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Position and movement of the equatorial electrojet over Ghana
Journal of Atmospheric andTerrestrial Physics, 1962,Vol.24,pp.491to502.Pergamon Press Ltd.Printed inNorthern Ireland
Position and movement of the equatorial electrojet over Ghana D. G. OSBORNE Department
of Physics, University
of Ghana
(Received 21 December 1961) Abstract-Measurements of absolute vertical field in order to locate the magnetic equator and of diurnal variation at two stations near this equator are described and interpreted. It is shown that the observed variability of the diurnal variation can be explained by supposing changes from day to day in the position and strength of the electrojet. The mean position of the jet axis lies very close to the magnetic equator for the period February and March 1961, but the axis moves from one day to another with a root mean square displacement of 46 km. The lack of dependence of jet strength of the normal current system introduces considerable errors in esti-
mates of magnetic variation based on supposedly fixed ratios between non-equatorial and equatorial stations. INTRODUCTION THE large horizontal diurnal variations found at equatorial stations like Huancayo were attributed by EUEDAL (1947, 1948) to a narrow band of current in the ionosphere flowing eastwards over the magnetic equator. This current is called the equatorial electrojet. A quantitative theory has been developed by BAKER and MARTY-N (1953), BAKER (1953) and others suggesting that the current is a reinforcement, due to increased ionospheric conductivity near the magnetic equator, of the current system responsible for quiet day diurnal variation (S,,). ONWUMECHILLI (1959) calculated the diurnal variation to be expected from a simple model electrojet. With suitably chosen parameters and the addition of a normal S, variation (estimated from records at stations outside the electrojet area) the variations predicted by the model fitted observations at a number of stations in Nigeria. He found that during the period 25 November 1956 to 21 January 1957 the electrojet in Nigeria had a width of about 440 km and was centred slightly south of the magnetic equator. FORBUSH and CASAVERDE (1961) found that the jet near Huancayo in South America for the period 1957-1959 was about 660 km wide and centred over the magnetic equator. RIVERS (personal communication) and WRIGHT (personal communication), on the basis of measurements made in Nigeria, suggested that the centre of the electrojet moves north or south of the magnetic equator on different days. Preliminary studies in Ghana which gave support to this suggestion were reported by OSBORNE (1960). This paper describes measurements to locate the magnetic equator in northern Ghana, gives mean values for diurnal variation at two stations in Ghana during February and March 1961 and interprets individual records to determine the position and movement of the equatorial electrojet. THE MAGNETIC EQUATOR The magnetic equator has been defined by VESTINE (1960, p. 474) as, “the globeencircling line along which the vertical component of the earth’s main magnetic 491
492
OSBORNE
D. G.
field is zero”. This definition is not very precise. In attempting to locate this equator the absolute vertical field component is measured at particular places and times and it is not easy to isolate the “main” field from the variations that occur. Similar problems were met in defining the position of the magnetic poles and are mentioned by VESTWE et ab. (1947a) and JONES (1948) and considered more fully by MAYAUD (1954). If values for the absolute vertical field are used directly in locating the position of the magnetic equator its calculated position fluctuates due to magnetic variation and disturbances. Near the magnetic equator variations in vertical field are greater in daytime than at night and for the survey in Ghana the position of zero mean vertical field for the hours 0000 to 0300 was chosen to define a point on the magnetic equator for that day. On 16 December 1960 absolute values of vertical field were read with a B.M.Z. at six stations on a north-south traverse across the region of the magnetic equator. Table 1. Values for vertical field for traverse on 16 December Site
Tamale airport Tamale-Bolgatanga Milepost 18 Milepost 28 Milepost 26 Milepost 24 Milepost 18 Tamale airport
1960
Latitude
Longitude
Time (hours)
9” 24.8’
0” 52.7’
0913
-589
9” 9” 9” 9” 9” 9”
0” 0” 0” 0” 0” 0”
1015 1041 1055 1107 1258 1654
-181 + 048 +006 -040 -185 -581
2 (Y)
road 40’ 48’ 46’ 45’ 40’ 24.8’
50’ 51’ 50’ 49’ 50’ 52.7’
Values for local survey on 15 December Latitude 9” 23.6’ 9” 24.4’ 9” 27’
1960
2 (Y) -605 -625 -530
The line of zero vertical field passed 39 km north of Tamale through the point 9” 46’ N, 50’ W (&Ol’). A later traverse further east showed that the line of zero field passed through the point 9” 41’ N, 0” 05’ W (&02’) near to a small anomaly and crossed the Greenwich meridian at about 9’ 40’ N. We are indebted to the Ghana Survey Department for the geographical co-ordinates used in this calculation. Fig. 1 shows the absolute value of the vertical component, in gammas, plotted against latitude for the traverse on 16 December 1960 at approximately 0” 50’ W. The field changes by 15 y for every kilometre moved along a north-south line. Using a variometer at Tamale during the period for each traverse it was possible to show that the diurnal variation produces an error of less than 1 km in the calculated position of the magnetic equator. The main studies of magnetic variation at Tamale were made during February and March 1961. The base line values for the vertical variometer were found using the B.M.Z. and the mean values for vertical field between 0000 and 0300
Position and ‘movement of the equatorial electrojet over Ghana
493
hours found for each day. Assuming that the meridional field gradient was still 15 y km-l the position of the magnetic equator for each night was calculated. The equator was found to move less than 0.7 km from its mean position over the whole
