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.