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Distances from auroral zones to the magnetic and geographic equators
0032-0633/82/101073~3.00/0 Pergamon Press Ltd.
Planet. SpaceSci. Vol. 30, No. 10, pp. 1073-1076, 1982 Printed in Great Britain.
DISTANCES
FROM AURORAL ZONES TO THE MAGNETIC AND GEOGRAPHIC EQUATORS K. D. COLE and P. F. B. WILLIAMS
Division of Theoretical and Space Physics, La Trobe University, Bundoora, 3083, Victoria, Australia (Received 9 February 1982) Abstract-Distance from amoral zone is a fundamental parameter in studies of disturbances produced in the thermosphere and ionosphere through the action of the solar wind. Calculations showing the great variation of the distances of the aurora1 “zones” from the magnetic equator and geographic equator are presented in diagrams. An aurora1 zone proximity index is proposed for use in correlative studies of upper atmosphere and of ionospheric disturbances.
INTRODUCTION
The dynamics of the thermosphere is controlled not only by electromagnetic radiation from the Sun but also by energy and momentum supplied by electric currents and the Lorentz force in the ionosphere, especially in the vicinity of auroras (e.g. Cole, 1962, 1975). Effects, such as new wind systems and the changes in composition of the neutral atmosphere which they transport to other parts of the globe from aurora1 regions, or the intensity of hydromagnetic waves originating in the aurora1 zone and transported via the ionosphere, or the intensity of internal gravity waves launched from aurora1 regions are extremely complex and require detailed numerical calculations for their modelling. However, in statistical studies of observations of such and other phenomena travelling from aurora1 regions, the simple notion of distance from the region may be useful. For this reason, calculations of such distances are provided here. Cole suggested that the instantaneous pattern of auroras is that of the polar ionospheric current system responsible for magnetic disturbances, i.e. different from aurora1 isochasms. See Cole and Jacka (1961). Feldstein (1963) showed that the pattern of visible auroras follows the shape of an oval. The deposition of energy into the upper atmosphere is related both to the corpuscular bombardment in aurora and electric current in the ionospheric environment. For the purpose of some statistical studies of relationships of aurora1 region phenomena to low and middle latitudes it is convenient to adopt isolines of zenithal aurora1 frequency (isoaurores) as aurora1 “zones”. These isoaurores have been shown to be close to curves of an equivalent latitude based upon the second adiabatic invariant of geomagnetically trapped
particles (see Bond and Jacka, 1962, 1963). The equivalent latitude is called 0, by Bond and Jacka. Distances have been calculated of the 03 = 22.5” and &= 30” aurora1 isoaurores from (a) the geomagnetic dip equator, and (b) the geographic equator. In the former case the distances were computed in three ways; firstly, along the geomagnetic meridians, secondly, along the geographic meridians and finally, via the shortest great circle distance from each point on the relevant equator. In the latter case distances were taken along the geographic meridians. TECHNIQUE
All distances were computed from manually digitized data using the great circle segments between adjacent digitization points. In the cases of distances along geomagnetic meridians and shortest great circles, computations were made at 5 degree intervals around the relevant equator. In the case of distances along geomagnetic meridians, computations were made at 10 degree intervals around the equator, with 13 unevenly spaced data points taken along each meridian. In all cases, the results were subjected to very mild filtering to reduce the jaggedness due to the digital technique. This filtering had no appreciable effect on the obvious trends observed. The dip equator used was hand digitized from the 100 km altitude data supplied in the United States Air Force Technical Report AFWL-TR-69144. Although this data is for 1970, whereas the data for geomagnetic longitude was for 1977.25, the variation would not be expected to change the results by more than 200 km. Geomagnetic longitude plots were obtained from the Australian Antarctic Division Technical Note “Invariant Geomagnetic Co-ordinates for the 1073
K.
