Characteristics of equatorial electrojet over India determined from a thick current shell model

Journal of Atmospheric and Solar-Terrestrial Physics 92 (2013) 105–115

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Characteristics of equatorial electrojet over India determined from a thick current shell model A.B. Rabiu a,n, C.A. Onwumechili b, N Nagarajan c, K Yumoto b a

Space Physics Laboratory, Department of Physics, Federal University of Technology, Akure, Nigeria 4813 Lackawanna St., College Park, MD 20740, USA c National Geophysical Research Institute, Hyderabad 500 007, India d Space Environment Research Center, Kyushu University, Hakozaki 6-10-1, Fukuoka 812-8581, Japan b

a r t i c l e i n f o

abstract

Article history: Received 1 March 2012 Received in revised form 24 September 2012 Accepted 21 October 2012 Available online 10 November 2012

For the first time the five parameters required to fully describe Onwumechili’s composite thick current shell model format of equatorial electrojet have been evaluated from a single autonomous set of ground data at solar minimum. The thick current shell model, which takes into account the vertical ionospheric currents, permits both the width and the thickness of the jet to be determined simultaneously. The mean annual values of the electrojet parameters evaluated over India sector are: the peak intensity of the forward current at its centre, 62.97 7 2.73 A/km; the peak intensity of the return current, 19.43 7 2.49 A/km; the ratio of the peak return to the peak forward current intensity, 0.312 7 0.052; the total forward current flowing between the current foci, 19.017 1.74 kA; half of the latitudinal width or the focal distance from the current centre, 2.7 7 0.181; the distance of the peak return current location from the current centre, 5.31 70.191; the half thickness of the peak current density, 0.063 70.0031; the latitudinal extent of the current from its centre, 9.25 72. 081; and the dip latitude of the equatorial electrojet EEJ centre  0.190 70.0031. The dip latitude of the centre of EEJ exhibits a consistent northward migration towards the dip equator from the rising of the jet at dawn from an annual average of  0.1931 to about  0.1861 at about 1100 h LT, after which it begins to recede southward towards the dusk. Our results show that the electrojet becomes more (less) intensified as the centre of the electrojet moves northwards (southwards) towards (away from) the dip equator. The diurnal variation of the thickness of the EEJ is opposite that of its current intensity and half width. The thickness of equatorial electrojet EEJ exhibits a consistent diurnal variation such that it decreases from about 0.0661 at dawn to the minimum at about 1100 h LT and then begins to increase towards the dusk. The wider (thicker) the EEJ, the stronger (weaker) the EEJ strength. The order of seasonal variation of the mean daytime current intensity Jo and forward current Ifwd is E4 D4 J. However, the diurnal variations of the EEJ parameters exhibit seasonal dependence as the order of seasonal variation is not uniform at every hour of daytime for all the parameters. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Equatorial electrojet Models Ionospheric currents Equatorial ionosphere

1. Introduction The study of equatorial ionosphere and its current systems has continued to gain attention (e.g., Jadhav et al., 2002a,b; Doumouya et al., 2003; Stening, 2003; Holme et al. 2004; Manoj et al. 2006; Denardini et al. 2009; Shume et al. 2010, 2011; Kelley et al. 2012; Klimenko et al. 2012) due to its increasing significance in the earth-satellite communication, applications in space weather studies and source field problems in magnetotellurics. The daytime dynamo E region of the ionosphere in the neighbourhood of magnetic dip equator have been identified to consist of

n

Corresponding author. Tel.: þ234 8030 7057 87. E-mail address: [email protected] (A.B. Rabiu).

1364-6826/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jastp.2012.10.014

two layers of currents responsible for the quiet solar daily variations; one known as the worldwide Sq, flowing at an altitude of 118 77 km (Onwumechili, 1992a, 1997a), the other one is the intense non-uniform eastward current named as equatorial electrojet, EEJ, by Chapman (1951) which flows at a lower altitude of 10672 km (Richmond, 1973; Onwumechili, 1997a). EEJ is accompanied by a return current system (Onwumechili, 1992a,b; Rabiu and Nagarajan, 2008). Since Chapman (1951) presented the first model of equatorial electrojet, a number of improved models have been proposed (Onwumechili, 1966a,b,c; Untiedt, 1967; Richmond, 1973; Suzuki, 1973; Fambitakoye and Mayaud, 1976). Onwumechili (1966a,b,c, 1967) presented a two dimensional model of the continuous current distribution responsible for EEJ, having both width and thickness represented in the same model unlike others.

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The current distribution of Onwumechili (1966a,b,c) model, henceforth designated as OM66, has been used by several authors to model equatorial electrojet, for examples Onwumechili and Agu (1980), Onwumechili and Ezema (1992), Oko et al. (1996), Rigoti et al. (1999), Jadhav et al. (2002a). The simplification of OM66 into measurable magnetic field components necessary for evaluation of model parameters resulted in two current shell formats, one known as the thick current shell format and the other known as thin current shell format. The latter is the approximation of the former. With the exception of Onwumechili and Ezema (1992), who applied the OM66 in its thick current shell format to POGO satellite data and evaluated the five parameters, the others have used the approximation known as the thin shell format. The parameters that fully describe the OM66 are defined in Appendix A after Onwumechili (1966a,b,c). Onwumechili and Ogbuehi (1967) and Onwumechili et al. (1989) used satellite data to evaluate three parameters K, a, and a from the thin shell format; Oko et al. (1996) evaluated only three parameters jo (obtainable from K or k), a, a, using the thin current shell format; Rigoti et al. (1999) evaluated three model parameters jo, a, a, for Brazilian sector using the thin current shell format with a set of ground data; Jadhav et al. (2002a) also employed the thin current shell format using Orsted satellite data between April 1999 and March 2000 to evaluate three parameters K, a, and a. Electrojet models computed under the thin-shell approximation have been shown to be inadequate by Untiedt (1967), Sugiura and Poros (1969), and Richmond (1973) due to the neglect of vertical currents. It is observed that parameters of the thick current shell of OM66 employed by Onwumechili and Ezema (1992) were evaluated at high solar activity period, 1967–1969, and results were published only for 11 and 12 h local time. Onwumechili (1997a) highlighted the many successes of his continuous current distribution over the years and noted that the five model parameters have never been obtained from a single autonomous set of ground data using the thick current shell, since its introduction. The thick current shell format of the model, which takes into account both the width and the thickness of the jet, contains all the five parameters in a nonlinear form that makes it complicated for trivial attempt. It is a composite format capable of describing in detail the latitudinal and vertical flow of the EEJ. The primary objective of this work is to evaluate all the five parameters that completely define the continuous current distribution of the equatorial electrojet from a single set of ground data during low solar activity for the first time since its introduction, and generate the daytime hourly profiles of the model and electrojet parameters over the Indian sector with a view to produce results that have hitherto not been obtained with ground magnetic data.

