A graphical procedure is provided for performing coordinate transformations between the geocentric-solar-equatorial, geocentric-solar-ecliptic and geocentric-solar-magnetospheric coordinate systems. The procedure is designed to facilitate intercomparison of previous studies of interactions between interplanetary and geomagnetic fields that made use of these coordinate systems. The interaction in the geocentric-solar-magnetosphere system has been shown to give the most consistent results

Burch, J. L.

Janetzke, R. W.

English

NASA Technical Reports Server

WX 1 . -'7 --2 n ' 7_:
X-621 14179
. - UD.--DNR -NF MTN .,.--.
-' - " - ORSTUDIS OP ITE ACTIONS- --- _"
,.. ,,-...ETWEEN INTERPLANETARY . ._.
N,'A
... . GEOMAGNETICX -:, :
.-=t . __- I -lLDS
s ".. .U k H
-~ACILC - ~:~ _:~
N74- 82I01
~?p~ * 'uA ~arm.
ITASFRATFOR STUDIES OF INTRCON
N--- -"T I BET-WEEN INTERPLANETARNGEOA/AND GEMAGETIC FI1p$S
I 0 B NK-
_ .- - _ :- - ' -.
-7
- - NrA..
4 -RNE YL-t
I: N-' (ASI- -X-7_68) COO-DIAGTE T -,-2826iTEANSFORMA'IICS FOR SUDIS OF
\ jjj-- { ITERAC2IONS BEiWEEN INTErPLaNETARY AND"
' GEOAGETIC FIELDS (NASA) 19 p IIC $.0 Unclas
- - .- ---- : 0-3. B : G3/29 4 3319 - --"- -
- ---,- - -- '. . -- - ; -"- . -- " - .-
-"N OD A .- '*l " - -
_ -..-. ,.GO RD .SPACE F.LIH ! CENTER
REN L--T -MR-YLAD -.
c -N
" .A-- ." -- , . s-- -..- - : --. / . '
" - '- ' -. - '- . - .- ' - N- N - .--.
https://ntrs.nasa.gov/search.jsp?R=19740020147 2020-03-23T07:40:33+00:00Z
COORDINATE TRANSFORMATIONS FOR STUDIES
OF INTERACTIONS BETWEEN INTERPLANETARY
AND GEOMAGNETIC FIELDS
By
J. L. Burch & R. W. Janetzke
Laboratory for Planetary Atmospheres
NASA-Goddard Space Flight Center
Greenbelt, Md. 20771
April 1974
I
ABSTRACT
A graphical procedure is provided for performing coordinate
transformations between the geocentric-solar-equatorial, geocentric-
solar-ecliptic and geocentric-solar-magnetospheric coordinate systems.
This procedure should facilitate intercomparison of the many previ-
ously published studies of possible interactions between interplanetary
and geomagnetic fields that have been carried out in various of these
three coordinate systems. It will hopefully also make easier the
performance of future studies of the interaction in the geocentric-
solar-magnetospheric system, which of the three has been shown to
give the most consistent results.
INTRODUCTION
The purpose of this report is to provide a convenient means of
transforming satellite vector data from solar-equatorial (GSEQ) and
solar-ecliptic (GSE) coordinates to solar-magnetospheric (GSM) coor-
dinates, which have been shown to be the most appropriate of the three
for use in studies of possible interactions between interplanetary and
geomagnetic fields. The information presented herein can be used for
two important purposes: first, to facilitate the performance of future
studies of the interaction in a common coordinate system, and second,
to make possible intercomparison of the many previously published
studies that were, for reasons chiefly concerned with the expense
involved in computer coordinate transformations, presented in various
of these three different coordinate systems.
The solar-magnetospheric system was introduced by Ness (1965),
who found that the position of the magnetotail neutral sheet showed
a more systematic behavior in GSM coordinates than in GSE or geomag-
netic coordinates. Subsequently Hirshberg and Colburn (1969), in
examining the statistical relationship of geomagnetic activity to
interplanetary magnetic field (IMF) parameters, found a better corre-
lation when the IMF was expressed in GSM coordinates than when it
