An inherently mass-conserving semi-implicit semi-Lagrangian discretization of the deep-atmosphere global non-hydrostatic equations

Following previous work on an inherently mass-conserving semi-implicit (SI) semi-Lagrangian (SL) discretization of the two-dimensional (2D) shallow-water equations and 2D vertical slice equations, that approach is here extended to the 3D deep-atmosphere, non-hydrostatic global equations. As with the reduced-dimension versions of this model, an advantage of the approach is that it preserves the same basic structure as a standard, non-mass-conserving, SISL version of the model. Additionally, the model is simply switchable to hydrostatic and/or shallow-atmosphere forms. It is also designed to allow simple switching between various geometries (Cartesian, spherical, spheroidal). The resulting mass-conserving model is applied to a standard set of test problems for such models in spherical geometry and compared with results from the standard SISL version of the model.