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首页> 外文期刊>Journal of Geophysical Research, A. Space Physics: JGR >A computationally compact representation of Magnetic-Apex and Quasi-Dipole coordinates with smooth base vectors
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A computationally compact representation of Magnetic-Apex and Quasi-Dipole coordinates with smooth base vectors

机译：一个计算的紧凑表示Magnetic-Apex和Quasi-Dipole坐标平滑的基向量

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摘要

Many structural and dynamical features of the ionized and neutral upper atmosphere are strongly organized by the geomagnetic field, and several magnetic coordinate systems have been developed to exploit this organization. Quasi-Dipole coordinates are appropriate for calculations involving horizontally stratified phenomena like heightintegrated currents, electron densities, and thermospheric winds; Modified Apex coordinates are appropriate for calculations involving electric fields and magnetic field-aligned currents. The calculation of these coordinates requires computationally expensive tracing of magnetic field lines to their apexes. Interpolation on a precomputed grid provides faster coordinate conversions, but requires the overhead of a sufficiently fine grid, as well as finite differencing to obtain coordinate base vectors. In this paper, we develop a compact and robust representation of the transformation from geodetic to Quasi-Dipole ( QD), Apex, and Modified Apex coordinates, by fitting the QD coordinates to spherical harmonics in geodetic longitude and latitude. With this representation, base vectors may be calculated directly from the expansion coefficients. For an expansion truncated at order 6, the fitted coordinates deviate from the actual coordinates by a maximum of 0.4°,and typically by 0.1°. The largest errors occur in the equatorial Atlantic region.Compared to interpolation on a pre-computed grid, the spherical harmonic representation is much more compact and produces smooth base vectors. An algorithm for efficiently and concurrently computing scalar and vector spherical harmonic functions is provided in the appendix. Computer code for producing the expansion coefficients and evalt ating the fitted coordinates and base vectors is included in the auxiliary material.
机译：许多的结构和动力学特性电离和中性的上层大气强烈组织的地磁场,和几个磁坐标系统已经开发出来利用这个组织。适合计算坐标包括水平分层现象heightintegrated电流,电子密度,和thermospheric风;适合计算坐标电场和磁场field-aligned电流。坐标计算需要昂贵的跟踪磁场线的弯角。预先计算的网格提供插值更快的坐标转换,但要求的开销足够细网格,以及有限差分获得协调基地向量。健壮的表示的转换大地Quasi-Dipole (QD),先端,修改顶点坐标,通过拟合QD球面谐波在大地坐标经度和纬度。基向量可能直接从计算膨胀系数。订单6截短,安装坐标偏离实际坐标的最大值0.4°,通常由0.1°。发生在大西洋赤道地区。在预先计算网格插值,球面谐波表示得多紧凑而产生平滑的基向量。同时算法有效球面谐波计算标量和向量在附录中提供的功能。代码产生膨胀系数evalt操作安装坐标和基地向量是包含在辅助材料。

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