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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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This paper describes the numerical treatment (Ring Average) to relax the time step in finite difference schemes when using spherical/cylindrical coordinates with axis singularities. The Ring Average is used to develop a high-resolution thermosphere-ionosphere coupled community model. This technique is not only a significant improvement in space weather modeling capability, but can also be adapted to more general finite difference solvers for hyperbolic equations in spherical/polar geometries.
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https://doi.org/10.5194/gmd-2020-243
https://doi.org/10.5194/gmd-2020-243

Submitted as: development and technical paper 23 Sep 2020

Submitted as: development and technical paper | 23 Sep 2020

Review status: a revised version of this preprint was accepted for the journal GMD and is expected to appear here in due course.

Development of high-resolution Thermosphere–Ionosphere Electrodynamics General Circulation Model (TIE-GCM) using Ring Average technique

Tong Dang1,2,3,5, Binzheng Zhang4,5, Jiuhou Lei1,2,3, Wenbin Wang5, Alan Burns5, Han-li Liu5, Kevin Pham5, and Kareem A. Sorathia6 Tong Dang et al.
  • 1CAS Key Laboratory of Geospace Environment, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, China
  • 2Mengcheng National Geophysical Observatory, University of Science and Technology of China, Hefei, China
  • 3CAS Center for Excellence in Comparative Planetology, Hefei, China
  • 4Department of Earth Sciences, the University of Hong Kong, Pokfulam, Hong Kong SAR, China
  • 5High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO, USA
  • 6Applied Physics Laboratory, Johns Hopkins University, Laurel, MD, USA

Abstract. When solving hydrodynamic equations in spherical/cylindrical geometry using explicit finite difference schemes, a major difficulty is that the time step is greatly restricted by the clustering of azimuthal cells near the pole due to the Courant-Friedrichs-Lewy condition. This paper adapts the azimuthal averaging-reconstruction (Ring Average) technique to finite difference schemes in order to mitigate the time step constraint in spherical/cylindrical coordinates. The finite-difference Ring Average technique averages physical quantities based on an effective grid and then reconstructs the solution back to the original grid in a piece-wise, monotonic way. The algorithm is implemented in a community upper atmospheric model Thermosphere-Ionosphere Electrodynamics General Circulation Model (TIE-GCM), with horizontal resolution up to 0.625 × 0.625 in the geographic longitude-latitude coordinates, which enables the capability of resolving critical mesoscale structures within the TIE-GCM. Numerical experiments have shown that the Ring Average technique introduces minimal artifacts in the polar region of the GCM solutions, which is a significant improvement compared to the commonly used low-pass filtering techniques such as the fast Fourier transform method. Since the finite-difference adaption of the Ring Average technique is a post-solver type algorithm, which requires no changes to the original computational grid and numerical algorithms, it has also been implemented in much more complicated models with extended physical/chemical modules such as the coupled Magnetosphere Ionosphere Thermosphere (CMIT) model and the Whole Atmosphere Community Climate Model with thermosphere and ionosphere eXtension (WACCM-X). The implementation of the Ring Average techniques in both models enables CMIT and WACCM-X to perform global simulations with a much higher resolution than that used in the community versions. The new technique is not only a significant improvement in space weather modeling capability, but can also be adapted to more general finite difference solvers for hyperbolic equations in spherical/polar geometries.

Tong Dang et al.

 
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Tong Dang et al.

Tong Dang et al.

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Short summary
This paper describes the numerical treatment (Ring Average) to relax the time step in finite difference schemes when using spherical/cylindrical coordinates with axis singularities. The Ring Average is used to develop a high-resolution thermosphere-ionosphere coupled community model. This technique is not only a significant improvement in space weather modeling capability, but can also be adapted to more general finite difference solvers for hyperbolic equations in spherical/polar geometries.
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