Online Learning of Entrainment Closures in a Hybrid Machine Learning Parameterization
Abstract
This work integrates machine learning into an atmospheric parameterization to target uncertain mixing processes while maintaining interpretable, predictive, and well-established physical equations. We adopt an eddy-diffusivity mass-flux (EDMF) parameterization for the unified modeling of various convective and turbulent regimes. To avoid drift and instability that plague offline-trained machine learning parameterizations that are subsequently coupled with climate models, we frame learning as an inverse problem: Data-driven models are embedded within the EDMF parameterization and trained online in a one-dimensional vertical global climate model (GCM) column. Training is performed against output from large-eddy simulations (LES) forced with GCM-simulated large-scale conditions in the Pacific. Rather than optimizing subgrid-scale tendencies, our framework directly targets climate variables of interest, such as the vertical profiles of entropy and liquid water path. Specifically, we use ensemble Kalman inversion to simultaneously calibrate both the EDMF parameters and the parameters governing data-driven lateral mixing rates. The calibrated parameterization outperforms existing EDMF schemes, particularly in tropical and subtropical locations of the present climate, and maintains high fidelity in simulating shallow cumulus and stratocumulus regimes under increased sea surface temperatures from AMIP4K experiments. The results showcase the advantage of physically constraining data-driven models and directly targeting relevant variables through online learning to build robust and stable machine learning parameterizations.
Copyright and License
© 2024 The Author(s). Journal of Advances in Modeling Earth Systems published by Wiley Periodicals LLC on behalf of American Geophysical Union. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Acknowledgement
We thank Zhaoyi Shen, Anna Jaruga, and Haakon Ervik for significant contributions to the development of the EDMF, which is the basis of this calibration work. This research was supported by Schmidt Sciences, LLC, by the U.S. National Science Foundation (Grant number AGS-1835860), and by the Office of Naval Research (Grant number N00014-23-1-2654). Tom Beucler acknowledges partial funding from the Swiss State Secretariat for Education, Research and Innovation (SERI) for the Horizon Europe project AI4PEX (Grant agreement ID: 101137682).
Data Availability
The calibration pipeline and underlying EDMF model used for this work are available as open-source Julia packages. The EDMF single column model is TurbulenceConvection.jl v1.3.6, available at https://doi.org/10.5281/zenodo.13733436 (Kawczynski et al., 2024). The calibration pipeline for the EDMF is implemented in CalibrateEDMF.jl v0.8.1 (https://doi.org/10.5281/zenodo.13738494) (Lopez-Gomez et al., 2024), and the underlying ensemble Kalman inversion algorithms are part of EnsembleKalmanProcesses.jl v1.1.5 (https://doi.org/10.5281/zenodo.10146103) (Dunbar et al., 2023). Visualization tools for calibration results are available alongside the calibration data at https://doi.org/10.5281/zenodo.13743167 (Christopoulos, 2024). The PyCLES large-eddy simulation output used for calibration is available on CaltechDATA (Z. Shen, 2022).
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Additional details
- National Science Foundation
- AGS‐1835860
- Office of Naval Research
- N00014‐23‐1‐2654
- State Secretariat for Education, Research and Innovation
- Horizon Europe project AI4PEX 101137682
- Accepted
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2024-10-21Accepted
- Available
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2024-11-14Published online
- Available
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2024-11-14Version of Record online
- Caltech groups
- Division of Geological and Planetary Sciences
- Publication Status
- Published