Latitude
Fig. 1. Vertical field at different latitudes (distances north of Tamale are shown). period. It was therefore concluded that the definition of the magnetic equator by night-time values of vertical field is a suitable one and that this equator passes 39 km north of Tamale. DIURNAL VARIATION Measurements of magnetic variation were taken at Tamale (9” 24’ N, 0” 53’ W) using an Askania GV-3 variograph and at Legon (5’ 38’ N, 0” 11’ W) using two Gulf flux-gate magnetometers mounted to record separately changes in vertical and northward horizontal field components. Due to a fault in the apparatus the values for vertical field at Legon had later to be rejected. The parameters required for the calculation were the variations in the vertical and horizontal fields at Tamale and the horizontal field at Legon. These were recorded for thirty-five complete days in February and March 1961 which form an effectively random sample of The period was fairly quiet magnetically. days near to the Spring equinox. Hourly means were found, the value taken for any hour being the mean for the preceding hour (thus the value written for 0900 hours is the mean for the period 0800-0900). The means of these hourly values over the thirty-five days are given in Table 2 and plotted in Fig. 2, the base-line adopted for each component being its mean value for the hours 0100, 0200 and 0300. From top to bottom the curves represent horizontal field at Tamale, H,, and at Legon, H,, and the vertical field at Tamale, 2,. Plotting the mean value for the hour on the ordinate for the hour has effectively advanced the curves by half an hour. The curves are of the type expected at equatorial stations such as these. A narrow electrojet current near the magnetic equator would produce a greater
494
D. G. OSBORNE Table 2. Mean hourly values Hour
0100 0200 0300 0400 0500 0600 0700 0800 0900 1000 1100 1200
0100
ET
2,
HL
Hour
H,
-01 00 00 02 02 04 05 17 47 83 105 106
00 00 01 01 01 01 01 03 06 09 10 10
-01 00 01 04 05 07 10 18 33 47 51 48
1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400
89 67 42 23 15 11 07 03 00 -01 -01 -01
0600
/ 200
/ 800
&I! 07 04 02 --01 -03 -03 -01 -01 -01 00 00 00
fft 36 23 15 06 07 03 02 -02 -04 -03 -04 -02
2* 30
HCWS Fig. 2. Mean diurnal variation.
diurnal range in H at Tamale than at Legon. Underneath the jet (at Tamale) the diurnal range in 2 would be small, although to one side of it (at Legon) it would be large. The variation curves for individual days differ somewhat from the mean. Curves for Hr and HL follow the same pattern each day with considerable differences in amplitude but only slight shifts of phase. The vertical variation at Tamale, Z,, changes from day to day both in amplitude and phase. On one day it was of opposite phase to that of the mean, on others it showed a minimum in the early morning or late afternoon instead of near mid-day. The amplitude changes in the horizontal variations can be attributed to changes in strength of the 8, current system and of the electrojet. The more complicated
Position
and movement
of the equatorial
eleotrojet
over Ghana
495
changes in the variation of vertical field at Tamale can be explained by supposing that the electrojet moves further to the north or south at different times. It is clear that the vertical field at Tamale due to the jet would change sign if the centre of the jet moved south of the station. In order to determine the position and movement of the electrojet it is first necessary to define what is meant by its position. The definition adopted is that the axis of the equatorial electrojet is the line on the earth’s surface where the jet produces no vertical component of magnetic field. North and south of this line the jet will produce upwards and downwards fields respectively. Calculations were made to estimate the position of the jet axis each day at the hour when the horizontal field at Tamale was a maximum. This approximates to the time of maximum jet current intensity because the normal diurnal variation and the jet variation have approximately the same phase. The calculations required comparison of ranges for different components at Tamale and Legon and for this purpose the range was defined as the difference between the value of the component for the hour of maximum horizontal field at Tamale and the mean value for the hours 0100, 0200 and 0300 of the same day. For these night-time hours the effect of the jet should be very small. Another reason for choosing this definition for range is that the horizontal component may pass through a minimum during the afternoon on certain days and the full diurnal range does not, therefore, indicate the difference between fields with and without the jet. POSITION OF THE EQUATORIAL ELECTROJET It may be assumed that the magnetic variation at a station near to the electrojet is the sum of a normal variation and a jet effect. If the jet is a reinforcement of the normal current system the two terms &ill not be independent of each other. The expressions Range H,, Jet H, and Normal H, represent the observed horizontal diurnal range at Legon, the part of this due to the jet and the part due to normal variation respectively. Replacing L with T indicates Tamale instead of Legon. The ranges are measured according to the definition already given. Using this symbolism the assumption made is that Range H,
= Jet H,
+ Normal H,
(1)
for a station X. A similar relation holds for the vertical component 2. ONWUMECHILLI (1959) postulates as a model for the electrojet a uniform horizontal band of current of strengthj units per unit width at a height h and with a half-width w. The magnetic field produced by such a current at a distance x from the axis is given by Jet H, and
= 2j tan-l
Jet 2,
=jln
2wh
1 1
+ (x2 - w”) + (x + M2 + (Z - w)2
(3)
These ranges are proportional to the current intensity in the jet. Their ratio is independent of current intensity and for a jet of fixed width at a constant height depends only on x, the distance from the axis.