1074
D. COLE and P.
Epoch 1977.25” by J. S. Boyd. These coordinates were computed using a spherical harmonic expansion of an updated version of the 1975 IGRF coordinates. The major errors involved would lie in the choice of non-contemporary maps of aurora1 zones, geomagnetic meridians and dip equator. However, since the greatest variation between the aurora1 zones used and the computed geomagnetic latitudes of 22.5 degrees and 30.0 degrees North and South on the map of geomagnetic coordinates is no more than about 2 degrees North or South (i.e. + 200 km approximately), and the drift of the Earth’s main field over the 7; years from the time
F.
B. WILLIAMS
of the dip equator used to the date of the geomagnetic meridians is about .45 degrees North (i.e. approximately 45 km North) and about 1.8 degrees West (corresponding to a variation in the North-South direction of about -C1.5 degrees or 150 km at the sharpest gradient of the equator), the inaccuracy is not expected to be more than, at very worst, + 400 km. DISTANCE CALCULATIONS
Results of distance calculations are displayed in Figs. 1, 2 and 3. Note the large percentage variation with longitude of the distances to the mag-
~
-60 GEOGRAPHIC
I_ONGl,“OE
0 at
OIP EQUATOR
al
via GEOGRAPHIC
(degrees1
FIG. 1. DISTANCE FROM NORTHERN AURORAL ZONES TO DIP EQUATOR.
-
via GEOMAGNETIC mendians
- - -
“!aS$TEST
~
via GECGRAPHIC meridians
great
6500
FIG. 2. DISTANCE FROM SOUTHERN AURORAL ZONES TO DIP EQUATOR.
1075
Distances from aurora1 zones to the magnetic and geographic equators
-
_---\ /’
9cm-
- \ \
/
NORTHERN 22.Y zone -
SOUTHERN 22.Y zone
-
NORTHERN 300 mrw
- -~
Y)UTHERN
\ 5cm-l -180
FIG.~.
-120
-EC GEOGRAPHIC
AURORAL ZONE PROXIMITY
From a study of the points on the aurora1 zones which were at shortest great circle distance from the selected equatorial points, it becomes obvious that certain limited segments of the aurora1 zones were predominant. Thus it might be expected that the effects of these aurora1 regions might predominate at the equator. Similarly, by selecting points around the aurora1 zones and finding the corresponding points on the equators which are closest, it becomes apparent that large sections of the aurora1 zones are closest to short segments of the equators. In an attempt to evaluate the relative effect the proximity of an aurora1 zone may have on any point on the equators (or in fact on any point on the globe), an index was derived as the integral around the aurora1 zone of the inverse distance from the zone to the point in question; I Zone
dslS
/
-A.
120 LO\GlTUDE
180
(d&T
DISTANCEFROMAURORALZONESTOGEOGRAPHICEQUATORVIAGEOGRAPHICMERIDIANS.
netic dip equator which are more pronounced for the Southern than the Northern Hemisphere. Also note the increase of this longitude variation as the aurora1 zone moves equatorwards. Such large variations should show up in statistical analyses of data measuring aurora1 zone effects on the upper atmosphere and ionosphere in middle and low latitudes.
i.e.
300 me
\
/
where s is the displacement around the aurora1 zone, and S is the distance to the reference (e.g. equatorial) point.
For computational purposes this was approximated by: 360” So/S where s is evaluated at 5 degree intervals Z (geographic longitude) around the zone in question. The index thus defined was computed for points at 5 degree intervals around the dip and geographic equators, with reference to both 22.5 and 30.0 degree Northern and Southern aurora1 zones. The average of the Northern and Southern values was also computed (see Figs. 4 and 5).
