A mixed finite-element, finite-volume, semi-implicit discretisation for atmospheric dynamics: Spherical geometry

Abstract

The reformulation of the Met Office’s dynamical core for weather and climate prediction previously described by the authors is extended to spherical domains using a cubed- sphere mesh. This paper updates the semi-implicit mixed finite-element formulation to be suitable for spherical do- mains. In particular the finite-volume transport scheme is extended to take account of non-uniform, non-orthogonal meshes and uses an advective-then-flux formulation so that increment from the transport scheme is linear in the diver- gence. The resulting model is then applied to a standard set of dry dynamical core tests and compared to the exist- ing semi-implicit semi-Lagrangian dynamical core currently used in the Met Office’s operational model.