NORi: An ML-Augmented Ocean Boundary Layer Parameterization

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. Combining highly expressive neural networks with a physically grounded base closure proves 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.

59 pages, 20 figures, submitted to Journal of Advances in Modeling Earth Systems (JAMES). This is version 3, updated based on reviews from 3 anonymous reviewers after initial submission to JAMES

References in corpus (13)

• FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators
• GraphCast: Learning skillful medium-range global weather forecasting
• Stiff Neural Ordinary Differential Equations
• The KPP boundary layer scheme: revisiting its formulation and benchmarking one-dimensional ocean simulations relative to LES
• Universal Differential Equations for Scientific Machine Learning
• Data-driven subgrid-scale modeling of forced Burgers turbulence using deep learning with generalization to higher Reynolds numbers via transfer learning
• A posteriori learning for quasi-geostrophic turbulence parametrization
• Parameterizing Vertical Mixing Coefficients in the Ocean Surface Boundary Layer using Neural Networks
• Learned Coarse Models for Efficient Turbulence Simulation
• Challenges of learning multi-scale dynamics with AI weather models: Implications for stability and one solution
• High-level, high-resolution ocean modeling at all scales with Oceananigans
• The Ensemble Kalman Inversion Race
• A Framework for Hybrid Physics-AI Coupled Ocean Models