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  • Perspective
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Iterative integration of deep learning in hybrid Earth surface system modelling

Abstract

Earth system modelling (ESM) is essential for understanding past, present and future Earth processes. Deep learning (DL), with the data-driven strength of neural networks, has promise for improving ESM by exploiting information from Big Data. Yet existing hybrid ESMs largely have deep neural networks incorporated only during the initial stage of model development. In this Perspective, we examine progress in hybrid ESM, focusing on the Earth surface system, and propose a framework that integrates neural networks into ESM throughout the modelling lifecycle. In this framework, DL computing systems and ESM-related knowledge repositories are set up in a homogeneous computational environment. DL can infer unknown or missing information, feeding it back into the knowledge repositories, while the ESM-related knowledge can constrain inference results of the DL. By fostering collaboration between ESM-related knowledge and DL systems, adaptive guidance plans can be generated through question-answering mechanisms and recommendation functions. As users interact iteratively, the hybrid system deepens its understanding of their preferences, resulting in increasingly customized, scalable and accurate guidance plans for modelling Earth processes. The advancement of this framework necessitates interdisciplinary collaboration, focusing on explainable DL and maintaining observational data to ensure the reliability of simulations.

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Fig. 1: Answering the grand environmental challenges through integrating Earth system modelling and deep learning.
Fig. 2: Comparison between outputs from Earth surface system models and hybrid models.
Fig. 3: Computational logics of hybrid models.
Fig. 4: A framework for iterative integration of Earth surface system modelling and deep learning.

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References

  1. Steffen, W. et al. The emergence and evolution of Earth system science. Nat. Rev. Earth Environ. 1, 54–63 (2020).

    Article  Google Scholar 

  2. Bowman, D. M. et al. Vegetation fires in the Anthropocene. Nat. Rev. Earth Environ. 1, 500–515 (2020).

    Article  Google Scholar 

  3. Zipkin, E. F. et al. Addressing data integration challenges to link ecological processes across scales. Front. Ecol. Environ. 19, 30–38 (2021).

    Article  Google Scholar 

  4. Knight, J. & Harrison, S. The impacts of climate change on terrestrial Earth surface systems. Nat. Clim. Change 3, 24–29 (2013).

    Article  Google Scholar 

  5. Chen, M. et al. Geographic modeling and simulation systems for geographic research in the new era: some thoughts on their development and construction. Sci. China Earth Sci. 64, 1207–1223 (2021).

    Article  Google Scholar 

  6. Luttge, A., Arvidson, R. S., Fischer, C. & Kurganskaya, I. Kinetic concepts for quantitative prediction of fluid-solid interactions. Chem. Geol. 504, 216–235 (2019).

    Article  Google Scholar 

  7. Pelletier, J. D. Quantitative Modeling of Earth Surface Processes (Cambridge Univ. Press, 2008).

  8. Meir, P., Cox, P. & Grace, J. The influence of terrestrial ecosystems on climate. Trends Ecol. Evol. 21, 254–260 (2006).

    Article  Google Scholar 

  9. Zhang, Z. Carbon mitigation potential afforded by rooftop photovoltaic in China. Nat. Commun. 14, 2347 (2023).

    Article  Google Scholar 

  10. Zhu, R. et al. GIScience can facilitate the development of solar cities for energy transition. Adv. Appl. Energy 10, 100129 (2023).

    Article  Google Scholar 

  11. Lee, C. A., Gasster, S. D., Plaza, A., Chang, C.-I. & Huang, B. Recent developments in high performance computing for remote sensing: a review. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 4, 508–527 (2011).

    Article  Google Scholar 

  12. Li, S. et al. Geospatial Big Data handling theory and methods: a review and research challenges. ISPRS J. Photogramm. Remote Sens. 115, 119–133 (2016).

    Article  Google Scholar 

  13. Thorp, H. H. ChatGPT is fun, but not an author. Science 379, 313 (2023).

    Article  Google Scholar 

  14. LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015).

    Article  Google Scholar 

  15. Camps-Valls, G., Tuia, D., Zhu, X. X. & Reichstein, M. Deep Learning for the Earth Sciences: A Comprehensive Approach to Remote Sensing, Climate Science and Geosciences (Wiley, 2021).

  16. Chen, M. et al. Artificial intelligence and visual analytics in geographical space and cyberspace: research opportunities and challenges. Earth Sci. Rev. 241, 104438 (2023).

    Article  Google Scholar 

  17. Goldstein, E. B., Coco, G. & Plant, N. G. A review of machine learning applications to coastal sediment transport and morphodynamics. Earth Sci. Rev. 194, 97–108 (2019).

    Article  Google Scholar 

  18. Qian, Z. et al. Deep Roof Refiner: a detail-oriented deep learning network for refined delineation of roof structure lines using satellite imagery. Int. J. Appl. Earth Obs. Geoinf. 107, 102680 (2022).

