Applications of generalized vertical coordinates in ocean circulation models

Abstract

Two types of generalized vertical coordinates are introduced to reduce model errors in calculating the baroclinic pressure gradient (BPG), advection term and horizontal mixing in tracer equations in a three-dimensional (3D) ocean circulation model. These two types of vertical coordinates are defined as the generalized terrain-following coordinate (GTC) and generalized piecewise terrain-following coordinate (GPTC). The main feature of the GTC is the use of a series of constant-depth levels in the water column above the sea bottom. The GPTC differs from the GTC in which the depth differences between two adjacent grids are reduced, especially in the bottom layer over steep topography. Performances of these two vertical coordinate systems are assessed first in two types of idealized numerical experiments with a tall seamount and continuously varying bottom slope respectively. The model results in the tall seamount experiment demonstrate that both the GTC and GPTC perform well in reducing the model errors in the BPG over the steep topography, and greatly alleviate the spurious diapycnal mixing in terrain-following coordinate models. In the continuously varying bottom slope experiment, both the GTC and GPTC perform better than the z-level coordinate in simulating the 3D currents. The performances of the GTC and GPTC are further assessed by examining prognostic simulations of 3D currents and hydrography in the Yellow and East China Seas with realistic external forcing and bottom topography. The model results in the third experiment demonstrate that the GPTC restrains the overestimated upward climbing of the bottom cold water in comparison with other coordinates. The GPTC also performs better than the GTC and the conventional sigma-layer coordinate in simulating the shoreward intrusion of relatively high-salinity subsurface waters, intermediate low-salinity waters and the Yellow Sea bottom cold waters. By comparison, the GTC simulates the Kuroshio, the Slope Counter-Current and their seasonal variability significantly better than other coordinates.