Transcript DIURNAL VARIATION OF THE CENTER OF EQUATORIAL ELECTROJET

ON THE MORPHOLOGY OF
EQUATORIAL ELECTROJET OVER
INDIAN SECTOR
A. Babatunde Rabiu1, and Nandini Nagarajan2
1Department
of Physics, Federal University of Technology, Akure,
NIGERIA
2National Geophysical Research Institute, Hyderabad 500 007,
INDIA.
[email protected], [email protected]
International Advanced School on Space Weather, 2-19 May, 2006, ICTP,Trieste
Outline
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



Introduction
Presentation of Model
Results
Discussions
Conclusions
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

Introduction
The E region of the equatorial ionosphere consists of two
layers of currents responsible for the quiet solar daily
variations in Earth’s magnetic field: the worldwide Sq,
(altitude 118 +7 km), & the equatorial electrojet, EEJ,
(altitude 106 + 2 km)
Equatorial electrojet EEJ- the intense ionospheric current
flowing eastwards within the narrow strip flanking the dip
equator, responsible for the observed enhanced horizontal
magnetic field intensity at the magnetic equatorial
neighbourhood. (Chapman, 1951)
Most of studies on electrojet focused on noon time period as
the ranges of the magnetic field intensities were fitted into
models in order to evaluate the electrojet characteristics.
Increasing
interest
in
modeling
the
geomagnetic
observations necessitates the need for examination of every
aspect of the variation field for accurate formulation and
evaluation of model parameters
Fig. 1. Relative positions of the magnetic and geographic equators
Manifestations of EEJ
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


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

Spatial structures of its intense current density
configurations & regular temporal variations of its
current system
magnetic fields of its current system
the ionospheric plasma density irregularities generated
by the turbulent flow of the EEJ current
the electric fields and ionospheric plasma drifts in the dip
equatorial zone
the quiet counter equatorial electrojet CEJ
temporal variabilities of the above phenomenon.
Central objectives


To explore the thick shell format of a
continuous current distribution model to
evaluate the morphology of equatorial
electrojet at the Indian sector
To study the transient variations of the
landmark parameters of the EEJ
Model Evaluation
Onwumechili (1966a, b, c; 1967) presented a two dimensional
empirical model of the continuous current distribution
responsible for EEJ as:
j = jo a2(a2 + x2)b2(b2 + z2) / (a2 + x2)2 (b2 + z2)2 (1)
Where j (µA 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 dimension by introducing the coordinate y or
longitude Ø or eastwards local time t. j0 is the current
density at the centre, a and b are constant latitudinal and
vertical scale lengths respectively,  and  are
dimensionless parameters controlling the current distribution
latitudinally and vertically respectively. It is a meridional
plane model, which in this simple form has to be applied to
specific longitudes or local times. The model is a realistic
model having both width and thickness.
Model Evaluation contd.
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 = constant) as
a result of the current distribution in (1) as follows:
(sg. z) P4 X = ½ k [(1+)(v + v +2a)(u + b)2
+ 2(1- )(v + v + 4a -2a)(u + b)
+ (1+ )(v + v + 2a)(v + a)2] (2)
- (sg.x) P4 Z = ½ k [(1+ )(1+ )(u + b)3 + ((1+ )(1+ )(u + b)2
+ (1+ )(v + v + 3a - a) (v + a) (u + b)
- (1- ) b (v + v + 3a - a) (v + a)] (3)
Where P2 = (u + b)2 + (v + a)2
(4)
k = 0.1π2abj0
(5)
u = /x/ and v= /z/
(6)
sg.x = sign of (x/u) and is ± 1 when x = 0
(7)
sg.z = sign of (z/v) and is ± 1 when z= 0
(8)
Equations 2 and 3 give the horizontal and vertical magnetic field variations respectively,
due to thick current shell format.
Model Evaluation contd.
0° dip latitude does not coincide with the center of the EEJ (Oko,
et al., 1996). Therefore we chose to write an expression for the
electrojet axis x0, in terms of the dip latitude, , as:
u =  - x0
(9)
Where x0 is the dip latitude of the current center.
Introducing equation 9 in equations 2 and 3 results in a set of pair
of non-linear equations. The non-linear model was applied to
four data points, each with a pair of simultaneously measured
horizontal H and vertical Z variation field components.
Model Evaluation contd
Simultaneously recorded hourly horizontal H and vertical Z
field values were obtained from 5 stations, in the solar
minimum year 1986. (Sunspot number R = 13.4).
These hourly horizontal and vertical field values were
treated for hourly departures, non-cyclic 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 resultant system of eight non-linear equations with five
unknown model parameters and one unknown physical
parameter (jo, a, , b, , x0 ) were subjected to nonlinear least square optimisation method. (Rabiu and
Nagarajan, 2005).
Coordinates of the geomagnetic
observatories
Station
Code
Geog.
Dip latitude
Trivandrum
TRD
Lat. N°
8.29
Ettaiyapuram
ETT
9.10
78.00
0.50
10.23
11.4
17.42
77.47
79.7
78.55
2.14
3.28
9.33
Kodaikanal
KOD
Annamalainagar ANN
Hyderabad
HYB
long °E
76.57
(°N)
0.20
Fig. 2. Geographical distributions of the geomagnetic observatories

the half thickness p km or degree at half of
the peak current density:
p2 = b2 [( -1) + {1+ ( -1)2}½ ]

