A stabilized proper orthogonal decomposition reduced-order model for large scale quasigeostrophic ocean circulation

In this paper, a stabilized proper orthogonal decomposition (POD) reduced-order model (ROM) framework is developed for the barotropic vorticity equation. Two different closure ideas are utilized in order to model truncated modes in the ROMs. We apply the POD-ROMs to mid-latitude simplified oceanic basins, which are standard prototypes of more realistic large-scale ocean dynamics. Two closure schemes are used to model the effects of the discarded POD modes: a mode dependent eddy viscosity closure model and a Smagorinsky-type model. A sensitivity analysis with respect to the free eddy viscosity stabilization parameter is performed for various POD-ROMs with different numbers of POD modes. The POD-ROM results are validated against the Munk layer resolving direct numerical simulations using a fully conservative fourth-order Arakawa scheme. A comparison with the standard Galerkin POD-ROM without any stabilization or closure is also included in our investigation. For a four-gyre ocean circulation problem, the new POD-ROM closure models show significant improvements in accuracy over the standard Galerkin model. This first step in the numerical assessment of the POD-ROMs shows that they could represent a computationally efficient tool for large scale oceanic simulations over long time intervals.