496
D. G. OSBORNE
The model jet predicts ranges in agreement with the means of observations in Nigeria for the period December 1956 to January 1957 if h = 100 km and w = 220 km. The real jet may be much more complicated than the model and the field produced may include a part due to an induced current system in the earth, but the simple model has been given parameters which allow for this and enable ranges to be predicted which agree with observation. Using these parameters the values of the predicted vertical and horizontal fields due to the jet, and their ratio, have been calculated for different distances, x, from the electrojet axis and plotted as Fig. 3. For the range -150 < x: < 150 km the ratio changes almost linearly with x. In order to use the data available from measurements of variation at Tamale and Legon to estimate the position of the electrojet a number of approximations are made. These are now listed and discussed. 1. The observed horizontal diurnal range at Legon is regarded as a normal variation unaffected by the jet. Its mean value is 48 y. Legon is about 4” south of the magnetic equator and the model jet proposed by ONWUMECHILLIpredicts a jet effect with a mean range of 8 y at this distance from the axis. 2. The normal diurnal range in horizontal field at Tamale is taken to be the same as the normal horizontal range at Legon. The form of the S, current system in equatorial regions, excluding the electrojet effect, would not be expected to give very different horizontal variations at stations only 400 km apart. Using a relation suggested by ONWUMECHILLI(1959) the calculated mean normal horizontal ranges for Tamale and Legon are 53 and 59 y respectively. But this relation is based on tables compiled by VESTINE et al. (1947a) for the years 1922-1933 using data from 100 observatories of which only five were in Africa and the accuracy of the calculated ranges is uncertain. 3. The vertical diurnal variation at Tamale is attributed solely to the jet. A vertical variation due to underground anomaly should be in phase with the horizontal variation and could not account for the wide difference in range and phase of the vertical variation at Tamale from day to day. Near the magnetic equator the vertical variation due to the normal S, current system should be small and is ignored. 4. The final approximation made is to assume that the ratio of the vertical to the horizontal field due to the jet at Tamale fits the curve predicted by OXWUMECHILLI’S model jet and shown in Fig. 3. Thus the value of this ratio on any day enables x, the distance between Tamale and the electrojet axis, to be read off from the graph. The approximations already stated give the horizontal jet range at Tamale as the difference between the observed horizontal ranges at Tamale and Legon, or Jet H, = Range H, - Range H,.
(4)
It would be expected that since this model jet fits observations in Nigeria at stations some 500 km east of those used in Ghana it would also apply to measurements in Ghana. Changes in jet width would also change the ratio of the vertical to horizontal fields produced at Tamale, but these could not cause the large changes which are observed.
Position and movement of the equatorial electrojet over Ghana
497
I-
-I Tamoi
Legon I - 500
1-1 -400
-300 x,
-200
km
-100
100
IO
North from axis
Fig. 3. Horizontal, and vertical fields produced by a model jet of unit bwrrent strength, and their ratio, at different distances from the jet axis. The positions of Tamale and Legon are shown for a jet centred over the magnetic equator.
The exact calculation of the separate jet and normal effects at a station like Tamale requires measurements of variation on the same days at stations lying north and south away from the electrojet but in equatorial regions. If further stations were sited also near to the jet it would be nnnecess~ry to use the predictions from a model jet to determine the form of the ratio curve in Fig. 3. Until such measurements are made it is necessary to make approximations of the type listed above. The calculation for the mean position of the jet is now given. The mean maximum value of horizontal field at Tamale over the thirty-five days occurs for the hour 1100-1200. The mean values for this hour are: Range HT = 106 y, Range HL = 48 y, Range 2, = 10 y. Using the approximations described the jet produces a mean horizontal field at Tamale of 58 y and a mean vertical field of 10 y. The ratio of the ranges is lo/58 (= o-172) and the mean value of x is 51 km. The error from instrumental causes arises mainly in measuring the small change in vertical field at Tamale and introduces a probable error in the calculated value of x of about 3 km. Correcting for the approximations made in calculating the horizontal jet range by adding S y to
D. G. OSBORNE
498
allow for the jet effect at Legon and 6 y for the difference in normal horizontal ranges between Legon and Tamale changes the value of x from 51 to 42 km. Although these corrections are inexact it is important that they change the calculated value of x by only 9 km and it would seem reasonable to claim that over the thirty-five days the probable mean position of the jet axis is 42 f 10 km north of Tamale. The magnetic equator passes 39 & 2 km north of Tamale so that the mean position of the jet axis lies very close to the magnetic equator. JET POSITION EACH DAY The position of the jet axis at the time of maximum horizontal field at Tamale (normally the hour 1100-1200) was calculated for each day making the approximations indicated. The mean value for this position is 53 km north of Tamale, with ‘a standard error for the mean calculated from the scatter of values on individual days of 8 km. This compares well with an uncorrected value of the axis position, calculated from the mean diurnal ranges over the period, of 51 km north of Tamale. The calculated position of the axis on each day is shown in Fig. 4. The position
20
28
March
IO
20
1961 Fig. 4. Location of jet axis at time of maximum on different days.
&l,“dPY
varies considerably, the root mean square displacement from the mean position The uncertainty in calculating any being 46 km, almost half a degree of latitude. one position is less than 10 km. Attempting to correct for the approximations involved would shift the mean but leave a similar change in position for each day. The daily movement of the jet is deduced from the variability in the diurnal variation at Tamale, this variability may be taken as an indication of the movement regardless of the detailed approximations involved in deriving its numerical value. It can be shown that different possible models for the jet shift the calculated mean position for the axis but make only a small difference in the calculated
Position and movement
of the equatorial electrojet over Ghana
499
displacement from the mean from day to day. The corrections suggested for the mean ranges due to the jet effect at Legon and the difference in normal variation at Tamale and Legon cannot be applied to the values for individual days. COMPARISONWITH VALUES FROM IBADAN Due to malfunction of the apparatus values for the vertical field variation at Instead, the vertical field variation at Ibadan was Legon had to be rejected. compared with the calculated behaviour of the jet on each day. The magnetic observatory at Ibadan is at 7” 26.6’ N, 3” 54’ E and about 250 km south of.the magnetic equator. Hourly values for the magnetic components at Ibadan during February and March 1961 were made available for the purpose of comparison. The daily variation in vertical field at Ibadan is large and is due almost entirely to the jet. On days when the jet current is stronger than usual the range in vertical field at Ibadan should be greater. It may be supposed that the strength of the jet current is indicated by the strength of the horizontal range due to the jet at Tamale and that the current strengths at Tamale and in the jet due north of Ibadan are similar on the same day. Hence the relation between horizontal range due to the jet at Tamale and vertical range at Ibadan was examined. The coefficient of correlation was 0.78 averaged thirty-five days. By contrast the correlation coefficient between horizontal and vertical ranges at Ibadan over the first fifteen days of this period is only 0.29, the horizontal range there being mainly a normal, non-jet, variation. The observed vertical range at Ibadan depends on both the strength and position of the electrojet. Its ratio to the horizontal jet field at Tamale should be independent of jet strength and dependent only on jet position. Fig. 5 shows the _ =A I.6 -
1.4 -
.
