Wyman, B. L., 1996: A step-mountain coordinate general circulation model: Description and validation of medium-range forecasts. Monthly Weather Review, 124(1), 102-121.

Abstract: The step-mountain or eta vertical coordinate has been a proposed solution for eliminating the numerical errors encountered when calculating the pressure gradient force along sloping surfaces. The main objectives of this paper are to describe the development of a global general circulation model using the eta coordinate and to verify the capabilities of the model for medium-range forecasts. First, the treatment of the polar boundary and the polar filtering are presented. To verify the polar treatment, numerical results using the shallow-water equations are presented. Second, various physical parameterizations are incorporated into the multilevel eta coordinate model. Model integrations for several January cases are presented to validate the model.

The similarity of the eta coordinate formulation to the terrain-following sigma coordinate allows the model to be run using either vertical coordinate. Thus, model comparisons are performed with the eta and sigma coordinate versions of the general circulation model, keeping the same physical parameterizations. Additional comparisons are made with a sigma coordinate spectral model.

As a validation of the model, 10-day integrations are made from four observed initial conditions at several horizontal resolutions. At relatively low resolution, forecast results slightly favor the spectral and sigma coordinate models. However, at higher resolution, forecast skill scores for the eta coordinate model are indistinguishable from those of the sigma models. Additional results are presented to demonstrate the advantages the advantages of the eta coordinate near steep topography and the potential deficiency of the eta coordinate in connection with the surface boundary layer treatment.