Introduction
Plasma convection in the high-latitude ionosphere is one of the key pieces of information for the magnetosphere–ionosphere–thermosphere coupling. The
convection has an influence on plasma irregularity generation and transport
e.g., the fine structure of the polar cap aurora
e.g., energy deposition into the thermosphere
e.g., and even the initial evolution of substorms
e.g.. Hence, plasma drift measurements in the high-latitude
ionosphere are of considerable importance.
Plasma convection can be measured in several different ways. The Super
Dual Auroral Radar Network (SuperDARN) consists of dense networks of
ground-based radars, which measure line-of-sight (LOS) drift speed of
decametre-scale ionospheric irregularities. By combining drift measurements
from several radars, maps of plasma velocity can be derived. The SuperDARN global convection maps typically depict data captured every 1–2 min. The Defense
Meteorological Satellite Program (DMSP) satellites also measure ion drift
velocities regularly. The SuperDARN and DMSP observations have been conducted
nearly continuously and on a regular basis. Occasionally, ground-based
optical instruments e.g. and Global Positioning System (GPS)
receivers e.g. can track ionospheric irregularities to
estimate plasma drift velocity.
Although high-latitude plasma convection has been monitored with a number of
methods, each has its own limitations. SuperDARN radars cannot measure the
convection when there are no decametre-scale irregularities in the
ionosphere, which limits its performance during extremely low and high
geomagnetic activity. The DMSP measurements are constrained by the satellite
orbits, which have poor spatial coverage in the post-midnight and post-noon
local time (LT) sector. As for the temporal resolution, the convection data
for the polar region can be given only every ∼100 min, which is the
orbit period of the DMSP satellites. Furthermore, the along-track component
of the convection velocity measurements is hardly used because of poorer
quality compared with the cross-track components. Ground-based optical and/or
GPS observations can be a good supplement to SuperDARN and DMSP
observations, but the data coverage is usually limited to continental areas
where the instruments are located. In particular, the operation of optical
measurements is normally restricted to dark periods when the Sun is below the
horizon. Therefore, more independent measurements of high-latitude plasma
convection velocity are still warranted.
In this study we introduce an automatic method to estimate plasma drift
velocity in the high-latitude ionosphere using the Swarm constellation.
Though a similar method was used in case studies of and
, our method is fully automatic and needs no human intervention.
The three Swarm satellites carry instruments that directly measure ion drift
velocity (thermal ion imager in the electric field instrument suite).
However, this paper discusses another method for along-track plasma velocity
estimation, which solely uses electron density profiles measured by the
onboard Langmuir Probe (LP). In Sect. 2 we will briefly describe the
instruments and analysis methods. The statistical results will be shown and
discussed in Sect. 3. Finally, we summarize our results and draw conclusions
in Sect. 4.
Instruments and data processing
The Swarm constellation consists of three identical satellites, which were
launched on 22 November 2013 into a near-circular polar orbit (orbit
inclination angle ∼ 87.5∘) . The initial altitudes
of the three satellites were nearly the same (∼500 km) during the
commissioning phase until mid-January 2014, after which satellite orbits gradually separated regarding altitudes and longitudes. Not all the instruments were
in full operation during the commissioning phase. Here we use only the
initial electron density data measured by the Swarm LP. Further, we consider
the data between 09 December 2013 and 15 January 2014 (hereafter, “the
mission period of interest”), when the three satellites were at similar
altitudes and longitudes.
During the mission period of interest the ascending nodes of the Swarm orbits
were generally located between 10:00 and 14:00 LT, i.e. the satellite tracks
were close to the noon–midnight meridian. The zonal separation of adjacent
orbital planes was less than 1∘ near the equator (i.e. <110 km)
(e.g. ; Fig. 1), which decreases further at high latitudes.
The latitudinal separation of the three satellites was non-negligible.
