ON THE MORPHOLOGY OF ON THE MORPHOLOGY OF EQUATORIAL ELECTROJET OVER EQUATORIAL ELECTROJET OVER

INDIAN SECTORINDIAN SECTOR

A. Babatunde RabiuA. Babatunde Rabiu11, and Nandini Nagarajan, and Nandini Nagarajan22

11Department of Physics, Federal University of Technology, Department of Physics, Federal University of Technology, Akure, NIGERIAAkure, NIGERIA

22National Geophysical Research Institute, Hyderabad 500 National Geophysical Research Institute, Hyderabad 500 007, INDIA.007, INDIA.

22tunderabiu@yahoo.com, tunderabiu@yahoo.com, 22nandini@ngri.res.innandini@ngri.res.in

International Advanced School on Space Weather, 2-19 May, 2006, ICTP,Trieste

OutlineOutline

IntroductionIntroduction Presentation of ModelPresentation of Model ResultsResults DiscussionsDiscussions ConclusionsConclusions

IntroductionIntroduction The E region of the equatorial ionosphere consists of The E region of the equatorial ionosphere consists of

two layers of currents responsible for the quiet solar two layers of currents responsible for the quiet solar daily variations in Earth’s magnetic field: the worldwide daily variations in Earth’s magnetic field: the worldwide Sq, (altitude 118 Sq, (altitude 118 ++7 km), & the equatorial electrojet, 7 km), & the equatorial electrojet, EEJ, (altitude 106 EEJ, (altitude 106 ++ 2 km) 2 km)

Equatorial electrojet EEJ- the intense ionospheric current Equatorial electrojet EEJ- the intense ionospheric current flowing eastwards within the narrow strip flanking the flowing eastwards within the narrow strip flanking the dip equator, responsible for the observed enhanced dip equator, responsible for the observed enhanced horizontal magnetic field intensity at the magnetic horizontal magnetic field intensity at the magnetic equatorial neighbourhood. (Chapman, 1951)equatorial neighbourhood. (Chapman, 1951)

Most of studies on electrojet focused on noon time Most of studies on electrojet focused on noon time period as the ranges of the magnetic field intensities period as the ranges of the magnetic field intensities were fitted into models in order to evaluate the were fitted into models in order to evaluate the electrojet characteristics. electrojet characteristics.

Increasing interest in modeling the geomagnetic Increasing interest in modeling the geomagnetic observations necessitates the need for examination of observations necessitates the need for examination of every aspect of the variation field for accurate every aspect of the variation field for accurate formulation and evaluation of model parametersformulation and evaluation of model parameters

Fig. 1. Relative positions of the magnetic and geographic equators

Manifestations of EEJManifestations of EEJ

Spatial structures of its intense current densitySpatial structures of its intense current density configurations & regular temporal variations of its configurations & regular temporal variations of its

current systemcurrent system magnetic fields of its current systemmagnetic fields of its current system the ionospheric plasma density irregularities the ionospheric plasma density irregularities

generated by the turbulent flow of the EEJ currentgenerated by the turbulent flow of the EEJ current the electric fields and ionospheric plasma drifts in the electric fields and ionospheric plasma drifts in

the dip equatorial zonethe dip equatorial zone the quiet counter equatorial electrojet CEJthe quiet counter equatorial electrojet CEJ temporal variabilities of the above phenomenon.temporal variabilities of the above phenomenon.

Central objectives Central objectives

To explore the thick shell format of a To explore the thick shell format of a continuous current distribution model continuous current distribution model to evaluate the morphology of to evaluate the morphology of equatorial electrojet at the Indian equatorial electrojet at the Indian sectorsector

To study the transient variations of To study the transient variations of the landmark parameters of the EEJthe landmark parameters of the EEJ

Model EvaluationModel EvaluationOnwumechili (1966a, b, c; 1967) presented a two Onwumechili (1966a, b, c; 1967) presented a two

dimensional empirical model of the continuous dimensional empirical model of the continuous current distribution responsible for EEJ as:current distribution responsible for EEJ as:

j = jo aj = jo a22(a(a22 + + xx22)b)b22(b(b22 + + zz22) / (a) / (a22 + x + x22))22 (b (b22 + z + z22))22 (1) (1)

