Stochastic data-driven model of mesoscale and submesoscale eddies in gyre circulation

Planetary flows and large scale circulation systems are characterised by an interaction between scales that range over several orders of magnitude, with contributions given by mesoscale and submesoscale dynamics. Resolving numerically  such interactions for realistic configuration is, however, far beyond reach. Any large-scale simulation must then rely on parameterizations of the effects of the small scales on  the large scales. In this work, a stochastic parameterization is proposed based on a decomposition of the flow in terms of a smooth-in-time large-scale contribution and a random fast-evolving uncorrelated small-scale part  accounting for  mesoscales and submesoscales unresolved eddies. This  approach, termed modelling under location uncertainty (LU) [4], relies on a stochastic version of Reynolds Transport Theorem to cast physically meaningful conservation principles in this scale-separated framework. Such a scheme has been successfully applied to several large-scale models of the  ocean dynamics [1, 2, 3, 5]. Here a LU version of the  hydrostatic primitive equations is  implemented within the  NEMO community code (https://www.nemo-ocean.eu) with a data-driven approach to establish the spatial correlation of the fast evolving scales. In comparison to a corresponding deterministic counterpart, this stochastic large-scale representation  is shown to improve, in terms of the eastward jet resolution and variabilities, the  flow prediction of an idealized wind forced double gyre circulation. The results are assessed through several statistical criterion as well as an energy transfer analysis [2,5].
[1] W. Bauer, P. Chandramouli, B. Chapron, L. Li, and E. Mémin. Deciphering the
role of small-scale inhomogeneity on geophysical flow structuration: a stochastic approach.
Journal of Physical Oceanography, 50(4):983-1003, 2020.
[2] W. Bauer, P. Chandramouli, L. Li, and E. Mémin. Stochastic representation of
mesoscale eddy effects in coarse-resolution barotropic models. Ocean Modelling, 151:101646,
2020.
[3] Rüdiger Brecht, Long Li, Werner Bauer and Etienne Mémin. Rotating Shallow
Water Flow Under Location Uncertainty With a Structure-Preserving Discretization. Journal of
Advances in Modeling Earth Systems, 13, 2021MS002492.
[4], E. Mémin Fluid flow dynamics under location uncertainty,(2014), Geophysical & Astrophysical Fluid Dynamics, 108, 2, 119–146.
[5] V. Resseguier, L. Li, G. Jouan, P. Dérian, E. Mémin, B. Chapron, (2021), New trends in ensemble forecast strategy: uncertainty quantification for coarse-grid computational fluid dynamics, Archives of Computational Methods in Engineering.