Swarm-B was the leading satellite, while Swarm-A (later by <∼1 min) and
Swarm-C (later by <∼3 min than Swarm-B) followed in that order. Under
this formation the three satellites were nearly aligned along one orbit track
at high latitudes, like pearls on a string. They could encounter similar
plasma density structures one satellite after another.
A schematic diagram showing the relative motion of the Swarm
satellites and plasma density structures.
Figure 1 shows our strategy to estimate along-track plasma drift speed using
a pair of the Swarm satellites. The horizontal axis represents Universal Time
(UT), and the vertical axis represents the distance from the equator. The red
and green lines are the trajectories of Swarm-A and Swarm-B, respectively.
Both satellites are assumed to move with the same speed, vSwarm.
The blue area signifies the path of a plasma density structure. Its speed
along the Swarm orbit (vplasmaalong-track) and the
morphological shape are assumed to be time-independent during the passages of
the Swarm satellites (a few minutes). As mentioned previously, Swarm-A is
behind Swarm-B by about <∼1 min: this time difference is denoted as
Δtpole-X, which means pole-crossing time difference. The
difference between the times when Swarm-B and Swarm-A encounter the plasma
density structure is not Δtpole-X. Since the plasma
density structure is also moving, there appears an additional time
difference, Δtxcorr. This additional time difference can
be estimated by cross-correlating the two density profiles measured by
Swarm-B and Swarm-A. Applying simple trigonometric equations to Fig. 1, the
plasma drift speed along the Swarm track
(vplasmaalong-track) can be estimated from the
known values of vSwarm (∼7.5 km s-1), Δtpole-X (obtained from the Swarm ephemeris data) and Δtxcorr (obtained from the Swarm LP data cross-correlation):
vplasmaalong-track=Δtxcorr×vSwarmΔtpole-X+Δtxcorr.
Note that the plasma density profiles measured by the Swarm satellites differ
from the “true snapshots” of the density structure. True snapshots can be
obtained only when vSwarm becomes infinite (i.e. when the green
and red lines in Fig. 1 become vertical). The only two assumptions used to
derive Eq. (1) are the time independence of
(a) vplasmaalong-track and (b) the morphology of
the plasma density structure. These assumptions can be justified by the fact
that vSwarm (about 7500 m s-1) is usually much faster than
vplasmaalong-track (of the order of
100 m s-1). Note also that
vplasmaalong-track is the speed with respect to
a ground observer. A plasma density irregularity fixed in geographic
coordinates (e.g. above Greenland) would be encountered by different Swarm
satellites at the same location. As a result, Δtxcorr
becomes 0, which yields a zero value for
vplasmaalong-track.
In applying this method to Swarm LP data, we use the leading satellite,
Swarm-B as the reference satellite. We first divide the Swarm-B (leading
satellite) data into 1 min segments, which are advanced in steps of 20 s
through the continuous Swarm-B data stream. For example, the first segment of
the Swarm-B data lasts from 00:00:00 to 00:01:00 UT, and the next data
interval from 00:00:20 to 00:01:20 UT. Segments containing a single data gap longer than 1 s or cumulated gaps longer than or equal to 20 % of the expected segment length are neglected. In both hemispheres only data within ±5 min
(∼±2300 km) around the peaks of absolute geographic latitude (GLAT)
are considered because the inter-satellite zonal distance becomes larger at
lower latitudes. As a next step we also divide the Swarm-A and Swarm-C data
into 1 min data segments, taking into account the time difference of the
pole crossing (Δtpole-X) with respect to Swarm-B
see also. In this way all the 1 min data segments from the
three satellites correspond to nearly the same location. Note that |Δtpole-X| should be ≤40 min in order for the segments to be
analysed further.
Figure 2 shows one example of plasma density profiles processed in the
above-mentioned way. In this figure different colours are used for the
satellites: red for Swarm-A, green for Swarm-B, and blue for Swarm-C. The
satellite tracks are shown in geographic coordinates in panel (a) while panel
(b) presents those in apex magnetic latitude and magnetic local time (MLT)
coordinates. Small circles in Fig. 2a–b correspond to the time stamps given
in panels (c)–(e) while the triangle denotes the start of the time series.
