A method for preserving nominally-resolved flow patterns in low-resolution ocean simulations: Dynamical system reconstruction

Abstract

Accurate representation of large-scale flow patterns in low-resolution ocean simulations is one of the most challenging problems in ocean modelling. The main difficulty is to correctly reproduce effects of unresolved small scales on the resolved large scales. For this purpose, most of current research is focused on development of parameterizations directly accounting for the small scales. In this work we propose an alternative to the mainstream ideas by showing how to reconstruct a dynamical system from the available reference solution data (our proxy for observations) and, then, how to use this system for modelling not only large-scale but also nominally-resolved flow patterns at low resolutions. This approach is advocated as a part of the novel framework for data-driven hyper-parameterization of mesoscale oceanic eddies in non-eddy-resolving models. The main characteristic of this framework is that it does not require to know the physics behind large–small scale interactions to reproduce both large and small scales in low-resolution ocean simulations. We tested it in the context of a three-layer, statistically equilibrated, steadily forced quasigeostrophic model for the beta-plane configuration and showed that non-eddy-resolving solution can be substantially improved towards the reference eddy-resolving benchmark. The proposed methodology robustly allows to retrieve a system of equations governing reduced dynamics of the observed data, while the additional adaptive nudging counteracts numerical instabilities by keeping solutions in the region of phase space occupied by the reference fields. Remarkably, its solutions simulate not only large-scale but also small-scale flow features, which can be nominally resolved by the low-resolution grid. In addition, the proposed method reproduces realistic vortex trajectories. One of the important and general conclusions that can be drawn from our results is that not only mesoscale eddy parameterization is possible in principle but also it can be highly accurate (up to reproducing individual vortices) for significantly reduced dynamics (down to 30 degrees of freedom). This conclusion provides great optimism for the ongoing parameterization studies, which are still far away from being completed.