An alternative approach to the ocean eddy parameterization roblem

It is typical for low-resolution ocean simulations to miss not only small- but also large-scale patterns of the flow dynamics compared with their high-resolution analogues. It is usually attributed to the inability of coarse-grid models to properly reproduce the effects of the unresolved small-scale dynamics on the resolved large scales. In part, the reason for that is that coarse-grid models fail to at least keep the coarse-grid solution within the region of phase space occupied by the reference solution  (the high-resolution solution projected onto the coarse grid). 

In this presentation we discuss two methods to solve this problem: (1) computation of the image point in the phase space restricted to the region of the reference flow dynamics, and (2) reconstruction of a dynamical system from the available reference solution data. The proposed methods show encouraging results for both low- and high-dimensional phase spaces.

One of the important and general conclusions that can be drawn from our results is that not only mesoscale eddy parameterisation is possible in principle but also it can be highly accurate (up to reproducing individual vortices). This conclusion provides great optimism for the ongoing parameterisation studies.