Abstract

High-order filtering with isotropy of a local-domain data defined at an arbitrary location on the sphere, with an application to scale-decomposition of mean sea level pressure field, was investigated. The equation of high-order filter was based on the implicit hyper-diffusion of 8th-order, which was discretized by the Fourier-finite element method (FFEM). In order to apply the FFEM high-order filter to a local-domain data which is not represented with two-dimensional array, a rotation of coordinates was performed. The geometry of the rotated local domain was made to be either a polar cap (polar cap domain) or a symmetric window with respect to the Equator (Equatorial symmetric domain) to reduce the anisotropy of the local domains caused by the metric effect of spherical coordinates. The rotated local domains are extended by padding artificial data to match the boundary condition of vanishing gradient. The performance of the filters for the symmetric- or asymmetric- domain, was compared for both initial fields defined with an analytic function and the observed meteorological data. It turned out that the filters on the local domains with symmetry, i.e., the polar cap domain and the Equatorial symmetric domain, produced improved results over the local domains with asymmetry: Asymmetric error pattern between the northern and southern boundary, which is typical of the window domain defined on the middle latitude (or between the pole and the Equator), is reduced appreciably and the improvement is shown to become more significant for the window-domain closer to the pole. Through tests with wind fields, the performance of the filters on the polar cap domain and the Equatorial symmetric domain was found comparable to each other. The advantage of polar cap filter, being not available for the Equatorial symmetric domain filter, was illustrated by conducting a scale decomposition and composite analysis of the mean sea level pressure that requires the data manipulations such as a zonal averaging as well as azimuthal-phase shifting.

中文翻译：

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球面局部域的各向同性高阶滤波器

摘要

研究了在球体上任意位置定义的局部数据各向同性的高阶滤波及其在平均海平面压力场的尺度分解中的应用。高阶滤波器方程基于8阶隐式超扩散，并通过傅立叶有限元法（FFEM）离散化。为了将FFEM高阶滤波器应用于未用二维数组表示的局部域数据，执行了坐标旋转。旋转局部区域的几何形状做成相对于赤道的极帽（极帽区域）或对称窗口（赤道对称域），以减小由球坐标的度量效应引起的局部域的各向异性。通过填充人工数据来扩展旋转后的局部域，以匹配消失梯度的边界条件。针对使用解析函数定义的初始字段和观测到的气象数据，对对称或非对称域的过滤器性能进行了比较。事实证明，具有对称性的局部域（即极帽区域和赤道对称域）上的滤波器比具有非对称性的局部域产生了更好的结果：北边界和南边界之间的不对称误差模式是典型的在中纬度（比较分析功能定义的初始字段和观测到的气象数据。事实证明，具有对称性的局部域（即极帽区域和赤道对称域）上的滤波器比具有非对称性的局部域产生了更好的结果：北边界和南边界之间的不对称误差模式是典型的在中纬度（比较分析功能定义的初始字段和观测到的气象数据。事实证明，具有对称性的局部域（即极帽区域和赤道对称域）上的滤波器比具有非对称性的局部域产生了更好的结果：北边界和南边界之间的不对称误差模式是典型的在中纬度（或极点与赤道之间）明显减小，并且对于离极点较近的窗域，改进变得更加明显。通过风场测试，发现极帽区域和赤道对称区域的滤波器性能可比。通过进行比例分解和平均海平面压力的综合分析，需要进行纬向平均和方位相移等数据操作，可以说明极帽过滤器的优势（对于赤道对称域滤波器不可用）。 。