DISCUSSION
Of course it is understood that for any single aurora1 substorm the position at which it strikes the thermosphere and dumps energy is not yet predictable, therefore the distances and proximity index mentioned may only be useful in the analysis of large amounts of data concerned with the response of the thermosphere and other parts of the upper atmosphere, e.g. the mesosphere and stratosphere, to solar activity. Also it should be emphasised that isoauroras are determined on the basis of actual observations of auroras under a variety of disturbance conditions. The latitude of the mean positions of the polewards and equatorwards envelopes of aurora1 ovals as a function of the planetary magnetic disturbance K, has been discussed by Bond and Thomas (1971) who
1076
K. D. COLEand P. F. B. WILLIAMS
200I
-180
-120
FIG. 4.
-60 GEQjRAPHlC
-120
0 LONGITUDE
hJree:
120
PRO~MTYINDEXRELATIVETODIPEQUATOR.
ZlO-
200 -I -1eo
A’
’ L-l
-60 GEOGRAPHIC
-
NORTHERN
229
zone
---
SOUTHERN
22.5’
zone
-
AVERAGE
0 LONGITUDE
b&lo
120
FIG. ~.PROXIMITY INDEXRELATIVETOGEOGRAPHICEQUATOR.
compared Southern Hemisphere data with Northern Hemisphere data of Feldsteiu and Starkov (1%7). It would be appropriate to calculate distances and proximity indices for a wider range of 0s corresponding to all levels of Kp.
Acknowledgement-This work was first presented at the Antarctic and Southern Hemisphere Aeronomy Year Workshop at Alpbach, Austria, May 1978 in association with the 24th COSPAR Plenary Meeting.
REFERENCES
Bond, F. R. and Jacka, F. (1962). Aust. J. Phys. 15, 261. Bond, F. R. and Jacka, F. (1963). Aust. J. Phys. 16,514. Bond, F. R. and Thomas, I. C. (1971). Aust. J. Phys. 24, 97. Cole, K. D. (1%2). Aust. J. Phys. 15, 223. Cole, K. D. (1975). J. atmos. ten. Phys. 37, 939. Cole, K. D. and Jacka, F. (l%l). J. geophys. Res. 66, 1584. Feldstein, Ya. I. (1963). Geomag. Aeron. 3, 183. Feldstein, Ya. I. and Starkov. G. V. (1967). Planet. Space Sci. 15, 209.
Planet. SpaceSci. Vol. 30, No. 10, pp. 1073-1076, 1982 Printed in Great Britain.
DISTANCES
FROM AURORAL ZONES TO THE MAGNETIC AND GEOGRAPHIC EQUATORS K. D. COLE and P. F. B. WILLIAMS
Division of Theoretical and Space Physics, La Trobe University, Bundoora, 3083, Victoria, Australia (Received 9 February 1982) Abstract-Distance from amoral zone is a fundamental parameter in studies of disturbances produced in the thermosphere and ionosphere through the action of the solar wind. Calculations showing the great variation of the distances of the aurora1 “zones” from the magnetic equator and geographic equator are presented in diagrams. An aurora1 zone proximity index is proposed for use in correlative studies of upper atmosphere and of ionospheric disturbances.
