A Lagrangian vertical coordinate version of the ENDGame dynamical core. Part II: Evaluation of Lagrangian conservation properties

Abstract

A baroclinic instability test case is used to compare the Lagrangian conservation properties of three versions of a semi‐implicit semi‐Lagrangian dynamical core: one using a height‐based vertical coordinate and two using a Lagrangian vertical coordinate. The Lagrangian coordinate versions differ in the choice of target levels to which model levels are reset after each step—the first uses the initial model level heights while the second uses quasi‐Lagrangian target levels. A range of diagnostics related to Lagrangian conservation are computed, including global entropy, unavailable energy, cross‐isentrope mass flux, and consistency of potential temperature and potential vorticity with passive tracers and parcel trajectories. The global entropy, unavailable energy, and cross‐isentrope fluxes do not suggest any clear advantage or disadvantage from the use of a Lagrangian vertical coordinate, though the cross‐isentrope flux reveals a flaw in the formulation of the remapping of potential temperature in the Lagrangian coordinate model at the top boundary. The use of a Lagrangian vertical coordinate with quasi‐Lagrangian target levels improves the consistency among potential temperature as a dynamical variable, potential temperature as a tracer and potential temperature on Lagrangian particle trajectories. It also improves consistency between a potential vorticity tracer and potential vorticity on Lagrangian particle trajectories. However, it degrades the consistency between model and tracer potential vorticity, as well as between model potential vorticity and potential vorticity on Lagrangian trajectories. This degradation appears to be related to the slopes of model levels, which are greater in the version with quasi‐Lagrangian target levels.