Geomagnetic Coordinate System Research Articles

Geomagnetic, geocentric, and geodetic coordinate transformations

Abstract A requirement in geomagnetism is to make transformations between geocentric, geodetic (spheroidal), and geomagnetic coordinate systems. A few of these transformations may be included in textbooks, but we have never noted them all presented. This paper provides derivations and subroutines for conversion of spatial coordinates and Cartesian magnetic field components between any combinations of these three coordinate systems.

A new magnetic coordinate system for conjugate studies at high latitudes

Studying magnetically conjugate phenomena at very high latitudes requires a magnetic coordinate system that is smooth and well defined at the geographic poles. In addition, it should provide for accurate comparisons at different altitudes. In this report we present a variation on the corrected geomagnetic coordinate system that is well defined and smooth over the entire globe. It provides an analytic expression relating geographic coordinates, including altitude, to the magnetic coordinates. The coordinate system is produced by tracing magnetic field lines using the IGRF85 reference magnetic field model with time derivatives updating the model to 1988. An expansion of the relationship in terms of spherical harmonics has been determined, which then provides the required well‐defined and smooth relationship over the entire globe. Independent expansions for different altitudes show a smooth functional relationship of the coefficients of the expansion with altitude, and therefore simple interpolation schemes can be used to provide an appropriate expansion at any altitude between 0 km and approximately 600 km. By reversing the process, the inverse expansions relating the magnetic coordinates to geographic coordinates have also been determined. The effects of the seasonal variation in the Sun's declination along with the variation in the Sun's apparent position due to the eccentricity of the Earth's orbit result in a variation of nearly 1 hour of magnetic local time for a fixed UT over the course of a year. In many applications this variation may be important and should be included when presenting data in terms of magnetic latitude and MLT.

Global quiet day field variation model WDCA/SQ1

The quiet daily variations of the geomagnetic field, called Sq, have been modeled for the extremely quiet (solar‐terrestrial disturbance) conditions using the digital values from magnetograms obtained from a worldwide distribution of observatories. This model, WDCA/SQ1, has been deposited at World Data Center A for Solar Terrestrial Physics as a set of data files and a Fortran computer program for retrieving the quiet variation field values at any world location, day of the year, and time of day. The WDCA/SQ1 model does not yet contain a solar‐cycle adjustment; it is a best representation for the sunspot minimum period. Presently, the dependence on year is just an adjustment for the geomagnetic coordinate system. Nevertheless, even in active years the model provides an adequate description of the minimum Sq changes.

Problems with deducing ionospheric plasma convection patterns

It is well‐known that convection electric fields have an important effect on the ionosphere‐thermosphere system at high latitudes and that a quantitative understanding of their effect requires a knowledge of the plasma convection pattern. Consequently, convection electric fields have been measured by a variety of techniques, including satellite, rocket, and balloon‐borne probes, optical tracking of ionized barium clouds, incoherent scatter observations of drifting F region plasma, and coherent scatter observations of drifting E region irregularities. Since all of these measurement techniques provide information on only a limited spatial region at any time, the construction of the overall convection pattern requires a synthesis of data obtained at a variety of places and times. Some of the problems associated with this procedure are examined in this study using incoherent scatter radar data as an example. In this case the main problem stems from the great variability of the convection electric field. Even for very similar magnetic and IMF conditions, the synthesis of convection data obtained on different days produces a convection pattern which has a fairly large uncertainty. For the case considered, the uncertainty is sufficiently large so that the characteristic differences between the H. Volland [1978] and R. A. Heelis et al. [1982] convection models cannot be clearly identified. In comparison to this uncertainty, the uncertainties associated with assuming how corotation is driven and with transforming velocities between geographic and geomagnetic coordinate systems are negligible. The selection of the “correct” magnetic coordinate system is also less important in view of the convection variability.

Time variation of instantaneous equivalent Sq current system

We have examined the time variation of the instantaneous equivalent S q current system during 1–18 March 1980, by removing the averaged UT variation caused by the difference between geographic and geomagnetic coordinate systems. The additional current system thus obtained shows several typical patterns which explain the variation field. Some of them may be explained by the IMF polarity effect or by the geomagnetic disturbance field of polar origin, but others appear to be caused by the variation of the ionospheric dynamo. The latter lasts for several hours or sometimes for over ten hours and may be explained by the variation of diurnal or semi-diurnal tidal winds.

Longitude and Seasonal Variations of the Sq Current System

The ‘equivalent circuit method’ of deriving electric currents in the ionosphere from assumed values of conductivities and emf's has been described earlier. The ionosphere is represented as a large circuit network, with the Hall effect included, and this network is solved by an iterative procedure on a computer. A single tidal wind system, the ‘1—2’ mode, is used as the driving force of the dynamo. The winds are converted from the geographic to the geomagnetic coordinate system. The international geomagnetic reference field (IGRF) is used to provide magnetic field values for calculating the dynamo emf's and the conductivities. The agreement between the calculated and observed positions of the focuses of the current system is remarkable when we consider that no seasonal variation of the wind was included. Seasonal variations of the reversal times of the equatorial electrojet are obtained in rough agreement with observation, whereas the calculated variations of the intensity of the electrojet do not agree so well.

Numerical evaluation of the auroral orientation curves II

The parameters of importance in the evaluation of the auroral orientation curves have been examined. The original auroral orientation curves were obtained by graphical integration and the coordinate system was based on magnetic data for epoch 1945. These parameters have been tested by means of a numerical integration method and a revised geomagnetic coordinate system and it has been shown that the accuracy in the location of the auroral orientation curves when using these improvements is determined by the accuracy of the raw data. DOI: 10.1111/j.2153-3490.1969.tb00492.x

On the orientation of auroral arcs

Information on the direction of auroral arcs, mostly all sky camera data during IGY, has been collected and organized in a geomagnetic coordinate system, corrected by the higher order spherical harmonic terms.By means of interpolation and integration between the measured values it was possible to obtain curves in a polar plot representing auroral arcs over the polar region in the latitude range 64–90 degrees.The ovals of auroral arcs do not follow the corrected geomagnetic latitudes. They are furthest from the pole on the night-side e.g. 70.5° at 24, 79.9° at 06, 79.2° at 12 and 75.5° of latitude at 18 hours. A small dawn-dusk asymmetry has also been observed, the curves being closer to the pole at 06 hours than at 18 hours.In the polar region between latitudes 80–85° for a time interval around 1600 hours it has been found that the auroral arcs have an angle relative to the solar direction of about 20 degrees.The shape of the auroral orientation curves corresponds (in the auroral zone region) with the auroral oval based on the occurrence of aurora.

Latitude effect of solar cosmic radiation on February 23, 1956 with respect to the problem of effective geomagnetic coordinate system

According to the results of our considerations we state, that the best approximation to a unique mean trend of points for solar cosmic rays is reached if we use the conventional geomagnetic system as base and apply corrections for excentric dipole location. Though the points for some european and american stations are better aligned in the intermediate westward shifted system, there are observed at least two different trends.