Where Where jj (µA m-2) is the eastward current density at the (µA m-2) is the eastward current density at the point (point (x, zx, z). The origin is at the centre of the current, ). The origin is at the centre of the current, xx is northwards, and is northwards, and zz is downwards. The model is is downwards. The model is extensible to three dimension by introducing the extensible to three dimension by introducing the coordinate coordinate yy or longitude or longitude ØØ or eastwards local time or eastwards local time tt. . jj00 is the current density at the centre, is the current density at the centre, aa and and bb are are constant latitudinal and vertical scale lengths constant latitudinal and vertical scale lengths respectively, respectively, and and are dimensionless parameters are dimensionless parameters controlling the current distribution latitudinally and controlling the current distribution latitudinally and vertically respectivelyvertically respectively. It is a meridional plane . It is a meridional plane model, which in this simple form has to be applied to model, which in this simple form has to be applied to specific longitudes or local times. The model is a specific longitudes or local times. The model is a realistic model having both width and thickness. realistic model having both width and thickness.

Model Evaluation Model Evaluation contd.contd.Onwumechili (1966c) used the Biot-Savart law to obtain the Onwumechili (1966c) used the Biot-Savart law to obtain the

northwards X and vertical Z components of the magnetic northwards X and vertical Z components of the magnetic field variation with latitude on the horizontal plane field variation with latitude on the horizontal plane (v = (v = constantconstant) as a result of the current distribution in (1) as ) as a result of the current distribution in (1) as follows:follows:

(sg. z) P(sg. z) P44 X = ½ k [(1+ X = ½ k [(1+)(v + )(v + v +2v +2a)(u + b)a)(u + b)22 + 2(1- + 2(1- )(v + )(v + v + 4a -2v + 4a -2a)(u + b)a)(u + b)

+ (1+ + (1+ )(v + )(v + v + 2a)(v + a)v + 2a)(v + a)22] ] (2)(2)- (sg.x) P- (sg.x) P44 Z = ½ k [(1+ Z = ½ k [(1+ )(1+ )(1+ )(u + b))(u + b)33 + ((1+ + ((1+ )(1+ )(1+ )(u + b))(u + b)22

+ (1+ + (1+ )(v + )(v + v + 3a - v + 3a - a) (v + a) (u + b)a) (v + a) (u + b) - (1- - (1- ) b (v + ) b (v + v + 3a - v + 3a - a) (v + a)]a) (v + a)] (3)(3)

Where PWhere P2 2 = (u + b)= (u + b)2 2 + (v + a)+ (v + a)22 (4)(4)k = 0.1πk = 0.1π22abjabj00 (5)(5)

u = /x/ and v= /z/u = /x/ and v= /z/ (6)(6)sg.x = sign of (x/u) and is ± 1 when x = 0sg.x = sign of (x/u) and is ± 1 when x = 0 (7)(7)sg.z = sign of (z/v) and is ± 1 when z= 0sg.z = sign of (z/v) and is ± 1 when z= 0 (8)(8) Equations 2 and 3 give the horizontal and vertical magnetic field variations Equations 2 and 3 give the horizontal and vertical magnetic field variations

respectively, due to thick current shell format.respectively, due to thick current shell format.

Model Evaluation Model Evaluation contd.contd.

0° dip latitude does not coincide with the center of the EEJ 0° dip latitude does not coincide with the center of the EEJ (Oko, et al., 1996). Therefore we chose to write an (Oko, et al., 1996). Therefore we chose to write an expression for the electrojet axis xexpression for the electrojet axis x00, in terms of the dip , in terms of the dip latitude, latitude, , as: , as:

u = u = - x - x00 (9) (9)

Where xWhere x00 is the dip latitude of the current center. is the dip latitude of the current center.

Introducing Introducing equation 9equation 9 in in equations 2equations 2 and and 3 3 results in a results in a set of pair of non-linear equations. The non-linear set of pair of non-linear equations. The non-linear model was applied to four data points, each with a pair model was applied to four data points, each with a pair of simultaneously measured horizontal H and vertical Z of simultaneously measured horizontal H and vertical Z variation field componentsvariation field components. .

Model Evaluation Model Evaluation contdcontd

Simultaneously recorded hourly horizontal H and vertical Simultaneously recorded hourly horizontal H and vertical Z field values were obtained from 5 stations, in the Z field values were obtained from 5 stations, in the solar minimum year 1986. (Sunspot number R = solar minimum year 1986. (Sunspot number R = 13.4). 13.4).

