A ‘‘Vertically Lagrangian’’ Finite-Volume Dynamical Core for Global Models

A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water system. The 2D horizontalto-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split-explicit, with large time steps for scalar transport, and small fractional steps for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for remapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with ‘‘physical parameterizations’’ and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave-growth tests and long-term integrations using the Held–Suarez forcing are presented. Impact of the monotonicity constraint is discussed.