JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, A03213, doi:10.1029/2005JA011465, 2006
Modeling of the global distribution of ionospheric electric fields based
on realistic maps of field-aligned currents
Renata Lukianova1,2 and Freddy Christiansen3
Received 10 October 2005; revised 6 December 2005; accepted 19 December 2005; published 17 March 2006.
[1] A new approach for modeling the global distribution of ionospheric electric potentials
utilizing high-precision maps of FACs derived from measurements by the Ørsted and
Champ satellites as input to a comprehensive numerical scheme is presented. The
boundary conditions provide a correct treatment of the asymmetry of conductivity and
sources of electric potential between the northern and southern hemispheres. On the
basis of numerical simulation the basic convection patterns developed simultaneously in
both hemispheres for equinox and summer/winter solstices are obtained. A rather
complicated dependence of the convection patterns on season linked with the sign of IMF
BY is found. In particular, the combinations of BY > 0/summer and BY < 0/winter produce
the highest circular flow around the pole in comparison with the combinations of
BY < 0/summer and BY > 0/winter. The model predicts that the summer cross-polar
potentials are smaller than the winter potentials. The value of the ratio depends on the
combination of season/IMF BY sign. The ratio is found to be greater for the combination
of BY > 0/southern summer and BY < 0/northern summer. The smallest value is obtained
for the combination of BY < 0/southern summer and BY > 0/northern summer under
northward IMF conditions. At middle latitudes the main features of the MLT-profile of the
westward and equatorward electric field components are reproduced. The model
predicts that during solstice the equatorward component of the midlatitude electric field is
negative at all local times for BY < 0 and positive for BY > 0.
Citation: Lukianova, R., and F. Christiansen (2006), Modeling of the global distribution of ionospheric electric fields based on
realistic maps of field-aligned currents, J. Geophys. Res., 111, A03213, doi:10.1029/2005JA011465.
1. Introduction
[2] It has long been a goal of high-latitude experiments
and modeling to describe the entire ionospheric convection
system. Large-scale convection maps have been obtained
by averaging data over time and/or space. Ground-based
instruments usually provide good temporal but poor spatial
coverage. For satellites, many passes are required before
the whole polar region is covered. Heppner and Maynard
[1987] synthesized a sketched convection pattern looking
for characteristic signatures in the electric field from each
pass of DE-2. Rich and Hairston [1994] used a spatial
binning approach on several years of DMSP measurements. From chains of magnetometers data fitted to the
IMF conditions using linear regression, Papitashvili et al.
[1994] produced electric potential patterns. The AMIE
procedure [Richmond and Kamide, 1988] is a comprehensive approach combining observations from multiple instruments simultaneously, which has the advantage of
providing a ‘‘snapshot’’ of the convection pattern although
1
Department of Physics, St. Petersburg State University, St. Petersburg,
Russia.
2
Also at Arctic and Antarctic Research Institute, St. Petersburg, Russia.
3
Danish National Space Center, Copenhagen, Denmark.
Copyright 2006 by the American Geophysical Union.
0148-0227/06/2005JA011465$09.00
the method depends very much on the availability of
coincident data from multiple locations. AMIE results are
widely used in current research. Recently, a renewed
interest in the generation of global convection models
has showed up. Papitashvili and Rich [2002] extended
the previous results to construct a new model in which
the electric potential are scaled by DMSP satellite
observations. Weimer [1995, 2005] used a spherical
harmonic expansion to fit a pattern to sets of electric
potentials from DE-2 binned by IMF angle and magnitude.
Ruohoniemi and Greenwald [1996, 2005] averaged SuperDARN radar data and employed Laplace’s equation to
extrapolate the mapping.
[3] The majority of existing convection models are statistical or semiempirical ones. Pure numerical models are less
widely used. Two reasons for the lesser attention paid to
numerical modeling of the ionospheric convection can be
mentioned. First, there has until recently been a lack of
realistic maps of Birkeland field-aligned currents (FAC)
distribution that serve as a source of the electric potential.
Second, there has been an absence of appropriate algorithms
to utilize these maps. In order to calculate the electric
potential pattern within the northern or southern hemispheres, most authors have used the total distribution of
FACs flowing above the ionosphere in one hemisphere only.
