A New Hybrid Sigma-Pressure Vertical Coordinate with Smoothed Coordinate Surfaces

Abstract

Abstract An alternative hybrid sigma-pressure terrain-following coordinate is presented here that provides smoother coordinate surfaces over terrain by allowing a more rapid decay of the influence of smaller-scale topographic structures with height. This is accomplished by first defining a reference surface pressure that includes the influence of the underlying topography. A smoothed version of this reference surface pressure is then created that represents the larger-scale features of the topography, while the deviations from the smoothed profile contain the smaller-scale terrain structures. In the hybrid-sigma coordinate formulation presented here, the influences of these deviations in the reference surface pressure from their smoothed values are removed more rapidly with increasing height, thereby producing smoother coordinate surfaces. Testing this approach using several idealized simulations demonstrates a significant reduction in the artificial circulations compared to those arising with the basic sigma or the conventional hybrid sigma coordinate, confirming the beneficial aspects of the smoothed hybrid coordinate surfaces. The smoothed hybrid sigma-pressure coordinate proposed here provides flexibility in reducing the influence of the terrain on the coordinate surfaces and can be easily substituted for the basic hybrid sigma-pressure coordinate. Significance Statement Terrain-following vertical coordinates are widely employed in atmospheric numerical models because of their advantages in implementing boundary conditions at the surface. However, it is well known that these coordinates can promote artificial circulations due to numerical errors in computing horizontal pressure gradients and advection along the transformed coordinate surfaces. The purpose of this study is to improve the performance of a pressure-based terrain-following (sigma) hybrid vertical coordinate by selectively removing the influences of smaller-scale terrain features, which results in smoother coordinate surfaces. We demonstrate that this enhancement is beneficial in reducing numerical errors that are inherent in computing with terrain-following vertical coordinates.