    Google Scholar 

  19. Li, W. & Hsu, C.-Y. GeoAI for large-scale image analysis and machine vision: recent progress of artificial intelligence in geography. ISPRS Int. J. Geoinf. 11, 385 (2022).

    Article  Google Scholar 

  20. Reichstein, M. et al. Deep learning and process understanding for data-driven Earth system science. Nature 566, 195–204 (2019).

    Article  Google Scholar 

  21. Bergen, K. J., Johnson, P. A., de Hoop, M. V. & Beroza, G. C. Machine learning for data-driven discovery in solid Earth geoscience. Science 363, eaau0323 (2019).

    Article  Google Scholar 

  22. Sutton, R. The bitter lesson. Incomplete Ideas (13 March 2019); http://www.incompleteideas.net/IncIdeas/BitterLesson.html.

  23. Zhang, Q., Yang, L. T., Chen, Z. & Li, P. A survey on deep learning for Big Data. Inf. Fusion. 42, 146–157 (2018).

    Article  Google Scholar 

  24. Razavi, S. et al. Coevolution of machine learning and process-based modelling to revolutionize Earth and environmental sciences: a perspective. Hydrol. Process. 36, e14596 (2022).

    Article  Google Scholar 

  25. Bolton, T. & Zanna, L. Applications of deep learning to ocean data inference and subgrid parameterization. J. Adv. Model. Earth Syst. 11, 376–399 (2019).

    Article  Google Scholar 

  26. Sillmann, J. et al. Understanding, modeling and predicting weather and climate extremes: challenges and opportunities. Weather Clim. Extremes 18, 65–74 (2017).

    Article  Google Scholar 

  27. Kadow, C., Hall, D. M. & Ulbrich, U. Artificial intelligence reconstructs missing climate information. Nat. Geosci. 13, 408–413 (2020).

    Article  Google Scholar 

  28. Razavi, S. Deep learning, explained: fundamentals, explainability, and bridgeability to process-based modelling. Environ. Model. Softw. 144, 105159 (2021).

    Article  Google Scholar 

  29. Murray, A. B. et al. Geomorphology, complexity, and the emerging science of the Earth’s surface. Geomorphology 103, 496–505 (2009).

    Article  Google Scholar 

  30. Phillips, J. D. Amplifiers, filters and geomorphic responses to climate change in Kentucky rivers. Clim. Change 103, 571–595 (2010).

    Article  Google Scholar 

  31. Fisher, R. A. et al. Vegetation demographics in Earth system models: a review of progress and priorities. Glob. Change Biol. 24, 35–54 (2018).

    Article  Google Scholar 

  32. Jakeman, A. J., Letcher, R. A. & Norton, J. P. Ten iterative steps in development and evaluation of environmental models. Environ. Model. Softw. 21, 602–614 (2006).

    Article  Google Scholar 

  33. Ma, Z. et al. Activity-based process construction for participatory geo-analysis. GISci. Remote Sens. 58, 180–198 (2021).

    Article  Google Scholar 

  34. Hamilton, S. H., Pollino, C. A., Stratford, D. S., Fu, B. & Jakeman, A. J. Fit-for-purpose environmental modeling: targeting the intersection of usability, reliability and feasibility. Environ. Model. Softw. 148, 105278 (2022).

    Article  Google Scholar 

  35. Chen, M. et al. Position paper: open web-distributed integrated geographic modelling and simulation to enable broader participation and applications. Earth Sci. Rev. 207, 103223 (2020).

    Article  Google Scholar 

  36. Werner, B. T. Complexity in natural landform patterns. Science 284, 102–104 (1999).

    Article  Google Scholar 

  37. Anderson, P. W. More is different: broken symmetry and the nature of the hierarchical structure of science. Science 177, 393–396 (1972).

    Article  Google Scholar 

  38. Werner, B. T. & McNamara, D. E. Dynamics of coupled human–landscape systems. Geomorphology 91, 393–407 (2007).

    Article  Google Scholar 

  39. Klir, G. J. & Simon, H. A. The Architecture of Complexity (Springer, 1991).

  40. Heymann, M. & Dahan Dalmedico, A. Epistemology and politics in Earth system modeling: historical perspectives. J. Adv. Model. Earth Syst. 11, 1139–1152 (2019).

    Article  Google Scholar 

  41. Shen, C. & Phanikumar, M. S. A process-based, distributed hydrologic model based on a large-scale method for surface–subsurface coupling. Adv. Water Resour. 33, 1524–1541 (2010).

    Article  Google Scholar 

  42. Robinson, D. T. et al. Modelling feedbacks between human and natural processes in the land system. Earth Syst. Dynam. 9, 895–914 (2018).

