  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.

Atmospheric and Oceanic Physics;Fluid Dynamics