JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. A11, 1391, doi:10.1029/2002JA009313, 2002
Comparing a spherical harmonic model of the global electric
field distribution with Astrid-2 observations
S. Eriksson1 and L. G. Blomberg
Alfvén Laboratory, Royal Institute of Technology, Stockholm, Sweden
D. R. Weimer
Mission Research Corporation, Nashua, New Hampshire, USA
Received 5 February 2002; revised 13 June 2002; accepted 9 August 2002; published 21 November 2002.
[1] Electric field measurements provided by the double probe instrument on the Astrid-2
satellite are compared with the empirical Weimer electric field model for all magnetic local
times, except between 11 and 13 MLT, and poleward of 55 corrected geomagnetic
latitude (CGLat). We focus the model evaluation on its ability to predict the latitudinal
locations of the convection reversal boundaries for two-cell convection patterns and to
estimate the magnitude of the electric field above 55 CGLat. A total number of 780 polar
cap passes are employed from the Northern Hemisphere between January and July 1999.
The measured average electric field magnitude in the dawn-dusk meridian plane above 55
CGLat is generally 25% larger than the predicted field independent of the interplanetary
magnetic field (IMF) direction. The model shows a better correspondence with the
observed electric field for southward IMF than for northward IMF, with most cases
centered around Bz = 1.5 nT and r = 0.88. However, the agreement for northward IMF is
promising, and a few examples are shown to corroborate this fact. The observed and
predicted convection reversal boundary locations along the satellite track for southward
IMF are on the average found 2–3 CGLat apart in the dawn-dusk meridian plane but may
be as far apart as 9 CGLat. An initial investigation of the relative timing of a 20-min
averaging window for the IMF along the 20–25 min polar cap crossing suggests that a
time-dependent transfer function may be found that applies a higher weight to the input
solar wind data early in the pass and a lower weight later in the pass for an IMF window
that corresponds to the first half of the crossing and the opposite weight versus time
INDEX
dependence for an IMF window corresponding to the last half of the crossing.
TERMS: 2447 Ionosphere: Modeling and forecasting; 2463 Ionosphere: Plasma convection; 2475 Ionosphere:
Polar cap ionosphere; 2411 Ionosphere: Electric fields (2712); 2784 Magnetospheric Physics: Solar wind/
magnetosphere interactions; KEYWORDS: global electric field modeling, ionospheric convection
Citation: Eriksson, S., L. G. Blomberg, and D. R. Weimer, Comparing a spherical harmonic model of the global electric field
distribution with Astrid-2 observations, J. Geophys. Res., 107(A11), 1391, doi:10.1029/2002JA009313, 2002.
1. Introduction
[2] Most studies of high-latitude ionospheric convection
rely on measurements either from single satellites or from
radars. These methods share the common disadvantage of
not measuring the global instantaneous two-dimensional
potential distribution, which is important in studying the
solar wind-magnetosphere coupling such as the relative
contributions of dayside and nightside driving mechanisms
[Lockwood et al., 1990] to magnetospheric convection.
Several empirical models have been developed in the past
to provide analytical tools for the global potential distri1
Now at Laboratory for Atmospheric and Space Physics, University of
Colorado, Boulder, Colorado, USA.
Copyright 2002 by the American Geophysical Union.
0148-0227/02/2002JA009313$09.00
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bution, such as those by Heppner and Maynard [1987],
the data-derived model by Rich and Hairston [1994], and
the IZMEM model by Papitashvili et al. [1994], to
mention but a few examples. The technique of least error
fits of spherical harmonic coefficients to data from multiple satellite passes or from radar measurements was used
by Weimer [1995, 1996] and by Ruohoniemi and Greenwald [1996], respectively, to provide an analytical expression of the global potential distribution. The coefficients
are assumed to depend on the IMF, the solar wind
velocity and the Earth’s magnetic dipole tilt angle. The
Weimer model was recently improved [Weimer, 2001] to
incorporate a dependence on the solar wind electric field
and the dynamic pressure, as well as an optional dependence on the AL index. This is the first empirical model to
include the assumed effects of substorms on nightside
convection.
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ERIKSSON ET AL.: GLOBAL ELECTRIC FIELD MODEL EVALUATION
[3] The motivation for this study is to evaluate the
empirical satellite-based Weimer model [Weimer, 2001]
against an independent set of electric field observations by
examining the model’s ability to predict two-cell convection
reversal boundary (CRB) locations in latitude and the level
of correspondence for electric field magnitudes poleward of
55 CGLat. The results from such a comparative study have
implications for its successful application in, e.g., space
weather modeling. The independent set of measurements
from the double probe electric field instrument on the
Astrid-2 satellite is well suited for this study, since the
satellite is in a circular polar orbit at a nearly constant
altitude of 1000 km.
[4] The study is divided into four sections. First, we
compare the relative location of the convection reversal
boundaries (CRBs) as observed by Astrid-2 with that
predicted by the model along the satellite track (section
3). Second, we compare the average electric field magnitudes (section 4) in the dawn-dusk meridian plane, which
E ~
B
gives a rough measure of the strength of the ~
convection velocity. This is followed by a study of how
the IMF Bz influences the correspondence between the
model and the measured electric field (sections 4 and 5)
and an examination of the importance of timing the
response of ionospheric convection to the IMF and the
solar wind (section 6).