    Article  Google Scholar 

  43. Lü, G. et al. Geographic scenario: a possible foundation for further development of virtual geographic environments. Int. J. Digit. Earth 11, 356–368 (2018).

    Article  Google Scholar 

  44. Haarsma, R. J. et al. High resolution model intercomparison project (HighResMIP v1. 0) for CMIP6. Geosci. Model. Dev. 9, 4185–4208 (2016).

    Article  Google Scholar 

  45. Worley, P. H. et al. Performance of the Community Earth System Model. In Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis 1–11 (IEEE, 2011).

  46. Salcedo-Sanz, S. et al. Machine learning information fusion in Earth observation: a comprehensive review of methods, applications and data sources. Inf. Fusion. 63, 256–272 (2020).

    Article  Google Scholar 

  47. Lee, J.-G. & Kang, M. Geospatial Big Data: challenges and opportunities. Big Data Res. 2, 74–81 (2015).

    Article  Google Scholar 

  48. Ansari, S. et al. Unlocking the potential of NEXRAD data through NOAA’s Big Data partnership. Bull. Am. Meteorol. Soc. 99, 189–204 (2018).

    Article  Google Scholar 

  49. Ge, Y. et al. Progress of big geodata. Sci. Bull. 67, 1739–1742 (2022).

    Article  Google Scholar 

  50. Oussous, A., Benjelloun, F.-Z., Lahcen, A. A. & Belfkih, S. Big Data technologies: A survey. J. King Saud Univ. Comput Inf. Sci. 30, 431–448 (2018).

    Google Scholar 

  51. Karpatne, A. et al. Theory-guided data science: a new paradigm for scientific discovery from data. IEEE Trans. Knowl. Data Eng. 29, 2318–2331 (2017).

    Article  Google Scholar 

  52. Qian, Z. et al. Vectorized dataset of roadside noise barriers in China using street view imagery. Earth Syst. Sci. Data 14, 4057–4076 (2022).

    Article  Google Scholar 

  53. Clark, M. P., Kavetski, D. & Fenicia, F. Pursuing the method of multiple working hypotheses for hydrological modeling. Water Resour. Res. 47, WR009827 (2011).

    Article  Google Scholar 

  54. Beven, K. & Freer, J. Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology. J. Hydrol. 249, 11–29 (2001).

    Article  Google Scholar 

  55. Gentine, P., Pritchard, M., Rasp, S., Reinaudi, G. & Yacalis, G. Could machine learning break the convection parameterization deadlock? Geophys. Res. Lett. 45, 5742–5751 (2018).

    Article  Google Scholar 

  56. Tang, Y., Reed, P., Wagener, T. & Van Werkhoven, K. Comparing sensitivity analysis methods to advance lumped watershed model identification and evaluation. Hydrol. Earth Syst. Sci. 11, 793–817 (2007).

    Article  Google Scholar 

  57. Di Baldassarre, G., Schumann, G. & Bates, P. Near real time satellite imagery to support and verify timely flood modelling. Hydrol. Process. 23, 799–803 (2009).

    Article  Google Scholar 

  58. Kucera, P. A. et al. Precipitation from space: advancing Earth system science. Bull. Am. Meteor. Soc. 94, 365–375 (2013).

    Article  Google Scholar 

  59. See, S. & Adie, J. Challenges and opportunities for a hybrid modelling approach to Earth system science. CCF Trans. HPC 3, 320–329 (2021).

    Article  Google Scholar 

  60. Zhang, K. et al. Quantifying the photovoltaic potential of highways in China. Appl. Energy 324, 119600 (2022).

    Article  Google Scholar 

  61. Fuhrer, O. et al. Near-global climate simulation at 1 km resolution: establishing a performance baseline on 4888 GPUs with COSMO 5.0. Geosci. Model. Dev. 11, 1665–1681 (2018).

    Article  Google Scholar 

  62. Kratzert, F., Klotz, D., Brenner, C., Schulz, K. & Herrnegger, M. Rainfall–runoff modelling using long short-term memory (LSTM) networks. Hydrol. Earth Syst. Sci. 22, 6005–6022 (2018).

    Article  Google Scholar 

  63. Wei, X., Zhang, L., Yang, H.-Q., Zhang, L. & Yao, Y.-P. Machine learning for pore-water pressure time-series prediction: application of recurrent neural networks. Geosci. Front. 12, 453–467 (2021).

    Article  Google Scholar 

  64. Bihlo, A. A generative adversarial network approach to (ensemble) weather prediction. Neural Netw. 139, 1–16 (2021).

    Article  Google Scholar 

  65. Peng, X., Li, Q. & Jing, J. CNGAT: A graph neural network model for radar quantitative precipitation estimation. IEEE Trans. Geosci. Remote Sens. 60, 1–14 (2021).

