The Critical Role of Small-Scale Dissipation in Deriving Subgrid Forcing Within an Ocean Quasi-Geostrophic Model

Due to computational constraints, ocean numerical models are often executed on low-resolution (LR) grids. To maintain consistency between LR simulations and coarsened high-resolution (HR) solutions, a subgrid forcing term is commonly integrated into the LR model as a parameterization scheme. Although numerous data-driven parameterizations have been developed to establish the relationship between resolved LR variables and corresponding subgrid forcing, the accurate extraction of target subgrid forcing remains an open challenge that significantly impacts the performance of such parameterizations. Small-scale dissipation (ssd) operators are widely used to enhance numerical stability while introducing minimal energy dissipation; however, this study demonstrates that these operators critically influence the accurate representation of subgrid forcing: an aspect that has not been adequately addressed. Within a quasi-geostrophic ocean modeling framework, new formulations have been rigorously derived for subgrid forcing that explicitly accounts for ssd effects. Numerical experiments confirm that the proposed forcing enables LR simulations to reproduce coarsened HR results with high fidelity. This work demonstrates that greater attention to the specific numerical discretization scheme is required for the accurate extraction of subgrid forcing from HR simulations. Although these newly developed extraction algorithms are diagnostic in nature, they could provide accurate target data that facilitate the subsequent development of data-driven parameterization schemes.