The Sun-pointing E3msp spin axis component is not measured, while the roughly Earthward E1msp component completes the system. The corotation electric field ~
E = (~
w ~
r)
v~
B and the induced ~
B motional electric field are both
~
subtracted from the measured field prior to analysis, where
~
w is the Earth’s rotation, ~
r is the satellite location, ~
B is the
v is the satellite velocity in an
model magnetic field, and ~
inertial frame of reference. The remaining Earth-fixed
convection electric field in the dawn-dusk direction E2msp
is used for the comparison with the corresponding dawndusk component of the Weimer model electric field
[Weimer, 2001], which is derived from the model twodimensional potential distribution in the CGLat and MLT
coordinate system and scaled up to 1000 km altitude
E ~
B = 0.
assuming ~
2.2. Weimer Model of Ionospheric Convection
[8] The Weimer model is based on a least error fit of
spherical harmonic coefficients using electric field data
from 2645 polar cap passes of the Dynamics Explorer 2
satellite [Maynard et al., 1981] and IMF and solar wind data
from the IMP 8 and ISEE 3 spacecraft. The ionospheric
model electric potential is expressed as a function of MLT
(f) and corrected geomagnetic colatitude (q) as
ðq; fÞ ¼
ðl;3Þ
4 min
X
X
l¼0
2. Methodology
2.1. Astrid-2 Electric Field
[5] The Swedish Astrid-2 microsatellite was launched on
10 December 1998 into an 83 inclination circular polar
orbit at 1000 km altitude. The spin-stabilized satellite, with
a roughly Sun-pointing spin axis, was in operation until the
end of July 1999 [Blomberg et al., 1999; Marklund et al.,
2001]. A final set of 780 orbits in the Northern Hemisphere
is selected that covers all magnetic local times (MLT)
between January and July 1999, except for an approximately 2-hour window between 11 and 13 MLT. The main
selection criteria was that the maximum CGLat reached for
each orbit must be larger than 80 and that ACE solar wind
data are available for each case.
[6] The corrected geomagnetic (CGM) latitude, CGLat,
and longitude of a point in space is defined by tracing the
IGRF magnetic field line through the specified point to the
dipole geomagnetic equator, then returning to the same
altitude along the dipole field line and assigning the
obtained dipole latitude and longitude as the CGM coordinates to the starting point. The magnetic local time (MLT)
is defined as follows. Assume that a geographic coordinate
is located at local midnight; that is, at some UT instance the
local geographic meridian is at 0000 LT and the coordinate
is directly antisunward of the geographic pole. If the Earth
rotates through an angle (measured in UT hours and
minutes) so that the coordinate’s local CGM meridian is
moved to 0000 MLT, then the station is directly antisunward
of the CGM pole. This UT instance (in hours and minutes)
would be ‘‘at local MLT midnight in UT.’’
[7] The measured electric field is transformed into a
coordinate system based on the IGRF 1998 model magnetic
B and the spin plane, where E2msp is the spin plane
field ~
B and positive toward dusk.
component, perpendicular to ~
ðAlm cos mf þ Blm sin mfÞPlm ðcos qÞ;
ð1Þ
m¼0
where Plm is the associated Legendre function. The
coefficients Alm and Blm for each of 16 IMF clock angle
intervals are functions of IMF magnitude in the GSM yzplane (BT), solar wind velocity (Vsw), proton number density
(np), and dipole tilt angle (m) on the form
2
Alm ¼ Rlm;0 þ Rlm;1 BaT Vsw þ Rlm;2 sin m þ Rlm;3 np Vsw
:
ð2Þ
The exponent a of BT in the solar wind electric field term is
taken as 2/3 and Rlm are the regression coefficients found
from the data. Since there are no final AL indices available
for 1999, it is not possible to study the optional substorm
influence of the model with the observed convection electric
field at this time.
2.3. Solar Wind Propagation From ACE
[9] The ACE solar wind monitor is located at the L1 point
during the Astrid-2 mission. Following the method adopted
by Weimer [2001], the corresponding state of the solar wind
for each polar cap crossing is determined by first delaying
the IMF and solar wind measurements by the solar wind
propagation delay to an assumed steady magnetopause
location at xGSE = 10 RE, using the xGSE component of
Vsw. Another 10 min delay is added to account for the
average propagation time along magnetic field lines from
the magnetopause to the ionosphere. The final IMF averaging time window is started 20 min before the first encounter
with the ionospheric convection electric field and ends at
the opposite convection electric field boundary. These two
boundaries are taken as the time when Astrid-2 passes 55
CGLat moving poleward and equatorward, respectively. It
is assumed that the IMF 20 min prior to any measurement
affects that measurement owing to the global ionospheric
ERIKSSON ET AL.: GLOBAL ELECTRIC FIELD MODEL EVALUATION
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Figure 1. The latitudinal position of all 139 morningside (top row) and eveningside (bottom row)
convection reversal boundary (CRB) events for passes that enters and exits within the dawn 4 < MLT < 8
and dusk 16 < MLT < 20 sectors at 55 CGLat for IMF Bz < 0. The measured CRB positions are marked
by a circle, while the predicted CRB positions are located at the end of the vertical bars. The left column
examines the CRB dependence on IMF Bz, while the right column examines the IMF By dependence.
