An Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory

The improvement of overall uniformity and smoothness of spherical icosahedral grids, the basic framework of atmospheric models, is a key to reducing simulation errors. However, most of the existing grid optimization methods have optimized grid from different aspects and not improved overall uniformi...

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Autores principales:	Fuli Luo, Xuesheng Zhao, Wenbin Sun, Yalu Li, Yuanzheng Duan
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	optimal transformation theory uniform grid optimized spherical icosahedral grid area uniformity interval uniformity Meteorology. Climatology QC851-999
Acceso en línea:	https://doaj.org/article/f97b87ef082545e9930a90c5088b6a9a
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id	oai:doaj.org-article:f97b87ef082545e9930a90c5088b6a9a
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spelling	oai:doaj.org-article:f97b87ef082545e9930a90c5088b6a9a2021-11-25T16:45:48ZAn Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory10.3390/atmos121115162073-4433https://doaj.org/article/f97b87ef082545e9930a90c5088b6a9a2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-4433/12/11/1516https://doaj.org/toc/2073-4433The improvement of overall uniformity and smoothness of spherical icosahedral grids, the basic framework of atmospheric models, is a key to reducing simulation errors. However, most of the existing grid optimization methods have optimized grid from different aspects and not improved overall uniformity and smoothness of grid at the same time, directly affecting the accuracy and stability of numerical simulation. Although a well-defined grid with more than 12 points cannot be constructed on a sphere, the area uniformity and the interval uniformity of the spherical grid can be traded off to enhance extremely the overall grid uniformity and smoothness. To solve this problem, an overall uniformity and smoothness optimization method of the spherical icosahedral grid is proposed based on the optimal transformation theory. The spherical cell decomposition method has been introduced to iteratively update the grid to minimize the spherical transportation cost, achieving an overall optimization of the spherical icosahedral grid. Experiments on the four optimized grids (the spring dynamics optimized grid, the Heikes and Randall optimized grid, the spherical centroidal Voronoi tessellations optimized grid and XU optimized grid) demonstrate that the grid area uniformity of our method has been raised by 22.60% of SPRG grid, −1.30% of HR grid, 38.30% of SCVT grid and 38.20% of XU grid, and the grid interval uniformity has been improved by 2.50% of SPRG grid, 2.80% of HR grid, 11.10% of SCVT grid and 11.00% of XU grid. Although the grid uniformity of the proposed method is similar with the HR grid, the smoothness of grid deformation has been enhanced by 79.32% of grid area and 24.07% of grid length. To some extent, the proposed method may be viewed as a novel optimization approach of the spherical icosahedral grid which can improve grid overall uniformity and smoothness of grid deformation.Fuli LuoXuesheng ZhaoWenbin SunYalu LiYuanzheng DuanMDPI AGarticleoptimal transformation theoryuniform gridoptimized spherical icosahedral gridarea uniformityinterval uniformityMeteorology. ClimatologyQC851-999ENAtmosphere, Vol 12, Iss 1516, p 1516 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	optimal transformation theory uniform grid optimized spherical icosahedral grid area uniformity interval uniformity Meteorology. Climatology QC851-999
spellingShingle	optimal transformation theory uniform grid optimized spherical icosahedral grid area uniformity interval uniformity Meteorology. Climatology QC851-999 Fuli Luo Xuesheng Zhao Wenbin Sun Yalu Li Yuanzheng Duan An Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory
description	The improvement of overall uniformity and smoothness of spherical icosahedral grids, the basic framework of atmospheric models, is a key to reducing simulation errors. However, most of the existing grid optimization methods have optimized grid from different aspects and not improved overall uniformity and smoothness of grid at the same time, directly affecting the accuracy and stability of numerical simulation. Although a well-defined grid with more than 12 points cannot be constructed on a sphere, the area uniformity and the interval uniformity of the spherical grid can be traded off to enhance extremely the overall grid uniformity and smoothness. To solve this problem, an overall uniformity and smoothness optimization method of the spherical icosahedral grid is proposed based on the optimal transformation theory. The spherical cell decomposition method has been introduced to iteratively update the grid to minimize the spherical transportation cost, achieving an overall optimization of the spherical icosahedral grid. Experiments on the four optimized grids (the spring dynamics optimized grid, the Heikes and Randall optimized grid, the spherical centroidal Voronoi tessellations optimized grid and XU optimized grid) demonstrate that the grid area uniformity of our method has been raised by 22.60% of SPRG grid, −1.30% of HR grid, 38.30% of SCVT grid and 38.20% of XU grid, and the grid interval uniformity has been improved by 2.50% of SPRG grid, 2.80% of HR grid, 11.10% of SCVT grid and 11.00% of XU grid. Although the grid uniformity of the proposed method is similar with the HR grid, the smoothness of grid deformation has been enhanced by 79.32% of grid area and 24.07% of grid length. To some extent, the proposed method may be viewed as a novel optimization approach of the spherical icosahedral grid which can improve grid overall uniformity and smoothness of grid deformation.
format	article
author	Fuli Luo Xuesheng Zhao Wenbin Sun Yalu Li Yuanzheng Duan
author_facet	Fuli Luo Xuesheng Zhao Wenbin Sun Yalu Li Yuanzheng Duan
author_sort	Fuli Luo
title	An Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory
title_short	An Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory
title_full	An Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory
title_fullStr	An Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory
title_full_unstemmed	An Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory
title_sort	overall uniformity optimization method of the spherical icosahedral grid based on the optimal transformation theory
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/f97b87ef082545e9930a90c5088b6a9a
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An Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory

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