(2)
Half of the latitudinal width or the focal
distance of the current w km or degree:
w2 = -a2/ 
(3)
-0.18
dip latitude (deg)
0
-0.184
4
8
12
16
20
24
Local Time (Hrs)
-0.188
-0.192
-0.196
Fig.1. Diurnal variation of electrojet centre
Fig.3. Diurnal variation of the electrojet center for E
–season
Half thickness (degrees)
EEJ Thickness
demonstrates
 a consistent
diurnal variation
across the
seasons
0.06
0.05
0.04
6
8
10
12
14
16
18
Local Time (Hrs)
0.07
0.06
0.05
0.04
6
8
10
12
14
16
18
Local Time (Hrs)
Half thickness
(degrees)
about 0.06642º at
dawn to the
minimum at
about 1100 hr LT
and then begin to
increase towards
the dusk
Half thickness (degrees)
 decrease from
0.07
0.07
0.06
0.05
0.04
6
8
10
12
14
Local Time (Hrs)
Fig. 1. Diurnal Variation of Half Thickness of EEJ
Fig 4. Diurnal variation of half Thickness of EEJ
16
18
Half width (deg)
3.5
3
2.5
2
6
8
10
12
14
16
18
Local tim e (Hrs )
Half width (deg)
3.5
3
2.5
2
6
8
10
12
14
16
18
14
16
18
Half width (deg)
Local time (Hrs)
3.5
3
2.5
2
6
8
10
12
Local tim e (Hrs )
Fig. 2. Diurnal variation of Half width
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
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Our result: mean annual
6.94 + 0.41 km
Rocket-borne magnetometers
(Sastry, 1970) bottom half:
7 km
Wind model (electrodynamic ) Anandarao &
Ragharavao (1987) bottom half:
8 km
relative consistency !
Comparison of our Half width values with literatures at 1100 LThr
degrees
km
mean
SD
Mean
SD
our result
2.83
0.3
314.13
33.3
Yakob and Khana 1963
2.61
289.71
Anandarao & Raghavarao
1987
2.5
277.5
onwumechili & Ezema 1992
2.74
0.09
304.14
9.99
Oko et al 1996
2.88
0.08
319.68
8.88
Jadhav et al. (2002) ORSTED 2.0
222.0
Luhr et al (2004) CHAMP
421.8
3.8
relative consistency !
Discussion
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The variation of the dip latitude of the center of EEJ, x0, clearly
demonstrates a consistent diurnal pattern, which described a
northwards shift towards the dip equator from the rising of 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
southwards 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. (1986) (-0.29 + 0.02°) result
obtained from thin shell format.
With mean value of -0.1911 + 0.0031°, it is obvious that the
center of EEJ is not necessarily at the dip equator in agreement
with results of Srivastava (1992) and Onwumechili (1997)
among others. This further implies that the equatorial electrojet
axis does not coincide with the dip equator.
Obviously the center of the jet is, however, close to the dip
equator at about local noon (1000 LT) and always coincides
with the hour of occurrence of the maximum peak forward
current intensity, peculiar to the region of study, on any day.
Discussion contd.
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Richmond (1973) showed that a meridional wind of 10 ms-1
shifts the jet center by 0.8 km.
Anandarao and Raghavarao (1987) revealed that meridional
winds shift the center of the jet either southwards or
northwards depending upon whether the wind is northwards
or southwards.
Anandarao and Raghavarao (1987) have found that a steady
northward wind of 100 ms-1 is capable of shifting the center
of EEJ southwards by 0.5º.
Forbes (1981) concluded that shifting of electrojet axis can
be responsible for day-today variability of electrojet intensity.
Discussion contd.


Diurnal variation of the jet center, x0, follow the satellite
observation of Jadhav (2002a), contradicts results
reported in literatures based on thin shell format for EEJ
current, and confirm the long term assertion of Forbes
and Lindzen (1976) 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. This is further stressed
by the fact that our electrojet center, 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.
Discussion contd.
Anandarao and Raghavarao (1987) ..
 showed that a positive (negative) wind shear
decreases (increases) the width (thickness) of the
jet.

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.
Conclusions
With mean value of -0.1911 + 0.0031°, it is obvious
that the center of equatorial electrojet is not
necessarily at the dip equator and implies that the
equatorial electrojet axis does not coincide with the
dip equator.
The
equatorial electrojet center is observed to
migrate northwards towards the dip equator from
the dawn such that it is closer to the dip equator at
about local noon and then reclined southwards
towards the dusk.
The
model result wholly confirmed the satellite
observational results and partly contradicted the
results hitherto obtained from approximate thin
shell model.
Conclusions contd
the
The mean annual half thickness and half width for
solar minimum year 1986 (Sunspot number R =
13.4) is 0.0625 + 0.0037º (6.93 + 0.41 km) and
2.68 + 0.23º ()respectively.
exhibit
The thickness and width of equatorial electrojet EEJ
consistent diurnal variations.
dawn
The thickness decreases from about 0.06642º at
to the minimum at about 1100 hr LT and then
begin to increase towards the dusk.
Conclusions
contd
maximum
The width increases with the sunrise, reaches
at about 1100 hr LT and then begin to
decrease towards the dusk
intensity
The dynamics of the variation of electrojet
and thickness shows that electrojet
shrinks as its intensity increases
near
The thin current shell model best fits only the
local noon jet observation, as the electrojet
is thinnest at period of maximum intensity.
Acknowledgements


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
World Data Centre-C2, Kyoto University,
Kyoto, Japan.
National Geophysical Research Institute
(NGRI), Hyderabad, India.
Third World Academy of Sciences TWAS,
Trieste, Italy,
CSIR (Government of India) for awarding
Research Fellowships.
Organisers of, and the co-participants at,
the International Advanced School on
Space Weather, ICTP, Trieste
THANK YOU
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