Mathematically, it implies the statement of a Dirichlet or
Neumann boundary condition on the equatorial boundary of
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LUKIANOVA AND CHRISTIANSEN: MODELING OF THE IONOSPHERIC ELECTRIC FIELD
Figure 1. Sketch illustrating the statement of boundary
value problem for the ionospheric shells. Arrows represent
the geomagnetic field lines. Calculation area is shaded.
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season, and by hemisphere, the same parameterization can
be further applied for the convection model. The modeled
convection patterns are expected to be in accordance with
ground and satellite observations of the ionospheric electric
field. The validation of this can be provided by a comparison with results from existing models.
[5] The outline of the paper is as follows. In the second
section, we describe the model including the statement of
the problem, the boundary conditions, and the algorithm.
The modeling results are presented in the third section. We
calculate the global electric potential distribution under
different IMF conditions for equinox and solstice. In this
section we obtain the basic convection patterns in both
northern and southern polar region, and the results are
compared to other models. We also discuss the electric
fields located below the polar cap boundary. The final
section is a summary of the modeling results.
2. Model Description
the high-latitude region. The effect of electrical coupling
between hemispheres is generally neglected. However, an
asymmetry in the interhemispheric distribution of FACs and/
or conductivity is a common feature of ionospheric electrodynamics. The IMF BY component produces antisymmetric
convection between the northern and southern polar caps,
known as the Svalgaard-Mansurov effect. The IMF BY is
also responsible for an interhemispheric asymmetry in the
FAC distribution with respect to the noon meridian [Taguchi
et al., 1993; Papitashvili et al., 2002]. Additionally, significant difference in the northern and southern cap potential
drops has been observed under jBZ/BYj < 1 conditions [Lu et
al., 1994], as well as under seasonal conditions of winter in
one hemisphere and summer in the other [Papitashvili and
Rich, 2002]. Thus a mutual influence of the opposite
hemispheres and a penetration of the electric field to middle
latitudes may be quite significant.
[4] Up to now, none of the ionospheric convection models
has utilized direct measurements of FACs as input. This
implies that the main link of magnetosphere-ionosphere
coupling has not been taken explicitly into account. Since
the early results of Iijima and Potemra [1976], no comprehensive studies of FAC distributions were carried out, until
the emergence of a new generation of low-orbiting satellites
with high-precision magnetometers (Ørsted, Champ) and
the low-precision multiple Iridium satellites. These spacecrafts are providing an enormous database of magnetic field
variations above the ionosphere, resulting in the appearance
of qualitatively new FAC models [Waters et al., 2001;
Papitashvili et al., 2002] parameterized by the IMF direction/strength, by season, and by hemisphere. Currently, the
technique of space measurements of FACs is developing
rapidly. This motivates us to attempt a new approach for
modeling the global distribution of the ionospheric electric
potential utilizing the high-precision maps of FACs derived
from measurements by modern constellation of satellites as
an input for a comprehensive numerical scheme. The
boundary conditions provide a correct treatment of the
asymmetry of conductivity and sources of electric potential
between hemispheres. Modeling the ionospheric electric
fields in their interhemispheric conjugation allows us to
obtain their variations at lower latitudes. Since the FAC
model is fully parameterized by the IMF conditions, by
[6] For an ‘‘open’’ model of the magnetosphere, electrical
conjugation between polar cap ionospheres of northern and
southern hemispheres via the geomagnetic field is negligible. Outside of the polar caps, however, this conjugation is
important. The equation of electric current continuity:
div J ¼ j00 sin c;
ð1Þ
where J is the height-integrated horizontal ionospheric
current, j00 is the field-aligned current, and c is the
magnetic inclination, is solved on a grid covering the twodimensional ionospheric shell with specified heightintegrated conductivity in spherical coordinate system (q is
the geomagnetic colatitude, j is the geomagnetic longitude).