    Google Scholar 

  66. Zhou, L. & Zhang, R.-H. A self-attention–based neural network for three-dimensional multivariate modeling and its skillful ENSO predictions. Sci. Adv. 9, eadf2827 (2023).

    Article  Google Scholar 

  67. Mousavi, S. M., Ellsworth, W. L., Zhu, W., Chuang, L. Y. & Beroza, G. C. Earthquake transformer — an attentive deep-learning model for simultaneous earthquake detection and phase picking. Nat. Commun. 11, 3952 (2020).

    Article  Google Scholar 

  68. Montavon, G., Samek, W. & Müller, K.-R. Methods for interpreting and understanding deep neural networks. Digital Signal. Process. 73, 1–15 (2018).

    Article  Google Scholar 

  69. Gómez-Chova, L., Tuia, D., Moser, G. & Camps-Valls, G. Multimodal classification of remote sensing images: a review and future directions. Proc. IEEE 103, 1560–1584 (2015).

    Article  Google Scholar 

  70. Dalla Mura, M. et al. Challenges and opportunities of multimodality and data fusion in remote sensing. Proc. IEEE 103, 1585–1601 (2015).

    Article  Google Scholar 

  71. Zhu, R. et al. Deep solar PV refiner: a detail-oriented deep learning network for refined segmentation of photovoltaic areas from satellite imagery. Int. J. Appl. Earth Obs. Geoinf. 116, 103134 (2023).

    Google Scholar 

  72. Hong, D. et al. More diverse means better: multimodal deep learning meets remote-sensing imagery classification. IEEE Trans. Geosci. Remote Sens. 59, 4340–4354 (2020).

    Article  Google Scholar 

  73. Fan, R. et al. Fine-scale urban informal settlements mapping by fusing remote sensing images and building data via a transformer-based multimodal fusion network. IEEE Trans. Geosci. Remote Sens. 60, 1–16 (2022).

    Google Scholar 

  74. Ives, A. R. et al. Statistical inference for trends in spatiotemporal data. Remote Sens. Environ. 266, 112678 (2021).

    Article  Google Scholar 

  75. Li, X., Zhang, C. & Li, W. Building block level urban land-use information retrieval based on Google Street View images. GISci. Remote Sens. 54, 819–835 (2017).

    Article  Google Scholar 

  76. Zhang, K. et al. Using street view images to identify road noise barriers with ensemble classification model and geospatial analysis. Sustain. Cities Soc. 78, 103598 (2022).

    Article  Google Scholar 

  77. Zhong, T. et al. Assessment of solar photovoltaic potentials on urban noise barriers using street-view imagery. Renew. Energy 168, 181–194 (2021).

    Article  Google Scholar 

  78. Bousmalis, K., Silberman, N., Dohan, D., Erhan, D. & Krishnan, D. Unsupervised pixel-level domain adaptation with generative adversarial networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition 3722–3731 (IEEE, 2017).

  79. Hess, P., Drüke, M., Petri, S., Strnad, F. M. & Boers, N. Physically constrained generative adversarial networks for improving precipitation fields from Earth system models. Nat. Mach. Intell. 4, 828–839 (2022).

    Article  Google Scholar 

  80. He, X., Chen, Y. & Ghamisi, P. Heterogeneous transfer learning for hyperspectral image classification based on convolutional neural network. IEEE Trans. Geosci. Remote Sens. 58, 3246–3263 (2019).

    Article  Google Scholar 

  81. Raissi, M., Perdikaris, P. & Karniadakis, G. E. 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 (2019).

    Article  Google Scholar 

  82. Shi, X. et al. Deep learning for precipitation nowcasting: a benchmark and a new model. Adv. Neural. Inf. Process. Syst. 30, 5617–5627 (2017).

    Google Scholar 

  83. Stevens, B. & Bony, S. What are climate models missing? Science 340, 1053–1054 (2013).

    Article  Google Scholar 

  84. Gao, Z. et al. in Deep Learning for the Earth Sciences: A Comprehensive Approach to Remote Sensing, Climate Science, and Geosciences 218–239 (Wiley, 2021).

  85. Lobry, S., Marcos, D., Murray, J. & Tuia, D. RSVQA: visual question answering for remote sensing data. IEEE Trans. Geosci. Remote Sens. 58, 8555–8566 (2020).

    Article  Google Scholar 

  86. Chai, S., Xu, Z., Jia, Y. & Wong, W. K. A robust spatiotemporal forecasting framework for photovoltaic generation. IEEE Trans. Smart Grid 11, 5370–5382 (2020).

    Article  Google Scholar 

  87. Boers, N. et al. Complex networks reveal global pattern of extreme-rainfall teleconnections. Nature 566, 373–377 (2019).

    Article  Google Scholar 

  88. Sambasivan, N. et al. ‘Everyone wants to do the model work, not the data work’: data cascades in high-stakes AI. In Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems 1–15 (ACM, 2021).

