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

Abstract

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.