2. Presentation of the model Onwumechili (1966a,b,c, 1967) presented a two dimensional model of the continuous current distribution responsible for EEJ as:   2 2 j ¼ jo a2 a2 þ ax2 b ðb þ bz2 Þ ð1Þ  2 2 a2 þ x2 ðb þz2 Þ2 where j (mA m  2) is the eastward current density at the point (x, z). The origin is at the centre of the current, x is northwards and z is downwards. The model is extensible to three dimensions by introducing the coordinate y or longitude | or eastwards local time t. j0 is the current density at the centre, a and b are constant latitudinal and vertical scale lengths, respectively, a and b are dimensionless parameters controlling the current distribution latitudinally and vertically, respectively. It is a meridional plane

model, which has to be applied to specific longitudes or local times in this simple form. Once the five parameters jo, a, a, b, b are determined by fitting observational data, a number of physical parameters of the current and its magnetic field can be calculated from them. Onwumechili (1966c) used the Biot–Savart law to obtain the northwards X and vertical Z components of the magnetic field variation with latitude on the horizontal plane (v ¼constant) as a result of the current distribution in (1) as follows: 1 h 2 ðsg: zÞ P 4 X ¼ k ð1 þ bÞðv þ av þ 2aaÞðu þbÞ 2 þ 2ð1 bÞbðv þ av þ 4a2aaÞðu þbÞ þ ð1 þ bÞðv þ av þ2aÞðv þaÞ2  ðsg:xÞ P 4 Z ¼

ð2Þ

1 h 3 2 k ð1 þ aÞð1 þ bÞðu þ bÞ þ ð1 þ aÞð1 bÞbðu þbÞ 2 þ ð1 þ bÞðv þ av þ 3aaaÞðv þaÞðu þ bÞ ð3Þ ð1bÞbðv þ av þ 3aaaÞðv þaÞ

In Eqs. (2) and (3): 2

P2 ¼ ðu þ bÞ þ ðv þ aÞ2

ð4Þ

k ¼ 0:1p2 abj0

ð5Þ

u ¼ 9x9 and v ¼ 9z9

ð6Þ

  sg:x ¼ sign of x=u and is 7 1 when x ¼ 0

ð7Þ

  sg:z ¼ sign of z=v and is 7 1 when z ¼ 0

ð8Þ

Eqs. (2) and (3) give the horizontal and vertical magnetic field variations respectively, due to thick current shell format. With some simplifying assumptions, the thick current shell format represented by Eqs. (2) and (3) were approximated to give the horizontal and vertical magnetic field variations respectively, due to thin current shell format as: ðsg:zÞP4 X ¼ 1=2 Ka½ðv þ av þ2aaÞðu þ bÞ

2

2

þ ðv þ avþ 2aÞðv þ aÞ 

ð9Þ 2

ðsg:xÞP4 Z ¼ 1=2 Kaðu þ bÞ½ð1 þaÞðu þ bÞ þ ðv þav þ 3a aaÞðv þ aÞ

ð10Þ

where; K ¼ 0:2pJ 0

ð11Þ

Or Ka ¼ kð1 þ bÞ

ð12Þ

K is the magnetic field, being the magnetic field of an infinite plane current sheet with constant intensity J0 (A km  1). It should be noted that b, the parameter that controls the vertical scale of the current is conspicuously missing in the thin shell format field (Eqs. (9) and (10)). In the neighbourhood of dip equator northwards component X and horizontal component H are approximately equal as the inclination is very small, therefore DXE DH. DZ and DH are measurable field components at observatories; v is the current altitude taken to be 106 km (0.961) as determined by rocket and satellite measurements (Onwumechili, 1997a,b). u is the dip latitude of the point of observation (Onwumechili, 1967; Oko et al.,1996). 3. Methodology The centre of the equatorial electrojet does not necessarily coincide with the dip latitude (Onwumechili, 1967). Oko et al. (1996) introduced xo as the dip latitude of the electrojet centre and

A.B. Rabiu et al. / Journal of Atmospheric and Solar-Terrestrial Physics 92 (2013) 105–115

thus presented the dip latitude of the stations as u¼ d  xo, where d is the dip latitude of the observatory. Substituting d  xo for u in Eqs. (2) and (3) and rewriting them yield: ðsg:zÞP 4 X½k½ð1 þ bÞðv þ av þ2aaÞðd  xo þbÞ

Table 2 Daytime Seasonal and annual means of the evaluated model parameters with their standard deviations (SD). Parameters

2

þ 2ð1bÞbðv þ av þ 4a 2aaÞðd  xo þ bÞ þ ð1þ bÞðv þ av þ 2aÞðv þ aÞ2  ¼ 0

ð13Þ 3

2

ðsg:xÞP 4 Z½k½ð1 þ aÞð1 þ bÞðdxo þ bÞ þ ð1 þ aÞð1bÞbðdxo þ bÞ

k (100A) SD a (1) SD

þ ð1þ bÞðv þ av þ3aaaÞðv þ aÞðdxo þ bÞ

a

ð1bÞbðv þ av þ 3aaaÞðv þ aÞ ¼ 0

SD b (1) SD

ð14Þ

It is obvious from Eqs. (13) and (14) that both H and Z which are measurable quantities at magnetic observatories are individually expressible in terms of k, a, a, b, b, v, d, and xo. The first five parameters (k, a, a, b, and b) are the model parameters; xo is a parameter of the current; d and v are known values at any point of observation. Eqs. (13) and (14), thus reflect a nonlinear function F (k, a, a, b, b, xo) of magnetic field variations in each of the components X and Z, can be written such that F ðk,a, a,b, b,xo Þ ¼ 0

ð15Þ

For each hour, we applied Eqs. (13) and (14) to a set of simultaneously derived electrojet index pairs Hi and Zi for a set of four data stations each at dip latitude ui (i¼1–4), so we have a set of 8 nonlinear simultaneous equations. Hence the model parameters are over-determined. Simultaneously recorded hourly horizontal H and vertical Z field values were obtained from five stations whose coordinates are shown in Table 1. These hourly horizontal and vertical geomagnetic field intensity values were treated for hourly departures, noncyclic and Dst variations to ensure absolute quiet condition as required. The electrojet index was obtained by subtracting the hourly values of worldwide Sq as obtained at Hyderabad, a station just outside of electrojet, from other four stations that fall within the electrojet influence. The current distribution described an external field and so it became necessary to separate the internal field from the external field. It is known that the observed values of H and Z are algebraic sum of the external ionospheric current and internal effects, such that:

DHe þ DHi ¼ DH

ð16Þ

DZe DZi ¼ DZ

ð17Þ

Onwumechili (1997a) reported the ratios of 0.28þ0.08 and 0.17þ0.02 for DHi/DHe and DZi/DZe, respectively, found in excellent agreement with Davis et al. (1967). We used these ratios to filter out the internal field from the observed values such that DH and DZ reflect the variation field due to external source of interest, the ionosphere. We therefore generated a hourly profiles of EEJ index in H and Z due to external current systems of Eq. (1) for selected 60 quiet days of the solar minimum year 1986 (Sunspot number R¼13.4). We obtained the monthly mean Table 1 Coordinates of the geomagnetic observatories. Station

Trivandrum Ettaiyapuram Kodaikanal Annamalainagar Hyderabad

Code

TRD ETT KOD ANN HYB

Geog. coordinates Lat. 1N

Long. 1E

8.29 9.10 10.23 11.4 17.42

76.57 78.00 77.47 79.7 78.55

Dip latitude (1N)

0.20 0.50 2.14 3.28 9.33

107

b SD

Annual means

Seasons E

J

D

98.128 8.503 3.689 0.01  1.87 0.34 0.079 0.004 0.499 0.033

94.432 5.051 3.683 0.008  2.01 0.21 0.081 0.003 0.512 0.02

95.653 5.83 3.685 0.01  1.96 0.23 0.08 0.003 0.508 0.023

96.071 6.148 3.686 0.009  1.95 0.24 0.08 0.003 0.506 0.024

Table 3 Annual mean hourly values of the parameters using thick current shell model. Local time (h)