  89. Zhang, Z. et al. Vectorized rooftop area data for 90 cities in China. Sci. Data 9, 66 (2022).

    Article  Google Scholar 

  90. Goldstein, E. B. et al. Labeling poststorm coastal imagery for machine learning: measurement of interrater agreement. Earth Space Sci. 8, e2021EA001896 (2021).

    Article  Google Scholar 

  91. Geiger, R. S. et al. ‘Garbage In, Garbage Out’ revisited: what do machine learning application papers report about human-labeled training data? Quant. Sci. Stud. 2, 795–827 (2021).

    Article  Google Scholar 

  92. Samsi, S., Mattioli, C. J. & Veillette, M. S. Distributed deep learning for precipitation nowcasting. In 2019 IEEE High Performance Extreme Computing Conference (HPEC) 1–7 (IEEE, 2019).

  93. Rasp, S., Pritchard, M. S. & Gentine, P. Deep learning to represent subgrid processes in climate models. Proc. Natl Acad. Sci. USA 115, 9684–9689 (2018).

    Article  Google Scholar 

  94. Flato, G. M. Earth system models: an overview. WIREs Clim. Change 2, 783–800 (2011).

    Article  Google Scholar 

  95. Brandt, M. et al. An unexpectedly large count of trees in the West African Sahara and Sahel. Nature 587, 78–82 (2020).

    Article  Google Scholar 

  96. Tung, F. & Mori, G. Deep neural network compression by in-parallel pruning-quantization. IEEE Trans. pattern Anal. Mach. Intell. 42, 568–579 (2018).

    Article  Google Scholar 

  97. Jouppi, N. P., Young, C., Patil, N. & Patterson, D. A domain-specific architecture for deep neural networks. Commun. ACM 61, 50–59 (2018).

    Article  Google Scholar 

  98. Shen, H. & Zhang, L. Mechanism-learning coupling paradigms for parameter inversion and simulation in Earth surface systems. Sci. China Earth Sci https://doi.org/10.1007/s11430-022-9999-9 (2023).

    Article  Google Scholar 

  99. Hunter, J. M. et al. Framework for developing hybrid process-driven, artificial neural network and regression models for salinity prediction in river systems. Hydrol. Earth Syst. Sci. 22, 2987–3006 (2018).

    Article  Google Scholar 

  100. Koppa, A., Rains, D., Hulsman, P., Poyatos, R. & Miralles, D. G. A deep learning-based hybrid model of global terrestrial evaporation. Nat. Commun. 13, 1912 (2022).

    Article  Google Scholar 

  101. Lv, X. et al. BTS: a binary tree sampling strategy for object identification based on deep learning. Int. J. Geogr. Inf. Sci. 36, 822–848 (2022).

    Article  Google Scholar 

  102. Sun, Z. et al. Improving the performance of automated rooftop extraction through geospatial stratified and optimized sampling. Remote Sens. 14, 4961 (2022).

    Article  Google Scholar 

  103. Vandal, T. et al. Deepsd: generating high resolution climate change projections through single image super-resolution. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 1663–1672 (ACM, 2017).

  104. Lanaras, C., Bioucas-Dias, J., Galliani, S., Baltsavias, E. & Schindler, K. Super-resolution of Sentinel-2 images: learning a globally applicable deep neural network. ISPRS J. Photogramm. Remote Sens. 146, 305–319 (2018).

    Article  Google Scholar 

  105. Schneider, T., Lan, S., Stuart, A. & Teixeira, J. Earth System Modeling 2.0: a blueprint for models that learn from observations and targeted high-resolution simulations. Geophys. Res. Lett. 44, 12–396 (2017).

    Article  Google Scholar 

  106. Eslami, E., Choi, Y., Lops, Y., Sayeed, A. & Salman, A. K. Using wavelet transform and dynamic time warping to identify the limitations of the CNN model as an air quality forecasting system. Geosci. Model. Dev. 13, 6237–6251 (2020).

    Article  Google Scholar 

  107. Han, J., Jentzen, A. & E, W. Solving high-dimensional partial differential equations using deep learning. Proc. Natl Acad. Sci. 115, 8505–8510 (2018).

    Article  Google Scholar 

  108. Gagne, D. J., Christensen, H. M., Subramanian, A. C. & Monahan, A. H. Machine learning for stochastic parameterization: generative adversarial networks in the Lorenz’96 model. J. Adv. Model. Earth Syst. 12, e2019MS001896 (2020).

    Article  Google Scholar 

  109. Jia, X. et al. Physics-guided machine learning for scientific discovery: an application in simulating lake temperature profiles. ACM/IMS Trans. Data Sci. 2, 1–26 (2021).

