Himmelfarb, J., Bansal, N., Lee, S.I., 2020. From local explanations to global understanding with explainable AI for trees. Nat. Mach. 2 (1), 56-67. doi: 10.1038/s42256-019-0138-9.

[50] Lyu, Y., Yong, B ., 2024. A novel double Machine Learning strategy for producing high-precision multi-source merging precipitation estimates over the Tibetan Plateau. Water Resour. Res. 60 (4), e2023WR035643. doi: 10.1029/2023WR035643.

[51] Lyu, Y., Yong, B., Huang, F., Qi, W.Q., Tian, F.Q., Wang, G.Q., Zhang, J.Y., 2024. Investigating twelve mainstream global precipitation datasets: which one performs better on the Tibetan Plateau? J. Hydrol. 633, 130947. doi: 10.1016/j.jhydrol.2024.130947.

[52] Ma, Z.Q., Xu, J.T., He, K., Han, X.Z., Ji, Q.W., Wang, T., Xiong, W.T., Hong, Y., 2020. An updated moving window algorithm for hourly-scale satellite precipitation downscaling: a case study in the Southeast Coast of China. J. Hydrol. 581, 124378. doi: 10.1016/j.jhydrol.2019.124378.

[53] Mardian, J ., 2022. The role of spatial scale in drought monitoring and early warning systems: a review. Environ. Rev. 30 (3), 438-459. doi: 10.1139/er-2021-0102.

[54] Materia, S., García, L.P., van Straaten, C., Sungmin, O., Mamalakis, A., Cavicchia, L., Coumou, D., de Luca, P., Kretschmer, M., Donat, M., 2024. Artificial intelligence for climate prediction of extremes: state of the art, challenges, and future perspectives. Wiley Clim. Change 15 (6), e914. doi: 10.1002/wcc.914.

[55] Mondal, S., Mishra, A.K., Leung, R., Cook, B., 2023. Global droughts connected by linkages between drought hubs. Nat. Commun. 14 (1), 144. doi: 10.1038/s41467-022-35531-8.

[56] Mosaffa, H., Ciabatta, L., Filippucci, P., Sadeghi, M., Brocca, L., 2025. HR-PrecipNet: a machine learning framework for 1-km high-resolution satellite precipitation estimation. J. Hydrol. 658, 133217. doi: 10.1016/j.jhydrol.2025.133217.

[57] Moura Ramos Filho, G., Hugo Rabelo Coelho, V., da Silva Freitas, E., Xuan, Y.Q., Brocca, L., das Neves Almeida, C., 2022. Regional-scale evaluation of 14 satellite-based precipitation products in characterising extreme events and delineating rainfall thresholds for flood hazards. Atmos. Res. 276, 106259. doi: 10.1016/j.atmosres.2022.106259.

[58] Muñoz-Sabater, J., Dutra, E., Agustí-Panareda, A., Albergel, C., Arduini, G., Balsamo, G., Boussetta, S., Choulga, M., Harrigan, S., Hersbach, H., Martens, B., Miralles, D.G., Piles, M., Rodríguez-Fernández, N.J., Zsoter, E., Buontempo, C., Thépaut, J.N., 2021. ERA5-Land: a state-of-the-art global reanalysis dataset for land applications. Earth Syst. Sci. Data 13 (9), 4349-4383. doi: 10.5194/essd-13-4349-2021.

[59] Ombadi, M., Risser, M.D., Rhoades, A.M., Varadharajan, C., 2023. A warming-induced reduction in snow fraction amplifies rainfall extremes. Nature 619 (7969), 305-310. doi: 10.1038/s41586-023-06092-7.

[60] Peleg, N., Marra, F., Fatichi, S., Paschalis, A., Molnar, P., Burlando, P., 2018. Spatial variability of extreme rainfall at radar subpixel scale. J. Hydrol. 556, 922-933. doi: 10.1016/j.jhydrol.2016.05.033.

[61] Qin, R.Z., Zhao, Z.Y., Xu, J., Ye, J.S., Li, F.M., Zhang, F., 2022. HRLT: a high-resolution (1 d, 1 km) and long-term (1961-2019) gridded dataset for surface temperature and precipitation across China. Earth Syst. Sci. Data 14 (11), 4793-4810. doi: 10.5194/essd-14-4793-2022.

[62] Rampal, N., Gibson, P.B., Sherwood, S., Abramowitz, G., 2024. On the extrapolation of generative adversarial networks for downscaling precipitation extremes in warmer climates. Geophys. Res. Lett. 51 (23), e2024GL112492. doi: 10.1029/2024GL112492.

