F. E. Yan

F. E. Yan, J. Mak, Y. Wang

'Data' plays a central role in data-driven methods, but is not often the subject of focus in investigations of machine learning algorithms as applied to Earth System Modeling related problems. Here we consider the case of eddy-mean interaction in rotating stratified turbulence in the presence of lateral boundaries, a problem of relevance to ocean modeling, where the eddy fluxes contain dynamically inert rotational components that are expected to contaminate the learning process. An often utilized choice in the literature is to learn from the divergence of the eddy fluxes. Here we provide theoretical arguments and numerical evidence that learning from the eddy fluxes with the rotational component appropriately filtered out results in models with comparable or better skill, but substantially improved robustness. If we simply want a data-driven model to have predictive skill then the choice of data choice and/or quality may not be critical, but we argue it is highly desirable and perhaps even necessary if we want to leverage data-driven methods to aid in discovering unknown or hidden physical processes within the data itself.

Fei Er Yan, Hugo Frezat, Julien Le Sommer et al.

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.