This study makes progress towards a data-driven parameterization for mesoscale oceanic eddies. To demonstrate the concept and reveal accompanying caveats, we aimed at replacing a computationally expensive, standard high-resolution ocean model with its inexpensive low-resolution analogue augmented by the parameterization. We considered eddy-resolving and non-eddy-resolving double-gyre ocean circulation models characterized by drastically different solutions due to the nonlinear mesoscale eddy effects. The key step of the proposed approach is to extract from the high-resolution reference solution its eddy field varying in space and time, and then to use this information to improve the low-resolution analogue model.

By interactively coupling both the continuously supplied history of the eddy field and the explicitly modeled low-resolution large-scale flow, we obtained the additional eddy forcing term which modified the low-resolution model and significantly augmented its solutions. This eddy forcing term represents the action of the eddy field, its coupling with the large-scale flow and is a key dynamical constraint imposed on the augmentation procedure.

Although the augmentation drastically improved the low-resolution circulation patterns, it did not recover the robust, intrinsic, large-scale low-frequency variability (LFV), which is an important feature of the high-resolution solution. This is by itself an important (negative) result that has significant implication for any data-driven eddy parameterization, especially, given the fact that we used the most complete information about the space–time history of the eddy fields. Note, when we supplied the reference (true) eddy forcing, rather than just the eddy field, the LFV was recovered. This suggests that the LFV is crucially dependent on the details of the space–time eddy forcing/large-scale flow correlations, which are not fully respected by the proposed augmentation procedure.

In order to overcome the deficiency and recover the LFV, we statistically filtered the augmented low-resolution model solution by projecting it onto the leading Empirical Orthogonal Functions (EOFs) of the large-scale component of the high-resolution reference solution. This operation allowed us to remove spurious effects associated with higher EOFs. We tested and confirmed that without using the data-driven eddy information this filtering alone cannot augment the low-resolution solution; but in conjunction with the eddy information, it produced desirable outcome.

Moreover, as a natural step towards parameterization, we took advantage of data-driven stochastic inverse modeling to obtain inexpensive emulators of the eddy field and showed generally promising results of augmenting the coarse-resolution model with the obtained emulators. Our results showed that obtaining the LFV characteristics for the eddy parameterization, which is already capable of reproducing the large-scale flow pattern, should become a standard parameterization requirement, but it can be challenging to meet.