Development of a high-order global dynamical core using the discontinuous Galerkin method for an atmospheric large-eddy simulation (LES) and proposal of test cases: SCALE-DG v0.8.0

Abstract. Focusing on the future global atmospheric simulations with a grid spacing of O(10–100 m), we developed a global nonhydrostatic atmospheric dynamical core with high-order accuracy by applying a discontinuous Galerkin method (DGM) for horizontal and vertical discretization. Furthermore, considering a global large-eddy simulation (LES), a Smagorinsky–Lilly turbulence model was introduced to the proposed global dynamical core in the DGM framework. By conducting several tests with various polynomial (p) orders, the impact of the high-order DGM on the accuracy of the numerical simulations of atmospheric flows was investigated. To show high-order numerical convergence, a few modifications were made in the experimental setup of existing test cases. In addition, we proposed an idealized test case to verify global-LES models, which is a global extension of an idealized planetary boundary layer (PBL) turbulence experiment performed in our previous studies. The error norms from the deterministic test cases, such as the linear-advection and gravity-wave tests, showed an optimal convergence rate achieved by an approximately p+1-order spatial accuracy when the temporal and round-off errors were sufficiently small. In the climatic test cases, such as the Held–Suarez test, the kinetic energy spectra indicated the advantage of effective resolution when large polynomial orders were used. In the LES experiment, the global model provided a reasonable vertical structure of the PBL and energy spectra because the results under shallow-atmosphere approximation reproduced those obtained in the plane computational domain well.