Development of high-order global dynamical core using discontinuous Galerkin method for atmospheric LES and proposal of test cases: SCALE-DG v0.8.0

Abstract. Focusing on future global atmospheric simulations with grid spacing of O(10–100 m), we developed a global nonhydrostatic atmospheric dynamical core with high-order accuracy by applying discontinuous Galerkin method (DGM) both horizontally and vertically. Further, 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 orders (p), the impact of high-order DGM on 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 validate global LES models, which is a global extension of idealized planetary boundary layer (PBL) turbulence experiment performed in our previous studies. The error norms from the deterministic test cases, such as linear advection and gravity wave test cases, show an optimal order of spatial accuracy with about p + 1-order when the temporal and round-off errors are sufficiently small. In the climatic test cases, such as the Held-Suarez test, the kinetic energy spectra indicate the advantage of effective resolutions when large polynomial orders are used. In the LES experiment, the global model provided a reasonable vertical structure of PBL and energy spectra since the results under shallow atmosphere approximation well reproduce those obtained in the plane computational domain.