    Article  Google Scholar 

  110. Zhu, X. et al. Comparison of two optimized machine learning models for predicting displacement of rainfall-induced landslide: a case study in Sichuan Province, China. Eng. Geol. 218, 213–222 (2017).

    Article  Google Scholar 

  111. Rasp, S. Coupled online learning as a way to tackle instabilities and biases in neural network parameterizations: general algorithms and Lorenz 96 case study (v1. 0). Geosci. Model. Dev. 13, 2185–2196 (2020).

    Article  Google Scholar 

  112. Yang, Z. et al. Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions. J. Thorac. Dis. 12, 165 (2020).

    Article  Google Scholar 

  113. Qian, Z., Liu, X., Tao, F. & Zhou, T. Identification of urban functional areas by coupling satellite images and taxi GPS trajectories. Remote Sens. 12, 2449 (2020).

    Article  Google Scholar 

  114. Amini, A., Dolatshahi, M. & Kerachian, R. Adaptive precipitation nowcasting using deep learning and ensemble modeling. J. Hydrol. 612, 128197 (2022).

    Article  Google Scholar 

  115. Li, G. & Choi, Y. HPC cluster-based user-defined data integration platform for deep learning in geoscience applications. Comput. Geosci. 155, 104868 (2021).

    Article  Google Scholar 

  116. Sun, A. Y. & Scanlon, B. R. How can Big Data and machine learning benefit environment and water management: a survey of methods, applications, and future directions. Environ. Res. Lett. 14, 073001 (2019).

    Article  Google Scholar 

  117. Venkatakrishnan, S. V., Bouman, C. A. & Wohlberg, B. Plug-and-play priors for model based reconstruction. In 2013 IEEE Global Conference on Signal and Information Processing 945–948 (IEEE, 2013).

  118. Shen, H. et al. Coupling model- and data-driven methods for remote sensing image restoration and fusion: improving physical interpretability. IEEE Geosci. Remote Sens. Mag. 10, 231–249 (2022).

    Article  Google Scholar 

  119. Goldstein, E. B. & Coco, G. Machine learning components in deterministic models: hybrid synergy in the age of data. Front. Environ. Sci. 3, 00033 (2015).

    Article  Google Scholar 

  120. Gelbrecht, M., Boers, N. & Kurths, J. Neural partial differential equations for chaotic systems. New J. Phys. 23, 043005 (2021).

    Article  Google Scholar 

  121. Mahjoubi, S., Barhemat, R., Guo, P., Meng, W. & Bao, Y. Prediction and multi-objective optimization of mechanical, economical, and environmental properties for strain-hardening cementitious composites (SHCC) based on automated machine learning and metaheuristic algorithms. J. Clean. Prod. 329, 129665 (2021).

    Article  Google Scholar 

  122. Goldstein, E. B., Coco, G., Murray, A. B. & Green, M. O. Data-driven components in a model of inner-shelf sorted bedforms: a new hybrid model. Earth Surf. Dynam. 2, 67–82 (2014).

    Article  Google Scholar 

  123. Bar-Sinai, Y., Hoyer, S., Hickey, J. & Brenner, M. P. Learning data-driven discretizations for partial differential equations. Proc. Natl Acad. Sci. USA 116, 15344–15349 (2019).

    Article  Google Scholar 

  124. Kraft, B., Jung, M., Körner, M., Koirala, S. & Reichstein, M. Towards hybrid modeling of the global hydrological cycle. Hydrol. Earth Syst. Sci. 26, 1579–1614 (2022).

    Article  Google Scholar 

  125. Zubov, K. et al. NeuralPDE: automating physics-informed neural networks (PINNs) with error approximations. https://doi.org/10.48550/arXiv.2107.09443 (2021).

  126. Chen, T. Q., Rubanova, Y., Bettencourt, J. & Duvenaud, D. K. Neural ordinary differential equations. Adv. Neural Inf. Process. Syst. 31, 6571–6583 (2018).

  127. Hagenauer, J. & Helbich, M. A geographically weighted artificial neural network. Int. J. Geogr. Inf. Sci. 36, 215–235 (2022).

    Article  Google Scholar 

  128. Li, H. & Weng, Y. Physical equation discovery using physics-consistent neural network (PCNN) under incomplete observability. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining 925–933 (ACM, 2021).

  129. Ma, Z. et al. Customizable process design for collaborative geographic analysis. GISci. Remote Sens. 59, 914–935 (2022).

    Article  Google Scholar 

  130. Zhang, W. et al. Application of machine learning, deep learning and optimization algorithms in geoengineering and geoscience: comprehensive review and future challenge. Gondwana Res. 109, 1–17 (2022).

    Article  Google Scholar 

  131. Massonnet, F. et al. Replicability of the EC-Earth3 Earth system model under a change in computing environment. Geosci. Model. Dev. 13, 1165–1178 (2020).

