NORi: An ML-Augmented Ocean Boundary Layer Parameterization

TL;DR

NORi introduces a physics-based ML parameterization for ocean boundary layer turbulence using neural ODEs, trained on simulations to accurately capture entrainment and improve climate model stability.

Contribution

This work presents a novel ML-augmented boundary layer parameterization that combines physical principles with neural networks, demonstrating superior stability and generalization in climate simulations.

Findings

NORi accurately predicts boundary layer entrainment across various conditions.

It maintains numerical stability over 100-year simulations with long time steps.

NORi performs comparably to traditional $k$-$ extepsilon$ closures in seasonal boundary layer evolution.

Abstract

NORi is a machine learning (ML) parameterization of ocean boundary layer turbulence that is physics-based and augmented with neural networks. NORi stands for neural ordinary differential equations (NODEs) Richardson number (Ri) closure. The physical parameterization is controlled by a Richardson number-dependent diffusivity and viscosity. The neural ODEs are trained to capture the entrainment through the base of the boundary layer, which cannot be represented with a local diffusive closure. The parameterization is trained using large-eddy simulations in an "a posteriori" fashion, where parameters are calibrated with a loss function that explicitly depends on the actual time-integrated variables of interest rather than the instantaneous subgrid fluxes, which are inherently noisy. NORi conserves tracers by design, uses realistic nonlinear thermodynamics, and demonstrates excellent prediction and generalization capabilities in capturing entrainment dynamics under different convective strengths, background stratifications, rotation, and wind forcings. NORi is shown to simulate the seasonal evolution of the boundary layer at Ocean Weather Station Papa with similar performance to the state-of-the-art two-equation $k$-$\epsilon$ closure. When implemented in a double-gyre simulation, it is numerically stable for at least 100 years, despite only being trained on two-day horizons, and can be run with time steps as long as one hour. The highly expressive neural networks, combined with a physically rigorous base closure, prove to be a robust paradigm for designing parameterizations for climate models: data required and training cost are drastically reduced, inference performance can be directly optimized as a primary objective, and numerical stability is implicitly promoted through training.