A Lagrangian vertical coordinate version of the ENDGame dynamical core. Part I: Formulation, remapping strategies, and robustness

Abstract

Previous work provides evidence that Lagrangian conservation and related properties of a numerical model dynamical core can be improved by the use of a Lagrangian or quasi‐Lagrangian vertical coordinate (LVC). Most previous model developments based on this idea have made the hydrostatic approximation. Here the LVC is implemented in a non‐hydrostatic compressible Euler equation dynamical core using almost identical numerical methods to ENDGame, the operational dynamical core of the Met Office atmospheric Unified Model. This enables a clean comparison of LVC and height‐coordinate versions of the dynamical core using numerical methods that are as similar as possible. Since Lagrangian surfaces distort over time, model level heights are continually reset to certain “target levels” and the values of model fields are remapped onto their new locations. Different choices for these target levels are discussed, along with remapping strategies that focus on different conservation or balance properties. Sample results from a baroclinic instability test case are presented. The LVC formulation is found to be rather less robust than the height‐coordinate version; some reasons for this are discussed.