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| Titel |
Uncertainties in field-line tracing in the magnetosphere. Part II: the complete internal geomagnetic field |
| VerfasserIn |
D. M. Willis, J. Robin Singh, K. S. C. Freeman |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
0992-7689
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| Digitales Dokument |
URL |
| Erschienen |
In: Annales Geophysicae ; 15, no. 2 ; Nr. 15, no. 2, S.181-196 |
| Datensatznummer |
250012626
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| Publikation (Nr.) |
 copernicus.org/angeo-15-181-1997.pdf |
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| Zusammenfassung |
| The discussion in the preceding paper is
restricted to the uncertainties in magnetic-field-line 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 ± δgnm and hnm ± δhnm). 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 the
locations 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
harmonic coefficients. As in the preceding paper, however, 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. |
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