5:15 PM - 7:15 PM
[MGI30-P05] Introduction of moist process to an global atmospheric dynamical core using discontinuous Galerkin method and validation with a moist Held-Suarez test
Keywords:High-order fluid scheme, Dynamics-Physics coupling, Idealized numerical experiment of global atmospheric model with moist process
Introduction
In future high-resolution atmospheric simulations such as global large-eddy simulations (LES), Kawai & Tomita, (2021) indicated that the required discretization accuracy is higher than that of conventional dynamical cores wiht low-order accuracy to ensure that the discretization errors do not dominate over the effect of turbulent schemes. Focusing on the discontinuous Galerkin method (DGM), which is characterized by its simplicity of high-order strategy and high computational locality, we have develped a regional and global atmospheric dynamical core using DGM, SCALE-DG (Kawai & Tomita, 2025). One of our next challenges is to investigate dynamics-physical coupling strategies considering the effective resolution of the dynamical cores. In Herrington et al. (2019), it is known that evaluating physical processes on finite element nodes in the spectral element method results in numerical structures along element boundaries. To investigate the behavior of dynamics-physics coupling in the DGM framework, we previously performed a moist warm bubble experiment in a regional setting. Further, we recently introduced a moist process to our global DG dynamical core and conducted the moist Held-Suarez experiment (Thatcher & Jablonowski, 2016); hereafter referred to as TJ16). In this presentation, we show the preliminary results.
Moist Held-Suarez test using global DG dynamical core
[Model and experimental setup] The dynamical process is based on a system of fully compressible nonhydrostatic equations in cubed-sphere coordinates. For spatial discretization, nodal DGM (e.g., Hesthaven & Warburton, 2007) is applied. The computational domain is divided using hexahedral elements. According to the order (p) of the discretization accuracy, (p+1)3 degrees of freedom are located in each element. For the numerical flux, Rusanov fluxes are used for the inviscid terms. In addition, a higher-order modal filter is applied for numerical stabilization. The transport of water vapor is calcualted by a non-negative guarantee scheme (Light & Durran, 2016). For the termporal discretization, we adopt a third-order horizontal explicit and vertical implicit (HEVI) scheme. As simplified physical processes, in addition to the Newtonian cooling and Rayleigh friction as in the original Held-Suarez experiment, a large-scale condensation, vertical mixing in the planetary boundary layer, and surface flux schemes are used. We note that the tedencies with these schemes are evaluated at the nodes of the finite elements. The horizontal grid spacing at the equator is approximately set to 156 km with p=7, and the time integration is performed during 1200 days.
[Results] Figure (a) shows the meridional distribution of the atmospheric field in a statistical equilibrium state. The spatial patterns and intensities of general circulation reproduce well the results of TJ16. The upper panel of Fig. (b) shows the meridional distribution of precipitation rate. The peak value at the equator is about twice higher than that of TJ16, and the latiduial width is narrower than that of TJ16. The global-mean value is 2.1 mm/day, which is well similar with that in TJ16. However, as shown in the lower panel of Fig. (b), we have a bias problem which is statistically large precipitation along the element boundaries; It corresponds to larger precipitation peak at the equator compared to the result in TJ16. Also in a DG dynamical core, we confirmed an issue of the numerical structure near the element boundaries as pointed out by previous studies using the spectral element method (e.g., Herrington et al. (2019)). To alleviate this problem, by using a spatial filter, we may need to coarse flow fields represented by the DGM or the physics tendencies evaluated on the nodes. As our next task, we plan to investigate the effect of such techniques and to consider the fundamental causes of the bias along the element boundaries.
In future high-resolution atmospheric simulations such as global large-eddy simulations (LES), Kawai & Tomita, (2021) indicated that the required discretization accuracy is higher than that of conventional dynamical cores wiht low-order accuracy to ensure that the discretization errors do not dominate over the effect of turbulent schemes. Focusing on the discontinuous Galerkin method (DGM), which is characterized by its simplicity of high-order strategy and high computational locality, we have develped a regional and global atmospheric dynamical core using DGM, SCALE-DG (Kawai & Tomita, 2025). One of our next challenges is to investigate dynamics-physical coupling strategies considering the effective resolution of the dynamical cores. In Herrington et al. (2019), it is known that evaluating physical processes on finite element nodes in the spectral element method results in numerical structures along element boundaries. To investigate the behavior of dynamics-physics coupling in the DGM framework, we previously performed a moist warm bubble experiment in a regional setting. Further, we recently introduced a moist process to our global DG dynamical core and conducted the moist Held-Suarez experiment (Thatcher & Jablonowski, 2016); hereafter referred to as TJ16). In this presentation, we show the preliminary results.
Moist Held-Suarez test using global DG dynamical core
[Model and experimental setup] The dynamical process is based on a system of fully compressible nonhydrostatic equations in cubed-sphere coordinates. For spatial discretization, nodal DGM (e.g., Hesthaven & Warburton, 2007) is applied. The computational domain is divided using hexahedral elements. According to the order (p) of the discretization accuracy, (p+1)3 degrees of freedom are located in each element. For the numerical flux, Rusanov fluxes are used for the inviscid terms. In addition, a higher-order modal filter is applied for numerical stabilization. The transport of water vapor is calcualted by a non-negative guarantee scheme (Light & Durran, 2016). For the termporal discretization, we adopt a third-order horizontal explicit and vertical implicit (HEVI) scheme. As simplified physical processes, in addition to the Newtonian cooling and Rayleigh friction as in the original Held-Suarez experiment, a large-scale condensation, vertical mixing in the planetary boundary layer, and surface flux schemes are used. We note that the tedencies with these schemes are evaluated at the nodes of the finite elements. The horizontal grid spacing at the equator is approximately set to 156 km with p=7, and the time integration is performed during 1200 days.
[Results] Figure (a) shows the meridional distribution of the atmospheric field in a statistical equilibrium state. The spatial patterns and intensities of general circulation reproduce well the results of TJ16. The upper panel of Fig. (b) shows the meridional distribution of precipitation rate. The peak value at the equator is about twice higher than that of TJ16, and the latiduial width is narrower than that of TJ16. The global-mean value is 2.1 mm/day, which is well similar with that in TJ16. However, as shown in the lower panel of Fig. (b), we have a bias problem which is statistically large precipitation along the element boundaries; It corresponds to larger precipitation peak at the equator compared to the result in TJ16. Also in a DG dynamical core, we confirmed an issue of the numerical structure near the element boundaries as pointed out by previous studies using the spectral element method (e.g., Herrington et al. (2019)). To alleviate this problem, by using a spatial filter, we may need to coarse flow fields represented by the DGM or the physics tendencies evaluated on the nodes. As our next task, we plan to investigate the effect of such techniques and to consider the fundamental causes of the bias along the element boundaries.