I.2 -
X,
km
North
from
Tomole
Fig. 5. (Vertical field range at Ibadan)/(calculated horizontal jet field at Tamale) plotted against position of the electrojet.
500
D. G. OSBORNE
ratio of the ranges (Range &/Jet HT) plotted against the calculated distance of the jet axis from Tamale (2) for each day. An approximately linear relationship holds. The point A refers to a day of high magnetic disturbance (10 March 1961) with K, = 7” over the relevant period. For this day the jet strength was very weak and hence its exact value proportionately more uncertain and this point was rejected. The point B is for the preceding day when the values were distorted by an anomalous maximum due to a sudden storm commencement at about 1330 hours. Excluding these two extreme points the correlation coefficient is 0.76 over the,remaining thirty-three days, showing that the vertical field produced at Ibadan by the jet is greater when the jet axis lies further to the north of Tamale. This suggests that over this short period the mean maximum vertical range due to the jet occurs some distance south of Ibadan. The high correlation between the ratio of the ranges and the electrojet position supports the calculations which established that position. If the line in Fig. 5 is extrapolated the intercept on the x axis is at -204 km. If the jet axis ever lay as much as 204 km south of Tamale it should also pass directly over Ibadan, producing zero vertical field there as the extrapolated curve suggests. STRENGTH OF THE ELECTROJET The diurnal ranges of horizontal field at Tamale and Legon were compared for each day. The horizontal range at Legon is due mainly to the normal S, current system. The difference between the horizontal range at Tamale on any day and the range at Legon for the same day is due almost entirely to the electrojet current strength on that day. Fig. 6 is a scatter diagram for (Range H, - Range HL) against (Range HL) on different days; hence it is approximately a plot of electrojet The coefficient of correlation is strength against the strength of the S, system. 0.36 over thirty-five days. Although this is statistically significant the dependence of the electrojet current on the S, current is very weak. As the horizontal range at Legon includes a small effect from the electrojet the true correlation between electrojet current and the strength of the normal S, current system must in fact be slightly less than 0.36 over the 35day period. FORBUSH and C~ASAVERDE(1961, p. 29) give similar evidence for thinking the electrojet to be practically independent of the normal current strength. This independence is surprising if the electrojet is a reinforcement of the normal current system, for although the enhancement of conductivity may vary from day to day it would be expected t’hat days with a stronger S, current would show a stronger jet current as well. The jet has a weaker dependence on the normal current system than present theories suggest and it is possible that the jet and S, currents are in different regions of the ionosphere. From Fig. 6 it is clear that for any individual day it is useless to predict the diurnal range at Legon by multiplying the measured range at Tamale by a constant factor. If the equatorial electrojet strengt,h does not depend on the strength of the normal current system the ratio of horizontal ranges between any stations near the jet and others far away will vary greatly from day to day. In considering the earth’s main magnetic field VESTINE et al. (1947a) calculated the amplitude of S, on individual days on the basis of observed diurnal variations at Huancayo, close
Position
and movement
of the equatorial
electrojet
over Ghana
501
60-
.
.
.
0
I IO
20
30 Raw
Fig. 6. Difference
between
40 H,.
50
60
70
80
y
horizontal ranges at Tamale and Legon horizontal range at Legon.
plotted
against
to the jet. The variations at other latitudes were calculated from these and used to correct the measured field at particular places and times for the effect of diurnal Later, VESTINE et al. (1947b) gave diagrams to show the changes of variation. diurnal variation with latitude. The weak correlation between jet and S, current systems makes these calculations of questionable value for the determination of diurnal variation on individual days. CoNCLUsIoNs It has been shown that the mean position of the axis of the equatorial electrojet during February and March 1961 lay in the region 42 f 8 km north of Tamale. The magnetic equator passed 39 f 2 km north of Tamale. There was a wide scatter in the axis position from day to day with a root mean square displacement of about 46 km. The approximations used in the calculation have been examined and the results substantiated by comparison with measurements made at Ibadan. No relation between the displacement and various suggested causative factors has been found. There is no simple relationship between the strengths of the electrojet current and the normal S, current system on different days. Acknowledgements--I wish to thank Professor R. W. H. WRIGHT for his help with this work, Dr. A. ONWUMECHILLI for supplying hourly values of magnetic components at Ibadan and the Ghana Meteorological Department for helping to maintain the Askania variograph at Tamale.
502
D. G. OSBORNE REFERENCES
BAKJZRW. G, BAKER W. G. and MARTYN D. F. E~EDAL J. EGEDAL J. FORBUSH S. E. and CASAVERDE M. JONES H. S. MAYAUD P. N.
1953 1953 1947 1948 1961 1948 1954
ON~~JMECHILLI A. OSBORNE D. G. VESTINE L.
1959 1960 1960
VESTINE L. et al. VESTINE L. et al.
1947a 1947b
Phil. Trans. A 246, 295. Phil. Trana. A 246, 281. Terr. Magn. Atmos. Elect. 52, 449. Nature, Lond. 161, 443. Carnegie Inst. Wash., Publ. No. 620. Polar Rec. 5, 148. Expeditions Polaires Franc&es, Resultats Scienti$ques, Fast 1, SXV. 2, 113. J. Atmosph. Terr. Phys. 13, 235. Proc. 12th Assembly, I.U.G.G. In press. Physics of the Upper Atmosphere (Ed. by J. A. RATCLIFFE). Academic Press, New York. Carnegie Inst Wash., Publ. No. 578. Carnegie Inst. Wash., Publ. No. 580.
