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 using 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.