Figure 1 gives a sketch of the ionospheric shell. According
to the statement of the boundary value problem and the
algorithm developed by Lukianova et al. [1997], we divide
the ionospheric shell into three subregions (referred to as
a = 1, 2, and 3) as follows. Northern (a = 1) and southern
(a = 2) polar caps with boundaries at the colatitudes q1
and q2 = p q1, respectively, are uncoupled with respect
to electric potential. On the remaining portion of the
sphere (a = 3) the Earth’s closed magnetic field lines are
taken to be equipotential for conjugate points on opposite
hemispheres. This allows us to solve equation (1) on each
half of the low-latitude subregion (a = 3). For definiteness,
let it be the northern half from the polar boundary at q1 to
a specified equator boundary at q3 (this area is denoted by
‘‘N’’ in the sketch). The boundary q3 is set latitudinally
away from the equator to avoid a division by zero in the
expression for the components of conductivity tensor. The
sum of conductivities and sources at conjugate points of
‘‘N’’ and ‘‘S’’ is used in every point. Further we omit the
sign ‘‘N’’ for a = 3 subregion and obtain the following
boundary value problem:
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div J 1 ¼ j1
for q q1
ð2Þ
div J 2 ¼ j2
for p q1 q < p
ð3Þ
div J 3 ¼ j3
for q1 q q3
ð4Þ
LUKIANOVA AND CHRISTIANSEN: MODELING OF THE IONOSPHERIC ELECTRIC FIELD
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where Ja is the height-integrated horizontal ionospheric
current and ja is the radial component of FACs in the
corresponding subregions. Three subregions (a = 1, 2, 3)
are connected by the boundary conditions as follows:
U1 ðq1 ; jÞ ¼ U3 ðq1 ; jÞ ¼ U2 ðq2 ; jÞ
ð5Þ
J1 ðq1 ; jÞ J3 ðq1 ; jÞ ¼ J2 ðq2 ; jÞ
ð6Þ
J3 ðq3 ; jÞ ¼ 0
ð7Þ
where Ua is the ionospheric electric potential in the
corresponding subregions.
[7] Boundary condition (5) means that no discontinuity in
the electric potential across the boundary of the polar cap
and between the boundaries of opposite caps. Condition (6)
means that any possible discontinuities of the longitudinal
components of ionospheric currents across the boundaries
of the northern and southern caps compensate each other
through the currents leaking across these boundaries into the
lower latitudes. Condition (7) means the absence of current
across the equator. The quantities Ua and Ja are connected
by Ohm’s law:
J a ¼ Sa ðrUa Þ
ð8Þ
where Sa is the height-integrated conductivity tensor
including both Hall and Pedersen conductivity.
[8] Equations (2) – (7) are solved numerically using an
iteration technique. To obtain (2) – (7) in iterative form, we
use the term:
Zaðnþ1Þ ¼ Uaðnþ1Þ UaðnÞ =tðnþ1Þ
ð9Þ
where n is the number of iteration, t(n+1) is the relaxation
parameter obtained by method adopted from Vladimirov
and U(n+1)
are the electric potential
[1981], and U(n)
a
a
distribution obtained at iteration n and (n+1), respectively.
[9] Following the recommendation of Samarsky and
Nikolaev [1978], we include into the left side of equations
(2) – (4) a regularizer R, specifically, the angular component
of the Laplace operator,
R divðrÞ D
ð10Þ
This is useful because R admits the separation of variables
making the solution of the problem (2)– (7) easier. Now in
terms of Za equations (2) – (4) have the form:
div rZaðnþ1Þ þ div J ðanÞ ¼ ja
ð11Þ
The boundary condition (5) is satisfied in each iteration
step. In terms of Za, it has the form (the vertical line means
the boundary at corresponding qa):
ðnþ1Þ Z2
ðn Þ ðnÞ ¼ U2 U1 =tðnþ1Þ
ð12aÞ
ðnþ1Þ Z3
ðnÞ ðnÞ ¼ U3 U1 =tðnþ1Þ
ð12bÞ
ðnþ1Þ Z1
q1
q2
ðnþ1Þ Z1
q1
q3
q2
q1
q1
q1
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The iterative counterparts of boundary conditions (6) – (7)
are
ðnþ1Þ ðnþ1Þ @Z2
@Z3
ðnÞ ðnÞ ðnÞ ¼ J1 J2 J3 q1
q2
q3
@q @q ðnþ1Þ @Z1
@q
q1
q2
q1
ð13Þ
ðnÞ ¼ J3 q3
ðnþ1Þ @Z3
@q
ð14Þ
q3
(n+1)
It is obvious, if U(n)
! U*a as n ! 1, U*a is a
a ! Ua
solution of (2) – (7). It is also obvious that if the iteration
! 0) the solution of (11) – (14) is
process converges (Z(n+1)
a
equal to the solution of (2) – (7). We can express the solution
of (11) as a Fourier series:
Zaðnþ1Þ ¼
Xk¼2m
k¼2m
Cak ðqÞ eikj
ð15Þ
where Cak(q) are the complex-valued coefficients depending
solely on the colatitude. Taking into account (8), by a finite
difference scheme over a two-dimensional grid (q, j), we
obtain an approximation for div Ja and Ja in (11) and (13) –
(14). Substitution of (15) into (11) – (14) gives the onedimensional boundary value problem for Fourier coefficients. The corresponding three systems of linear algebraic
equations are solved by the sweep method (Gauss method
for the system of equations with three-diagonal matrix). In
order to connect the subregions a = 1, 2, 3 the system of six
equations containing a pair of boundary grid points from
each of them is singled out and solved separately. Finally,
by inverse Fourier transform and obtain
we restore Z(n+1)
a
. Having the potential distribution we can calculate the
U(n+1)
a
zonal and meridional components of the electric field
strength as follows:
Eq ¼ @U =@q
ð16Þ
Ej ¼ 1= sin q @U =@j
ð17Þ
The described technique needs the distribution of ionospheric conductivity. Both the solar UV conductance and
the auroral precipitation-enhanced conductance contribute
to Sa. The solar UV contribution can be calculated from the
10.7 cm solar radio flux proxy and the zenith angle.