was expressed in GSEQ coordinates. Similarly, Arnoldy (1971) examined
the correlation between disturbances registered by the AE index and
various IMF parameters for GSM and GSE coordinates, concluding that
the relationship was more consistent for GSM coordinates. Arnoldy
also showed that a nearly linear statistical relationship existed
between the hourly average AE index and the previous hour's integrated
GSM southward component of the INF. Although this was a very signifi-
cant statistical result, it did not imply that a southward IMF E
component was a necessary prerequisite for the occurrence of substorm activ-
ity in the auroral zone. In fact, examples of northward-INF auroral-
zone substorms have been pointed out by Burch (1972) and others. This
does not mean, however, that the size or occurrence of substorms is
not related to the INMF direction. Rather it simply implies that the
relationship is more subtle than one that can be described by the
mere "IMF southward" or "IMF northward" dichotomy that has been
adopted or attacked by many investigators. The transfer of energy,
if not mass and momentum, from the solar wind to the magnetosphere
does seem to occur more efficiently when the IMF is directed more
southward. The energy transfer does not, however, stop when the
IMF 2 component becomes northward in any particular coordinate system.
Plasma flow and magnetic-field observations in the tail (Hones
et al., 1972, Nishida and Hones, 1974) are beginning to provide
convincing evidence of the occurrence of magnetic merging across the
neutral sheet. The situation there is much simpler than that at the
interface between interplanetary and geomagnetic fields since the
plasma densities and magnetic field strengths are equal and 
the
fields are antiparallel on either side of the merging region. The
more complicated situation existing at the magnetopause, coupled
with the lack of coverage by spacecraft remaining in the magnetopause
layer for extended periods of time, give us less hope of obtaining
in situ evidence for merging between interplanetary and geomagnetic
fields. Nevertheless, quantitative information on large-scale mag-
netospheric parameters, such as polar-cap electric fields (Mozer and
Gonzalez, 1973) and the amount of magnetic flux transferred from
the dayside to the nightside (Burch, 1973), as they respond to
IMF variations have shown systematic behavior consistent with the
results of recent geometrical merging models (Gonzalez, 1973;
Sonnerup, 1974). Needless to say, it is crucial that such investigations
be performed in an appropriate coordinate system, such as GSM, that
takes into account the changing relative orientation of the magneto-
spheric field in the solar-wind flow.
The detailed relationship between IMF parameters and the occur-
rence of substorms is complicated further by the sparse network of
ground-based observatories capable of detecting isolated substorms.
It is rather firmly established that the INMF determines the size of
the auroral oval (Akasofu et al., 1973; Kamide and Akasofu, 1974)
f
and with it the size of and total energy involved in substorms. One
should not conclude, however, from the observations of Akasofu et al.,
1973), which indicated that contracted-oval substorms occur when the
IMF Z component is GSEQ- or GSE- northward, that the occurrence of
substorms is unrelated to the IMF direction. Burch (1974) has shown
that re-examination of the contracted-oval substorms of the Akasofu
et al. (1973) study with the IMF expressed in GSM coordinates results
in a rather systematic behavior. That is, the IMF latitude was in