Position and movement of the equatorial electrojet over Ghana D. G. OSBORNE Department
of Physics, University
of Ghana
(Received 21 December 1961) Abstract-Measurements of absolute vertical field in order to locate the magnetic equator and of diurnal variation at two stations near this equator are described and interpreted. It is shown that the observed variability of the diurnal variation can be explained by supposing changes from day to day in the position and strength of the electrojet. The mean position of the jet axis lies very close to the magnetic equator for the period February and March 1961, but the axis moves from one day to another with a root mean square displacement of 46 km. The lack of dependence of jet strength of the normal current system introduces considerable errors in esti-
mates of magnetic variation based on supposedly fixed ratios between non-equatorial and equatorial stations. INTRODUCTION THE large horizontal diurnal variations found at equatorial stations like Huancayo were attributed by EUEDAL (1947, 1948) to a narrow band of current in the ionosphere flowing eastwards over the magnetic equator. This current is called the equatorial electrojet. A quantitative theory has been developed by BAKER and MARTY-N (1953), BAKER (1953) and others suggesting that the current is a reinforcement, due to increased ionospheric conductivity near the magnetic equator, of the current system responsible for quiet day diurnal variation (S,,). ONWUMECHILLI (1959) calculated the diurnal variation to be expected from a simple model electrojet. With suitably chosen parameters and the addition of a normal S, variation (estimated from records at stations outside the electrojet area) the variations predicted by the model fitted observations at a number of stations in Nigeria. He found that during the period 25 November 1956 to 21 January 1957 the electrojet in Nigeria had a width of about 440 km and was centred slightly south of the magnetic equator. FORBUSH and CASAVERDE (1961) found that the jet near Huancayo in South America for the period 1957-1959 was about 660 km wide and centred over the magnetic equator. RIVERS (personal communication) and WRIGHT (personal communication), on the basis of measurements made in Nigeria, suggested that the centre of the electrojet moves north or south of the magnetic equator on different days. Preliminary studies in Ghana which gave support to this suggestion were reported by OSBORNE (1960). This paper describes measurements to locate the magnetic equator in northern Ghana, gives mean values for diurnal variation at two stations in Ghana during February and March 1961 and interprets individual records to determine the position and movement of the equatorial electrojet. THE MAGNETIC EQUATOR The magnetic equator has been defined by VESTINE (1960, p. 474) as, “the globeencircling line along which the vertical component of the earth’s main magnetic 491
492
OSBORNE
D. G.
field is zero”. This definition is not very precise. In attempting to locate this equator the absolute vertical field component is measured at particular places and times and it is not easy to isolate the “main” field from the variations that occur. Similar problems were met in defining the position of the magnetic poles and are mentioned by VESTWE et ab. (1947a) and JONES (1948) and considered more fully by MAYAUD (1954). If values for the absolute vertical field are used directly in locating the position of the magnetic equator its calculated position fluctuates due to magnetic variation and disturbances. Near the magnetic equator variations in vertical field are greater in daytime than at night and for the survey in Ghana the position of zero mean vertical field for the hours 0000 to 0300 was chosen to define a point on the magnetic equator for that day. On 16 December 1960 absolute values of vertical field were read with a B.M.Z. at six stations on a north-south traverse across the region of the magnetic equator. Table 1. Values for vertical field for traverse on 16 December Site
Tamale airport Tamale-Bolgatanga Milepost 18 Milepost 28 Milepost 26 Milepost 24 Milepost 18 Tamale airport
1960
Latitude
Longitude
Time (hours)
9” 24.8’
0” 52.7’
0913
-589
9” 9” 9” 9” 9” 9”
0” 0” 0” 0” 0” 0”
1015 1041 1055 1107 1258 1654
-181 + 048 +006 -040 -185 -581
2 (Y)
road 40’ 48’ 46’ 45’ 40’ 24.8’
50’ 51’ 50’ 49’ 50’ 52.7’
Values for local survey on 15 December Latitude 9” 23.6’ 9” 24.4’ 9” 27’
1960
2 (Y) -605 -625 -530
The line of zero vertical field passed 39 km north of Tamale through the point 9” 46’ N, 50’ W (&Ol’). A later traverse further east showed that the line of zero field passed through the point 9” 41’ N, 0” 05’ W (&02’) near to a small anomaly and crossed the Greenwich meridian at about 9’ 40’ N. We are indebted to the Ghana Survey Department for the geographical co-ordinates used in this calculation. Fig. 1 shows the absolute value of the vertical component, in gammas, plotted against latitude for the traverse on 16 December 1960 at approximately 0” 50’ W. The field changes by 15 y for every kilometre moved along a north-south line. Using a variometer at Tamale during the period for each traverse it was possible to show that the diurnal variation produces an error of less than 1 km in the calculated position of the magnetic equator. The main studies of magnetic variation at Tamale were made during February and March 1961. The base line values for the vertical variometer were found using the B.M.Z. and the mean values for vertical field between 0000 and 0300
Position and ‘movement of the equatorial electrojet over Ghana
493
hours found for each day. Assuming that the meridional field gradient was still 15 y km-l the position of the magnetic equator for each night was calculated. The equator was found to move less than 0.7 km from its mean position over the whole
Latitude
Fig. 1. Vertical field at different latitudes (distances north of Tamale are shown). period. It was therefore concluded that the definition of the magnetic equator by night-time values of vertical field is a suitable one and that this equator passes 39 km north of Tamale. DIURNAL VARIATION Measurements of magnetic variation were taken at Tamale (9” 24’ N, 0” 53’ W) using an Askania GV-3 variograph and at Legon (5’ 38’ N, 0” 11’ W) using two Gulf flux-gate magnetometers mounted to record separately changes in vertical and northward horizontal field components. Due to a fault in the apparatus the values for vertical field at Legon had later to be rejected. The parameters required for the calculation were the variations in the vertical and horizontal fields at Tamale and the horizontal field at Legon. These were recorded for thirty-five complete days in February and March 1961 which form an effectively random sample of The period was fairly quiet magnetically. days near to the Spring equinox. Hourly means were found, the value taken for any hour being the mean for the preceding hour (thus the value written for 0900 hours is the mean for the period 0800-0900). The means of these hourly values over the thirty-five days are given in Table 2 and plotted in Fig. 2, the base-line adopted for each component being its mean value for the hours 0100, 0200 and 0300. From top to bottom the curves represent horizontal field at Tamale, H,, and at Legon, H,, and the vertical field at Tamale, 2,. Plotting the mean value for the hour on the ordinate for the hour has effectively advanced the curves by half an hour. The curves are of the type expected at equatorial stations such as these. A narrow electrojet current near the magnetic equator would produce a greater
494
D. G. OSBORNE Table 2. Mean hourly values Hour
0100 0200 0300 0400 0500 0600 0700 0800 0900 1000 1100 1200
0100
ET
2,
HL
Hour
H,
-01 00 00 02 02 04 05 17 47 83 105 106
00 00 01 01 01 01 01 03 06 09 10 10
-01 00 01 04 05 07 10 18 33 47 51 48
1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400
89 67 42 23 15 11 07 03 00 -01 -01 -01
0600
/ 200
/ 800
&I! 07 04 02 --01 -03 -03 -01 -01 -01 00 00 00
fft 36 23 15 06 07 03 02 -02 -04 -03 -04 -02
2* 30
HCWS Fig. 2. Mean diurnal variation.
