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

Abstract

Our previously described reformulation of the Met Office's dynamical core for weather and climate prediction is extended to spherical domains using a cubed-sphere mesh. We update the semi-implicit mixed finite-element formulation to be suitable for spherical domains. 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 divergence. The resulting model is then applied to a standard set of dry dynamical core tests and compared with the existing semi-implicit semi-Lagrangian dynamical core currently used in the Met Office's operational model.