On the choice of training data for machine learning of geostrophic mesoscale turbulence

Abstract: '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.