K (100A)

a (1)

a

b (1)

b

0600 0700 0800 0900 1000 1100 1200 1300 1400 1500 1600 1700 1800

88.895 90.214 93.598 99.595 103.964 105.168 103.509 102.919 96.484 92.948 91.016 90.402 90.211

3.671 3.675 3.682 3.69 3.696 3.696 3.695 3.695 3.691 3.686 3.682 3.678 3.676

 2.22  2.17  2.03  1.78  1.61  1.58  1.66  1.69  1.95  2.09  2.16  2.17  2.17

0.083 0.083 0.081 0.078 0.076 0.076 0.077 0.077 0.08 0.082 0.083 0.083 0.083

0.533 0.528 0.515 0.49 0.474 0.47 0.478 0.482 0.507 0.521 0.528 0.529 0.528

Mean SD

96.071 6.148

3.686 0.009

 1.95 0.24

0.08 0.003

0.506 0.024

equatorial electrojet strength at each local time. Five international quiet days IQDs were selected per month. The hourly values of the model parameters k, a, a, b, b, and xo were evaluated employing some subroutines in MATLAB environment using optimization method engaging Eqs. (13) and (14) as described above. We estimated the model parameters at every hour and took the seasonal means according to Llyod’s classification as presented by Eleman (1973): Equinox ‘E’ season (March, April, September, October), June ‘J’ solstice (May, June, July, August) and December ‘D’ solstice (November, December, January, February). Table 2 presents the seasonal and annual means of the evaluated model parameters with their standard deviations. Table 3 presents the annual mean hourly values of the parameters. Onwumechili (1966c) further presented the physical parameters of the current and its magnetic field in terms of the model parameters described and evaluated above. The physical parameters obtained include: the peak current density jo A km  2, the peak intensity of the forward current Jo (A km  1) at its centre, the peak intensity of the return current Jm (A km  1), the ratio of the peak return to the peak forward current intensity Jm/Jo, the total forward current IFwd (kA) flowing between the current foci, half of the latitudinal width or the focal distance w (degrees) from the current centre, the distance xm (degrees) of the peak return current location from the current centre, the half thickness p (km or degree) at half of the peak current density, and the latitudinal extent of the current L1 (degrees) from its centre. These parameters are given as jo ¼ 

k  0:1p2 ab

ð18Þ

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K ¼ 0:1p2 ð1 þ bÞbjo

ð19Þ

Jo ¼

K 0:2p

ð20Þ

Jm ¼

J o a2 4ða1Þ

ð21Þ

1986. Table 4 presents the summary of day time means of the EEJ parameters over the three seasons with their annual means.

4. Discussion 4.1. Model parameters

2

Jm a ¼ Jo 4ða1Þ

ð22Þ

" IFwd ¼ aJo ðaÞ1=2 þ ð1þ aÞtan1

w2 ¼  p2 ¼ b

2

1

!# ð23Þ

ðaÞ1=2

a2

ð24Þ

a

  o1=2  2 ðb1Þ þ 1 þ ðb1Þ

ð25Þ

    L1 a L1 a1 þ ¼ tan1 L1 a a a þ1

ð26Þ

Onwumechili et al. (1989) called w, xm, xo, p and L1 the landmark parameters measuring the distances of equatorial electrojet. While jo, Jo, Jm, IFwd and ratio J m =Jo are referred to as the current parameters measuring the currents of the electrojet. The daytime hourly values of these parameters were evaluated for all the 60 international quiet days of the solar minimum year Table 4 Summary of daytime means of the EEJ parameters ( the symbols are defined in the text). Parameters

Jo (A km  1) SD Jm (A km  1) SD Jm/Jo SD Ifwd (kA) SD o

W (% ) SD o

Xm ( % ) SD o

P (% ) SD o

L1 ( % ) SD o Xo ( % )

SD

Seasons

Annual means

E

J

D

64.04 3.86  18.6 3.6  0.294 0.073 19.73 2.55 2.77

62.09 2.3  20.21 2.06  0.327 0.045 18.44 1.4 2.64

62.77 2.54  19.62 2.28  0.314 0.049 18.86 1.58 2.68

62.97 2.73  19.48 2.49  0.312 0.052 19.01 1.74 2.7

0.27 5.39

0.14 5.24

0.16 5.29

0.18 5.31

0.29 0.062

0.15 0.063

0.17 0.063

0.19 0.063

0.004 10.51

0.003 8.4

0.003 8.85

0.003 9.25

3.81  0.189 0.004

1.27  0.19 0.002

1.58  0.19

K ¼ kð1 þ bÞ=a

ð27Þ

and obtained the daytime mean of 30.96717.12 nT. A high positive correlation coefficient of 0.974 and p-value of 4.9  10  9 ()0.05) exist between our estimated magnetic constant from our thick current shell and that of Oko et al. (1996) obtained

2.08  0.19

0.003

Table 5 gives the comparison of noontime means of evaluated model parameters with available piecewise data from literature for Indian sector. Seasonal and annual means of the evaluated model parameters k, a, a, b, b for the Indian sector are displayed in Table 2 with their standard deviations. These seasonal values have no basis for comparison in literatures as only noontime values of a (1.5670.01) and a (3.5770.04) were reported for equinox noontime by Oko et al. (1996). Rather most literatures, including Onwumechili (1997a,b), discussed the seasonal variations of the derived parameters, from this model. Table 3 presents the mean annual hourly values of the model parameters for daytime (0700–1700). Table 5 compares noontime model parameters from our work with the available ones in the literature, indicating the data source (ground or satellite) and the type of current shell format employed. Obviously, the thin current shell format permits direct evaluation of only the latitudinal parameters a, a, and an implicit function of current density j0 in terms of the magnetic constant K which is not shown in Table 4. The values of a, a, b, and b compare so well with the existing values as they all fall within the appropriate limits of standard deviations. The value of b as measured by satellite and adopted for so long as 8.5 70.5 km (Onwumechili, 1997a) equivalent of 0.0767 70.00451 is in excellent agreement with our value of 0.08070.0031. The significant variation in our own parameter k (96077615 A) and the only available basis for comparison, that of Onwumechili and Ezema (1992), 172,383 71319 A can be accounted for by the solar activity difference in the periods of data acquisition. Model parameter k by definition is directly proportional to the current density (see Eq. (5)). We estimated the parameter for low solar activity period (sunspot number¼13.4), while Onwumechili and Ezema (1992) considered high solar activity period (average sunspot number¼101.7) using available satellite data and analytical procedure. Oko et al. (1996) estimated thin current shell parameters for low solar activity period (R¼13.4) and obtained lower current density than Onwumechili and Ezema (1992). We estimated the magnetic constant, K, expressed by definition (Onwumechili, 1997a,b) as:

0.003

Table 5 Comparison of noontime means of evaluated model parameters with available piecewise data from literature for Indian sector. Data type (model format)

Model parameters k SD (amp)

Ours Onwumechili and Ogbuehi (1967) Onwumechili et al. (1989) Onwumechili and Ezema (1992) Onwumechili (1992b) Oko et al. (1996)

Ground data (thick) Satellite data (thin) Satellite data (thin) Satellite data (thick) Rocket data Ground data (thin)