There are actually three individual satellite tracks in panels (a)–(b).
However, the three satellite tracks are hardly distinguishable, consistent
with the assumption that the data segments shown in panels (c)–(e)
correspond approximately to the same location. Panel (b) shows that the three
satellites were on the prenoon side and poleward of 80∘ in magnetic
latitude (MLAT).
An example of Swarm LP data: (a) satellite track in
geographic coordinates, (b) satellite track in apex magnetic
latitude and MLT coordinates, (c–e) electron density measured by
the LP onboard Swarm-A (red), Swarm-B (green), and Swarm-C (blue). Circles in
panels (a)–(b) correspond to the time stamps of panels
(c)–(e), and triangles mark the start of the time series.
The green lines overplotted in panels (c) and (e) represent the density profile
measured by Swarm-B but time-shifted by Δtpole-X.
Panels (c)–(e) present electron density measured by the Swarm LP. Note the
different time stamps of the three panels. The satellite altitudes given in
panels (c)–(e) agree with one another within 1 km. Swarm-B (panel d, green)
first passed the polar region and encountered plasma density structures.
About 1 min after Swarm-B, Swarm-A (panel c, red) passed the same region.
About 2 min after Swarm-B, Swarm-C (panel e, blue) passed the same region.
The three density profiles appear strikingly similar, only displaced along
the x axis.
The green lines overplotted in panels (c) and (e) represent the density profile
measured by Swarm-B (panel d, green) but time-shifted by Δtpole-X: this is the plasma density profile the trailing Swarm
satellites (Swarm-A or Swarm-C) would encounter if the along-track plasma
drift speed was 0
vplasmaalong-track=0. We
cross-correlate this profile (time-shifted Swarm-B profile) with those of the
respective trailing satellites (Swarm-A or Swarm-C). All profiles are
linearly detrended and interpolated in an automatic way prior to cross-correlation. For both of
the Swarm-B–A and Swarm-B–C pairs, cross-correlation between the density
profiles leads to maximum correlation coefficients (Rmax) higher than
0.8. The time shift corresponding to the maximum correlation coefficient is
used to estimate the additional time difference (Δtxcorr)
in Fig. 1. Then the along-track velocity of the plasma density profile
vplasmaalong-track is obtained from
Eq. (1). Each satellite pair (i.e. Swarm-B–A and Swarm-B–C) leads to one
value of along-track velocity of the plasma density profile
vplasmaalong-track. In Fig. 2 the
calculation results of 700 (620) m s-1 are listed for the Swarm-B–A
(for Swarm-B–C) pairs, which agree with each other to within 13 %. Note that a
positive velocity corresponds to plasma drift in the flight direction of the
Swarm satellites (negative velocity corresponds to plasma drift ramming into
Swarm). Hence, the along-track velocity of the plasma density profile is
nearly anti-sunward in the example shown in Fig. 2.
Statistical results and discussion
Velocity estimation using Swarm
We applied the method described in Sect. 2 to all the Swarm observations
between 09 December 2013 and 15 January 2014. To check the
robustness and consistency of velocity estimates, only those days are used when
all the three satellites observed electron density, i.e. a day is neglected
when one of the satellites did not operate the onboard LP. Further, we only
consider the polar passes with significant fluctuations in plasma density. If
no substructures are observed, the density profiles seen by the three Swarm
satellites are likely to be similar, with a high maximum correlation
coefficient for Δtxcorr=0. This would indicate a zero
along-track velocity even though the plasma is moving. We remove the slowly
varying background from the plasma density profile by means of a
Savitzky–Golay filter (order: 2; window size: 31 data points). Considering the filter cutoff period, the residual density is constrained to fluctuations of less than about 80 km scales. If the mean
absolute value of the residual is smaller than 1.2×104 cm-3, the orbit segment is omitted in further data
processing.
