Online Learning of Entrainment Closures in a Hybrid Machine Learning Parameterization

• Published in: Journal of advances in modeling earth systems 2024-11, Vol.16 (11), p.n/a
• Main Authors: Christopoulos, Costa, Lopez‐Gomez, Ignacio, Beucler, Tom, Cohen, Yair, Kawczynski, Charles, Dunbar, Oliver R. A., Schneider, Tapio
• Format: Article
• Language: English
• Subjects: Boundary conditions; Climate; Climate change; Climate models; Cumulus clouds; Distance learning; Entrainment; General circulation models; Global climate; Humidity; Machine learning; Mixing; Mixing processes; Neural networks; Online instruction; Parameter estimation; Parameterization; Parameters; Partial differential equations; Phase transitions; Sea surface temperature; Simulation; Stratocumulus clouds; Subtropical climates; Surface temperature; Variables; Vertical profiles
• ISSN: 1942-2466; 1942-2466
• DOI: 10.1029/2024MS004485

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. Plain Language Summary In this research, we aim to improve projections of the Earth's climate response by creating a hybrid model that integrates machine learning (ML) into parts of an existing atmospheric model that are less certain. This integration improves our hybrid model's performance, particularly in tropical and subtropical oceanic regions. Unlike previous approaches that first trained the ML and then ran the host model with ML embedded, we train the ML while the host model is running in a single column, which makes the model more stable and reliable. Indeed, when tested under conditions with higher sea surface temperatures, our model accurately predicts outcomes even in scenarios that were not encountered during the ML training. Our study highlights the value of combining ML and traditional atmospheric models for more robust and data‐dri