[63] Rampal, N., Gibson, P.B., Sood, A., Stuart, S., Fauchereau, N.C., Brandolino, C., Noll, B., Meyers, T., 2022. High-resolution downscaling with interpretable deep learning: rainfall extremes over New Zealand. Weather Clim. Extrem. 38, 100525. doi: 10.1016/j.wace.2022.100525.

[64] Rentschler, J., Salhab, M., Jafino, B.A ., 2022. Flood exposure and poverty in 188 countries. Nat. Commun. 13, 3527. doi: 10.1038/s41467-022-30727-4.

[65] Sha, Y.K., Schreck, J.S., Chapman, W., Gagne, D.J.II, 2025. Improving AI weather prediction models using global mass and energy conservation schemes. J. Adv. Model. Earth Syst. 17 (11), e2025MS005138. doi: 10.1029/2025MS005138.

[66] Shahriari, B., Swersky, K., Wang, Z.Y., Adams, R.P., de Freitas, N., 2016. Taking the human out of the loop: a review of Bayesian optimization. Proc. IEEE 104 (1), 148-175. doi: 10.1109/JPROC.2015.2494218.

[67] Shen, C.P., Appling, A.P., Gentine, P., Bandai, T., Gupta, H., Tartakovsky, A., Baity-Jesi, M., Fenicia, F., Kifer, D., Li, L., Liu, X.F., Ren, W., Zheng, Y., Harman, C.J., Clark, M., Farthing, M., Feng, D.P., Kumar, P., Aboelyazeed, D., Rahmani, F., Song, Y.L., Beck, H.E., Bindas, T., Dwivedi, D., Fang, K., Höge, M., Rackauckas, C., Mohanty, B., Roy, T., Xu, C.G., Lawson, K., 2023. Differentiable modelling to unify machine learning and physical models for geosciences. Nat. Rev. Earth Environ. 4 (8), 552-567. doi: 10.1038/s43017-023-00450-9.

[68] Sokol, Z., Szturc, J., Orellana-Alvear, J., Popová, J., Jurczyk, A., Célleri, R., 2021. The role of weather radar in rainfall estimation and its application in meteorological and hydrological modelling -a review. Remote Sens. 13 (3), 351. doi: 10.3390/rs13030351.

[69] Sun, J., Yang, K., He, X.G., Wang, G.L., Wang, Y., Yu, Y., Lu, H., 2025. Causal pathways underlying global soil moisture-precipitation coupling. Nat. Commun. 16, 8935. doi: 10.1038/s41467-025-63999-7.

[70] Sun, Q.H., Miao, C.Y., Duan, Q.Y., Ashouri, H., Sorooshian, S., Hsu, K.L., 2018. A review of global precipitation data sets: data sources, estimation, and intercomparisons. Rev. Geophys. 56 (1), 79-107. doi: 10.1002/2017rg000574.

[71] Sun, S.C., Nai, C.Y., Pan, B.X., Li, W.T., Li, L., Li, X., Foufoula-Georgiou, E., Lin, Y.L., 2026. Fusion of multi-source precipitation records via coordinate-based generative models. Nat. Commun. 17 (1), 1227. doi: 10.1038/s41467-025-67987-9.

[72] Sun, Y.J., Deng, K.F., Ren, K.J., Liu, J., Deng, C.J., Jin, Y.J., 2024. Deep learning in statistical downscaling for deriving high spatial resolution gridded meteorological data: a systematic review. ISPRS J. Photogramm. Remote Sens. 208, 14-38. doi: 10.1016/j.isprsjprs.2023.12.011.

[73] Sutanto, S.J., van der Weert, M., Blauhut, V., Van Lanen, H.A.J., 2020. Skill of large-scale seasonal drought impact forecasts. Nat. Hazards Earth Syst. Sci. 20 (6), 1595-1608. doi: 10.5194/nhess-20-1595-2020.

[74] Tang, G.Q., 2021. Characterization of the systematic and random errors in satellite precipitation using the multiplicative error model. IEEE Trans. Geosci. Remote Sens. 59 (7), 5407-5416. doi: 10.1109/TGRS.2020.3028525.

[75] Tang, G.Q., Clark, M.P., Papalexiou, S.M., Ma, Z.Q., Hong, Y., 2020. Have satellite precipitation products improved over last two decades? A comprehensive comparison of GPM IMERG with nine satellite and reanalysis datasets. Remote Sens. Environ. 240, 111697. doi: 10.1016/j.rse.2020.111697.