To avoid false velocity estimation, we impose a rather strict condition for
the morphological similarity between plasma density profile pairs: the
maximum cross-correlation between plasma density profiles should be higher
than 0.65. Figure 3 shows the correlation diagram of the along-track
plasma drift speed obtained by the Swarm-B–A pair and the Swarm-B–C pair.
Each data point in Fig. 3 corresponds to one 1 min data segment, as shown
in Fig. 2. Blue and red crosses represent observations in the Northern and
Southern Hemisphere, respectively. Note that speed estimates exceeding
1 km s-1 are omitted from the figure. Figure 3 shows that the two
independent speed estimates from the two satellite pairs exhibit high
correlation (∼0.9), and most values are concentrated around the line of
perfect correspondence (unity slope). This good agreement suggests that the
method for plasma velocity estimation (Eq. 1) is reliable and robust except
for a few outliers.
Correlation diagram between the along-track plasma drift speed
obtained by the Swarm-B–A pair and the Swarm-B–C pair. Each data point
corresponds to one 1 min data segment, as shown in Fig. 2. Blue and red
crosses represent observations in the Northern and Southern Hemisphere,
respectively. The dashed line represents perfect correspondence between the
abscissa and the ordinate.
Note that the leading satellite, Swarm-B was used as the reference satellite
in producing Fig. 3. We have repeated the same procedure while changing the
reference satellite to Swarm-A and Swarm-C. All the results (figures not
shown) look qualitatively similar to Fig. 3, with the correlation coefficient
between the abscissa and the ordinate being 0.83 (0.96) when Swarm-A
(Swarm-C) is used as the reference satellite.
conducted similar analyses using Swarm data (for a few cases of
polar cap patches). In Table 1 of the along-track plasma drift
speed is (1) mostly below 500 m s-1, with a mean of about
280 m s-1, and (2) occasionally below 100 m s-1. In Fig. 3 we
can see that the range of -500 to +500 m s-1 contains the majority
of the population. Hence, our Fig. 3 generally agrees with ;
this also supports the validity of our method.
In Fig. 3 we can see that the along-track plasma convection speed is mostly
positive (negative) in the Northern (Southern) Hemisphere. During the mission
period of interest, the Swarm orbital directions point approximately from noon
to midnight in the Northern Hemisphere (NH) and reversed in the Southern
Hemisphere (SH). As positive velocity corresponds to plasma drift in the flight
direction of the Swarm satellites (see Sect. 2), Fig. 3 shows that the
plasma drift is generally from noon to midnight (i.e. anti-sunward) in both
hemispheres, especially for high speeds beyond about ±300 m s-1.
The numbers of data points in Fig. 3 are 70 and 417 for the NH and SH,
respectively. This ratio of 1 to 6 (=0.17) in favour of the Southern
Hemisphere can be explained in the following way. First, we should consider
sampling bias. The total number of paired (e.g. between Swarm-B and Swarm-A)
1 min data segments analysed, as described in Fig. 2, is 39 353 and 39 485
for the NH and SH, respectively: the ratio between the former and the latter
is about unity. Second, found that 40 % (60 %) of
plasma density irregularities observed at |MLAT|≥55∘ by the
CHAMP (Challenging Minisatellite Payload) satellite belong to the NH (SH).
The irregularities' natural preference for the SH can contribute to the
hemispheric asymmetry in our Fig. 3. The sampling bias (about unity) in
combination with irregularities' natural preference for the SH (0.67) would
result in a north-to-south ratio of 0.67 (=1×0.67), which is still
insufficient to explain the ratio observed in Fig. 3 (0.17). Hemispheric
asymmetry in distributions of the MLAT ranges analysed in this study, which
will be discussed at the end of this subsection, can make an additional
contribution. However, further study is needed to elucidate quantitatively
the hemispheric asymmetry in the number of events shown in Fig. 3.
|MLAT| dependence of the along-track plasma drift speed obtained
by (a) the Swarm-B–A pair and (b) by the Swarm-B–C pair.
