A method for reducing pressure gradient errors improving the sigma coordinate stretching function: An idealized flow patterned after the Libyan near-shore region with the POM

Abstract

A technique for reducing the effects of pressure gradient errors in terrain-following models based on the vertical distribution of layers is proposed in this study. The basic idea is to find a vertical distribution that reduces the cumulative pressure gradient error estimated over the whole domain. The technique is applied to the sigma coordinate Princeton Ocean Model (POM), where the vertical distribution of layers is defined by a horizontally uniform stretching function. The cumulative error is used to measure the difference between the z-level-based pressure gradient approximation, used as “ground truth”, and the pressure gradient in sigma coordinates after interpolating the density field to sigma coordinate locations. A vertical stretching function which reduces the cumulative error is sought by iterative methods that need some additional constraints in order to avoid non-useful results (e.g. wildly varying layer thicknesses based on the derived stretching function). Two simple expressions for the cumulative error based on barotropic and baroclinic errors are tested. With the POM model the baroclinic one is found to be the most effective. Improvements are found in the internal current field and on the time evolution of the density distribution. Beneficial effects on the external mode, however, cannot be excluded in the long term. The technique can be used on any pressure gradient scheme adopted; however, iterative methods are applicable only to cases, or to portions of the domain, in which the vertical stretching function is horizontally uniform (sigma, pure ‘quasi’ z-level and hybrid sigma- z level coordinate systems). The application of the technique to generalized vertical coordinate systems (temporarily setting the vertical coordinate as sigma) can be used to establish to which kind of cumulative error the model is sensitive, information useful in building vertical and horizontal adaptive grids that reduce the effects of pressure gradient errors.