Comparison of Terrain Effects in Divergent versus Non-Divergent Barotropic Models

The effects of including terrain in divergent and non-divergent, single-level barotropic models are examined in detail using a global spectral model. The non-divergent model solves the barotropic vorticity equation, while the divergent model solves the shallow water equations. In both models, the impact of terrain is evaluated by examining the evolution of the predicted heights of a pressure surface. Four simulations with initially zonal flow were run for each model using a two-dimensional Gaussian mountain shape for terrain, with two different mean fluid depths of 5,000 m and 7,500 m, and two different peak mountain heights of 2,000 m and 4,000 m. One additional simulation was completed using real North American terrain, also with initially zonal flow. As the mean fluid depth was decreased, greater differences in the predicted height fields between the two models were observed, with the shallow water model producing a more amplified leeside trough. The differences are caused by increased convergence downstream of the terrain in the shallow water model compared to the barotropic vorticity equation model as the mean fluid depth is decreased. As the mean fluid depth is increased in the shallow water model, the two different models show little difference.