Uncertainties in field-line tracing in the magnetosphere. Part II: the complete internal geomagnetic field
Uncertainties in field-line tracing in the magnetosphere. Part II: the complete internal geomagnetic field
复制标题
磁层中场线追踪的不确定性。
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
K. Freeman
中科院分区：
文献类型：
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作者：
D. Willis;J. Singh;K. Freeman
前一篇文章的讨论仅限于磁层磁场直线跟踪中的不确定性，这些不确定性是由定义内部地磁场的轴对称部分的球谐系数(即Gn0±δGn0)中公布的标准误差引起的。基于轴对称场线解析方程的这些不确定性的数值估计与基于沿磁场线的逐步数值积分的独立计算估计非常一致。这一比较证实了本文使用的计算机程序的准确性，该程序用于估计磁场线跟踪中的不确定度，该不确定度是由定义完整(非轴对称)内部地磁场的全集球谐系数(即GNm±θGNm和HNm±θHnm)公布的标准误差引起的。提出了一种算法，大大减少了在磁场线跟踪中估计这些不确定性所需的计算时间。对一般情况下(1≤n≤10)内磁场的轴对称部分和限制情况下(0≤m≤n，1≤n≤3)内磁场进行了数值计算，验证了算法的有效性。在此基础上，假设该算法可以在否则计算时间长得令人望而却步的情况下可靠地使用。对于完整的内部地磁场，以2RE的标称偶极距离穿过地磁赤道的磁力线的地心距离的最大特征不确定度通常为100公里。以6RE的标称偶极距离穿过地磁赤道的磁力线的相应特征不确定度通常为500公里。给出了显示与磁层中磁场线跟踪有关的特征不确定性的直方图和散点图，以供一系列说明性例子使用。最后，给出了所选地球物理观测站共轭点位置的最大不确定度估计。对磁层磁场线跟踪中的不确定性的数值估计，包括地球物理观测站共轭点位置的相关不确定性，应视为“第一近似”，因为这些估计仅与公布的全套球面损伤系数的标准误差一样准确。然而，与前一篇论文一样，随着球谐系数标准误差的进一步确定，本文开发的所有计算技术都可以用来对磁层磁场线跟踪中的不确定度进行更现实的估计。
The discussion in the preceding paper is restricted to the uncertainties in magnetic-field-iine tracing in the magnetosphere resulting from published standard errors in the spherical harmonic coefficients that define the axisymmetric part of the internal geomagnetic field (i.e. gn0 ± δgn0). Numerical estimates of these uncertainties based on an analytic equation for axisymmetric field lines are in excellent agreement with independent computational estimates based on stepwise numerical integration along magnetic field lines. This comparison confirms the accuracy of the computer program used in the present paper to estimate the uncertainties in magnetic-field-line tracing that arise from published standard errors in the full set of spherical harmonic coefficients, which define the complete (non-axisymmetric) internal geomagnetic field (i.e. gnm ± θgnm and hnm ± θhnm). An algorithm is formulated that greatly reduces the computing time required to estimate these uncertainties in magnetic-field-line tracing. The validity of this algorithm is checked numerically for both the axisymmetric part of the internal geomagnetic field in the general case (1 ≤ n ≤ 10) and the complete internal geomagnetic field in a restrictive case (0 ≤ m ≤ n, 1 ≤ n ≤ 3). On this basis it is assumed that the algorithm can be used with confidence in those cases for which the computing time would otherwise be prohibitively long. For the complete internal geomagnetic field, the maximum characteristic uncertainty in the geocentric distance of a field line that crosses the geomagnetic equator at a nominal dipolar distance of 2 RE is typically 100 km. The corresponding characteristic uncertainty for a field line that crosses the geomagnetic equator at a nominal dipolar distance of 6 RE is typically 500 km. Histograms and scatter plots showing the characteristic uncertainties associated with magnetic-field-line tracing in the magnetosphere are presented for a range of illustrative examples. Finally, estimates are given for the maximum uncertainties in the locations of the conjugate points of selected geophysical observatories. Numerical estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, including the associated uncertainties in thelocations of the conjugate points of geophysical observatories, should be regarded as “first approximations” in the sense that these estimates are only as accurate as the published standard errors in the full set of spherical harmomic coefficients. As in the preceding paper, howerver, all computational techniques developed in this paper can be used to derive more realistic estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, following further progress in the determination of more accurate standard errors in the spherical harmonic coefficients.