9607 7 615

172827 1319

a SD (1)

a

b SD (1)

b

3.686 7 0.009 4.2707 1.04 2.937 7 0.171 3.342 7 0.081

 1.95 7 0.24  1.59 7 0.08  1.86 7 0.06  1.53 7 0.08

0.0807 0.003

0.5067 0.024

0.0797 0.001 0.0707 0.017

0.526 7 0.018 0.396 7 0.335

3.5707 0.040

 1.56 7 0.02

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directly from thin current shell format. This demonstrates a high level of significance and gives credence to the approach we have taken. 4.2. Diurnal variations of the landmark parameters Fig. 1. presents the diurnal variations of the seasonal means of the landmark distances. While the diurnal variations of the seasonal means of the landmark measures of the EEJ current are illustrated in Fig. 2. Figs. 3 and 4 present the diurnal variations of the annual means of the landmark distances and the landmark measures of EEJ current, respectively. Some of the results obtained in this work have basis for comparison in literatures that have utilized thin shell model for EEJ current distribution and have been discussed extensively. For example the diurnal variations of peak intensity of the forward electrojet current Jo, forward currents Ifwd, peak intensity of the return current Jm and the ratio of the peak intensity of the return current to forward current

109

Jm/Jo have been discussed in Oko et al. (1996), Onwumechili (1997a) and Jadhav et al. (2002a) among others. Table 6 compares our results with those obtained by Oko et al. (1996) using a thin shell format within the same sector, while Table 7 compares the means of the 1100 LT and 1200 LT from our results with those of earlier workers obtained from ground and satellite data sets. We chose to discuss the results we consider outstanding and have new information for the understanding of the behaviour of EEJ in the sector under study. The peak intensity of the forward electrojet current Jo, forward currents Ifwd, peak intensity of the return current Jm and the ratio of the peak intensity of the return current to forward current Jm/Jo all demonstrated similar pattern of diurnal variation as seen in Figs. 2 and 4. They all exhibit an increase from the dawn towards a maximum at about noon mostly 1100 LT and then a decrease towards the dusk, with the rising rate always greater than the decaying rate in all situations. This pattern of variation was only observed in peak intensity of the forward electrojet current Jo,

Fig. 1. Diurnal variations of the seasonal mean hourly values of the landmark distances of EEJ parameters over India.

Fig. 2. Diurnal variations of the seasonal mean hourly values of the landmark measures of the of EEJ current over India.

110

A.B. Rabiu et al. / Journal of Atmospheric and Solar-Terrestrial Physics 92 (2013) 105–115

Fig. 3. Diurnal variations of the annual mean hourly values of the landmark distances of EEJ parameters over India.

Fig. 4. Diurnal variations of the annual mean hourly values of the landmark measures of the of EEJ current over India.

forward currents Ifwd, and peak intensity of the return current Jm by Oko et al. (1996) and has been well discussed by them. On the average the electrojet peaks at about 1100 LT on most days of the E and J seasons while it peaks at about 1200 LT on most days in D season. E season happened to be the season with very intense EEJ and it has been observed that intense EEJ tends to peak earlier than less intense ones (Arora, 1972; Rigoti et al., 1999; Onwumechili 1997a,b; Rabiu et al., 2007). The electrojet builds up faster on intense days and quickly attain maximum value earlier than less intense days (Rabiu et al., 2007). However, Oko et al. (1996) obtained a different pattern of diurnal variation for the ratio Jm/Jo, in their Fig. 2., such that the ratio maintains an almost steady value from dawn till about 0900 LT when it begins to rise steadily till dusk. Using the thin shell format Oko et al. (1996) have obtained a ratio Jm /Jo which is lower before noon than afternoon. We also got an annual prenoon mean value of 0.29870.057 and postnoon mean value of 0.32470.051 which means more currents return in the post maximum regime than pre maximum regime of the EEJ. The overall mean value of

the ratio 0.31270.052 which implies that average of one-third of the forward current is returned on any particular day; this is in accordance with literatures for example Oko et al. (1996). Onwumechili (1997a, b) following the Singh and Cole (1987, 1988) discussed various physical mechanisms responsible for the forward and the return currents of the EEJ as well as the electric fields that drive all the parts of the EEJ circuits; their arguments favour our observation. Onwumechili (1992a) noted that Singh and Cole (1987, 1988) have investigated the divergence east–west current phenomenon more than most authors. Singh and Cole (1987) found out that the divergence of east–west current results in a non-zero large value of meridional current polarization electrostatic field at the equator. This requires and leads to an additional proportionate zonal electrostatic field distribution. They reported that the ‘‘dynamo emf’s in the equatorial and low latitude regions do not cause significant current to flow out into mid or high latitudes. Most of the transverse currents leaving the generating region of the equatorial ionosphere return back along paths extending not far out from the

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generating region. This effect is consistent with the decrease of field line integrated conductivities with increasing latitude, which does not favour the flow path for closing electric current lying in the high latitude ionosphere’’. Singh and Cole (1988) explained how the EEJ current closes by discussing a basic theory which relates ionospheric conductivties with EEJ structure. They stated that the current returns between the equator and 41 as ‘‘the meridional transverse current fall sharply to zero’’ within this region. ‘‘This implies that below 41 latitude the closing current starts flowing out of the meridional plane in the zonal direction, creating or joining the main stream of the EEJ current. Physically the change in flow direction from meridional to zonal is caused by the harp gradient of field line integrated FLI conductivity’’. The diurnal variation of the dip latitude of the centre of EEJ, xo, is illustrated in the topmost panel of Figs. 1 and 3.This clearly demonstrates a consistent diurnal pattern, which described a northward migration towards the dip equator from the rising of the jet at dawn at an annual average of 0.1931 at 0700 to about 0.1861 at about 1100, thus becoming closer to the dip equator at the peak intensity period of the jet after which it begins to recede southward towards the dusk. The rate of morning northward migration is higher than that of southward recession towards the dusk. Magnitude wise this diurnal observation is in consistency with the Orsted satellite observational result of Jadhav et al. (2002a) and contradicts Oko et al. (1996) ( 0.29þ0.02) result obtained from thin shell format. With mean value of  0.190 þ0.0031, it is obvious that the centre of EEJ is not necessarily at the dip equator

Table 6 Comparison the annual daytime means of our result with those obtained from the thin shell model by Oko et al. (1996) using same data set. Parameters

Our results

Oko et al. (1996)

Jo (A km  1) SD Jm (Akm  1) SD Jm/Jo SD Ifwd (kA) SD w (1) SD Xm (1) SD p (1) SD L1 (1) SD Xo (1) SD

62.97 2.73  19.48 2.49  0.312 0.052 19.01 1.74 2.7 0.18 5.31 0.19 0.063 0.003 9.25 2.08  0.19 0.003

49.28 27.24  11.74 6.49  0.238 0.078 16.89 9.08 2.89 0.12 5.45 0.2 – – 11.96 1.03  0.15 0.17