diurnal range in H at Tamale than at Legon. Underneath the jet (at Tamale) the diurnal range in 2 would be small, although to one side of it (at Legon) it would be large. The variation curves for individual days differ somewhat from the mean. Curves for Hr and HL follow the same pattern each day with considerable differences in amplitude but only slight shifts of phase. The vertical variation at Tamale, Z,, changes from day to day both in amplitude and phase. On one day it was of opposite phase to that of the mean, on others it showed a minimum in the early morning or late afternoon instead of near mid-day. The amplitude changes in the horizontal variations can be attributed to changes in strength of the 8, current system and of the electrojet. The more complicated
Position
and movement
of the equatorial
eleotrojet
over Ghana
495
changes in the variation of vertical field at Tamale can be explained by supposing that the electrojet moves further to the north or south at different times. It is clear that the vertical field at Tamale due to the jet would change sign if the centre of the jet moved south of the station. In order to determine the position and movement of the electrojet it is first necessary to define what is meant by its position. The definition adopted is that the axis of the equatorial electrojet is the line on the earth’s surface where the jet produces no vertical component of magnetic field. North and south of this line the jet will produce upwards and downwards fields respectively. Calculations were made to estimate the position of the jet axis each day at the hour when the horizontal field at Tamale was a maximum. This approximates to the time of maximum jet current intensity because the normal diurnal variation and the jet variation have approximately the same phase. The calculations required comparison of ranges for different components at Tamale and Legon and for this purpose the range was defined as the difference between the value of the component for the hour of maximum horizontal field at Tamale and the mean value for the hours 0100, 0200 and 0300 of the same day. For these night-time hours the effect of the jet should be very small. Another reason for choosing this definition for range is that the horizontal component may pass through a minimum during the afternoon on certain days and the full diurnal range does not, therefore, indicate the difference between fields with and without the jet. POSITION OF THE EQUATORIAL ELECTROJET It may be assumed that the magnetic variation at a station near to the electrojet is the sum of a normal variation and a jet effect. If the jet is a reinforcement of the normal current system the two terms &ill not be independent of each other. The expressions Range H,, Jet H, and Normal H, represent the observed horizontal diurnal range at Legon, the part of this due to the jet and the part due to normal variation respectively. Replacing L with T indicates Tamale instead of Legon. The ranges are measured according to the definition already given. Using this symbolism the assumption made is that Range H,
= Jet H,
+ Normal H,
(1)
for a station X. A similar relation holds for the vertical component 2. ONWUMECHILLI (1959) postulates as a model for the electrojet a uniform horizontal band of current of strengthj units per unit width at a height h and with a half-width w. The magnetic field produced by such a current at a distance x from the axis is given by Jet H, and
= 2j tan-l
Jet 2,
=jln
2wh
1 1
+ (x2 - w”) + (x + M2 + (Z - w)2
(3)
These ranges are proportional to the current intensity in the jet. Their ratio is independent of current intensity and for a jet of fixed width at a constant height depends only on x, the distance from the axis.
