Data-driven stochastic parameterization of multi-scale flow interactions in ocean models

Oceanic flows typically include multi-scale motions featuring highly nonlinear and small transient structures such as jets and vortices. Such features couple in a non-trivial way with large-scale components of the flows, that in turn, modify the evolution of the latter. Therefore, in order to reliably model the large-scale oceanic flow, one still needs to resolve these evanescent transient features (with typical length scales of 10-100 kilometers depending on the latitude). However, resolving such small-scale features by brute-force computing is still out of question even despite significantly increased capabilities of modern high performance computing systems.

To overcome this computational problem, we consider a data-driven approach to parameterize the effect of the small-scales on the large-scales in a classic double-gyre oceanic model, where flow dynamics is known to be heavily affected by the multi-scale interactions. Given a relatively short dataset produced by a high-resolution model that resolves all the necessary scales, we diagnose the forcing relating to the multi-scale oceanic interactions.

The low-resolution version of the model is augmented by the information about such forcing and also by emulating the transient small-scale features with a nonlinear stochastic process that incorporates memory effects. As a result of this augmentation procedure, the low-resolution solution demonstrates similar spectral characteristics and the spatial structure of its flow as in the corresponding high-resolution reference dataset.