Automatic mapping of geomagnetic field & electric current flow in ionospher

Cain, J. C.

Neilon, J. R.

English

NASA Technical Reports Server

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AWGWST 15. 1963 JOWRNAL OF GEOPHYSICAL RSSEARCH VOL. 68, No. 16  
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( Automatic Mapping of the Geomagnetic Field?&: - --  . .  
JOSEPH C. CAIN c*,4k 1 
JAMES R. NEILON (b24*LJ 
- NASA, Goddard Space Flight Center, Greenbelt, Maryland 
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U. S. Weather Bureau, Suitland, Maryland ___ - /os 6 
Abstract. Spheric harmonic representations are used to illustrate the application of the 
This technique is also applied to the representation of model S, fluctuations by maps of elec- 
tric current flow in the ionosphere. A ~ l r H b e  
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field is analyzed, and the 
discuss the application of the field-contouring 
techniques developed at the U. S. Weather Bu- 
reau to  the illustration of the geomagnetic field 
and its time changes. This study, an outgrowth 
of the work with Vanguard 3 (19597) magnetic 
data [Cain et at,  19621 and the analysis of mag- 
netic survey data [Jensen and Cain, 19621, was 
made in connection with preparation for analysis 
of the magnetic data to be obtained with the 
polar orbiting geophysical observatory [Ludwig, 
19631. 
The need for a general system of rapid illus- 
tration in geomagnetism has arisen with the 
advent of methods dowing automatic process- 
ing of large quantities of data. The techniques 
have been found of value not only for illustrab 
ing the results themselves but also in investigat- 
ing the various steps of analyses. 
Contouring procedure. The procedure fol- 
lowed [Bedient and Neilon, 19623 is first t o  
produce coarse grid point values of the function 
t o  be contoured and then to perform a two- 
dimensional quadratic interpolation to locate 
the contour lines on a much h e r  grid. In  the 
application illustrated here the original field is 
computed on a %-inch grid 39 units in latitude 
and 55 units in longitude, a total of 2145 points. 
The interpolation is then performed by means 
of Bessel’s central difference interpolation for- 
mula (second degree) to  produce a further &vi- 
sion of this interval by a factor of 8 SO that  
the ‘decision field’ is a two-dimensional 1/16-inch 
lpresented at the 44th Annual Meeting of the 
plotter pen instructions are generated on a 1/8- 
inch square grid for drawing contours between 
the ‘high’ and ‘low’ points in the field. The avail- 
able variable control features include the selec- 
tion of a particular contour and the contour 
interval t o  be used. The contour programs in- 
clude sufficient corrections to compensate for 
the dynamics of the plotter system with a spe- 
cified electronic filter network. 
1960.0 magnetic field. The magnetic field il- 
lustrated here is that computed by Jensen and 
Cain [1962] for the epoch of 1960.0 using a se- 
lected set of 7400 magnetic field observations 
for the period 1940-1961. Figures 1, 2, 3, and 4 
represent the contours of F ,  H ,  2, and I ,  respec- 
tively, from this 48-term spherical harmonic 
expansion. (The map projection is a modifica- 
tion of the Miller Cylindrical [Miller, 19421 as 
published by Army Map Senice.) The three- 
digit numbers printed in the open areas are 
the highs and lows in the fields positioned 
approximately a t  the decimal point of the num- 
bers. The large-scale kinks that usually appear 
in manually contoured magnetic maps are sig- 
nificantly absent from these four figures. How- 
ever, there are slight waves in a few of the lines, 
owing to the 1/8-inch grid spacing and to the 
dynamics of the plotting system. These small 
irregularities vary for different plotting equip- 
ment. Tests have shown that, on the map scales 
illustrated, the contours are accurate to about 
+lo of latitude. The pen speed for this system 
is about 20 cm/sec, so that the average plotting 
time is of the order of 3 minutes for each map. 
To compare this relatively smoothed version 
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AGU in Washington, D. C., April 23, 1963. 
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of the ficld with a more complex map, in Figure 
5 the Z-component contours have been plotted 
from the 512-term expansion of Jensen and 
Whitulcer [1960]. Comparing the chart of this 
higher-order expansion with Figure 3 shows that 
it is possible with this plotting system to illus- 
trate much more detail than that contained in 
a 48-term expansion. That Figure 5 is not as 
detailed as the original 1955 Z charts (USN 
Hydrographic Office), from which the data for 
the original analysis were taken, is due primar- 
ily to  the fact that this analysis utilized data a t  
only 10" intervals in latitude and longitude. This 
additional smoothing could not have occurred in 
the contouring, since the plotting system utilized 
a grid of 2145 points, whereas the original analy- 
sis by  Jensen and Whitaker only employed ap- 
proximately 614 observed values of 2. With this 
particular grid system i t  should be possible to  
represent spherical harmonic expansions of the 
field containing more than the 512 coefficients 
used. Of course, the possible map detail is lim- 
ited only by the input data and scale of the map 
being used, so that any degree of detail can be 
represented by suitably expanding the scale and 
plotting the map by sections. 
Magnetic variations. This technique of auto- 
matic plotting has also been investigated for the 
illustration of the time variations in the field as 
well as the main field itself. This application is 
illustrated here only by the representation of 
the quiet solar daily variations S,. Figure 6 plots 
an idealized ionospheric current system com- 
puted by M. Sugiura (private communication) 
from a set of harmonic coefficients [Chapman 
and Bartels, 19401 representing the averaged 
quiet field variations a t  the equinoxes. Although 
this particular representation was produced 
from analytic functioiis, i t  is likely that the 
system will be adaptable t o  the illustration of 
worldwide magnetic variations on a synoptic 
basis either by representative ionospheric cur- 
rent stream functions or simply by  contouring 
changes in specific components as abstracted 
from magnetic variometer records. 
, 
Acknowledgment. We wish to acknowledge the 
able assistance of S. Hendricks in preparing the 
diagrams. 
, 
REFERENCES 
Bedient, H. A,, and J. R. Neilon, Automatic pro- 
duction of meteorological contour charts, Con- 
ference on Data Handling, Reduction, and In- 
terpretation in Geophysics, York town Heights, 
New York ,  1962. 
Cain, J. C., I. R. Shapiro, J. D. Stolarik, and J. P. 
Heppner, Vanguard 3 magnetic field observa- 
tions, J .  Geophys. Res., 6'7, 5055-5069, 1962. 
Chapman, S., and J .  Bartels, Geomagnetism, vol. 
2, p. 692, Table 4, Clnrendon Press, Oxford, 1940. 
Jcnsen, D. C., and J .  C. Cain, An interim geomag- 
netic field (abstract), J .  Geophys. Res., 67, 3568- 
3569, 1962. 
Jcnsen, D. C., and W. A. Whitaker, A spherical 
harmonic analysis of the geomagnetic field (ab- 
stract), J .  Geophys. Res., 65, 2500, 1960. 
Imlwig, G. H., The orbiting gcophysicnl obscrva- 
tories, Spncc Sci. Rev . ,  in press, 1963. 
Miller, 0. M., Notes on cylindricnl world map prc- 
jections, Geograph. Rev. ,  S2, 424, 1942. 
(Manuscript reccivcd June 3, 1963.) 
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Automatic mapping of the geomagnetic field

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