111

in agreement with results of Srivastava (1992) and Onwumechili (1997a) among others. This further implies that the equatorial electrojet axis does not coincide with the dip equator. Obviously the centre of the jet is, however, close to the dip equator at about local noon (1100 LT) and always coincides with the hour of occurrence of the maximum peak forward current intensity, peculiar to the region of study (along 791E), on any day. The geographical locus of the dip equator is slightly different as we go to higher altitudes (especially in the American sector), as per International Geomagnetic Reference Field IGRF simulations. In other words, the vertical profile of the locus of the dip equator is a kind of ‘‘tilted’’ with respect to the zenith. Richmond (1973) showed that a uniform southward meridional wind of 10 m s  1 shifts the jet centre by 0.83 km (0.00751). Anandarao and Raghavarao (1987) have found that a steady northward wind of 100 m s  1 is capable of shifting the centre of EEJ southwards by 0.51. Further calculations of the effects of zonal and meridional winds on the EEJ done by Anandarao and Raghavarao (1987) revealed that meridional winds shift the centre of the jet either southwards or northwards depending upon whether the wind is northwards or southwards. Kane and Rastogi (1977) reported such a shift in the EEJ centre from ground based magnetometer data from a chain of closely spaced stations in Africa. Forbes (1981) has concluded that shifting of electrojet axis can be responsible for day-to-day variability of electrojet intensity. Our results show that the electrojet becomes more (less) intensified as the centre of the electrojet moves northwards (southwards) towards (away from) the dip equator. The pattern of the diurnal variation of the jet centre, x0, obtained in this work follows the satellite observation of Jadhav et al. (2002a), but contradicts results reported in literatures based on thin shell format for EEJ current including that of Oko et al. (1996). We chose to uphold this result and strengthen the fact that thin shell approximation is only a representation of approximate noontime equatorial magnetic variations, and fail to take into account local time variations of the electrojet as proposed by Forbes and Lindzen (1976). This is further stressed by the fact that our electrojet centre, x0, is minimum and closer to the dip equator at about local noon. Forbes and Lindzen (1976) have demonstrated the defects and inconsistencies in using a thin shell approximation in the vicinity of the magnetic equator. Preliminary results on the thickness and width of EEJ in Indian zone had been discussed by Rabiu and Nagarajan (2007). Their results were obtained when only the five model parameters of the model described by Eqs. (13) and (14) were evaluated with a fixed diurnal value for the dip latitude of the electrojet centre. This present effort considered the electrojet centre as a variable and reproduced results that we feel must be more reliable. Interestingly similar diurnal variation patterns were obtained in the width and thickness of the electrojet though with slightly different values. Hence we improve on the discussions presented

Table 7 Comparison of noon time means of 11 and 12 LT with results from ground data, POGO satellite data and CHAMP data. Authors

Our result SD Oko et al. (1996) SD Onwumechili and Ezema (1992) (SD) Luhr et al. (2004)

Data source

Ground data (thin) POGO sat data (high solar activity) CHAMP satellite

Parameters Jo (Akm  1)

Jm (Akm  1)

Jm/Jo

Ifwd (kA)

W (1)

Xm (1)

P (1)

L1 (1)

xo (1)

66.23 1.72 81.35 14.95 210.5 18.8

 16.53 1.46  19.44 3.9  47.8 4.27

 0.2505 0.0277  0.2378 0.0059  0.2271 0.0169 0.33

21.1 1.18 27.49 5.19 69.5 6.7

2.91 0.13 2.89 0.08 2.73 0.06 3.8

5.54 0.14 5.43 0.14 5.11 0.14 5.0

0.06 0.002 – – 0.063 0.003

11.69 2.44 11.92 0.71 12.4 1.07

 0.187 0.002  0.21 0.13

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by Rabiu and Nagarajan (2007) on inter-relationship between width and thickness of EEJ as well as their variations. The thickness of equatorial electrojet EEJ exhibits a consistent diurnal variation throughout the seasons as illustrated in the bottom panel of Figs. 1 and 3. It decreases from about 0.0661 at dawn to the minimum at about 1100 h LT and then begins to increase towards the dusk. This is the first derivation of this diurnal variation of the thickness of the EEJ from the continuous current distribution model and so the result has no basis for comparison in the literatures that have employed the thin current shell format of the model. Anandarao and Raghavarao (1987) noticed that a negative (positive) wind shear decreases (increases) the thickness of the jet. The fact that the thickness of the electrojet is minimum at about noon further shows that the model of the thin current shell is very suitable only for noon periods as noted by Forbes and Lindzen (1976). Generally the intensity of the EEJ increases from dawn towards noon when it maximized and begin to decline towards the setting of the sun in consistency with the augmentation of the dynamo theory by the solar activity as observed by Onwumechili and Ezema (1977). The dynamics of the variation of electrojet intensity and thickness shows that electrojet shrinks as its intensity increases. Maynard et al. (1965) have long determined the vertical distribution of the EEJ over India by launching four rockets from near the magnetic equator at Thumba. They identified a short distance from the centre where the main current is thicker with lower peak density. Sastry (1970) studied the parameters of the EEJ by rocket-borne magnetometers and obtained a thickness of about 14–15 km. The bottom half and top half of EEJ thickness obtained turned out to be 7 km (0.0631) and 8 km (0.0721), respectively; while Anandarao and Raghavarao (1987) model gives 8 km (0.0721) and 10 km (0.0901), respectively. Our result, 6.99370.333 km (0.06370.0031), is relatively consistent with the values of the bottom half thickness reported by the duo. Singh and Misra (1967) compared maximum integrated electrojet current with the maximum current density measured by rocket and found the thickness of electrojet layer to be about 17.5 km. Anandarao and Raghavarao (1987) studied the effects of zonal and meridional winds on equatorial electrojet at 1100 h LT by solving electrodynamic equations, and found both the halfwidth and thickness of the EEJ to be at about 2.51 and 16–18 km (corresponding to half-thickness of 0.07211 - 0.08111) respectively. These results are in excellent agreement with our result. Our mean half width w is 2.9570.191 at 1100 LT which is in accordance with the results of Onwumechili and Ogbuehi (1967) (3.8170.811); Onwumechili and Ezema (1992) ( 2.7470.091); and Oko et al. (1996) (2.8870.081); and Anandarao and Raghavarao (1987) (2.51). Table 8 compares our present values of the half width at 1100 LT with those available from different sources in literatures. Anandarao and Raghavarao (1987) have found negative currents Table 8 Comparison of our half width values with literatures at 1100 LT hr. Authors

Our result Yacob and Khana (1963) Anandarao and Raghavarao (1987) Onwumechili and Ezema (1992) Oko et al. (1996) Jadhav et al. (2002a). ORSTED Rabiu and Nagarajan (2007) Yacob (1966) Ozoemena and Onwumechili (1988). POGO Sat Ivers et al. (2002)

(deg)

(km)

Mean

SD

Mean

SD

2.95 2.61 2.5 2.74 2.88 2.0 2.83 2.62 2.22 3.0

0.13 327.45 14.43 289.71 277.5 0.09 304.14 9.99 0.08 319.68 8.88 222.0 0.3 314.13 33.3 291 0.43 246 48 333