Two data points for IMF Bz < 10 nT are excluded from the figure to obtain a better resolution for the
majority of events.
convection reconfiguration time [Weimer, 2001, and references therein]. The Astrid-2 satellite is observed to cross the
high-latitude ionosphere poleward of 55 CGLat in 20– 24
min which translates into an IMF averaging window length
of 40– 44 min. The resolution of the ‘‘Level 2’’ ACE data
prior to averaging is 4 min, and model input parameters are
in GSM coordinates.
3. Comparison of the Dawn and Dusk Convection
Reversal Boundaries
[10] We examine the model performance in predicting the
CRBs for IMF Bz < 0 conditions and the relatively simple
two-cell convection pattern as observed by Astrid-2 polar
cap passes in the Northern Hemisphere. A CRB is defined
here as the location of zero electric field in the dawn-dusk
direction. The analysis is limited to passes that enters and
exits the dawn 4 < MLT < 8 sector and the dusk 16 < MLT <
20 sector at 55 CGLat. A total number of 139 orbits satisfy
the Bz < 0 condition of all 312 orbits that pass within these
sectors.
[11] Separating each pass in its pair of a morningside and
eveningside CRB location for both the measured and the
predicted data sets, we note that there is a characteristic IMF
dependence of their absolute latitudinal CRB positions.
Figure 1 illustrates the morningside and eveningside position in CGLat versus IMF Bz (left column) and IMF By
(right column) as measured by Astrid-2 (circle) and pre-
dicted by the Weimer model. The predicted CRB positions
are found at the end of the vertical bars. Note that the CRBs
shift from a duskward offset to a dawnward offset as By
changes sign from negative to positive. This is an expected
result [e.g., Shue and Weimer, 1994] that may be explained
by an IMF By-dependent magnetotail rotation about the
Sun-Earth line [e.g., Siscoe and Sanchez, 1987]. We also
observe the expected trend that the CRB locations expand
equatorward as the IMF Bz component becomes increasingly more negative. As we separate the eveningside Bydependent CRB distributions by a horizontal line at CGLat
= 79, we note the apparent separation of the Bz-dependent
distributions in two subsets, each indicating the same IMF
Bz-dependence. Figure 1 shows, moreover, that where there
are more extreme differences between the observed and
model CRB locations, the model is most often in the
middle. The bars point down (equatorward) where the
observed locations are high, and the bars point up (poleward) where the observed locations are low.
[12] We shall hereby examine whether there is any
systematic behavior in the magnitude or the direction of
the relative CRB differences (length of the vertical bars in
Figure 1) to the solar wind input. The model performance in
predicting the CRBs is quantified by the latitudinal difference between the location of the observed and predicted
CRB, where m and e denote the dawnside (morning)
and duskside (evening) differences, respectively. A negative
value signifies that the observed CRB lies equatorward of
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ERIKSSON ET AL.: GLOBAL ELECTRIC FIELD MODEL EVALUATION
Figure 2. Measured (black and red) and model electric field (green) versus time above 55 CGLat for
four examples of the relative positions of the measured (red) and the model (green) CRBs (see text for
type definitions). The red curve is a 60-sec running average of the measured 1-sec resolution electric field
(black curve). The blue curve shows the Weimer potential (in kV) along the Astrid-2 orbit. Entry and exit
locations in CGLat and MLT are shown in the lower left and right corners, respectively. A vertical dotted
line marks the instance of maximum CGLat. Model input parameters from ACE are shown in the upper
right corners for the propagation time in the top left of each plot. The correlation coefficient (r) and the
standard deviation of the magnitude of the differences (sdev) are calculated between the red and green
smoothed electric fields. The time in UT (top right) refers to the start point at 55 CGLat. See color
version of this figure at back of this issue.
the model CRB. We may therefore define four types of
situations according to the relative latitudinal positions of
the model and the observed CRB. Type ‘‘A’’ denotes that
both the morning and evening model cells are shifted
duskward relative to the observed ones. Type ‘‘B’’ denotes
that both model cells are found poleward of the observed
cells. Types ‘‘C’’ and ‘‘D’’ correspond to a dawnward and
equatorward model shift, respectively.
[13] Figure 2 illustrates an example of the observed and
predicted electric fields of each type for which a maximum
correlation is found between the Weimer model and the
Astrid-2 convection electric fields. The dawnside and duskside CRB latitudinal differences for these cases are found in
the upper left corner of each plot together with the estimated
propagation time (tp) from ACE. The black curve shows the
1-sec resolution Astrid-2 duskward electric field component, while the red curve is the approximately 60-sec
running average of the same. The duskward component of
the derived Weimer model electric field along the Astrid-2
orbit is shown as a green curve, while the blue curve is the
along-track Weimer electric potential (kV). The solar wind
input parameters to the model as well as the start time (UT)
at the point of entry are shown explicitly in the upper right
corners. The correlation coefficient and standard deviation
between the 60-sec running average Astrid-2 electric field
(red curve) and the Weimer electric field (green curve) are
found at the bottom.
