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

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.