An Embedded Bottom Boundary Layer Formulation for Z-Coordinate Ocean Models

Abstract

An embedded bottom boundary layer (EBBL) scheme is developed to improve the bottom topographic representation in z-coordinate ocean general circulation models. The EBBL scheme is based on the combined techniques of an embedded topography-following slab, an explicit turbulent bottom boundary layer (BBL), and a generalized pressure gradient formulation. The coupling between the interior z-level model and the EBBL model is achieved by exchanging entrainment/detrainment and pressure gradients at the bottom layer surface, which allows temporal and spatial variations. The EBBL is implemented into one of the most widely used z-coordinate models, the Modular Ocean Model (MOM). A test problem with a source of dense water on a slope is used. The new EBBL produces significantly more realistic plume spreading than the existing BBL scheme of Killworth and Edwards and is comparable to the results from a topography-following coordinate model (SCRUM), which is believed to be more suitable for such a problem. Calculation of the momentum budget demonstrates that the improved representation of the downslope pressure gradient formulation plays an important role in the simulations of dense slope flows. Sensitivity experiments with different grid sizes, model parameters, and density contrast between the cold source water and the warm interior water are carried out to test the robustness of the EBBL scheme. In contrast to the BBL model of Killworth and Edwards, which tends to diffuse too much dense water along isobaths, the EBBL model allows dense water to sink across isobaths through a very thin bottom layer into the deep ocean. Even in the coarser-resolution case (1/4° and 15 levels) the EBBL produces more realistic deep water than the existing BBL with higher resolution (1/8° and 30 levels), and at only one-eighth the computational cost. It is therefore concluded that the EBBL scheme presented here is cost effective and robust to model resolution and mixing parameters, and should be easily implemented in any nontopography-following coordinate ocean model.