Seasonal and diurnal variations are taken into account
using the estimates by Robinson and Vondrak [1984]. The
Kp-dependent model of Hardy et al. [1987] is used to
calculate the auroral contribution. The auroral conductivity
is combined with the solar radiation conductivity as the
square root of the sum of the squares. Note that the effective
numerical scheme allows a rather steep gradient of the
conductivity and sources. Depending on the conductivity
and FAC distribution, the solution (2) – (7) gives the
potential distribution. In particular, it can be substantially
different but not independent in the two hemispheres.
3. Calculations
3.1. Patterns of Ionospheric Potentials
[10] Recently, a new model of FACs has been derived
from magnetic field measurements from the Ørsted and
Champ satellites parameterized by IMF strength and direc-
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Table 1. Numbers of the IMF Clock-Angle Orientation
IMF BZ
IMF BY
Number
<0
<0
6
=0
7
=0
>0
8
<0
5
=0
0
>0
>0
1
<0
4
=0
3
>0
2
tion for summer, winter and equinox for both hemispheres
[Papitashvili et al., 2002]. We use these FAC patterns as
input for calculating of the global distribution of ionospheric electric potentials. In this paper we present convection patterns modeled for the IMF BT = (B2Z + B2Y)1/2 = 5 nT
and eight IMF clock-angle orientation (Table 1) under
conditions of December solstice and March equinox. For
the calculation, the boundaries q1, q2 and the equatorial
boundary q3 were set at 30 and 60 of geomagnetic
colatitude, respectively. The coordinate grid steps were
Dq = 1 and Dj = (360/128). Average values of the
parameters controlling the solar part of conductivity, specifically F10.7 = 120, UT = 12, and day = 80 (equinox),
day = 355 (solstice) were used. Taking into account the
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variation of average Kp with BZ, we choose Kp = 2 for
BZ 0 and Kp = 3 for BZ < 0.
[11] First, we consider winter solstice conditions. Figure 2
gives the convection patterns obtained in the northern winter
polar region. Figure 3 gives the result for the southern
summer polar region. The plots in paired Figures 2 and 3
are arranged as follows. The first, second, and third rows
present the maps of electric potential obtained for BZ > 0,
BZ = 0 and BZ < 0, respectively. The first, second, and
third plots in each row present the maps obtained for BY <
0, BY = 0, and BY > 0, respectively. Such an organization
of the plots according to the IMF clock-angle in GSM Y-Z
plane was used in previous works [e.g., Papitashvili et al.,
2002; Weimer, 2005] For easy comparison we organize the
plots in the same manner. One can see that the solstice
convection patterns from Figures 2 and 3 show a significant seasonal effect. First, the convection cells in the
winter hemisphere have more voltage than corresponding
cells in the summer hemisphere. Also, the shape of the
corresponding cells from the opposite polar caps is recog-
Figure 2. Isolines of the electric potential calculated for December solstice in the northern winter
hemisphere for nine IMF clock-angle orientations with contours every 5 kV (first and second rows) and
10 kV (third row). Minimum and maximum potentials are shown by number under each plot. Positive
and negative potential are marked by solid and dashed lines, respectively. Noon is at the top, and dawn is
to the right in each polar plot. Circles are drawn every 20 in magnetic latitude down to 50.