[14] The total number of cases for each type and the
resulting mean, maximum, minimum, and standard deviation of the dawnside and duskside CRB latitudinal differences, m and e, are displayed in Table 1. No apparent
dependence on IMF, solar wind density, or solar wind
electric field could be found for any one of these types as
might be expected when comparing type B with type D, or
types A and C, such as a stronger southward Bz for type B
than for type D, with type B two-cell convection patterns
Table 1. Statistical Information on the Relative Locations of the Two CRBs for a Measured and Modeled Two-Cell Convection Patterna
Type
Number
hmi
hei
max(jmj)
max(jej)
min(jmj)
min(jej)
std(jmj)
std(jej)
A
B
C
D
27
57
30
25
1.83
2.08
1.64
1.95
1.96
2.54
2.22
2.26
5.42
6.88
4.03
5.89
5.47
7.80
6.26
8.97
0.17
0.11
0.05
0.04
0.06
0.17
0.10
0.03
1.24
1.52
1.16
1.63
1.67
1.73
1.75
2.47
a
m and e refer to the morningside and eveningside CRBs, respectively.
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ERIKSSON ET AL.: GLOBAL ELECTRIC FIELD MODEL EVALUATION
Figure 3. The relative latitude separation between the measured (circle in Figure 1) and the predicted
CRB locations for the pair of morningside and eveningside CRBs. Type A is defined as those cases where
the morningside measured to predicted difference in CRB latitude is negative and the eveningside
difference is positive. The latitude measure is derived as the sum of the magnitude of these two
differences. See text for the complete set of type definitions.
located at lower latitudes for Astrid-2 as compared with the
model. This is further illustrated in Figure 3. However, it
seems that the offsets are minimized as IMF becomes
increasingly more negative (left column).
[15] There are a total of 14 ‘‘perfect matches’’ of all 139
passes, which is arbitrarily defined as the case when the
relative latitudinal differences between the observed and
model CRB locations at dawn and dusk are both <1
CGLat. Extending the limit to within 2 CGLat results in
49 ‘‘perfect matches.’’ As we move the limit up by increments of 1 CGLat, we get the distribution of the number of
‘‘perfect matches’’ as is displayed in Table 2. In 79% of the
cases the agreement is within 4 CGLat. This corresponds to
an 515 km distance at 1000 km altitude. Caution should
therefore be employed when applying the present model to
the study of convection reversal boundary locations at
spatial scales <500 km.
4. Comparing Observed and Model Electric Field
Magnitudes
[16] To what degree can the model provide a realistic
convection flow velocity in the high-latitude ionosphere?
One way to approach the subject is to compare the
smoothed (red curves) electric field observations and the
predicted model mean values (green curves) of the absolute
magnitude of the electric field above 55 CGLat. The data
set is separated into three categories; Bz > 1, Bz < 1, and
1 < Bz < 1 nT, respectively.
[17] Figure 4 illustrates the average of the absolute
electric field magnitude for the observed and modeled data
in each pass for these categories as well as a plot including
all the data. The optimum linear fits are shown in the upper
left corner of each plot using a least squares fit technique.
The solid line is the best linear fit, whereas the dotted line
corresponds to y = x. We observe that the measured average
electric field is larger in general than the predicted value by
25% for all data (r = 0.79) or by 31% for Bz < 1 nT
(r = 0.69), while the best correspondence is found for the
two Bz > 1 nT categories illustrated in the right column of
Figure 4. It should be noted, however, that the correlation
coefficient is lower for this category with r 0.60. As we
instead examine the actual electric fields (red and green
curves in Figure 2) point-by-point at 10-sec resolution for
all 780 passes, we find that the observed field is on the
average only 10% larger than the model field (see Figure 5).
In dividing the data set in two subgroups after IMF Bz, we
also observe a higher correlation for southward IMF than
for northward IMF, although the measured field is now 14%
larger than the predicted field for Bz < 0.
[18] The reason(s) for the deviation from the one-to-one
relationship between the observed and the predicted electric
fields is most likely found as a combination of the following: (1) The measured electric field may experience nonzero offsets at lower latitudes owing to inexact spin axis
Table 2. Number of Cases for Each 1 Bin With Both the
Dawnside and Duskside Model to Observation CRB Latitudinal
Relative Distance Being Less Than the Indicated Numbera
< 1
<2
<3
<4
<5
<6
<7
<8
<9
14
49
80
110
120
129
136
137
139
a
The total number of examined cases is 139.
