A high‐order vertical discretization method for a semi‐implicit mass‐based non‐hydrostatic kernel

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Most global models employ a vertical coordinate based on the moist hydrostatic pressure, and therefore do not conserve dry air mass. Such an issue should be taken seriously into account, especially in developing global high-resolution atmospheric models to address nonhydrostatic motions explicitly. In this article, we present a modified nonhydrostatic moist global spectral dynamical core using a dry-mass vertical coordinate, which conserves the mass of dry air naturally. In addition to the vertical coordinate, the modified dynamical core differs from the original Aladin-NH like dynamical kernel in the state variables employed. Specifically, a new temperature variable is introduced to formulate the governing equations and the mass continuity equation is expressed in terms of the dry air density. To assess its performance, an idealized splitting supercell test is conducted. Simulation results from both the modified and original dynamical cores are presented and compared. The results indicate that only the modified dynamic core is able to simulate the splitting supercell with good accuracy comparable to reference solutions from the Model for Prediction Across Scales (MPAS). K E Y W O R D SAladin-NH, dry-mass vertical coordinate, idealized supercell simulation, nonhydrostatic moist atmosphere, spectral dynamical core

Section: Solver Formulationsupporting

confidence: 65%

“…Actually, the present modified moist dynamical core is an extension of our previous works (Wu et al, ; Yang et al, , ). Following Bénard et al .…”

Section: Solver Formulationsupporting

confidence: 58%

A modified nonhydrostatic moist global spectral dynamical core using a dry‐mass vertical coordinate

Peng

Zhang

et al. 2019

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“…Our deep-atmosphere kernel is an extension of Yin-He Global Spectral Model (YHGSM) (Wu et al, 2011), and some standard tests for the YHGSM kernel have already been performed in Yang et al (2015). Hence, only deep-atmosphere effects are tested in this section, and the results validate the correctness and reliability of our deep-atmosphere dynamic core.…”

Section: Test Casesmentioning

confidence: 99%

A semi‐implicit deep‐atmosphere spectral dynamical kernel using a hydrostatic‐pressure coordinate

Yang

Song

et al. 2017

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Most of the present deep‐atmosphere models are based on finite‐difference schemes. This article proposes a novel deep‐atmosphere non‐hydrostatic spectral dynamical kernel with hydrostatic‐pressure based terrain‐following vertical coordinate. Contrary to finite‐difference methods, a spectral transform method is used for the horizontal discretization. The prognostic variables in our dynamical kernel are analogous to the typical ALADIN‐NH spectral model. A two time level semi‐implicit semi‐Lagrangian time‐stepping scheme is applied to enable large time steps and improve the efficiency of integration. A set of test cases are conducted to evaluate the accuracy and stability of the deep‐atmosphere dynamic kernel.

“…The parameters used in the steady-state case are set to T E 0 = 310 K, T P 0 = 240 K, b = 2, k = 3, Γ = 0.005. 38For the sake of brevity, we will refer to the original hybrid method described in Yang et al (2015) as the "Original Hybrid FE method" and to the modified method developed in our article as the "Gauss-based Hybrid FE method". The settings of the employed numerical methods are listed in Table 2.…”

Section: Steady-state Test Case For Global Modelmentioning

confidence: 99%

A modified hybrid finite‐element method for a semi‐implicit mass‐based non‐hydrostatic kernel

Yang

Song

et al. 2020

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A hybrid finite-element vertical discretization method for a semi-implicit mass-based non-hydrostatic kernel is a feasible high-order discretization approach which combines the advantages of both finite-differential and finite-element methods. In this article, we put forward a modified version of the existing hybrid finite-element method to reduce computation load and improve precision. A key feature of our modified method is the presence, in the enlarging step, of new levels which are not equally spaced, but rather based on Gaussian quadrature. A higher-order accuracy may be thus achieved with less enlarged levels by virtue of the properties of Gaussian quadrature. The modified method is also designed to fulfil the constraints required by the dynamic kernel, which themselves are crucial to ensure stability. A set of 2D and 3D test cases are conducted so as to confirm the accuracy and the stability of the new method.