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Figure 3. The same as Figure 2, but in the southern summer hemisphere.
nizably different even for the same IMF orientation. A
change of the IMF BY sign does not produce a simple
mirror antisymmetric change in convection patterns within
the same hemisphere. Also, the paired patterns from
opposite hemispheres, specifically the patterns for BY >
0/northern and BY < 0/southern (BY < 0/northern and BY >
0/southern) do not copy each other. It is worth to underline
the following features. For the IMF = 0 pattern, the winter
dusk cell dominates while in summer the positive dusk and
the negative dawn cell are more symmetric. For the IMF
BZ > 0 patterns, the winter dusk cell generally dominates
irrespective of the IMF BY sign. However, in the dayside
near-pole region one can identify an isolated convection cell
extended from the prenoon (BY < 0) or postnoon (BY > 0)
sector. During southern summer the convection vortex
surrounds the pole. The ionospheric plasma flows clockwise
or anticlockwise around the pole depending on the IMF BY
sign. For BY > 0 the dawn cell strongly dominates while the
dusk cell almost disappears. For BY = 0, the convection
system is marginal in winter cap and is barely structured in
summer cap. The IMF BZ < 0 patterns from both hemispheres show a customary two-cell convection system
slightly distorted according to the IMF BY effect.
[12] Figures 4 and 5 give the result of our calculation for
equinox in the northern and southern hemispheres, respectively. One can see that the two-cell convection system is
typical for all IMF orientations, although under northward
IMF conditions an additional BY-dependent vortex is developed near local noon. In contrast to solstice conditions,
during equinox the BY effect produces an antisymmetric
distortion of the convection cells in the opposite hemispheres. Without any influence of the BY component the
convection patterns display interhemispheric symmetry. The
peculiarity of the IMF BZ > 0 patterns is that the dusk cell
always extends to the dawnside across the pole. Under
southward IMF conditions a two-cell system with extended
dusk vortex is developed.
[13] From Figures 2 – 5 one can see that the patterns
obtained under different IMF and seasonal conditions are
in agreement with the commonly accepted understanding
of large-scale convection. They also show some smallerscale but notable peculiarities caused by the combined
action of different factors. Also, the convection vortices
are not confined within the high-latitude region. The
flow extends to lower latitudes where the electric potential is determined by the mutual electrodynamic influence
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Figure 4. The same as Figure 2, but for the equinox in the northern hemisphere.
of the opposite hemispheres. Indeed, below the boundary
between the regions of open and closed geomagnetic
field lines (denoted as q1 and q2) the electric potential
isolines show some kind of fracture. The features of
penetrated electric field will be considered in more details
in section 3.3.
3.2. Comparison With Other Models
[14] Convection patterns calculated for both northern
and southern hemispheres show all the main features
predicted by previous statistical models. Present modeling
was undertaken for different seasons and for the test
IMF/SW conditions, specifically the IMF BT = 5 nT, n =
5 cm3, V = 400 km/s. A quantitative comparison for one
of the most representative parameters is given in Figure 6.
This figure shows the voltage in the foci of the dawn
positive and dusk negative convection cells for eight the
IMF clock-angle orientations (see Table 1). We compare the
voltage obtained from present calculation with the voltage
predicted by DMSP and DISM models of Papitashvili and
Rich [2002] and DE2 model of Weimer [1995]. From
Figure 6 one can see that the voltage predicted by the
various models responds to the IMF rotation in the same
manner. The largest and the smallest values are achieved
under the IMF BZ < 0, BY = 0 and BZ > 0, BY = 0
conditions, respectively. Some greater uncertainty is in the
voltage of the southern dawn cell. The spread in results
from different models increases in this case. In particular,
one can suspect that during solstice the present model
slightly underestimates the voltage. During equinox the
southern dawn cell voltage shows too slight variations
with the IMF rotation. However, overall the present model
gives reasonable values of the voltage in the dawn and
dusk convection cells.
[15] Regarding the cross-polar potential it is interesting
to estimate the seasonal and the IMF clockangle effect.
Earlier, Papitashvili and Rich [2002] obtained the ratio
1.2 between the winter and summer cross-polar potential.