These hourly horizontal and vertical field values were These hourly horizontal and vertical field values were treated for hourly departures, non-cyclic and Dst treated for hourly departures, non-cyclic and Dst variations to ensure absolute quiet condition as variations to ensure absolute quiet condition as required. The electrojet index was obtained by required. The electrojet index was obtained by subtracting the hourly values of worldwide Sq as subtracting the hourly values of worldwide Sq as obtained at Hyderabad, a station just outside of obtained at Hyderabad, a station just outside of electrojet, from other four stations that fall within the electrojet, from other four stations that fall within the electrojet influence. electrojet influence.

The resultant system of eight non-linear equations with The resultant system of eight non-linear equations with five unknown model parameters and one unknown five unknown model parameters and one unknown physical parameter (physical parameter (jjoo, a, , a, , b, , b, , x, x00 ) ) were subjected to were subjected to non-linear least square optimisation method. (Rabiu non-linear least square optimisation method. (Rabiu and Nagarajan, 2005). and Nagarajan, 2005).

Coordinates of the geomagnetic Coordinates of the geomagnetic observatories observatories

Station Station Code Code Geog. Geog. Dip latitudeDip latitudeLat. N°Lat. N° long °Elong °E (°N) (°N)

TrivandrumTrivandrum TRDTRD 8.298.29 76.5776.57 0.200.20EttaiyapuramEttaiyapuram ETTETT 9.109.10 78.0078.00 0.500.50KodaikanalKodaikanal KODKOD 10.2310.23 77.4777.47 2.142.14Annamalainagar ANNAnnamalainagar ANN 11.411.4 79.779.7 3.283.28HyderabadHyderabad HYBHYB 17.4217.42 78.5578.55 9.339.33

Fig. 2. Geographical distributions of the geomagnetic observatories

the half thickness the half thickness pp kmkm or or degreedegree at at half of the peak current density: half of the peak current density:

pp22 = b = b22 [( [( -1) + {1+ ( -1) + {1+ ( -1) -1)22}}½½ ] ] (2)(2)

Half of the latitudinal width or the Half of the latitudinal width or the focal distance of the current w km or focal distance of the current w km or degree:degree:

ww22 = -a = -a22/ / (3)(3)

Fig.3. Diurnal variation of the electrojet center for E Fig.3. Diurnal variation of the electrojet center for E –season–season

Fig.1. Diurnal variation of electrojet centre

-0.196

-0.192

-0.188

-0.184

-0.18

0 4 8 12 16 20 24

Local Time (Hrs)

dip

latit

ud

e (

de

g)

Fig. 1. Diurnal Variation of Half Thickness of EEJ

0.04

0.05

0.06

0.07

6 8 10 12 14 16 18Local Time (Hrs)

Half

thic

kn

ess

(degre

es)

0.04

0.05

0.06

0.07

6 8 10 12 14 16 18Local Time (Hrs)

Half

th

ickn

ess

(degre

es)

0.04

0.05

0.06

0.07

6 8 10 12 14 16 18Local Time (Hrs)

Half

thic

kn

ess

(deg

rees)

Fig 4. Diurnal variation of half Thickness of EEJ

EEJ Thickness demonstrates

a consistent diurnal variation across the seasons

decrease from about 0.06642º at dawn to the minimum at about 1100 hr LT and then begin to increase towards the dusk

Fig. 2. Diurnal variation of Half width

2

2.5

3

3.5

6 8 10 12 14 16 18

Local time (Hrs)

Ha

lf w

idth

(d

eg

)

2

2.5

3

3.5

6 8 10 12 14 16 18

Local time (Hrs)

Half w

idth

(deg)

2

2.5

3

3.5

6 8 10 12 14 16 18

Local time (Hrs)

Ha

lf w

idth

(d

eg

)

Fig. 5. Diurnal variation of Half width of EEJ

Fig. 6. seasonal and annual means of Half Width and Thickness

Comparison of our Half thickness value with literatures

Our result: mean annual Our result: mean annual 6.94 6.94 ++ 0.41 0.41 kmkm

Rocket-borne magnetometers Rocket-borne magnetometers (Sastry, 1970) bottom half: (Sastry, 1970) bottom half: 7 km7 km

Wind model (electrodynamic ) Anandarao &Wind model (electrodynamic ) Anandarao &Ragharavao (1987) Ragharavao (1987) bottom half: bottom half: 8 8

kmkm

relative consistency !relative consistency !

meanmean SDSD Mean Mean SDSD

our resultour result 2.832.83 0.30.3 314.13314.13 33.333.3

Yakob and Khana 1963Yakob and Khana 1963 2.612.61 289.71289.71

Anandarao & Raghavarao Anandarao & Raghavarao 19871987

2.52.5 277.5277.5

onwumechili & Ezema onwumechili & Ezema 19921992

2.742.74 0.090.09 304.14304.14 9.999.99

Oko et al 1996Oko et al 1996 2.882.88 0.080.08 319.68319.68 8.888.88

Jadhav et al. (2002) Jadhav et al. (2002) ORSTEDORSTED

2.02.0 222.0222.0

Luhr et al (2004) CHAMPLuhr et al (2004) CHAMP 3.83.8 421.8421.8

degrees km

Comparison of our Half width values with literatures at 1100 LThr

relative consistency !relative consistency !