    Article  Google Scholar 

  132. Warnat-Herresthal, S. et al. Swarm learning for decentralized and confidential clinical machine learning. Nature 594, 265–270 (2021).

    Article  Google Scholar 

  133. Rackauckas, C. & Nie, Q. Differentialequations.jl — a performant and feature-rich ecosystem for solving differential equations in Julia. J. Open Res. Softw. 5, 151 (2017).

    Article  Google Scholar 

  134. Stokel-Walker, C. AI bot ChatGPT writes smart essays — should academics worry? Nature https://doi.org/10.1038/d41586-022-04397-7 (2022).

    Article  Google Scholar 

  135. Diffenbaugh, N. S. et al. The COVID-19 lockdowns: a window into the Earth System. Nat. Rev. Earth Environ. 1, 470–481 (2020).

    Article  Google Scholar 

  136. Zhu, R. et al. The effects of different travel modes and travel destinations on COVID-19 transmission in global cities. Sci. Bull. 67, 588–592 (2022).

    Article  Google Scholar 

  137. Wen, W., Yang, S., Zhou, P. & Gao, S. Impacts of COVID-19 on the electric vehicle industry: evidence from China. Renew. Sustain. Energy Rev. 144, 111024 (2021).

    Article  Google Scholar 

  138. Hoang, A. T. et al. Impacts of COVID-19 pandemic on the global energy system and the shift progress to renewable energy: opportunities, challenges, and policy implications. Energy Policy 154, 112322 (2021).

    Article  Google Scholar 

  139. Wu, X., Nethery, R. C., Sabath, M. B., Braun, D. & Dominici, F. Air pollution and COVID-19 mortality in the United States: strengths and limitations of an ecological regression analysis. Sci. Adv. 6, eabd4049 (2020).

    Article  Google Scholar 

  140. Wilkinson, M. D. et al. The FAIR guiding principles for scientific data management and stewardship. Sci. Data 3, 1–9 (2016).

    Article  Google Scholar 

  141. Barton, C. M. et al. How to make models more useful. Proc. Natl Acad. Sci. USA 119, e2202112119 (2022).

    Article  Google Scholar 

  142. Chen, M. et al. Teamwork-oriented integrated modeling method for geo-problem solving. Environ. Model. Softw. 119, 111–123 (2019).

    Article  Google Scholar 

  143. Tucker, G. E. et al. CSDMS: a community platform for numerical modeling of Earth surface processes. Geosci. Model. Dev. 15, 1413–1439 (2022).

    Article  Google Scholar 

  144. Rollins, N. D., Barton, C. M., Bergin, S., Janssen, M. A. & Lee, A. A computational model library for publishing model documentation and code. Environ. Model. Softw. 61, 59–64 (2014).

    Article  Google Scholar 

  145. Janssen, M. A., Pritchard, C. & Lee, A. On code sharing and model documentation of published individual and agent-based models. Environ. Model. Softw. 134, 104873 (2020).

    Article  Google Scholar 

  146. Samek, W., Montavon, G., Lapuschkin, S., Anders, C. J. & Müller, K.-R. Explaining deep neural networks and beyond: a review of methods and applications. Proc. IEEE 109, 247–278 (2021).

    Article  Google Scholar 

  147. Irrgang, C. et al. Towards neural Earth system modelling by integrating artificial intelligence in Earth system science. Nat. Mach. Intell. 3, 667–674 (2021).

    Article  Google Scholar 

  148. Trapp, R. J. et al. Changes in severe thunderstorm environment frequency during the 21st century caused by anthropogenically enhanced global radiative forcing. Proc. Natl Acad. Sci. USA 104, 19719–19723 (2007).

    Article  Google Scholar 

  149. Ma, Z. & Mei, G. Deep learning for geological hazards analysis: data, models, applications, and opportunities. Earth Sci. Rev. 223, 103858 (2021).

    Article  Google Scholar 

  150. Diffenbaugh, N. S. & Field, C. B. Changes in ecologically critical terrestrial climate conditions. Science 341, 486–492 (2013).

    Article  Google Scholar 

  151. Syvitski, J. P., Vörösmarty, C. J., Kettner, A. J. & Green, P. Impact of humans on the flux of terrestrial sediment to the global coastal ocean. Science 308, 376–380 (2005).

    Article  Google Scholar 

  152. Goswami, B. et al. Abrupt transitions in time series with uncertainties. Nat. Commun. 9, 48 (2018).

    Article  Google Scholar 

  153. Zhu, Z. et al. Documentation strategy for facilitating the reproducibility of geo-simulation experiments. Environ. Model. Softw. 163, 105687 (2023).

    Article  Google Scholar 

  154. Burnash, R. in Computer Models of Watershed Hydrology (ed. Singh, V.) 311–366 (Water Resources Publication, 1995).

  155. Tikhamarine, Y. et al. Rainfall-runoff modelling using improved machine learning methods: Harris hawks optimizer vs. particle swarm optimization. J. Hydrol. 589, 125133 (2020).