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Figure 4. The averages taken over the complete passages above 55 CGLat of the absolute electric field
magnitudes for Astrid-2 versus the derived Weimer model electric field. The data set is divided in three
subgroups after IMF Bz. Optimum linear fits and correlation coefficients are shown as well as the number
of cases in each group.
information, (2) the Weimer model field is unable [Weimer,
2001] to predict the large electric fields at the CRBs, or (3)
the measured field poleward of the CRBs may de facto be
larger than the predicted field. The second explanation is
probably the most important one, since the electric potentials at the CRBs do not have as sharp gradients or electric
fields as the actual fields owing to the resulting smoothing
of the spherical harmonic fitting process. This is, e.g.,
observed in Figure 2 on the dawnside for orbit 1127, where
the observed electric field is almost twice as large as the
predicted field. The same effect is e.g. seen in Figure 5b for
electric field magnitudes larger than, say 50 mV/m, with
higher densities of data points below (above) y = x for
negative ( positive) electric fields.
[19] The perhaps somewhat unexpected result, that the 10sec resolution data comparison yields better correlations
with the model electric field than was shown for the
averaged fields, may be explained using the same reasoning.
The total number of points at or near the CRBs are far less
than the number of points both poleward and equatorward of
the CRB regions. At the same time we expect optimal
correlations in the regions away from the CRBs. Thus when
using the 10-sec resolution data and binning the data from
many orbits together (see Figure 5), we expect a majority of
data points to be in the regions away from the CRB.
However, when first averaging the data from each pass for
all passes (see Figure 4) and then calculating the correlation
coefficient and regression parameters, it seems that the small
deviation in each pass is accumulated and overrated. The
result is that the 10-sec electric field comparison show
improved correlations over the averaged data set.
[20] In studying the distribution of the correlation coefficient between the observed and predicted electric fields for
the different solar wind input parameters, we note that the
model performs generally better for IMF Bz < 0 than for
Bz > 0. This is illustrated in Figure 6 that shows the square of
the correlation coefficient for all 780 orbits versus IMF Bz,
IMF By , the xGSM component of the solar wind velocity, and
the proton solar wind dynamic pressure. The vertical lines
mark the median value for each solar wind parameter, while
the horizontal line marks the median correlation coefficient
value of r = 0.79. It is seen that 72% of all 390 cases above
r = 0.79 are found on the lefthand side of the median at
about Bz = 0.0 nT, while only 28% are found on the opposite
side for IMF Bz > 0. The opposite is true for the other half
below r = 0.79. The corresponding analysis for the remaining three solar wind parameters do not indicate such a clear
offset as the Bz distribution does. The Bz distribution average
for the entire set is located at Bz = 1.5 nT and r = 0.88. It
thus seems that the model works better for Bz < 0 conditions
than for Bz > 0 conditions. This is not entirely unexpected,
owing to the limited ability of the parameterization of the
model potential to account for smaller scale structures in the
polar cap which are more frequent during positive IMF Bz.
5. Northward IMF
[21] Although the model works better for southward IMF
conditions, there are still some nice examples of good
correspondence between the model predictions and observations for northward IMF. Owing to the inherent dynamics
involved during northward IMF, we restrict the analysis to
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Figure 5. (a) Astrid-2 electric field versus Weimer electric field (red and green curves of Figure 2) for
all 431 northward IMF cases. Data resolution is one point every 10 seconds along each orbit. The
optimized linear fits and correlation coefficients are shown in the upper left corner. (b) Same format as
Figure 5a but for all 349 southward IMF cases. (c) Same format as Figure 5a but for the complete set of
all 780 cases.
describing a few cases rather than presenting a statistical
survey.
[22] There are 18 orbits of all 312 that pass through the
dawn-dusk MLT sectors defined previously that also satisfy
Bz > 3.0 nT and jBz/Byj > 2.0. Figure 7a shows three cases
which display a clear four-cell electric field signature and
one case (orbit 2173) of a distorted two-cell convection
pattern, as indicated by the Weimer potential curve (blue)
and the electric fields (red and green curves). The observed
electric field (black) is highly fluctuating as is expected for
these IMF conditions. Despite the rather poor mathematical
correlation, we note that there is a decent fit with four cells,
although the locations and magnitudes are not in qualitative
agreement.
[23] Figure 7b illustrates four additional events taken
from the set of 18 orbits. Note that only one case (orbit
881) displays a clear four-cell convection pattern which also
corresponds to the event of highest solar wind speed (Vx =
536 km/s). All four cases have a similar jBz/Byj ratio of 2.4
and a similar solar wind proton density of 5 cm3 but a
solar wind speed Vx that steadily increases from 380 km/s
(orbit 2240) to 536 km/s (orbit 881), clockwise in Figure 7b.
Moreover, the observed electric field for orbit 2397 is
suggestive of a combined lower latitude viscous cell and a
higher latitude lobe cell convection signature [e.g., Burch et
al., 1985; Crooker et al., 1998; Eriksson et al., 2002, and
references therein] that the model fails to predict on the
duskside, with a positive electric field embedded in a wider
region of negative electric field.
6. On the Importance of Individual Timing
[24] The Astrid-2 satellite crosses the region poleward of
55 CGLat in 20– 24 min, its maximum latitude located
above 80. It is most likely then that the IMF and solar wind
affecting the electric field measured early in the pass is
different from that affecting the electric field towards the
end of the polar cap crossing.