Discussion Discussion

The variation of the dip latitude of the center of EEJ, xThe variation of the dip latitude of the center of EEJ, x00, clearly , clearly demonstrates a consistent diurnal pattern, which described a demonstrates a consistent diurnal pattern, which described a northwards shift towards the dip equator from the rising of the northwards shift towards the dip equator from the rising of the jet at dawn and becoming closer to the dip equator at the jet at dawn and becoming closer to the dip equator at the peak intensity period of the jet after which it begins to recede peak intensity period of the jet after which it begins to recede southwards towards the dusk.southwards towards the dusk.

Magnitude wise this diurnal observation is in consistency with Magnitude wise this diurnal observation is in consistency with the Orsted satellite observational result of Jadhav et al (2002a) the Orsted satellite observational result of Jadhav et al (2002a) and contradicts Oko, et al. (1986) (-0.29 and contradicts Oko, et al. (1986) (-0.29 ++ 0.02 0.02°°) result ) result obtained from thin shell formatobtained from thin shell format. .

With mean value of -0.1911 With mean value of -0.1911 ++ 0.0031°, it is obvious that the 0.0031°, it is obvious that the center of EEJ is not necessarily at the dip equator in center of EEJ is not necessarily at the dip equator in agreement with results of Srivastava (1992) and Onwumechili agreement with results of Srivastava (1992) and Onwumechili (1997) among others. This further implies that the equatorial (1997) among others. This further implies that the equatorial electrojet axis does not coincide with the dip equator. electrojet axis does not coincide with the dip equator.

Obviously the center of the jet is, however, close to the dip Obviously the center of the jet is, however, close to the dip equator at about local noon (1000 LT) and always coincides equator at about local noon (1000 LT) and always coincides with the hour of occurrence of the maximum peak forward with the hour of occurrence of the maximum peak forward current intensity, peculiar to the region of study, on any day.current intensity, peculiar to the region of study, on any day.

Discussion contd.Discussion contd. Richmond (1973) showed that a meridional wind of Richmond (1973) showed that a meridional wind of

10 ms10 ms-1-1 shifts the jet center by 0.8 km. shifts the jet center by 0.8 km.

Anandarao and Raghavarao (1987) revealed that Anandarao and Raghavarao (1987) revealed that meridional winds shift the center of the jet either meridional winds shift the center of the jet either southwards or northwards depending upon whether southwards or northwards depending upon whether the wind is northwards or southwards. the wind is northwards or southwards.

Anandarao and Raghavarao (1987) have found that a Anandarao and Raghavarao (1987) have found that a steady northward wind of 100 mssteady northward wind of 100 ms-1-1 is capable of is capable of shifting the center of EEJ southwards by 0.5º.shifting the center of EEJ southwards by 0.5º.

Forbes (1981) concluded that shifting of electrojet Forbes (1981) concluded that shifting of electrojet axis can be responsible for day-today variability of axis can be responsible for day-today variability of electrojet intensity.electrojet intensity.

Discussion contd.Discussion contd.

Diurnal variation of the jet center, xDiurnal variation of the jet center, x00, follow the , follow the satellite observation of Jadhav (2002a), contradicts satellite observation of Jadhav (2002a), contradicts results reported in literatures based on thin shell results reported in literatures based on thin shell format for EEJ current, and confirm the long term format for EEJ current, and confirm the long term assertion of Forbes and Lindzen (1976) that thin shell assertion of Forbes and Lindzen (1976) that thin shell approximation is only a representation of approximation is only a representation of approximate noontime equatorial magnetic approximate noontime equatorial magnetic variations, and fail to take into account local time variations, and fail to take into account local time variations of the electrojet. This is further stressed by variations of the electrojet. This is further stressed by the fact that our electrojet center, xthe fact that our electrojet center, x00, is minimum , is minimum and closer to the dip equator at about local noon. and closer to the dip equator at about local noon.