[76] Tellman, B., Sullivan, J.A., Kuhn, C., Kettner, A.J., Doyle, C.S., Brakenridge, G.R., Erickson, T.A., Slayback, D.A., 2021. Satellite imaging reveals increased proportion of population exposed to floods. Nature 596 (7870), 80-86. doi: 10.1038/s41586-021-03695-w.

[77] van Jaarsveld, B., Wanders, N., Sutanudjaja, E.H., Hoch, J., Droppers, B., Janzing, J., van Beek, R.L.P.H., Bierkens, M.F.P., 2025. A first attempt to model global hydrology at hyper-resolution. Earth Syst. Dynam. 16 (1), 29-54. doi: 10.5194/esd-16-29-2025.

[78] Wang, T.C., Li, Z., Ma, Z.Q., Gao, Z., Tang, G.Q., 2023. Diverging identifications of extreme precipitation events from satellite observations and reanalysis products: a global perspective based on an object-tracking method. Remote Sens. Environ. 288, 113490. doi: 10.1016/j.rse.2023.113490.

[79] Wei, L.Y., Jiang, S.H., Dong, J.Z., Ren, L.L., Liu, Y., Zhang, L.Q., Wang, M.H., Duan, Z., 2023. Fusion of gauge-based, reanalysis, and satellite precipitation products using Bayesian model averaging approach: determination of the influence of different input sources. J. Hydrol. 618, 129234. doi: 10.1016/j.jhydrol.2023.129234.

[80] Wu, H.J., Su, X.L., Huang, S.Z., Singh, V.P., Zhou, S., Tan, X.Z., Hu, X.T., 2025. Decreasing dynamic predictability of global agricultural drought with warming climate. Nat. Clim. Chang. 15, 411-419. doi: 10.1038/s41558-025-02289-y.

[81] Xia, H.M., Wang, K.C., 2024. PreciDBPN: a customized deep learning approach for hourly precipitation downscaling in eastern China. Atmos. Res. 311, 107705. doi: 10.1016/j.atmosres.2024.107705.

[82] Xu, Q.S., Bamber, J.L., Thuerey, N., Boers, N., Bates, P., Camps-Valls, G., Shi, Y.L., Zhu, X.X., 2025a. Physically consistent and uncertainty-aware learning of spatiotemporal dynamics. arXiv: 2510.21023. https://arxiv.org/abs/2510.21023.

[83] Xu, Q.S., Shi, Y.L., Bamber, J.L., Tuo, Y., Ludwig, R., Zhu, X.X., 2025b. Physics-aware machine learning revolutionizes scientific paradigm for process-based modeling in hydrology. Earth Sci. Rev. 271, 105276. doi: 10.1016/j.earscirev.2025.105276.

[84] Xu, Y., Tang, G.Q., Li, L.J., Wan, W., 2024a. Multi-source precipitation estimation using machine learning: clarification and benchmarking. J. Hydrol. 635, 131195. doi: 10.1016/j.jhydrol.2024.131195.

[85] Xu, Z.H., Sun, H., Zhang, T., Xu, H.Y., Wu, D., Gao, J.H., 2024b. The high spatial resolution drought response index (HiDRI): an integrated framework for monitoring vegetation drought with remote sensing, deep learning, and spatiotemporal fusion. Remote Sens. Environ. 312, 114324. doi: 10.1016/j.rse.2024.114324.

[86] Yin, J.Z., Meo, C., Roy, A., Bou Cher, Z., Lică, M., Wang, Y.B., Imhoff, R., Uijlenhoet, R., Dauwels, J., 2024. Precipitation nowcasting using physics informed discriminator generative models. In: 2024 32nd European Signal Processing Conference (EUSIPCO). IEEE, Lyon, France, pp. 967-971. doi: 10.23919/EUSIPCO63174.2024.10715141 August 26-30 2024.

[87] Zhou, B.T., Qian, J., 2021. Changes of weather and climate extremes in the IPCC AR6. Adv. Clim. Change Res. 17 (6), 713-718. doi: 10.12006/j.issn.1673-1719.2021.167.

[88] Zhou, S., Yu, B.F., Zhang, Y., 2023. Global concurrent climate extremes exacerbated by anthropogenic climate change. Sci. Adv. 9 (10), eabo1638. doi: 10.1126/sciadv.abo1638.