    Article  Google Scholar 

  156. Harbaugh, A. W. MODFLOW-2005, the US Geological Survey Modular Ground-water Model: The Ground-water Flow Process Vol. 6 (US Department of the Interior, US Geological Survey Reston, 2005).

  157. Ali, A. S. A., Ebrahimi, S., Ashiq, M. M., Alasta, M. S. & Azari, B. CNN-Bi LSTM neural network for simulating groundwater level. Environ. Eng. 8, 1–7 (2022).

    Google Scholar 

  158. Laflen, J. M., Lane, L. J. & Foster, G. R. WEPP: a new generation of erosion prediction technology. J. Soil Water Conserv. 46, 34–38 (1991).

    Google Scholar 

  159. Senanayake, S. & Pradhan, B. Predicting soil erosion susceptibility associated with climate change scenarios in the Central Highlands of Sri Lanka. J. Environ. Manag. 308, 114589 (2022).

    Article  Google Scholar 

  160. Ferro, V. & Porto, P. Sediment delivery distributed (SEDD) model. J. Hydrol. Eng. 5, 411–422 (2000).

    Article  Google Scholar 

  161. Buscombe, D. SediNet: a configurable deep learning model for mixed qualitative and quantitative optical granulometry. Earth Surf. Process. Landf. 45, 638–651 (2020).

    Article  Google Scholar 

  162. Turner, D. B. Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling (CRC, 2020).

  163. Zhang, Q., Fu, F. & Tian, R. A deep learning and image-based model for air quality estimation. Sci. Total Environ. 724, 138178 (2020).

    Article  Google Scholar 

  164. Skamarock, W. C. et al. A Description of the Advanced Research WRF Version 2 (National Center for Atmospheric Research, Mesoscale and Microscale Meteorology Division, 2005).

  165. Sato, H., Itoh, A. & Kohyama, T. SEIB–DGVM: a new dynamic global vegetation model using a spatially explicit individual-based approach. Ecol. Model. 200, 279–307 (2007).

    Article  Google Scholar 

  166. Jung, M. et al. The FLUXCOM ensemble of global land–atmosphere energy fluxes. Sci. Data 6, 74 (2019).

    Article  Google Scholar 

  167. Mondal, B. et al. Urban expansion and wetland shrinkage estimation using a GIS-based model in the East Kolkata wetland, India. Ecol. Indic. 83, 62–73 (2017).

    Article  Google Scholar 

  168. Wang, X. et al. Estimation of soil salt content (SSC) in the Ebinur Lake Wetland National Nature Reserve (ELWNNR), northwest China, based on a Bootstrap-BP neural network model and optimal spectral indices. Sci. Total Environ. 615, 918–930 (2018).

    Article  Google Scholar 

  169. Bailey, N. T. et al. The Mathematical Theory of Infectious Diseases and Its Applications (Griffin, 1975).

  170. Karemera, D., Oguledo, V. I. & Davis, B. A gravity model analysis of international migration to North America. Appl. Econ. 32, 1745–1755 (2000).

    Article  Google Scholar 

  171. Simini, F., Barlacchi, G., Luca, M. & Pappalardo, L. A deep gravity model for mobility flows generation. Nat. Commun. 12, 6576 (2021).

    Article  Google Scholar 

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Acknowledgements

The authors thank M. Reichstein for his comments on the manuscript. M.C. acknowledges funding from the National Key R&D Program of China under no. 2022YFF0711604. G.L. acknowledges funding by the National Natural Science Foundation of China under grant no. 41930648. Z.Y.M acknowledges funding from Key Scientific and Technological Project of the Ministry of Water Resources. P.R.C under no. SKS-2022001. N.B. acknowledges funding by the Volkswagen foundation, by the European Union’s Horizon 2020 research and innovation program under grant agreement no. 820970 and under the Marie Sklodowska-Curie grant agreement no. 956170, as well as by the German Federal Ministry of Education and Research under grant no. 01LS2001A.

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M.C. and Z.Q. initiated the writing and co-led the design and writing of the article. G.L. conceptualized and supervised this article. All co-authors provided input on the manuscript text, figures and discussion of scientific content.

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Correspondence to Min Chen or Guonian Lü.

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Community Surface Dynamics Modeling System (CSDMS): https://csdms.colorado.edu/

Open Geographic Modeling and Simulation (OpenGMS): https://geomodeling.njnu.edu.cn/

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Chen, M., Qian, Z., Boers, N. et al. Iterative integration of deep learning in hybrid Earth surface system modelling. Nat Rev Earth Environ 4, 568–581 (2023). https://doi.org/10.1038/s43017-023-00452-7

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