Stochastic Data‐Driven Parameterization of Unresolved Eddy Effects in a Baroclinic Quasi‐Geostrophic Model.

In this work, a stochastic representation based on a physical transport principle is proposed to account for mesoscale eddy effects on the large‐scale oceanic circulation. This stochastic framework arises from a decomposition of the Lagrangian velocity into a smooth‐in‐time component and a highly oscillating noise term. One important characteristic of this random model, without any external forcing and damping, is that it conserves the total energy of the resolved flow for any realization. The proposed stochastic formulation is successfully implemented in a well established multi‐layered quasi‐geostrophic dynamical core. The empirical spatial correlation of the unresolved noise is calibrated from the eddy‐resolving simulation data. In particular, a stationary correction drift can be introduced in the noise through Girsanov transformation. This non‐intuitive term appears to be important in reproducing on a coarse mesh the eastward jet of the wind‐driven double‐gyre circulation. In addition, a projection method has been proposed to constrain the noise to act along the iso‐surfaces of the vertical stratification. The resulting noise enables us to improve the intrinsic low‐frequency variability of the large‐scale current. Plain Language Summary: Accurate numerical simulation of the ocean and the atmosphere is important for understanding complex patterns in climate science. Unfortunately, the high‐dimensional geophysical fluid dynamics contain a wide range of spatio‐temporal scales with complex interactions. In order to maintain affordable computational time, only large‐scale representations of the geophysical flows of interest are simulated. However, the effect of the unresolved scales on the resolved component must be carefully taken into account to minimize the errors of truncation. In the present work, we stick to a specific stochastic formulation that represents the physical principles of the resolved large scales and parameterizes the statistical properties of the unresolved small scales. Such random formulation is successfully tested in numerical simulations of a simplified ocean mesoscale model, in which the structure of the unresolved flow is calibrated from a finite sequence of reference data. The resulting model enables to represent accurately the statistics of the resolved flow component. In addition, numerical results show that an adequate modeling of the unresolved dynamics leads to a significant improvement of the intrinsic variability for the large‐scale ocean models. These findings are important for future developments of ocean and atmosphere climate models. Key Points: A stochastic transport formulation is used to parameterize the effects of the unresolved eddies on the resolved flowThe structure of unresolved flow is calibrated from data and a projection method is proposed to parameterize its dynamicsThe proposed random models on coarse resolutions enable to reproduce the eastward jet and the intrinsic variability of ocean wind‐driven circulation [ABSTRACT FROM AUTHOR]