due to wind shears centred at about 61 on either side of the dip equator. This lends credence to the claims of the strong wind effects. Jadhav et al. (2002a) found out that 30% of the zonal variability of EEJ could be explained by ‘‘variability of the migrating tides and suggested that besides conductivity, atmospheric tides play important roles in defining the zonal variability of the EEJ’’. Bedinger (1977) observed a vertical profile of an horizontal neutral winds during a strong EEJ in Peru, which is distinctively different from profiles observed previously at other times and locations. Forbes (1981) and Anandarao and Raghavarao (1979) have explained the structural variability of equatorial electrojet in terms of wind effects. The half width of the electrojet as inferred from ground magnetometer data by Yacob and Khana (1963) is 290 km (2.611), while the shear wind model of Anandarao and Raghavarao (1987) yields about 275 km ( 2.451). Ivers et al. (2002) applied signal processing techniques in the frequency domain to the total intensity data of six consecutive months from the Ørsted Overhauser scalar magnetometer and obtained the electrojet half width of 31. These values tally with our estimation (299.7720.0 km, 2.7070.181). Anandarao and Raghavarao (1987) have shown that a positive (negative) wind shear decreases (increases) the width of the jet. Hysell et al. (2002) carried out theoretical, computational and experimental analysis of the effects of large winds on the lowlatitude E region ionosphere and the equatorial electrojet in particular. Their model shows that the horizontal wind component drastically modifies the vertical polarization electric field in the electrojet and found out that that strong winds and wind shears are present in the E region over Jicamarca. Forbes (1981) reviewed various studies that have been performed on the effects of winds on electrojet. Oko et al. (1996) does not really show any relationship between the width and intensity of the electrojet. The half width obtained from the thin shell model in their Figure 2 shows a decrease from around dawn towards dusk, while the current intensity demonstrates a rise from dawn towards a peak at about 1100 h LT and then a decrease towards dusk. More recently Jadhav et al. (2002b) showed, in their Figure 5 using Orsted satellite data, that the width of EEJ current system is largest in the American sector, and responsible for the strong peak in the EEJ strength at 2701E. Sugiura and Poros (1969) worked on a meridional current model of EEJ and obtained a stronger EEJ at Peru with half width of about 2.51 while India with weaker EEJ strength has smaller half width of 21. Earlier on, Ogbuehi and Onwumechili (1964) reported that the jet over Nigeria broadens (that is, increases in width) as the Sun moves over it. Of course, the EEJ intensifies as the Sun moves over it (see Figs. 1 and 3). This increase in width of EEJ with increasing current intensity was observed by CHAMP in the works of Luhr et al. (2004) who concluded that ‘‘high current densities are accompanied by wider electrojet channels’’. Our derived half width as reflected in the second panel from bottom of Figs. 1 and 3 clearly demonstrates that the EEJ becomes wider from an average value of about 2.51 at the dawn with the rising of the Sun and attain maximum value of 2.951 at the highest jet intensity (about 1100 LT) before reducing to about 2.51 at the dusk. Therefore, the wider the EEJ the stronger the EEJ strength. One of the outstanding results we obtained using the thick current shell is the diurnal variation of the thickness of the EEJ which is opposite of its current intensity and half width. So the thicker the EEJ the weaker it becomes. Anandarao and Raghavarao (1987) noted that the zonal wind shears can decrease or increase the width of jet by as much as 100% depending upon their direction, strength and altitude, and concluded that ‘‘if the width of the jet is increased, then the thickness would decrease and vice versa’’. This explanation fits our result. We propose that it is the

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effective change in thickness of the jet that is responsible for the variation of its intensity. Comparison of our results with the results of Oko et al. (1996) obtained for Indian sector using the approximate thin shell format shows a discrepancy outside the neighbourhood of local noon. This further buttressed the mathematical deduction of Forbes and Lindzen (1976), who used a system of equations to show that EEJ becomes thinnest at local noon time and therefore expected that a thin shell model such as used by Oko et al. (1996) should only be appropriate to local noon time when the equatorial electrojet becomes thinnest. 4.3. Seasonal variation of electrojet parameters The diurnal variations of the EEJ parameters exhibit seasonal dependence as the order of seasonal variation is not uniform at every hour of daytime for all the parameters. The hour of maximum current intensity Jo was evaluated for each season and the premaximum mean values taken as the mean of the hourly values of each parameter between 0700 and the hour of maximum inclusive. While the post-maximum mean values were evaluated by simply Table 9 Distribution of season of maximum values of the EEJ parameters in India. Season of maximum values Parameters

Pre-maximum regime

Post-maximum regime

Mean daytime

Xo L1 p w Xm Jo Jm Jm/Jo Ifwd

J E J E E E J J E

J D J D D D J J D

J E J E E E J J E

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averaging the hourly values of the different parameters over the hours between the maximum time and 1700 h local time. The distribution of season of maximum values of the parameters at different time regime is shown in Table 9. Fig. 5 illustrates the seasonal variation of the EEJ parameters at three different diurnal regimes; the pre-maximum period, post-maximum period and over the entire daytime (0700–1700 h). The distance measuring parameters that shows overall maximum variation in E season are L1, w and xm. This E season maximum is also observed in the current intensity Jo and forward current Ifwd. The maximum occurrence of the aforementioned parameters in E season is accompanied by minimum values of xo, p, Jm, and Jm/Jo. An obvious fact is that maximum EEJ intensity and forward current occurs simultaneously when the EEJ centre is closest to the dip equator and the electrojet is thinnest. The order of seasonal variation of the mean daytime current intensity Jo and forward current Ifwd is E4D4J, which actually follow classical order in the sector studied and have been exclusively discussed by several authors including Chapman and Raja Rao (1965), Patel and Rastogi (1978), Langel et al. (1993) and Oko et al. (1996). Chandra et al. (2000) found a linear relationship between the peak current density of EEJ measured by rocket and the daily range of H obtained on the ground in India. The equinoctial maxima have been attributed primarily to the corresponding variation of the index of horizontal electric field in the E-region by Rastogi (1993) and Chandra et al. (2000). Mainly the seasonal variation at the post maximum regime which represents the decaying daytime period of EEJ is found to be maximum in D season and minimum in J season. The order of pre-maximum seasonal variation is quite different from the order of post maximum seasonal variation in all parameters. L1, w, and xm have similar seasonal order at different time regime while xo and p share similar order different from others at different time regime. The difference in order of seasonal variation of the EEJ parameters at different time regime is surely a

Fig. 5. Seasonal variation of the EEJ parameters at three different diurnal regimes; E-season (in blue); J-season (in green) and D-season (in red) [along the x-axis (the horizontal axis), pre-maximum period mean values; post-maximum period mean values; mean daytime (0700–1700 h) values]. The names and units of the parameters indicated along the vertical axis are as listed in the text.

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reflection of the difference in the rising and decay rates of the EEJ discussed in Rabiu et al. (2007). This is evident in the asymmetry nature of the diurnal variation plots of EEJ mentioned by Rigoti et al. (1999) and underscores the fact that EEJ is not solely controlled by solar activity, but also by the dynamics of local winds. Percentage contribution of migratory tides to the variability of EEJ has been estimated as 30% by Jadhav et al. (2002a).

5. Conclusions We have shown that the full characteristics of EEJ can be obtained using the thick shell format of continuous current distribution density of Onwumechili (1966a,b,c) obtained from an empirical model by fitting geomagnetic data measured on ground. The thick shell format has been able to reproduce some parameters of the EEJ which tallied with satellite and rocket observations and met the expectation of wind based theoretical models. Most importantly we have demonstrated that the thick shell format is more capable of representing the diurnal and seasonal variation of EEJ over Indian sector than thin shell approximation, the results of which are summarized and presented. The five parameters that fully described the current distribution of EEJ have been evaluated using an autonomous set of ground data. The results obtained compare well with earlier piecewise obtained parameters. The mean noontime values of the model parameters k, a, a, b and b, are 96077615 A, 3.68670.0091, 1.9570.24, 0.08070.0031, and 0.50670.024, respectively. The mean annual values of the electrojet parameters evaluated over India sector are: the peak intensity of the forward current at its centre, 62.9772.73 A/km; the peak intensity of the return current, 19.43 72.49 A/km; the ratio of the peak return to the peak forward current intensity, 0.31270.052; the total forward current flowing between the current foci, 19.0171.74 kA; half of the latitudinal width or the focal distance from the current centre, 2.770.181; the distance of the peak return current location from the current centre, 5.317 0.191; the half thickness of the peak current density, 0.063 70.0031; the latitudinal extent of the current from its centre, 9.2572. 081; and the dip latitude of the electrojet centre  0.190 70.0031. The diurnal variation of the dip latitude of the centre of EEJ described a northward migration towards the dip equator from the rising of the jet at dawn at an annual average of 0.1931 at 0700 to about 0.1861 at about 1100, thus becoming closer to the dip equator at the peak intensity period of the jet after which it begins to recede southward towards the dusk. One of the outstanding results we obtained using the thick current shell is the diurnal variation of the thickness of the EEJ which is opposite of its current intensity and half width. The thickness of equatorial electrojet EEJ exhibits a consistent diurnal variation such that it decreases from about 0.0661 at dawn to the minimum at about 1100 h LT and then begins to increase towards the dusk. The wider (thicker) the EEJ, the stronger (weaker) the EEJ strength. The thick current shell model is shown to give better hourly representation of jet behaviour than thin shell format hitherto being used. The thin current shell model best fits only the near local noon jet observation, as the electrojet is thinnest at period of maximum intensity. The transient variation of the jet thickness is explained in terms of the wind shears in consistency with the electrodynamics of the dynamo region.

