Inability of low-resolution ocean models to simulate many important aspects of the large-scale general circulation is a common problem. In the view of physics, the main reason for this failure are the missed dynamical effects of the unresolved small scales of motion on the explicitly resolved large scale motions. Complimentary to this mainstream physics-based perspective, we propose to address this failure from the dynamical systems point of view, namely, as the persistent tendency of phase space trajectories representing the low-resolution solution to escape the right region of the corresponding phase space, which is occupied by the reference eddy-resolving solution. Based on this concept, we propose to use methods of constrained optimization to confine the low-resolution solution to remain within the correct phase space region, without attempting to amend the eddy physics by introducing a process-based parameterisation. This approach is advocated as a novel framework for data-driven hyper-parameterisation of mesoscale oceanic eddies in non-eddy-resolving models. We tested the idea in the context of classical, baroclinic beta-plane turbulence model and showed that non-eddy-resolving solution can be substantially improved towards the reference eddy-resolving benchmark.