[25] Assume that it takes 25 min for the satellite to
traverse the polar region above 55 CGLat. The IMF data
are therefore averaged over a 20 + 25 = 45 min long
interval, adding 20 min prior to the point of entry, since it
is assumed that the IMF 20 min prior to any measurement
affects that particular measurement. We then take the 20 min
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Figure 6. The square of the correlation coefficient versus IMF Bz (top left), IMF By (top right), xGSM
component of the solar wind velocity (bottom left) and the solar wind dynamic pressure (bottom right) for
all 780 cases. The vertical lines mark the median value for each parameter. The horizontal line marks the
median correlation coefficent, r = 0.79, i.e. r2 = 0.63. The distributions are thus separated in two halves
with 390 data points on each side of the median lines. The number of data points in each sector are shown
explicitly.
interval and shift it by incremental steps of 5 min within the
45 min period, starting at the point of entry. The resulting
five 20-min averaged intervals of the IMF within the 45 min
period thus correspond to five evenly distributed measurements along the satellite track.
[26] Since the Bz component of the IMF is expected to
have the greatest impact on the solar wind-magnetosphere
coupling, we limit the study to the following two cases. IMF
turns southward: Bz > 2.0 nT when Astrid-2 moves poleward at 55 CGLat and Bz < 2.0 nT when the satellite
passes 55 CGLat moving equatorward. There are six orbits
of all 780 that satisfy this criterion irrespective of local time.
Another seven orbits meet the opposite criterion of IMF
turning northward during the polar cap pass, Bz < 2.0 nT
at the 55 entry point and Bz > 2.0 nT at the exit point,
respectively.
[27] Figure 8a shows four examples of all six southward
turning events. The set of five Weimer electric fields, one
for each 5-min delayed 20 min averaging window, are
plotted on top of the smoothed Astrid-2 electric field
(black), as if each single set of IMF and solar wind data
results in a model potential distribution that would correspond to the entire polar cap crossing. The color code of
red, orange, green, light blue, and dark blue corresponds to
the sequence of five 20-min long windows separated by 5
min along the Astrid-2 orbit. The local times of the entry
and exit points are shown in the top left and right corners of
the plots, while the sequence of IMF Bz (nT), correlation
coefficient, and standard deviation of the differences (mV/
m) between the observed and predicted electric fields are
shown in the bottom half of the plots. We observe that the
red curve for the dusk-to-dawn orbits (2174 and 2418)
corresponds best with the measured field in the first half
of the pass, while the blue curves do a better job in the
second half. The optimum over the complete pass above 55
CGLat is given by the green curve. The midnight-to-noon
orbit 1687 suggests that the blue curve does the best job
across the whole pass. The smoothed electric field of the
dawn-to-dusk orbit 482 seems to fluctuate between the red
and blue curves. It is possible that the strong northward IMF
early in the pass affects the global state of convection more
than the southward IMF.
[28] Figure 8b illustrates a few examples for the opposite
case of a northward turning IMF. The electric field magnitudes of the dawn-to-dusk orbits 565 and 1025 are best
predicted by the red curves, whereas the CRB location
seems to correlate best for the blue curves. A maximum
correlation and minimum standard deviation are obtained
for the green curve of orbit 1931. The midnight-to-noon
orbit 1796 suggests that an optimized correspondence is
obtained for the red curve, rather than the blue curve, across
the whole pass. Note that this is just the opposite situation
to that of orbit 1687 for a southward turning IMF (see
Figure 8a).
[29] From studying Figure 8 it seems that a southward
IMF turning during the pass does have an improving effect
on the correlation and that a weighting scheme of the
individually delayed Weimer potentials could be found from
studying comparisons such as those described above. The
northward turning events are not as clear in this respect. The
ERIKSSON ET AL.: GLOBAL ELECTRIC FIELD MODEL EVALUATION
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Figure 7. (a) Three examples of a clear four-cell convection pattern and one example (2173) of a
distored two-cell convection pattern of those 18 dawn-dusk sector events that satisfy jBz/Byj > 2.0 and
Bz > 3.0 nT. Same format as in Figure 2. (b) Another four northward IMF cases of all 18 events. See color
version of this figure at back of this issue.
two dusk-to-dawn orbits (2174 and 2418) and the midnightto-noon orbit (1687) are consistent with the residual AMIE
potential patterns for negative changes in IMF Bz that grow
in magnitude and time but being fixed in location [Ridley et
al., 1997, 1998]. By comparing the two midnight-to-noon
orbits (1687 and 1796) it seems that a southward turning of
the IMF is a faster process than the northward turning, as
was noted by Hairston and Heelis [1995]. Here, we have
been using a ‘‘patched approximation’’ of a few different
potentials calculated from the solar wind parameters at a
few different times. This approach is computationally simple, yet it exemplifies the importance of properly accounting
for time variations. Eventually, for the purpose of comparing satellite electric field data with the Weimer model a
‘‘transfer function’’ should be used which relates the local
potential (and electric field) at the position of the satellite to
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ERIKSSON ET AL.: GLOBAL ELECTRIC FIELD MODEL EVALUATION
Figure 8. (a) Smoothed Astrid-2 electric field (black) and five Weimer electric field curves (colored)
corresponding to five 20-min long solar wind averaging intervals, each separated by 5 min along the
orbit, as the IMF turns southward during the crossing. The sequence of five 20-min averaged IMF Bz
values at the bottom of each plot (left to right) was used as input to the Weimer model producing the red,
orange, green, light blue, and dark blue curves, respectively. The other solar wind input parameters have
been omitted in the figure. (b) Same format as for Figure 8a but corresponding to a northward turning
IMF during the crossing. See color version of this figure at back of this issue.
the solar wind parameters during some prior time interval.