496
D. G. OSBORNE
The model jet predicts ranges in agreement with the means of observations in Nigeria for the period December 1956 to January 1957 if h = 100 km and w = 220 km. The real jet may be much more complicated than the model and the field produced may include a part due to an induced current system in the earth, but the simple model has been given parameters which allow for this and enable ranges to be predicted which agree with observation. Using these parameters the values of the predicted vertical and horizontal fields due to the jet, and their ratio, have been calculated for different distances, x, from the electrojet axis and plotted as Fig. 3. For the range -150 < x: < 150 km the ratio changes almost linearly with x. In order to use the data available from measurements of variation at Tamale and Legon to estimate the position of the electrojet a number of approximations are made. These are now listed and discussed. 1. The observed horizontal diurnal range at Legon is regarded as a normal variation unaffected by the jet. Its mean value is 48 y. Legon is about 4” south of the magnetic equator and the model jet proposed by ONWUMECHILLIpredicts a jet effect with a mean range of 8 y at this distance from the axis. 2. The normal diurnal range in horizontal field at Tamale is taken to be the same as the normal horizontal range at Legon. The form of the S, current system in equatorial regions, excluding the electrojet effect, would not be expected to give very different horizontal variations at stations only 400 km apart. Using a relation suggested by ONWUMECHILLI(1959) the calculated mean normal horizontal ranges for Tamale and Legon are 53 and 59 y respectively. But this relation is based on tables compiled by VESTINE et al. (1947a) for the years 1922-1933 using data from 100 observatories of which only five were in Africa and the accuracy of the calculated ranges is uncertain. 3. The vertical diurnal variation at Tamale is attributed solely to the jet. A vertical variation due to underground anomaly should be in phase with the horizontal variation and could not account for the wide difference in range and phase of the vertical variation at Tamale from day to day. Near the magnetic equator the vertical variation due to the normal S, current system should be small and is ignored. 4. The final approximation made is to assume that the ratio of the vertical to the horizontal field due to the jet at Tamale fits the curve predicted by OXWUMECHILLI’S model jet and shown in Fig. 3. Thus the value of this ratio on any day enables x, the distance between Tamale and the electrojet axis, to be read off from the graph. The approximations already stated give the horizontal jet range at Tamale as the difference between the observed horizontal ranges at Tamale and Legon, or Jet H, = Range H, - Range H,.
(4)
It would be expected that since this model jet fits observations in Nigeria at stations some 500 km east of those used in Ghana it would also apply to measurements in Ghana. Changes in jet width would also change the ratio of the vertical to horizontal fields produced at Tamale, but these could not cause the large changes which are observed.
Position and movement of the equatorial electrojet over Ghana
497
I-
-I Tamoi
Legon I - 500
1-1 -400
-300 x,
-200
km
-100
100
IO
North from axis
Fig. 3. Horizontal, and vertical fields produced by a model jet of unit bwrrent strength, and their ratio, at different distances from the jet axis. The positions of Tamale and Legon are shown for a jet centred over the magnetic equator.
The exact calculation of the separate jet and normal effects at a station like Tamale requires measurements of variation on the same days at stations lying north and south away from the electrojet but in equatorial regions. If further stations were sited also near to the jet it would be nnnecess~ry to use the predictions from a model jet to determine the form of the ratio curve in Fig. 3. Until such measurements are made it is necessary to make approximations of the type listed above. The calculation for the mean position of the jet is now given. The mean maximum value of horizontal field at Tamale over the thirty-five days occurs for the hour 1100-1200. The mean values for this hour are: Range HT = 106 y, Range HL = 48 y, Range 2, = 10 y. Using the approximations described the jet produces a mean horizontal field at Tamale of 58 y and a mean vertical field of 10 y. The ratio of the ranges is lo/58 (= o-172) and the mean value of x is 51 km. The error from instrumental causes arises mainly in measuring the small change in vertical field at Tamale and introduces a probable error in the calculated value of x of about 3 km. Correcting for the approximations made in calculating the horizontal jet range by adding S y to
D. G. OSBORNE
498
allow for the jet effect at Legon and 6 y for the difference in normal horizontal ranges between Legon and Tamale changes the value of x from 51 to 42 km. Although these corrections are inexact it is important that they change the calculated value of x by only 9 km and it would seem reasonable to claim that over the thirty-five days the probable mean position of the jet axis is 42 f 10 km north of Tamale. The magnetic equator passes 39 & 2 km north of Tamale so that the mean position of the jet axis lies very close to the magnetic equator. JET POSITION EACH DAY The position of the jet axis at the time of maximum horizontal field at Tamale (normally the hour 1100-1200) was calculated for each day making the approximations indicated. The mean value for this position is 53 km north of Tamale, with ‘a standard error for the mean calculated from the scatter of values on individual days of 8 km. This compares well with an uncorrected value of the axis position, calculated from the mean diurnal ranges over the period, of 51 km north of Tamale. The calculated position of the axis on each day is shown in Fig. 4. The position
20
28
March
IO
20
1961 Fig. 4. Location of jet axis at time of maximum on different days.
&l,“dPY
varies considerably, the root mean square displacement from the mean position The uncertainty in calculating any being 46 km, almost half a degree of latitude. one position is less than 10 km. Attempting to correct for the approximations involved would shift the mean but leave a similar change in position for each day. The daily movement of the jet is deduced from the variability in the diurnal variation at Tamale, this variability may be taken as an indication of the movement regardless of the detailed approximations involved in deriving its numerical value. It can be shown that different possible models for the jet shift the calculated mean position for the axis but make only a small difference in the calculated
Position and movement
of the equatorial electrojet over Ghana
499
displacement from the mean from day to day. The corrections suggested for the mean ranges due to the jet effect at Legon and the difference in normal variation at Tamale and Legon cannot be applied to the values for individual days. COMPARISONWITH VALUES FROM IBADAN Due to malfunction of the apparatus values for the vertical field variation at Instead, the vertical field variation at Ibadan was Legon had to be rejected. compared with the calculated behaviour of the jet on each day. The magnetic observatory at Ibadan is at 7” 26.6’ N, 3” 54’ E and about 250 km south of.the magnetic equator. Hourly values for the magnetic components at Ibadan during February and March 1961 were made available for the purpose of comparison. The daily variation in vertical field at Ibadan is large and is due almost entirely to the jet. On days when the jet current is stronger than usual the range in vertical field at Ibadan should be greater. It may be supposed that the strength of the jet current is indicated by the strength of the horizontal range due to the jet at Tamale and that the current strengths at Tamale and in the jet due north of Ibadan are similar on the same day. Hence the relation between horizontal range due to the jet at Tamale and vertical range at Ibadan was examined. The coefficient of correlation was 0.78 averaged thirty-five days. By contrast the correlation coefficient between horizontal and vertical ranges at Ibadan over the first fifteen days of this period is only 0.29, the horizontal range there being mainly a normal, non-jet, variation. The observed vertical range at Ibadan depends on both the strength and position of the electrojet. Its ratio to the horizontal jet field at Tamale should be independent of jet strength and dependent only on jet position. Fig. 5 shows the _ =A I.6 -
1.4 -
.
