NORi: An ML-Augmented Ocean Boundary Layer Parameterization

2025-12-03

AI Summary

This study addresses inaccurate and poorly generalizable entrainment representation in marine boundary layer (MBL) turbulence parameterization. We propose a physics-constrained neural ordinary differential equation (Neural ODE) framework. Methodologically, we construct a differentiable closure model controlled by the bulk Richardson number, incorporate diffusion–viscosity physical priors, employ a posterior training strategy that directly optimizes time-integrated quantities, and design a loss function sensitive to integration behavior; training data are derived from high-resolution large-eddy simulations. Our approach significantly enhances generalizability across varying convective intensities, background stratifications, Coriolis effects, and wind stresses, while ensuring long-term numerical stability. It supports hourly time steps and maintains stable integration for over 100 years in global-scale climate simulations—demonstrating robustness unattainable with conventional parameterizations. This work delivers a novel turbulence closure scheme that simultaneously satisfies physical consistency and expressive capacity for Earth system modeling.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Learning to Search

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

NORi is a machine-learned (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 NODEs 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 is designed for the realistic nonlinear equation of state of seawater and demonstrates excellent prediction and generalization capabilities in capturing entrainment dynamics under different convective strengths, oceanic background stratifications, rotation strengths, and surface wind forcings. NORi is numerically stable for at least 100 years of integration time in large-scale simulations, despite only being trained on 2-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 where data requirements are drastically reduced, inference performance can be directly targeted and optimized, and numerical stability is implicitly encouraged during training.

Problem

• Develops a machine-learned ocean turbulence parameterization using neural networks.
• Captures boundary layer entrainment dynamics not represented by local closures.
• Ensures numerical stability and generalization across varied oceanic conditions.

Innovation

• Machine-learned physics-based ocean turbulence parameterization
• Neural ODEs trained on large-eddy simulations for entrainment
• Stable long-term integration with reduced data requirements