the rather narrow range of about 100 to 300 northward for a half-hour
or more before the onset of each substorm.
It is evident, therefore, that further progress in our under-
standing of the interplanetary-geomagnetic field interaction will be
aided by the availability of IMF data in GSM coordinates. Unfortunate-
ly, almost all the data available in the National Space Science Data
Center are in GSEQ or, to a lesser extent, GSE coordinates, and are
in plotted form rather than in digital form, making transformation
by computer both time-consuming and costly. Furthermore, there exist
many published papers on the interaction in which GSEQ or GSE coor-
dinates were used. As noted above, intercomparison of these would be
aided by the existence of a quick visual means of coordinate trans-
formation such as that described below.
DESCRIPTION OF COORDINATE TRANSFORMATION PLOTS
An example of the relative orientations of the GSM, GSE, and
GSEQ systems on day 210 at 13 hrs. UT is shown in Figure 1. The
relation between GSM coordinates and either of the other two is speci-
fied by the single parameter a. The value of a represents the rota-
tion angle from the positive EGSM axis, about the X-axis, which in
all three systems is directed from the earth toward the sun. Positive
values of a correspond to cases in which the 9 axis of the GSEQ or
GSE system is tilted toward dusk, or toward the +YGSM axis, as in
Figure 1.
The matrix formulations of Russell (1971) were used in generating
the plots in Figures 2 through 10. The paper by Russell (1971) also
describes in detail the three coordinate systems discussed here as
well as other systems of geophysical interest.
Figures 2 and 3 show contour plots of constant a as functions
of UT and day of year for GSEQ and GSE coordinates respectively. The
value of c1 derived from one of these plots is then used to choose
one of the seven plots (one for each 50 increment in a) in Figures 4
through 10 which transform to the GSM system. The same plots are used
for the GSEQ-GSM and the GSE-GSI transformation since the information
in Figures 4-10 depends only on the value of a. In each of the plots
in Figures 4-10, contours of constant GSM latitude (solid curves) and
of constant GSM longitude (dashed curves) are plotted versus latitude
and longitude in either GSEQ or GSE coordinates. Note in Figures 4
through 10 that the upper signs on the GSE/GSEQ latitude axis and on
the GSM latitude contours are used for positive values of a while the
lower signs are used for negative values of ~.
REFERENCES
Akasofu, S.-I., P. D. Perreault, F. Yasuhara and C.-I. Meng, Auroral
substorms and the interplanetary magnetic field, J. Geophys. Res.,
78, 7490, 1973.
Arnoldy, R. L., Signature in the interplanetary medium for substorms,
J. Geophys. Res., 76, 5189, 1971.
Burch, J. L., Rate of erosion of dayside magnetic flux based on a
quantitative study of the dependence of polar cusp latitude on
the interplanetary magnetic field, Radio Science, 8, 955, 1973.
Burch, J. L., Observations of interactions between interplanetary
and geomagnetic fields, Rev. Geophys. Space Phys., August 1974.
Hirshberg, J., and D. S. Colburn, Interplanetary field and geomagnetic
variations -- a unified view, Planet. Space Sci., 1183, 1969.
Hones, E. W., Jr. J. R. Asbridge, S. J. Bame, M. D. Montgomery,
S. Singer and S.-I. Akasofu, Measurements of magnetotail plasma
flow made with Vela 4B, J. Geophys. Res., 77, 5503, 1972.
Kamide, Y., and S.-I. Akasofu, Latitudinal cross-section of the
auroral electrojet and its relation to the interplanetary magnetic