INTRODUCTION
The dynamics of the thermosphere is controlled not only by electromagnetic radiation from the Sun but also by energy and momentum supplied by electric currents and the Lorentz force in the ionosphere, especially in the vicinity of auroras (e.g. Cole, 1962, 1975). Effects, such as new wind systems and the changes in composition of the neutral atmosphere which they transport to other parts of the globe from aurora1 regions, or the intensity of hydromagnetic waves originating in the aurora1 zone and transported via the ionosphere, or the intensity of internal gravity waves launched from aurora1 regions are extremely complex and require detailed numerical calculations for their modelling. However, in statistical studies of observations of such and other phenomena travelling from aurora1 regions, the simple notion of distance from the region may be useful. For this reason, calculations of such distances are provided here. Cole suggested that the instantaneous pattern of auroras is that of the polar ionospheric current system responsible for magnetic disturbances, i.e. different from aurora1 isochasms. See Cole and Jacka (1961). Feldstein (1963) showed that the pattern of visible auroras follows the shape of an oval. The deposition of energy into the upper atmosphere is related both to the corpuscular bombardment in aurora and electric current in the ionospheric environment. For the purpose of some statistical studies of relationships of aurora1 region phenomena to low and middle latitudes it is convenient to adopt isolines of zenithal aurora1 frequency (isoaurores) as aurora1 “zones”. These isoaurores have been shown to be close to curves of an equivalent latitude based upon the second adiabatic invariant of geomagnetically trapped
particles (see Bond and Jacka, 1962, 1963). The equivalent latitude is called 0, by Bond and Jacka. Distances have been calculated of the 03 = 22.5” and &= 30” aurora1 isoaurores from (a) the geomagnetic dip equator, and (b) the geographic equator. In the former case the distances were computed in three ways; firstly, along the geomagnetic meridians, secondly, along the geographic meridians and finally, via the shortest great circle distance from each point on the relevant equator. In the latter case distances were taken along the geographic meridians. TECHNIQUE
All distances were computed from manually digitized data using the great circle segments between adjacent digitization points. In the cases of distances along geomagnetic meridians and shortest great circles, computations were made at 5 degree intervals around the relevant equator. In the case of distances along geomagnetic meridians, computations were made at 10 degree intervals around the equator, with 13 unevenly spaced data points taken along each meridian. In all cases, the results were subjected to very mild filtering to reduce the jaggedness due to the digital technique. This filtering had no appreciable effect on the obvious trends observed. The dip equator used was hand digitized from the 100 km altitude data supplied in the United States Air Force Technical Report AFWL-TR-69144. Although this data is for 1970, whereas the data for geomagnetic longitude was for 1977.25, the variation would not be expected to change the results by more than 200 km. Geomagnetic longitude plots were obtained from the Australian Antarctic Division Technical Note “Invariant Geomagnetic Co-ordinates for the 1073
K.
1074
D. COLE and P.
Epoch 1977.25” by J. S. Boyd. These coordinates were computed using a spherical harmonic expansion of an updated version of the 1975 IGRF coordinates. The major errors involved would lie in the choice of non-contemporary maps of aurora1 zones, geomagnetic meridians and dip equator. However, since the greatest variation between the aurora1 zones used and the computed geomagnetic latitudes of 22.5 degrees and 30.0 degrees North and South on the map of geomagnetic coordinates is no more than about 2 degrees North or South (i.e. + 200 km approximately), and the drift of the Earth’s main field over the 7; years from the time
F.
B. WILLIAMS
of the dip equator used to the date of the geomagnetic meridians is about .45 degrees North (i.e. approximately 45 km North) and about 1.8 degrees West (corresponding to a variation in the North-South direction of about -C1.5 degrees or 150 km at the sharpest gradient of the equator), the inaccuracy is not expected to be more than, at very worst, + 400 km. DISTANCE CALCULATIONS
Results of distance calculations are displayed in Figs. 1, 2 and 3. Note the large percentage variation with longitude of the distances to the mag-
~
-60 GEOGRAPHIC
I_ONGl,“OE
0 at
OIP EQUATOR
al
via GEOGRAPHIC
(degrees1
FIG. 1. DISTANCE FROM NORTHERN AURORAL ZONES TO DIP EQUATOR.
-
via GEOMAGNETIC mendians
- - -
“!aS$TEST
~
via GECGRAPHIC meridians
great
6500
FIG. 2. DISTANCE FROM SOUTHERN AURORAL ZONES TO DIP EQUATOR.
1075
Distances from aurora1 zones to the magnetic and geographic equators
-
_---\ /’
9cm-
- \ \
/
NORTHERN 22.Y zone -
SOUTHERN 22.Y zone
-
NORTHERN 300 mrw
- -~
Y)UTHERN
\ 5cm-l -180
FIG.~.