Forbes and Lindzen (1976) have demonstrated the Forbes and Lindzen (1976) have demonstrated the defects and inconsistencies in using a thin shell defects and inconsistencies in using a thin shell approximation in the vicinity of the magnetic approximation in the vicinity of the magnetic equator.equator.

Discussion contd.Discussion contd.

Anandarao and Raghavarao (1987) ..Anandarao and Raghavarao (1987) .. showed that a positive (negative) wind showed that a positive (negative) wind

shear decreases (increases) the width shear decreases (increases) the width (thickness) of the jet. (thickness) of the jet.

noted that the zonal wind shears can noted that the zonal wind shears can decrease or increase the width of jet by as decrease or increase the width of jet by as much as 100% depending upon their much as 100% depending upon their direction, strength and altitude, and direction, strength and altitude, and concluded that “if the width of the jet is concluded that “if the width of the jet is increased, then the thickness would increased, then the thickness would decrease and vice versa. decrease and vice versa.

ConclusionsConclusions With mean value of -0.1911 With mean value of -0.1911 ++ 0.0031°, it is 0.0031°, it is

obvious that the center of equatorial obvious that the center of equatorial electrojet is not necessarily at the dip equator electrojet is not necessarily at the dip equator and implies that the equatorial electrojet axis and implies that the equatorial electrojet axis does not coincide with the dip equator.does not coincide with the dip equator.

The equatorial electrojet center is observed to The equatorial electrojet center is observed to migrate northwards towards the dip equator migrate northwards towards the dip equator from the dawn such that it is closer to the dip from the dawn such that it is closer to the dip equator at about local noon and then reclined equator at about local noon and then reclined southwards towards the dusk. southwards towards the dusk.

The model result wholly confirmed the The model result wholly confirmed the satellite observational results and partly satellite observational results and partly contradicted the results hitherto obtained contradicted the results hitherto obtained from approximate thin shell model.from approximate thin shell model.

The mean annual half thickness and half width The mean annual half thickness and half width for the solar minimum year 1986 (Sunspot for the solar minimum year 1986 (Sunspot number R = 13.4) is 0.0625 number R = 13.4) is 0.0625 ++ 0.0037º (6.93 0.0037º (6.93 ++ 0.41 km) and 2.68 0.41 km) and 2.68 ++ 0.23º ()respectively. 0.23º ()respectively.

The thickness and width of equatorial The thickness and width of equatorial electrojet EEJ exhibit consistent diurnal electrojet EEJ exhibit consistent diurnal variations.variations.

The thickness decreases from about 0.06642º The thickness decreases from about 0.06642º at dawn to the minimum at about 1100 hr LT at dawn to the minimum at about 1100 hr LT and then begin to increase towards the dusk. and then begin to increase towards the dusk.

Conclusions Conclusions contdcontd

The width increases with the sunrise, The width increases with the sunrise, reaches maximum at about 1100 hr LT and reaches maximum at about 1100 hr LT and then begin to decrease towards the duskthen begin to decrease towards the dusk

The dynamics of the variation of electrojet The dynamics of the variation of electrojet intensity and thickness shows that intensity and thickness shows that electrojet shrinks as its intensity increaseselectrojet shrinks as its intensity increases

The thin current shell model best fits only The thin current shell model best fits only the near local noon jet observation, as the the near local noon jet observation, as the electrojet is thinnest at period of maximum electrojet is thinnest at period of maximum intensity. intensity.

Conclusions Conclusions contdcontd

AcknowledgementsAcknowledgements World Data Centre-C2, Kyoto World Data Centre-C2, Kyoto

University, Kyoto, Japan.University, Kyoto, Japan. National Geophysical Research National Geophysical Research

Institute (NGRI), Hyderabad, India. Institute (NGRI), Hyderabad, India. Third World Academy of Sciences Third World Academy of Sciences

TWAS, Trieste, Italy, TWAS, Trieste, Italy, CSIR (Government of India) for CSIR (Government of India) for

awarding Research Fellowships.awarding Research Fellowships. Organisers of, and the co-participants Organisers of, and the co-participants

at, the at, the International Advanced School on Space Weather, ICTP, Trieste

THANK YOUTHANK YOU

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Forbes J. M. and R. S. Lindzen, 1976. Atmospheric and solar tides and their electrodynamic effects-II, The equatorial electrojet. JoumaI of Atmospheric and Terrestrial Physics, Vol. 38, pp. 911-920.

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