Adjoint-based online learning of two-layer quasi-geostrophic baroclinic turbulence

TL;DR

This paper introduces online adjoint-based machine learning methods for modeling oceanic baroclinic turbulence, improving the accuracy and stability of parameterizations in Earth System Models by incorporating fluid dynamics during training.

Contribution

It develops and compares two online learning approaches, including an adjoint-based method and an approximation, for better turbulence parameterization in ocean models.

Findings

Online methods outperform offline in skill and stability.

Adjoint-based approach effectively incorporates fluid dynamics.

Guidelines provided for training setup and loss function design.

Abstract

For reasons of computational constraint, most global ocean circulation models used for Earth System Modeling still rely on parameterizations of sub-grid processes, and limitations in these parameterizations affect the modeled ocean circulation and impact on predictive skill. An increasingly popular approach is to leverage machine learning approaches for parameterizations, regressing for a map between the resolved state and missing feedbacks in a fluid system as a supervised learning task. However, the learning is often performed in an `offline' fashion, without involving the underlying fluid dynamical model during the training stage. Here, we explore the `online' approach that involves the fluid dynamical model during the training stage for the learning of baroclinic turbulence and its parameterization, with reference to ocean eddy parameterization. Two online approaches are considered: a full adjoint-based online approach, related to traditional adjoint optimization approaches that require a `differentiable' dynamical model, and an approximately online approach that approximates the adjoint calculation and does not require a differentiable dynamical model. The online approaches are found to be generally more skillful and numerically stable than offline approaches. Others details relating to online training, such as window size, machine learning model set up and designs of the loss functions are detailed to aid in further explorations of the online training methodology for Earth System Modeling.