-120
-EC GEOGRAPHIC
AURORAL ZONE PROXIMITY
From a study of the points on the aurora1 zones which were at shortest great circle distance from the selected equatorial points, it becomes obvious that certain limited segments of the aurora1 zones were predominant. Thus it might be expected that the effects of these aurora1 regions might predominate at the equator. Similarly, by selecting points around the aurora1 zones and finding the corresponding points on the equators which are closest, it becomes apparent that large sections of the aurora1 zones are closest to short segments of the equators. In an attempt to evaluate the relative effect the proximity of an aurora1 zone may have on any point on the equators (or in fact on any point on the globe), an index was derived as the integral around the aurora1 zone of the inverse distance from the zone to the point in question; I Zone
dslS
/
-A.
120 LO\GlTUDE
180
(d&T
DISTANCEFROMAURORALZONESTOGEOGRAPHICEQUATORVIAGEOGRAPHICMERIDIANS.
netic dip equator which are more pronounced for the Southern than the Northern Hemisphere. Also note the increase of this longitude variation as the aurora1 zone moves equatorwards. Such large variations should show up in statistical analyses of data measuring aurora1 zone effects on the upper atmosphere and ionosphere in middle and low latitudes.
i.e.
300 me
\
/
where s is the displacement around the aurora1 zone, and S is the distance to the reference (e.g. equatorial) point.
For computational purposes this was approximated by: 360” So/S where s is evaluated at 5 degree intervals Z (geographic longitude) around the zone in question. The index thus defined was computed for points at 5 degree intervals around the dip and geographic equators, with reference to both 22.5 and 30.0 degree Northern and Southern aurora1 zones. The average of the Northern and Southern values was also computed (see Figs. 4 and 5).
DISCUSSION
Of course it is understood that for any single aurora1 substorm the position at which it strikes the thermosphere and dumps energy is not yet predictable, therefore the distances and proximity index mentioned may only be useful in the analysis of large amounts of data concerned with the response of the thermosphere and other parts of the upper atmosphere, e.g. the mesosphere and stratosphere, to solar activity. Also it should be emphasised that isoauroras are determined on the basis of actual observations of auroras under a variety of disturbance conditions. The latitude of the mean positions of the polewards and equatorwards envelopes of aurora1 ovals as a function of the planetary magnetic disturbance K, has been discussed by Bond and Thomas (1971) who
1076
K. D. COLEand P. F. B. WILLIAMS
200I
-180
-120
FIG. 4.
-60 GEQjRAPHlC
-120
0 LONGITUDE
hJree:
120
PRO~MTYINDEXRELATIVETODIPEQUATOR.
ZlO-
200 -I -1eo
A’
’ L-l
-60 GEOGRAPHIC
-
NORTHERN
229
zone
---
SOUTHERN
22.5’
zone
-
AVERAGE
0 LONGITUDE
b&lo
120
FIG. ~.PROXIMITY INDEXRELATIVETOGEOGRAPHICEQUATOR.
compared Southern Hemisphere data with Northern Hemisphere data of Feldsteiu and Starkov (1%7). It would be appropriate to calculate distances and proximity indices for a wider range of 0s corresponding to all levels of Kp.
Acknowledgement-This work was first presented at the Antarctic and Southern Hemisphere Aeronomy Year Workshop at Alpbach, Austria, May 1978 in association with the 24th COSPAR Plenary Meeting.
REFERENCES
Bond, F. R. and Jacka, F. (1962). Aust. J. Phys. 15, 261. Bond, F. R. and Jacka, F. (1963). Aust. J. Phys. 16,514. Bond, F. R. and Thomas, I. C. (1971). Aust. J. Phys. 24, 97. Cole, K. D. (1%2). Aust. J. Phys. 15, 223. Cole, K. D. (1975). J. atmos. ten. Phys. 37, 939. Cole, K. D. and Jacka, F. (l%l). J. geophys. Res. 66, 1584. Feldstein, Ya. I. (1963). Geomag. Aeron. 3, 183. Feldstein, Ya. I. and Starkov. G. V. (1967). Planet. Space Sci. 15, 209.