Functionally, this can be expressed as
ðq; f; tÞ ¼ ðq; f; hF ð½t Tdel Tint ; t Tdel ÞiÞ;
ð3Þ
where hF([t Tdel Tint, t Tdel])i is the average of the
solar wind input parameters during the time interval [t Tdel Tint, t Tdel] or equivalently, the time interval of
length Tint ending at t Tdel, where Tdel accounts for the
ERIKSSON ET AL.: GLOBAL ELECTRIC FIELD MODEL EVALUATION
(minimum) propagation delay time between the solar wind
passing the monitoring spacecraft and the time when it starts
affecting the ionosphere.
7. Summary and Conclusions
[30] This is the first time that an electrodynamic model
has been thoroughly compared with an independent set of
electric field observations, resulting in an improved understanding of the model ability to predict CRB locations for
IMF Bz < 0 and the level of correspondence for electric field
amplitudes above 55 CGLat. The Weimer 2000 [Weimer,
2001] electric field model is evaluated by comparing its
electric field predictions with the measured convection
electric field using the Astrid-2 satellite at a near constant
altitude of 1000 km.
[31] The Weimer potentials are obtained by applying
ACE solar wind data. We derive an electric field in the
dawn-dusk direction from the predicted potential distribution along each Astrid-2 orbit and scale it to the satellite
altitude, rather than using the potential. The integration of
the measured electric field would result in larger relative
deviations from the model potential than the electric field
comparison. This stems from an integration of electric
field uncertainties on the order of 1 mV/m that would
result in electric potential offsets on the order of 20 kV at
the low-latitude end of the pass. The substorm AL index
option is not employed since there are no final AL indices
available for 1999. Comparisons are performed with 780
Astrid-2 passes in the Northern Hemisphere above 55
CGLat. The following conclusions can be drawn from the
analysis.
1. The morningside and eveningside latitudinal offsets
between the observed and the predicted CRB positions are
both <3 CGLat for 58% of all 139 examined orbits in the
dawn-to-dusk meridian plane for IMF Bz < 0 and the
prevailing two-cell convection pattern. A total number of 14
out of all 139 orbits are considered as perfect CRB matches
with model to measurement discrepancies at dawn and dusk
being <1 CGLat. The observed maximum offset was <9
(see Table 2). However, the relative model to observed
locations of morningside and eveningside CRBs as defined
by the four types A, B, C, and D do not clearly depend on
the input solar wind parameters, such as the magnitude of
IMF Bz or the direction of IMF By .
2. The measured mean magnitude of the electric field above
55 CGLat is in general larger than the predicted Weimer field
by 25% independent of IMF and by 31% for IMF Bz < 1.0 nT
and a correlation coefficient r = 0.69. The corresponding
difference for northward IMF is on the order of 10% but
exhibits a lower correlation coefficient (r = 0.60). By
examining the actual 10-sec resolution electric fields in a
point-by-point comparison, we found that this difference
decreased to 14% for southward IMF (r = 0.81) and to
an almost perfect match for northward IMF that showed a
lower correlation coefficient of r = 0.67 though. The
apparent improvement seen, e.g., for IMF Bz < 0 from
31% to 14% is an expected result that reflects the two
methods employed, since the use of the actual electric
fields provide a much larger set of data points with a
majority of points located away from the CRBs in regions
where the correlation is expected to be much better.
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3. The Weimer electric field model generally works
better in predicting the electric field magnitude for IMF
Bz < 0 than for Bz > 0, with a majority of events centered
around Bz = 1.5 nT and r = 0.88. We did not find any
significant trends or offsets, however, when examining the
possible influences from IMF By, solar wind velocity, or
the solar wind dynamic pressure. We note that a general
four-cell convection pattern is present in both data and
model prediction for several events in the dawn-dusk
meridian plane when Bz > 3.0 nT and jBz/Byj > 2.0 are
satisfied. However, there are not enough events to draw
any final conclusions as to the capability of the model to
fully reproduce these convection patterns for this data set,
such as the position of CRBs.
4. A clear southward turning of the IMF during the
polar cap passes suggests that an improved model
prediction is obtained at the end of the pass if a
correspondingly delayed set of IMF and solar wind is
used as input. These results show that for comparing
satellite electric field data with the Weimer model, ideally
a ‘‘transfer function’’ should be used which relates the
local potential (and electric field) at the position of the
satellite to the solar wind parameters during some prior
time interval.
