A computationally compact representation of Magnetic-Apex and Quasi-Dipole coordinates with smooth base vectors
TLDR
In this article, the authors developed 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.Abstract:
[1] 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 height-integrated 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 evaluating the fitted coordinates and base vectors is included in the auxiliary material.read more
Citations
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An update to the Horizontal Wind Model (HWM): The quiet time thermosphere
Douglas P. Drob,John T. Emmert,John W. Meriwether,Jonathan J. Makela,Eelco Doornbos,Mark Conde,Gonzalo Hernandez,John Noto,K. Zawdie,Sarah E. McDonald,J. D. Huba,Jeffrey Klenzing +11 more
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Magnetic Coordinate Systems
TL;DR: A review of the most common magnetic coordinate systems and how they are defined, where they are used, and how to convert between them can be found in this paper, where the definitions are presented based on the spherical harmonic expansion coefficients of the International Geomagnetic Reference Field (IGRF) and, in some of the coordinate systems, the position of the Sun which we show how to calculate from the time and date.
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TL;DR: This work focuses on studying the models' capability to reproduce observed ground magnetic field fluctuations, which are closely related to geomagnetically induced current phenomenon and supports NOAA SWPC in their selection of the next numerical model that will be transitioned into operations.
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The Geomagnetic Kp Index and Derived Indices of Geomagnetic Activity
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CM5, a Pre-Swarm Comprehensive Geomagnetic Field Model Derived from Over 12 Yr of CHAMP, Orsted, SAC-C and Observatory Data
TL;DR: A comprehensive magnetic field model named CM5 was derived from CHAMP, Orsted and SAC-C satellite and observatory hourly-means data from 2000 August to 2013 January using the Swarm Level-2 Comprehensive Inversion (CI) algorithm as mentioned in this paper.
References
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TL;DR: In this article, the authors present a dictionary of symbols for modeling the atmosphere, including equations of motion, coordinate and time systems, and initial orbit determination and estimation, as well as various perturbation techniques.
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Fundamentals of Astrodynamics and Applications
TL;DR: In this article, the authors present a dictionary of symbols for modeling the atmosphere, including equations of motion, coordinate and time systems, and initial orbit determination and estimation, as well as various perturbation techniques.
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Journal ArticleDOI
A new magnetic coordinate system for conjugate studies at high latitudes
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TL;DR: In this article, the authors presented a variation on the corrected geomagnetic coordinate system that is well defined and smooth over the entire globe, and provided an analytic expression relating geographic coordinates, including altitude, to the magnetic coordinates.
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