Improved Advection Schemes for Ocean Models

Abstract

Leonard?s widely used QUICK advection scheme is, like the Bryan?Cox?Semtner ocean model, based on a control volume form of the advection equation. Unfortunately, in its normal form it cannot be used with the leapfrog?Euler forward time-stepping schemes used by the ocean model. Farrow and Stevens overcame the problem by implementing a predictor?corrector time-stepping scheme, but this is computationally expensive to run. The present paper shows that the problem can be overcome by splitting the QUICK operator into an O(δx2) advective term and a velocity dependent biharmonic diffusion term. These can then be time-stepped using the combined leapfrog and Euler forward schemes of the Bryan?Cox?Semtner ocean model, leading to a significant increase in model efficiency. A small change in the advection operator coefficients may also be made leading to O(δx4) accuracy. Tests of the improved schemes are carried out making use of a global eddy-permitting ocean model. Results are presented from cases where the schemes were applied to only the tracer fields and also from cases where they were applied to both the tracer and velocity fields. It is found that the new schemes have the most effect in the western boundary current regions, where, for example, the warm core of the Agulhas Current is no longer broken up by numerical noise.