Design of a Dynamical Core Based on the Nonhydrostatic “Unified System” of Equations*

Abstract

Abstract This paper presents the design of a dry dynamical core based on the nonhydrostatic “unified system” of equations. The unified system filters vertically propagating acoustic waves. The dynamical core predicts the potential temperature and horizontal momentum. It uses the predicted potential temperature to determine the quasi-hydrostatic components of the Exner pressure and density. The continuity equation is diagnostic (and used to determine the vertical mass flux) because the time derivative of the quasi-hydrostatic density is obtained from the predicted potential temperature. The nonhydrostatic component of the Exner pressure is obtained from an elliptic equation. The main focus of this paper is on the integration procedure used with this unique dynamical core. In the implementation described in this paper, height is used as the vertical coordinate, and the equations are vertically discretized on a Lorenz-type grid. Cartesian horizontal coordinates are used along with an Arakawa C grid. A detailed description of the discrete equations is presented in the supplementary material, along with the rationale behind the decisions made during the discretization process. Only a short description is given here. To demonstrate that the model is capable of simulating a wide range of dynamical scales, the results from cyclone- and cloud-scale simulations are presented. The solutions obtained for the selected cloud-scale simulations are compared to those from a fully compressible, anelastic, and pseudo-incompressible models that (as far as possible) uses the same schemes used in the unified dynamical core. The results show that the unified dynamical core performs reasonably well in all these experiments.