Christiansen et al. [2002] obtained the summer/winter
ratio 1.5 for the R1 FAC. The seasonal ratio for each
IMF clock-angle (Table 1) derived from our model is
presented in Figure 7. The upper panel shows the ratio
between the northern winter and southern summer crosspolar potential (DUW and DUS, respectively) calculated
under December solstice conditions. The second panel
shows the same parameter for southern winter and northern summer during June solstice (corresponding convection patterns are not shown). One can see that the winter
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Figure 5. The same as Figure 2, but for the equinox in the southern hemisphere.
potential drop regularly exceeds the summer value. The
ratio varies significantly from 1.0 to 1.7 with the average
value of 1.3 for both the northern and southern winter.
This is a bit larger compared to the results of Papitashvili
and Rich [2002] who attributed the winter/summer potential difference mostly to the seasonal dependence of FACs.
Figure 7 also shows that in the northern cap, the value of
DUW/DUS is greater when the IMF BY > 0 while in the
southern cap this ratio is greater when the IMF BY < 0.
The effect is more clearly seen under conditions of
positive/zero BZ component. This is possibly caused by
the dependence of FACs on the sign of BY. Although the
FAC distribution obtained in [Papitashvili et al., 2002]
shows a general mirror asymmetry related to BY polarity
there is some difference in details especially for northward
IMF. On the other hand, because of conductivity gradients
resulting in an extension of the dusk convection cell, this
is favorable for the strengthening of convection in the
northern polar cap when the IMF BY > 0, or in the
southern polar cap when the IMF BY < 0. The combined
effect of seasonal and BY dependence of FAC can cause
changes in DUW/DUS. A similar effect was recently
detected by Ruohoniemi and Greenwald [2005]. These
results show greater variability of convection patterns than
a traditional scheme.
3.3. Electric Field at Lower Latitudes
[16] As it was pointed out by Weimer [2005], one of the
unresolved problems of ionospheric modeling is the determination of the electric fields penetrating to middle latitudes, since this field is located below the outer boundary of
the existed models. Although this aspect mostly concerns
the electrodynamics of geomagnetic storms, the seasonal
asymmetry in conductivity as well as the seasonal and the
IMF dependence of FACs affects the distribution of the
electric potential in the region of closed geomagnetic field
lines. In our model we can calculate the electric field as low
in latitude as 30– 20 from the equator. In this section we
present the variations of zonal and meridional component of
the electric field that determines the plasma motion along
the latitude and longitude, respectively, obtained from the
patterns considered above. The westward and equatorward
electric field component was calculated. First, we focus on
the seasonal effect and present the electric field variations at
high and middle latitudes obtained for equinox and northern
winter. To exclude the asymmetry caused by the BY effect,
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geomagnetic field lines where its behavior is controlled by
the electric potential distribution in the opposite polar caps.
As expected, the electric field decays more quickly during
the day than at night. This effect is clearly seen during both
equinox and solstice. The notable feature is that during
northern winter, a strong winter electric field decays more
rapidly with latitude than the weaker summer field. As a
result, the electric field from summer high latitudes and
the subauroral electric field from both hemispheres have
comparable amplitudes. Figure 9 demonstrates with better
resolution the profile of westward and equatorward components at middle latitudes (q = 45). It is seen that the
corresponding curves keep their form during both seasons.
Figure 9 indicates that the electric fields are mostly
eastward during the day, westward and poleward at night,
equatorward near dawn. Westward and equatorward components peak just before dawn. The poleward electric field
is strongest on the nightside.
[17] When the seasonal interhemispheric asymmetry in
conductivity and in FAC intensity is amplified with the BY –
related redistribution of FACs, the plasma flow at middle
latitude is also modified. Specifically, the flow is strongly
affected by the corresponding summer polar cap convection
pattern. Returning to Figures 2 and 3, one can see that under
northward IMF conditions the BY-related ionospheric plasma flows have the opposite direction in the northern
winter and southern summer polar caps (e.g., BY < 0
produces eastward (westward) flow in the northern
(southern) polar cap). Although the most intensive vortices
are confined within high-latitude regions, a recognizable
Figure 6. The electric potential in the foci of the dawn
positive and dusk negative convection cells for eight the
IMF clock-angle orientation according Table 1 under
December solstice (a) and March equinox (b) conditions.
