An adaptive vertical coordinate formulation for a nonhydrostatic model with flux-form equations

The concept of adaptive vertical coordinates is used to upgrade conventional terrain-following sigma coordinates to arbitrary hybrid coordinates. Compared with previous approaches for implementing adaptive coordinates, the method presented here combines unrestricted applicability to nonhydrostatic models with the capability to integrate the atmospheric equations in flux form. The coordinate is based on a three-dimensional field carrying the vertical position of the coordinate surfaces, which is made time dependent by introducing a prognostic equation. As a specific example, the adaptive coordinate is used to emulate a hybrid isentropic system. Idealized tests in which the coordinate surfaces are artificially moved reveal that the ensuing spurious motions are small enough to be negligible in realistic applications. Mountain wave tests demonstrate that the hybrid coordinate remains numerically stable under strong forcing. However, the model layer distribution established with the hybrid isentropic coordinate is not optimal for representing the dynamics of breaking gravity waves because the vertical distance between the model levels tends to be too large in the wave breaking region. On the other hand, real case studies demonstrate that the hybrid coordinate significantly improves the representation of the tropopause because of enhanced vertical resolution in the tropopause region.