A nestable, multigrid-friendly grid on a sphere for global spectral models based on Clenshaw-Curtis quadrature
A nestable, multigrid-friendly grid on a sphere for global spectral models based on Clenshaw-Curtis quadrature
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基于 Clenshaw-Curtis 求积的全局光谱模型的球体上可嵌套、多重网格友好的网格
DOI：
10.1002/qj.3282
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发表时间：
2018
影响因子：
8.9
通讯作者：
Ujiie M.
中科院分区：
文献类型：
--
作者：
Hotta D.;Ujiie M.
提出了一种新的球体网格系统，它允许直接实现基于球谐函数的谱方法和基于网格点的多重网格方法。新网格中的纬度网格点是等距的，并且使用克伦肖-柯蒂斯求积法执行纬度方向上的光谱变换。如果网格截断使得对于 N 的总截断波数至少有 2N+1 个纬度网格点，则使用该新网格和正交的光谱变换被证明在机器精度内是精确的。新的网格和求积法在浅水方程模型和全球 NWP 模型 JMA-GSM 的静水干动力核心上实施和测试。使用新求积法获得的积分结果与使用高斯网格上的传统高斯求积法获得的积分结果几乎相同。只需要对代码进行少量更改即可适应任何基于高斯的频谱模型以采用所提出的正交。
A new grid system on a sphere is proposed which allows for straightforward implementation of both spherical‐harmonics‐based spectral methods and gridpoint‐based multigrid methods. The latitudinal gridpoints in the new grid are equidistant and spectral transforms in the latitudinal direction are performed using Clenshaw–Curtis quadrature. The spectral transforms with this new grid and quadrature are shown to be exact within machine precision provided that the grid truncation is such that there are at least 2N+ 1 latitudinal gridpoints for the total truncation wavenumber ofN. The new grid and quadrature is implemented and tested on a shallow‐water equations model and the hydrostatic dry dynamical core of the global NWP model JMA‐GSM. The integration results obtained with the new quadrature are shown to be almost identical to those obtained with the conventional Gaussian quadrature on a Gaussian grid. Only minor code changes are required to adapt any Gaussian‐based spectral models to employ the proposed quadrature.