The upper and lower plot in panels (a) and (b) represent the
northern and southern hemispheres, respectively. Results are
represented as follows: the present model (thick line with
squares), DMSP model (thin line with circles), IZMEM/
DMSP model (dotted line with triangles), DE2 model
(dashed line with diamonds).
the IMF conditions of BZ < 0, BY = 0 were chosen. The
upper panel of Figure 8 shows the westward component in
both polar caps (q = 15) and just below the boundary
separating the regions of open and closed field lines (q =
30). The first and second plot in the panel gives the
result for March and December, respectively. The lower
panel of Figure 8, organized in the same manner, shows
the equatorward component. Figure 8 indicates that both
components effectively penetrate to the region of closed
Figure 7. Histogram of the ratio between the winter and
summer cross-polar potential for eight the IMF clock-angle
under December (upper panel) and June (lower panel)
solstice conditions.
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Corresponding high-latitude convection patterns were given
in the first row of Figures 2 – 3. From Figure 10 one can see
that the behavior of the westward component which determines meridional plasma flow is similar regarding to BY
polarity. However, equatorward component which determines zonal flow is negative for BY < 0 and positive for
BY > 0 at all local times. That implies opposite directions of
plasma circulation at middle latitudes. For BY < 0 (BY > 0)
the vortex with clockwise (anticlockwise) flow is extended
from the southern summer polar cap to the middle latitudes
of the northern winter hemisphere. This result illustrates
nicely that the mutual influence of opposite hemispheres
can modify the global convection.
4. Discussion and Conclusion
[18] We have performed numerical modeling of the
global distribution of the ionospheric electric field. A new
approach is to utilize realistic maps of FACs obtained from
Ørsted and Champ satellites as an input for the calculation
of convection systems which are developed simultaneously
in both hemispheres. From the conductivity side, both the
solar contribution and auroral precipitation contribution are
included. The convection patterns we have obtained reproduce all common features inherent in statistical models.
Besides that, some new remarkable features are seen.
[19] Very recently, Ruohoniemi and Greenwald [2005]
reported a rather complicated dependence of the convection
patterns on season. Analyzing SuperDARN data, these
authors found it necessary to link season with the sign of
IMF BY to fully characterize the dependence. In particular,
Figure 8. Westward component of the electric field in the
northern and southern polar caps (q = 15), and at
subauroral latitudes (q = 30) for the equinox and northern
winter (upper panel). The same for equatorward component
(lower panel).
portion of the electric field penetrates to middle latitudes. The
electrodynamic coupling of opposite hemispheres shows
itself in an expansion of the dominating direction of plasma
flow from summer to winter hemisphere. To demonstrate this
effect, in Figure 10 both components of midlatitude electric
field (q = 45) are presented. Upper and lower panels give
the results for IMF BY < 0 and BY > 0, respectively.
Figure 9. Westward and equatorward components of the
electric field at middle latitudes (q = 45) for the equinox
and northern winter.
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LUKIANOVA AND CHRISTIANSEN: MODELING OF THE IONOSPHERIC ELECTRIC FIELD
Figure 10. Westward and equatorward components of the
electric field at middle latitudes (q = 45) during northern
winter under conditions of the IMF BY < 0 (upper panel)
and BY > 0 (lower panel).
the combinations of BY > 0/summer and BY < 0/winter
produce the most circular flow around the pole in comparison with the combinations of BY < 0/summer and BY >
0/winter. In the frame of our model, the majority of the
effects described by Ruohoniemi and Greenwald [2005]
are nicely reproduced. An inspection of the BZ > 0 patterns
of Figures 2 and 3 show that the circumpolar vortex is more
pronounced in summer. The BY > 0/summer conditions are
the most favorable for the development of one-cell convection pattern in which the dawn cell dominates. There is no
the equivalent response of the dusk cell with respect to
BY < 0. The pattern of BY < 0/winter that is paired to
BY > 0/summer regarding to BY effect, shows a tendency
for the development of an isolated vortex of the dawn cell
near noon. These peculiarities imply a greater variability in
the convection cells associated with the combined influence of both the seasonal and IMF factors. Further
investigation of hemispheric asymmetries is needed.