We have also investigated the dependence of
vplasmaalong-track on |MLAT| in Fig. 4. The
top (bottom) panel presents vplasmaalong-track
obtained by the pair Swarm-A and Swarm-B (Swarm-C and Swarm-B). Black
triangles and red asterisks correspond to the NH and SH, respectively. As
|MLAT| increases, the upper bound of the along-track plasma convection
speed increases, while the lower bound stays more or less unchanged. That is
to say, vplasmaalong-track at lower |MLAT|
(e.g. at auroral regions) is generally lower, while
vplasmaalong-track at high |MLAT| (e.g.
inside the polar cap) can exhibit a wide range of values. This MLAT
dependence can be explained in the following way. Unless the interplanetary
magnetic field (IMF) is directed strongly northward, (1) the convection
velocity for |MLAT|≥80∘ (in the polar cap) on average has a
dominant noon-to-midnight component but (2) convection velocities at
|MLAT|<75∘ (in the auroral region) generally exhibit reduced
magnitude and/or deviations from the noon-to-midnight direction
(; Figs. 2–3). When the IMF is directed strongly northward,
the convection velocity shows complex patterns regardless of whether
|MLAT| is above 80∘ or below 75∘ (;
Figs. 2–3). As mentioned in the preceding paragraph, the Swarm orbital
directions are approximately aligned with the noon–midnight direction during
the mission period of interest. Hence, the along-track convection velocity
component measured by Swarm is likely to be larger in magnitude within the
polar cap than at auroral latitudes.
In Fig. 4 events in the NH are generally confined to the high-latitude region
of |MLAT|>75∘. On the other hand, a significant part (about
75 %) of the events in the SH comes from |MLAT|<75∘. This
hemispheric asymmetry is as expected from our data selection method described
in Sect. 2. Only data within ±5 min (approximately ±2300 km or ±20∘ in latitude) around the peaks of |GLAT| are selected and
analysed in this study. The offset between the geographic and geomagnetic
poles is larger in the SH than in the NH. Hence, wider ranges of |MLAT| can be
populated well by the selected and analysed Swarm data in the SH than in the NH.
Swarm–SuperDARN comparison
We further compared the data with independent ground observations conducted
by SuperDARN. To ensure that the plasma drift speed measured by Swarm does
not change within a few minutes (that is, to focus only on the bulk
population around the 1:1 correspondence line in Fig. 3), Swarm
vplasmaalong-track data are used only when they
satisfy the following conditions:
the mean of the two vplasmaalong-track estimates is smaller in magnitude than
1000 m s-1;
the difference in vplasmaalong-track for the Swarm-B–A pair
and the Swarm-B–C pair is smaller than 40 % of the mean of the two
vplasmaalong-track estimates (note that these
two estimates are separated in time by a few minutes); and
the MLT should be within ±3.5 h of noon or
midnight. Plasma convection in the dawn–dusk sector may exhibit strong
latitudinal shear, which may hinder the inter-instrument comparison due to
the proximity to the convection reversal boundary.
Plasma velocities from the SuperDARN map velocity data (at 2 min cadence) are
chosen for comparison when they satisfy the following conditions:
the centre point of each 1 min segment of Swarm-B data lies within ±1∘
in latitude and ±10∘ in longitude of the altitude adjustment
corrected geomagnetic (AACGM) coordinates of the SuperDARN grid point, and
within ±4 min in time and
more than one grid point of SuperDARN data satisfies Condition (1).
If satisfied, the SuperDARN map velocity data at those candidate grid points are
projected onto the horizontal velocity vector of Swarm-B orbit
vSwarmnorth,vSwarmeast
for each candidate grid point (displacement of the actual Swarm-B location
from the SuperDARN data point is neglected for simplicity);
averaged over different candidate grid points; and
compared with the along-track plasma speed estimation from Swarm electron density profiles vplasmaalong-track.