[32] Acknowledgments. This work was performed at the Alfvén
Laboratory, Royal Institute of Technology, Stockholm, Sweden.
[33] Arthur Richmond thanks Marc R. Hairston and Volodya Papitashvili for their assistance in evaluating this paper.
References
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Burch, J. L., P. H. Reiff, J. D. Menietti, R. A. Heelis, W. B. Hanson, S. D.
Shawhan, E. G. Shelley, M. Sugiura, D. R. Weimer, and J. D. Winningham, IMF By-dependent plasma flow and Birkeland currents in the dayside magnetosphere, 1, Dynamics Explorer observations, J. Geophys.
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Crooker, N. U., J. G. Lyon, and J. A. Fedder, MHD model merging with
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Eriksson, S., J. W. Bonnell, L. G. Blomberg, R. E. Ergun, G. T. Marklund,
and C. W. Carlson, Lobe cell convection and field-aligned currents poleward of the region 1 current system, J. Geophys. Res., 107(A8), 1185,
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Hairston, M. R., and R. A. Heelis, Response time of the polar ionospheric
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Heppner, J. P., and N. C. Maynard, Empirical high-latitude electric field
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microsatellite for auroral research, Ann. Geophys., 19, 589, 2001.
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523, 1981.
Papitashvili, V. O., B. A. Belov, D. S. Faermark, Y. I. Feldstein, S. A.
Golyshev, L. I. Gromova, and A. E. Levitin, Electric potential patterns
in the northern and southern polar regions parameterized by the interplanetary magnetic field, J. Geophys. Res., 99, 13,251, 1994.
Rich, F. J., and M. Hairston, Large-scale convection patterns observed by
DMSP, J. Geophys. Res., 99, 3827, 1994.
Ridley, A. J., G. Lu, C. R. Clauer, and V. O. Papitashvili, Ionospheric
convection during nonsteady interplanetary magnetic field conditions,
J. Geophys. Res., 102, 14,563, 1997.
Ridley, A. J., G. Lu, C. R. Clauer, and V. O. Papitashvili, A statistical study
of the ionospheric convection response to changing interplanetary mag-
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netic field conditions using the assimilative mapping of ionospheric electrodynamics technique, J. Geophys. Res., 103, 4023, 1998.
Ruohoniemi, J. M., and R. A. Greenwald, Statistical patterns of high-latitude convection obtained from Goose Bay HF radar observations,
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Shue, J.-H., and D. R. Weimer, The relationship between ionospheric convection and magnetic activity, J. Geophys. Res., 99, 401, 1994.
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Weimer, D. R., Models of high-latitude electric potentials derived with a
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L. G. Blomberg, Alfvén Laboratory, Royal Institute of Technology, SE10044 Stockholm, Sweden. (blomberg@plasma.kth.se)
S. Eriksson, Laboratory for Atmospheric and Space Physics, University
of Colorado, 1234 Innovation Drive, Boulder, CO 80303, USA.
(eriksson@lasp.colorado.edu)
D. R. Weimer, Mission Research Corporation, 589 West Hollis Street,
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ERIKSSON ET AL.: GLOBAL ELECTRIC FIELD MODEL EVALUATION
Figure 2. Measured (black and red) and model electric field (green) versus time above 55 CGLat for
four examples of the relative positions of the measured (red) and the model (green) CRBs (see text for
type definitions). The red curve is a 60-sec running average of the measured 1-sec resolution electric field
(black curve). The blue curve shows the Weimer potential (in kV) along the Astrid-2 orbit. Entry and exit
locations in CGLat and MLT are shown in the lower left and right corners, respectively. A vertical dotted
line marks the instance of maximum CGLat. Model input parameters from ACE are shown in the upper
right corners for the propagation time in the top left of each plot. The correlation coefficient (r) and the
standard deviation of the magnitude of the differences (sdev) are calculated between the red and green
smoothed electric fields. The time in UT (top right) refers to the start point at 55 CGLat.
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ERIKSSON ET AL.: GLOBAL ELECTRIC FIELD MODEL EVALUATION
Figure 7. (a) Three examples of a clear four-cell convection pattern and one example (2173) of a
distored two-cell convection pattern of those 18 dawn-dusk sector events that satisfy jBz/Byj > 2.0 and
Bz > 3.0 nT. Same format as in Figure 2. (b) Another four northward IMF cases of all 18 events.
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ERIKSSON ET AL.: GLOBAL ELECTRIC FIELD MODEL EVALUATION
Figure 8. (a) Smoothed Astrid-2 electric field (black) and five Weimer electric field curves (colored)
corresponding to five 20-min long solar wind averaging intervals, each separated by 5 min along the
orbit, as the IMF turns southward during the crossing. The sequence of five 20-min averaged IMF Bz
values at the bottom of each plot (left to right) was used as input to the Weimer model producing the red,
orange, green, light blue, and dark blue curves, respectively. The other solar wind input parameters have
been omitted in the figure. (b) Same format as for Figure 8a but corresponding to a northward turning
IMF during the crossing.
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