[20] Our calculation of the cross-polar potential drop for
the equinox, winter solstice, and summer solstice under
different IMF conditions give the following results. During
the equinox the northern and southern potential drops are
found to be practically equal. During solstice the winter
cross-polar potential (DUW) drop regularly exceeds the
summer one (DUS), but the ratio between these values
depends on the IMF conditions. There remains some
disagreement between models regarding the value of
cross-polar potential drop in northern and southern hemispheres. In particular, the models of Weimer [1995] and
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Ruohoniemi and Greenwald [2005] give an increase of
potential drop from winter to summer. However, our result
is generally consistent with the result of Papitashvili and
Rich [2002]. These authors described an overall decrease of
15% in potential drop in passing from winter to summer.
The effect was mostly attributed to the seasonal dependence
of FACs that changes the topological properties of the
dayside magnetopause. At the same time, our results do
not contradict to the finding of Ruohoniemi and Greenwald
[2005] pointed out that BY < 0 conditions are favorable for
an increase of DUS. Under BY > 0 conditions the value of
DUS was found to be smaller. Convection patterns from the
first row of Figure 3 show the same regularity. More
systematically, though more indirectly, this regularity is
obtained from variations of the ratio DUW/DUS. To investigate the combined seasonal/IMF effect, we examined the
dependence of DUW/DUS on the IMF clock-angle rotation.
The ratio is found to be greater for the combination of
BY > 0/southern summer and BY < 0/northern summer. The
smallest value of DUW/DUS is obtained for the combination
of BY < 0/southern summer and BY > 0/northern summer
(northward IMF). In other words, in the first two cases the
value of the potential drop in the winter polar cap exceeds
that of the summer polar cap more than in the last two cases.
Because we consider the winter and summer hemispheres in
their conjugation, the obtained regularity can be of the same
nature as an increase of DUS for BY < 0 and thus can be
attributed to merging site asymmetries [Crooker, 1992].
[21] Convection patterns presented in Figures 2– 5 are
confined within 50 CGM latitude. Actual outer boundary
of the region where we calculate the electric potential
distribution is set at 30 CGM latitude. Taking into account
the interhemispheric electrodynamic coupling allows us to
simulate the behavior of the meridional and zonal components of the electric field at middle latitudes. Calculations
give the following results. During equinox at middle latitudes the electric fields are westward at night and near
dawn, mostly eastward during the day, poleward at night
and near dusk, and equatorward near dawn. Westward and
equatorward components are peaked near dawn. Poleward
electric field is strongest on the nightside. The obtained
variations are in good agreement with observation and
modeling. Note that the MLT-profile of the westward and
equatorward components obtained from the present model
is similar to the variations derived from a Rise Convection
Model [e.g., Fejer and Emmert, 2003], providing an independent check of our model. Examination of the electric
field during solstice shows that although the electric field is
stronger in the winter polar cap, it is mostly confined within
high latitudes. In the summer polar cap and at middle
latitudes the electric field has comparable amplitudes,
implying a slower spatial decay. A combined influence of
the seasonal and IMF asymmetry reinforces the global
asymmetry in electric potential distribution. The simulation
shows that during solstice the equatorward component of
the mid-latitude electric field is negative at all local times
for BY < 0 and positive for BY > 0. This component
determines the zonal component of ionospheric plasma
flow. Thus the vortex with clockwise (anticlockwise) flow
can occupy the majority of the globe, although to our
present knowledge there are yet no direct observations
supporting this prediction.
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[22] Finally, we would like to mention two key elements
of the proposed model in the context of further work. First,
it can utilize high-precision maps of FACs. We believe that
further development of direct measurements of FACs will
improve the accuracy of the ionospheric electric field
modeling based on realistic FAC distribution. In particular,
better understanding of conductivity variations in relation to
FACs is needed. Second, taking into account the electrodynamic coupling of the opposite hemispheres, the model can
handle the electric field far below the auroral latitudes. It
allows a simulation of the electric field disturbances that
originate at the polar regions but cover a broad range of
latitudes in both hemispheres.
[23] Acknowledgments. Work of RL was partly supported by the
NATO grant PST.CLG.978252. We appreciate discussions with V. Pilipenko.
[24] Arthur Richmond thanks Vladimir Papitashvili and Colin Waters
for their assistance in evaluating this paper.
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F. Christiansen, Danish National Space Center, Copenhagen, Denmark.
R. Lukianova, Department of Physics, St. Petersburg State University, 38
Bering Street, St. Petersburg, 199397 Russia. ([email protected])
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