Acknowledgements Data for Trivandrum TRD, Kodaikanal KOD, Annamalainagar ANN, and Hyderabad HYB were obtained from World Data Centre-C2,

Kyoto University, Kyoto, Japan. Data for Ettaiyapuram ETT were obtained from the Director, National Geophysical Research Institute (NGRI), Hyderabad, India. One of us (ABR) is indebted to the Space Environment Research Center of the Kyushu University, Fukuoka, Japan, for a visiting appointment. The critical reviews provided by the anonymous referees are greatly acknowledged.

Appendix A Definitions and units of the parameters j (A m  2) the eastward current density at the point (x, z). Considering a 2-dimensional coordinate system with x northwards and z is downwards j0 (A m  2) the current density at the centre otherwise known as the peak current density a and b constant latitudinal and vertical scale lengths, respectively a and b are dimensionless parameters controlling the current distribution latitudinally and vertically, respectively. X (nT) northwards component of the magnetic field Z (nT) vertical component of the magnetic field H (nT) horizontal component of the magnetic field v (km or 1) the current altitude taken to be 106 km (0.961) K (nT) magnetic field of an infinite plane current sheet with constant intensity J0 (A km  1 u (1) the dip latitude of the point of observation xo (1) the dip latitude of the electrojet centre d (1) is the dip latitude of the observatory Jo (A km  1) the peak intensity of the forward current at its centre Jm (A km  1) the peak intensity of the return current Jm/Jo the ratio of the peak return to the peak forward current intensity IFwd (kA) the total forward current flowing between the current foci w (1) half of the latitudinal width or the focal distance from the current centre, xm (1) the distance of the peak return current location from the current centre p (km or 1) the half thickness at half of the peak current density L1 (1) the latitudinal extent of the current from its centre. References Anandarao, B.G., Raghavarao, R., 1979. Effects of vertical shears in the zonal winds on the electrojet. Space Research 19, 283–286. Anandarao, B.G., Raghavarao, R., 1987. Structural changes in the currents and fields of the equatorial electrojet due to zonal and meridional winds. Journal of Geophysical Research 92, 2514–2526. Arora, B.R., 1972. On abnormal quiet day variation in the low latitudes. Indian Journal of Meteorology and Geophysics 23, 195–198. Bedinger, J.F., 1977. Observation of neutral winds during an equatorial electrojet. Journal of Atmospheric and Terrestrial Physics 39, 241–242. Chandra, H., Sinha, H.S.S., Rastogi, R.G., 2000. Equatorial electrojet studies from rocket and ground measurements. Earth, Planets and Space 52 (111–120), 2000. Chapman, S., 1951. The equatorial electrojet as deduced from the abnormal current distribution above Huancayo and elsewhere. Archiv Fuer Meteorologie, Geophysik und Bioklimatologie, Serie A 4, 368–390. Chapman, S., Raja Rao, K.S., 1965. The H and Z variations along and near the equatorial electrojet in India, Africa and the Pacific. Journal of Atmospheric and Terrestrial Physics 27, 559–581. Davis, T.N., Burrows, K., Stolarik, J.D., 1967. A latitude survey of the equatorial electrojet with rocket-borne magnetometer. Journal of Geophysical Research 72, 1845–1861. Denardini, C.M., Abdu, M.A., Aveiro, H.C., 2009. Counter electrojet features in the Brazilian sector: simultaneous observation by radar, digital sounder and magnetometers. Annales Geophysicae 27, 1593–1603. Doumouya, V., Cohen, Y., Arora, B.R., Yumoto, K., 2003. Local time and longitude dependence of the equatorial electrojet magnetic effects. Journal of Atmospheric and Solar-Terrestrial Physics 65, 1265–1282.

A.B. Rabiu et al. / Journal of Atmospheric and Solar-Terrestrial Physics 92 (2013) 105–115

Eleman, F., 1973. In: Egeland, A., Holter, O., Omholt, A. (Eds.), The Geomagnetic Field in Cosmical Geophysics. Scandinavian University Books, Oslo, pp. 45–62, Chapter 3. Fambitakoye, O., Mayaud, P.N., 1976. Equatorial electrojet and regular daily variation SR: I. A determination of the equatorial electrojet parameters. Journal of Atmospheric and Terrestrial Physics 38, 1–17. Forbes, J.M., 1981. The equatorial electrojet. Reviews of Geophysics 19, 469–504. Forbes, J.M., Lindzen, R.S., 1976. Atmospheric and solar tides and their electrodynamic effects-II. The equatorial electrojet. JoumaI of Atmospheric and Terrestrial Physics 38, 911–920. Holme, R., James, M.A., Luhr, H., 2004. Magnetic field modelling from scalar-only data: resolving the Backus effect with the equatorial electrojet. Earth, Planets and Space 57, 1–8. Hysell, D.L., Chau, J.L., Fesen, C.G., 2002. Effects of large horizontal winds on the equatorial electrojet. Journal of Geophysical Research 107 (A8), 1214 10.1029/ 2001JA000217. Ivers, D., Stening, R., Turner, J., Winch, D., 2002. Equatorial electrojet from Ørsted scalar magnetic field observations. Journal of Geophysical Research 108 (A2), 1061, http://dx.doi.org/10.1029/2002JA009310 2003. Jadhav, G., Rajaram, M., Rajaram, R., 2002a. A detailed study of equatorial electrojet phenomenon using Ørsted satellite observations. Journal of Geophysical Research 107 (A8), 1175, http://dx.doi.org/10.1029/2001JA000183. Jadhav, G., Rajaram, M., Rajaram, R., 2002b. Main field control of the equatorial electrojet: a preliminary study from the Orsted data. Journal of Geodynamics 33, 157–171. Kane, R.P., Rastogi, R.G., 1977. Some characteristics of the equatorial electrojet in Ethiopia (East Africa). Indian Journal of Radio Space Physics 6, 85–101. Kelley, M.C., Ilma, R.R., Eccles, V., 2012. Reconciliation of rocket-based magnetic field measurements in the equatorial electrojet with classical collision theory. Journal of Geophysical Research 117 (A01311), 6, http://dx.doi.org/10.1029/ 2011JA017020. Klimenko, M.V., Klimenko, V.V., Zakharenkova, I.E., Pulinets, S.A., 2012. Variations of equatorial electrojet as possible seismo-ionospheric precursor at the occurrence of TEC anomalies before strong earthquake. Advances in Space Research 49 (3), 509–517. Langel, R.A., Purucker, M., Rajaram, M., 1993. The equatorial electrojet and associated currents as seen in Magsat data. Journal of Atmospheric and Terrestrial Physics 55, 1233–1269. Luhr, H., Maus, S., Rother, M., 2004. Noon-time equatorial electrojet: its spatial features as determined by the CHAMP satellite. Journal of Geophysical Research 109, A01306, http://dx.doi.org/10.1029/2002JA009656. Manoj, C., Luhr, H., Maus, S., Nagarajan, N., 2006. Evidence for short spatial correlation lengths of the noontime equatorial electrojet inferred from a comparison of satellite and ground magnetic data. Journal of Geophysical Research 111, A11312, http://dx.doi.org/10.1029/2006JA011855. Maynard, N.C., Cahill Jr., L.J., Sastry, T.S.G., 1965. Preliminary results of measurements of the equatorial electrojet over India. Journal of Geophysical Research 70, 1241–1245. Ogbuehi, P.O., Onwumechili, C.A., 1964. Daily and seasonal changes in the equatorial electrojet in Nigeria. Journal of Atmospheric and Terrestrial Physics 26, 889–898. Oko, S.O., Ezema, P.O., Onwumechili, C.A., 1996. Geomagnetically quiet day ionospheric currents over the Indian sector—II. Equatorial electrojet currents. Journal of Atmospheric and Terrestrial Physics. 58, 555–564. Onwumechili, C.A., 1966a. A new model of the equatorial electrojet current. Nigerian Journal of Science 1, 11–19. Onwumechili, C.A., 1966b. A three dimensional model of density distribution in ionospheric currents causing part of quiet day geomagnetic variations. IIe Symposium d’aeronomie equatoriale, Special publication of Annales de Geophysique, pp. 157–162. Onwumechili, C.A., 1966c. The magnetic field of a current model for part of geomagnetic Sq variations. IIe Symposium d’aeronomie equatoriale, Special publication of Annales de Geophysique, pp. 163–170. Onwumechili, C.A., 1967. Geomagnetic variations in the equatorial zone. In: Matsushita, S., Campbell, W.H. (Eds.), Physics of Geomagnetic Phenomena, vol. 1. Academic press, New York, pp. 425–507. Onwumechili, C.A., 1992a. Study of the return current of the equatorial electrojet. Journal of Geomagnetism and Geoelectricity 44, 1–42. Onwumechili, C.A., 1992b. A study of rocket measurements of ionospheric currents. V. Modelling rocket profiles of low latitude ionospheric currents. Geophysical Journal International 108, 673–682.