I.2 -
X,
km
North
from
Tomole
Fig. 5. (Vertical field range at Ibadan)/(calculated horizontal jet field at Tamale) plotted against position of the electrojet.
500
D. G. OSBORNE
ratio of the ranges (Range &/Jet HT) plotted against the calculated distance of the jet axis from Tamale (2) for each day. An approximately linear relationship holds. The point A refers to a day of high magnetic disturbance (10 March 1961) with K, = 7” over the relevant period. For this day the jet strength was very weak and hence its exact value proportionately more uncertain and this point was rejected. The point B is for the preceding day when the values were distorted by an anomalous maximum due to a sudden storm commencement at about 1330 hours. Excluding these two extreme points the correlation coefficient is 0.76 over the,remaining thirty-three days, showing that the vertical field produced at Ibadan by the jet is greater when the jet axis lies further to the north of Tamale. This suggests that over this short period the mean maximum vertical range due to the jet occurs some distance south of Ibadan. The high correlation between the ratio of the ranges and the electrojet position supports the calculations which established that position. If the line in Fig. 5 is extrapolated the intercept on the x axis is at -204 km. If the jet axis ever lay as much as 204 km south of Tamale it should also pass directly over Ibadan, producing zero vertical field there as the extrapolated curve suggests. STRENGTH OF THE ELECTROJET The diurnal ranges of horizontal field at Tamale and Legon were compared for each day. The horizontal range at Legon is due mainly to the normal S, current system. The difference between the horizontal range at Tamale on any day and the range at Legon for the same day is due almost entirely to the electrojet current strength on that day. Fig. 6 is a scatter diagram for (Range H, - Range HL) against (Range HL) on different days; hence it is approximately a plot of electrojet The coefficient of correlation is strength against the strength of the S, system. 0.36 over thirty-five days. Although this is statistically significant the dependence of the electrojet current on the S, current is very weak. As the horizontal range at Legon includes a small effect from the electrojet the true correlation between electrojet current and the strength of the normal S, current system must in fact be slightly less than 0.36 over the 35day period. FORBUSH and C~ASAVERDE(1961, p. 29) give similar evidence for thinking the electrojet to be practically independent of the normal current strength. This independence is surprising if the electrojet is a reinforcement of the normal current system, for although the enhancement of conductivity may vary from day to day it would be expected t’hat days with a stronger S, current would show a stronger jet current as well. The jet has a weaker dependence on the normal current system than present theories suggest and it is possible that the jet and S, currents are in different regions of the ionosphere. From Fig. 6 it is clear that for any individual day it is useless to predict the diurnal range at Legon by multiplying the measured range at Tamale by a constant factor. If the equatorial electrojet strengt,h does not depend on the strength of the normal current system the ratio of horizontal ranges between any stations near the jet and others far away will vary greatly from day to day. In considering the earth’s main magnetic field VESTINE et al. (1947a) calculated the amplitude of S, on individual days on the basis of observed diurnal variations at Huancayo, close
Position
and movement
of the equatorial
electrojet
over Ghana
501
60-
.
.
.
0
I IO
20
30 Raw
Fig. 6. Difference
between
40 H,.
50
60
70
80
y
horizontal ranges at Tamale and Legon horizontal range at Legon.
plotted
against
to the jet. The variations at other latitudes were calculated from these and used to correct the measured field at particular places and times for the effect of diurnal Later, VESTINE et al. (1947b) gave diagrams to show the changes of variation. diurnal variation with latitude. The weak correlation between jet and S, current systems makes these calculations of questionable value for the determination of diurnal variation on individual days. CoNCLUsIoNs It has been shown that the mean position of the axis of the equatorial electrojet during February and March 1961 lay in the region 42 f 8 km north of Tamale. The magnetic equator passed 39 f 2 km north of Tamale. There was a wide scatter in the axis position from day to day with a root mean square displacement of about 46 km. The approximations used in the calculation have been examined and the results substantiated by comparison with measurements made at Ibadan. No relation between the displacement and various suggested causative factors has been found. There is no simple relationship between the strengths of the electrojet current and the normal S, current system on different days. Acknowledgements--I wish to thank Professor R. W. H. WRIGHT for his help with this work, Dr. A. ONWUMECHILLI for supplying hourly values of magnetic components at Ibadan and the Ghana Meteorological Department for helping to maintain the Askania variograph at Tamale.
502
D. G. OSBORNE REFERENCES
BAKJZRW. G, BAKER W. G. and MARTYN D. F. E~EDAL J. EGEDAL J. FORBUSH S. E. and CASAVERDE M. JONES H. S. MAYAUD P. N.
1953 1953 1947 1948 1961 1948 1954
ON~~JMECHILLI A. OSBORNE D. G. VESTINE L.
1959 1960 1960
VESTINE L. et al. VESTINE L. et al.
1947a 1947b
Phil. Trans. A 246, 295. Phil. Trana. A 246, 281. Terr. Magn. Atmos. Elect. 52, 449. Nature, Lond. 161, 443. Carnegie Inst. Wash., Publ. No. 620. Polar Rec. 5, 148. Expeditions Polaires Franc&es, Resultats Scienti$ques, Fast 1, SXV. 2, 113. J. Atmosph. Terr. Phys. 13, 235. Proc. 12th Assembly, I.U.G.G. In press. Physics of the Upper Atmosphere (Ed. by J. A. RATCLIFFE). Academic Press, New York. Carnegie Inst Wash., Publ. No. 578. Carnegie Inst. Wash., Publ. No. 580.