Resolution and Algorithmic Influences on the Baroclinic Pressure Gradient in Finite Element-Based Hydrodynamic Models

摘要

In 3D shallow water models, the baroclinic pressure gradient (BPG) can become unstable or physically unrealistic in areas of rapidly changing topography and/or density fields. By using a 2D finite element x-z model, whose formulation uses the generalized wave continuity equation, we assess the impact on accuracy of three methods used to compute the BPG: the sigma coordinate method, the z-coordinate (level coordinate) method and a hybrid method that switches from sigma coordinates to z-coordinates at a prescribed depth. Resolution studies then look at horizontal and vertical resolution independently, and the interplay of the horizontal and vertical resolutions for these three methods of computing the BPG. Numerical experiments are carried out on several domains, from constant to rapidly changing bathymetry, with two different density fields, which vary only in the horizontal or vertical directions. Results thus far indicate that the z-coordinate method provides the least amount of error in the solution.