The deep-atmosphere Euler equations with a mass-based vertical coordinate

Abstract

The terrain-following hydrostatic pressure-coordinate system for the shallow-atmosphere Euler equations is generalized for deep atmospheres using a mass-based vertical coordinate. A consequent benefit is that an existing (shallow atmosphere) hydrostatic primitive-equations model, which uses a pressure-based terrain-following vertical coordinate, could be modified for non-hydrostatic deep-atmosphere applications, without the need to change the scientific and computing infrastructure substantially in which it is embedded.