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Onwumechili, C.A., 1997a. The Equatorial Electrojet. Gordon and Breach Science Publishers, Netherlands 627pp. Onwumechili, C.A., 1997b. Spatial and temporal distributions of ionospheric currents in subsolar elevations. Journal of Atmospheric and Solar-Terrestrial Physics 59, 1891–1899. Onwumechili, C.A., Agu, C.E., 1980. General features of the magnetic field of the equatorial electrojet measured by the POGO satellites. Planetary and Space Science 28, 1125–1130. Onwumechili, C.A., Ezema, P.O., 1977. On the course of the geomagnetic daily variation in low latitudes. Journal of Atmospheric and Terrestrial Physics 39, 1079–1086. Onwumechili, C.A., Ezema, P.O., 1992. Latitudinal and vertical parameters of the equatorial electrojet from an autonomous data set. Journal of Atmospheric and Terrestrial Physics. 54, 1535–1544. Onwumechili, C.A., Ogbuehi, P.O., 1967. Preliminary results on the equatorial electrojet in India. Journal of Geomagnetism and Geoelectricity 19 (1), 15–22. Onwumechili, C.A., Ozoemena, P.C., Agu, C.E., 1989. Landmark values of equatorial electrojet and the magnetic field along a meridian near noon. Journal of Geomagnetism and Geoelectricity 41, 443–459. Ozoemena, P.C., Onwumechili, C.A., 1988. Diurnal variations of equatorial electrojet parameters derived from POGO solstitial data. Journal of Atmospheric and Terrestrial Physics 50, 181–184. Patel, V.P., Rastogi, R.G., 1978. On the solar control of the quiet day geomagnetic variations near the magnetic equator. Current Science 47, 325–327. Rabiu, A.B., Nagarajan, N., 2007. Inter-relationships between the thickness, width and intensity of the equatorial electrojet in Indian sector. Bulletin of the Astronomical Society of India 35, 645–654. Rabiu, A.B., Nagarajan, N., 2008. Transient variation of electromagnetic induction due to Equatorial electrojet. Online Journal of Earth Sciences 2 (1), 1–8. Rabiu, A.B., Nagarajan, N., Saratchandra, K., 2007. Rising and decay rates of solar quiet daily variation and electrojet at equatorial region. Online Journal of Earth Sciences 1 (2), 85–92. Rastogi, R.G., 1993. Geomagnetic field variations at low latitudes and ionospheric electric fields. Journal of Atmospheric and Terrestrial Physics. 55, 1375–1381. Richmond, A.D., 1973. Equatorial electrojet I. Development of a model including winds and instabilities. Journal of Atmospheric and Terrestrial Physics 35, 1083–1103. Rigoti, A., Chamalaun, F.H., Trivedi, N.B., Padilha, A.L., 1999. Characteristics of the Equatorial Electrojet determined from an array of magnetometers in N–NE Brazil. Earth, Planets and Space 51, 115–128. Sastry, T.S.G., 1970. Diurnal change in the parameters of the equatorial electrojet as observed by rocket-borne magnetometers. Space Research 10, 778–785. Shume, E.B., Denardini, C.M., de Paula, E.R., Trivedi, N.B., 2010. Variabilities of the equatorial electrojet in Brazil and Peru´. Journal of Geophysical Research 115, A06306, http://dx.doi.org/10.1029/2009JA014984. Shume, E.B., De Paula, E.R., Kherani, E.A., Abdu, M.A., Denardini, C.M., 2011. Equatorial electrojet plasma irregularities observed during late afternoon by the 30 MHz coherent scatter radar in Sa~ o Luı´s, Brazil. Journal of Atmospheric and Solar-Terrestrial Physics 73, 1560–1567. Singh, R.N., Misra, K.D., 1967. Formation of equatorial electrojet current layers. Nature 214, 375–376. Singh, A., Cole, K.D., 1987. A numerical model of the ionospheric dynamo—II. Electrostatic field at equatorial and low latitudes. Journal of Atmospheric and Terrestrial Physics. 49, 529–537. Singh, A., Cole, K.D., 1988. Altitude and latitude dependence of the equatorial electrojet. Journal of Atmospheric and Terrestrial Physics. 50, 639–648. Srivastava, B.J., 1992. New results on the dip equator and the equatorial electrojet in India. Journal of Atmospheric and Terrestrial Physics 54, 871–880. Stening, R.J., 2003. Space weather in the equatorial ionosphere. Space Science Reviews 107 (263–271), 2003. Sugiura, M., Poros, D.J., 1969. An improved model equatorial electrojet with meridional current system. Journal of Geophysical Research 74, 4025–4034. Suzuki, A., 1973. Returning flow of the equatorial electrojet currents. Journal of Geomagnetism and Geoelectricity 25, 249–258. Untiedt, J., 1967. A model of the equatorial electrojet including meridional currents. Journal of Geophysical Research 72, 5799–5810. Yacob, A., 1966. Seasonal parameters of the equatorial electrojet at different longitudinal zones. Journal of Atmospheric and Terrestrial Physics. 28, 581–597. Yacob, A., Khana, K.B., 1963. Geomagnetic Sq variations and the parameters of the Indian electrojet for 1958, 1959. Indian Journal of Meteorology and Geophysics 14, 470–477.