Empirical and stochastic formulations of western boundary conditions

Abstract

High-frequency radar observations of surface current at 100 m resolution are used to stochastically determine the vorticity variability in the boundary layer between the Florida Current and the Florida coast. Using the empirical data, several formulations of the stochastic boundary condition (SBC) are then developed and evaluated for the parameterization of sub-grid scale variability along the western boundaries of an ocean general circulation model (OGCM). These SBCs are compared to both no-slip and free-slip boundary conditions along the western boundary of a channel model simulating separation of the boundary current at a cape, as well as simulations of the classic, wind-forced double-gyre circulation. Our studies indicate that simulated circulation patterns are sensitive to both the functional form of the SBC and the parameters used in a given formulation. In particular, a relatively simple, auto-regressive formulation of SBC can be applied to a coarse-resolution, eddy-permitting OGCM to increase flow turbulence and to affect the flow patterns in ways distinct from the standard, deterministic no-slip and free-slip boundary conditions. Correlation time scales of a few days to weeks, orders of magnitude larger than a typical time step of OGCM, are needed in the regression model for SBC. This formulation of SBC is shown to be effective in both quasi-geostrophic and shallow-water dynamics.