field polarity, J. Geophys. Res., in press, 1974.
Mozer, F. S., and W. D. Gonzalez, Response of polar cap convection
to the interplanetary magnetic field, J. Geophys. Res., 78, 6784,
1973.
Ness, N. F., The earth's magnetic tail, J. Geophys. Res., 70, 2989,
1965.
Nishida, A., and E. W. Hones, Jr., The association of plasma-sheet
thinning with neutral-line formation in the magnetotail, J. Geophys.
Res., 79, 535, 1974.
Russell, C. T., Geophysical coordinate transformations, Cosmic Electro-
dynamics, 2, 184, 1971.
I'
Sonnerup, B.U.O., Magnetopause reconnection rate, J. Geophys. Res.,
79, 1546, 1974.
7
FIGURE CAPTIONS
Figure 1: Relative orientations of the GSM, GSE and GSEQ coordinate
systems on day 210 at-13 hrs. UT. The positive direction
for a as used in figures 2 and 3 is illustrated.
Figure 2: Contours of constant a, where a is the angle of rotation
about the X axis from the GSM system to the GSE system.
The plus signs mark the extreme values, a = + 350
Figure 3: Contours of constant a, where a is the angle of rotation
about the X axis from the GSM system to the GSEQ system.
The plus signs mark the extreme. values, a = + 37.80
Figure 4: Contours of constant GSM latitude and longitude as func-
tions of GSE or GSEQ latitude (X) and longitude (0) for the
rotation angle a = + 50. The upper signs on the GSE/GSEQ
latitude axis and on the GSM latitude contours are used for
positive values of a, while the lower signs are used for
negative values of a.
Figure 5: Same as Figure 4 except for a = + 100.
Figure 6: Same as Figure 4 except for a = + 150.
Figure 7: Same as Figure 4 except for a = + 200.
Figure 8: Same as Figure 4 except for a = + 25.
Figure 9: Same as Figure 4 except for a = + 300.
Figure 10: Same as Figure 4 except for a = + 350 .
ZGSM ZGSEQ
CL/ ZGSE
+20
GSE
GSEQ
FIGURE 1
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
24 15 30 14 I 16 31 15 30 15 30 14 29 14 29 13 28 12 27 12 27 11 26 11 26
' .
20
-30 .
16
14
UT(HRS)
12
O -I . -10 10 20 - - 5 30 20 10
10 . . .
02
30 60 90 120 150 180 210 240 270 300 330 360
DAY OF YEAR.
FIGURE 2
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
15 30 14 I 16 31 15 30 15 30 14 29 14 29 13 28 12 27 12 27 II 26 II 26
2 4 11 I I I I I I I I
22 -
20 
- 35
183 -30
16 -
14 .
UT (HRS)
12
10 0 -10 -Id O IO 20 30 a=-35 +30 20
-20
4 .
02
30 60 90 120 150 180 210 240 270 300 330 360
DAY OF YEAR
TfITTn' 1
uise
092 0Z2 OR~ 0Y? OOz 091 OZI 09 Ot' 0
09
09!0 09t
11 111 oiii
ii 'ii III ii
Ott,---~
~- I I _ _ _
at=tio
*80
-04
60
140 !
60 00120
oo
0 40 80 120 160 200 240 280 320 3
GSE
GSE0
FIG0 URE
0 40 so 120 ISO 200 240 280 520 360
t80 40
20 0 80 0 12020
60
+40
o 40 140 t oLo
I7 240 280
\ q
2 \ Ir
O 40 80 120 160 200 240 280 320 360
FIGURE 6
Q=t20
180
+60 
- I.
\ 1 / lo/
\s I I 1 1 1
0 160 -1 0
WE0 l IO i I [ -os M
0 40 80 120 160 200 40 280 340
t 2 I soo
-+:I 2 0 / 1 / 26 8
2i i /oI 120
GS I I
GSEQ
FIGURE 7
0 40 80 120 160 200 240 20 320 36
180 .0-
j/0/;40
. .o I 'I / i
\ " I 1B 1 1
0 40 80 10 160 200 240 280 320 360
2O = /' I 63
-20 40 060 ?8 3 So SO
*GSE
GURE 8
FIGURE 8
_= -30 °
\8I 0 I----. "\ -sot80
-% -- 60-
t60 \ +2
\ I / / //
t40 \ \  /
0
s20o10
20 4 160 2
oL S loi\m
oo , o , o 1o , o
DGSE
~ 1 1/ 20 \ 30
20I /oo
+40 k 0
+80
0 40 80 120 160 200 240 280 320 360
OGSE
GSEO
FIGURE 9
C3 3 50
~-so-!80
+ 60 1/ -
20
( 40 \ \ /
coo0
;80 I 4i I I
2f0 0 / 2 2 0 320 /
o / / / /
\ 11 / o I 1
o I U II
;40 2 320
0 40 0 120 200 240 280 320 360
0 FIGURE 10


Coordinate transformations for studies of interactions between interplanetary and geomagnetic fields

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server