The results of this Swarm–SuperDARN comparison are shown in Fig. 5. The
x axis represents the mean of
vplasmaalong-track from the Swarm-A–B and B–C
pairs, while the y direction shows SuperDARN map velocities projected onto
the Swarm flight direction. The correlation coefficient of the two
plasma velocities estimated from Swarm and SuperDARN is about 0.75, and the
total number of common events is 34. Note also that most of the data points
in Fig. 5 are not too far from the line of perfect correspondence (i.e. the line
of unity slope). Nevertheless, the slope of the best fit lines is only 0.54
when we use the simple linear regression methods. This indicates that we
obtain clearly larger velocities from Swarm estimates than from SuperDARN
reconstructions. If we assume comparable uncertainties in the two data sets
(i.e. using the total linear regression method), the slope increases to 0.64,
which means the SuperDARN results are on average smaller by about 36 %.
However, the bias between the two types of measurements (about
50 m s-1; see Fig. 5) is quite small (i.e. much smaller than the
natural variation range in Fig. 5).
Correlation diagram for the along-track plasma drift speed
obtained by Swarm and SuperDARN. The diagonal line represents perfect
correspondence between the abscissa and ordinate.
We have repeated the same procedure while changing the reference satellite
from Swarm-B to Swarm-A and Swarm-C. All the results (figures not shown) look
qualitatively similar to Fig. 5, with the correlation coefficient between the
abscissa and the ordinate being 0.75 (0.67) when Swarm-A (Swarm-C) is used as
the reference satellite.
Reasons for the imperfect, though reasonable, agreement (R∼0.75) between
Swarm and SuperDARN estimates may be explained as follows. The SuperDARN map
velocity data represent large-scale convection patterns because of their beam
width and consequent grid spacing. This smoothing probably leads to smaller
velocities. In contrast, Swarm satellites track individual patches at high
latitudes. Hence, differences between large-scale convection patterns
(SuperDARN) and smaller-scale plasma drift features (Swarm), especially
around plasma density irregularities e.g., are
expected to result in a reduced correspondence between the two velocity
estimates. Furthermore, Fig. 4 demonstrate that the SuperDARN
velocity is on average 18 % lower in magnitude than that estimated from the motion
of pulsating auroral patches. These results can partly explain the systematic
underestimation in our Fig. 5 (underestimation by 36 %).
The multi-satellite method, which is based on a pearls-on-a-string constellation, can be a useful method to determine plasma velocity along
the string of satellites. After completion of the operational constellation
(by mid-April 2014), the Swarm-A and Swarm-C satellites are again at the same
altitudes with a small zonal separation (∼1.4∘ around the
equator). However, the temporal separation between the satellites is rather
small (∼9 s) such that the presented method can hardly be applied in a relable manner. According to Eq. (1), for example, an along-track plasma speed of
0.5 km s-1 will result in a 0.64 s time shift (Δtxcorr) between Swarm-A and Swarm-C observations. This time
difference is close to the nominal sampling period (0.5 s) of the Swarm LP;
therefore, improved methods are needed for the estimation of along-track
plasma speed from these data.
Summary and conclusion
Using electron density measured by the Swarm constellation between 01
December 2013 and 15 January 2014, we have estimated the along-track velocity
component of plasma convection within and around the polar cap. Our main
conclusions can be summarized as follows:
The velocity values estimated from two different satellite pairs agree well with each other.
Further, the velocity exhibits reasonable agreement with plasma velocity from SuperDARN,
at least for those cases which coincide with the Swarm observations. On
average, SuperDARN data reveal drift velocities smaller by 36 % than those
from the local Swarm observations.
In both hemispheres the estimated velocity is more frequently anti-sunward rather than sunward, as expected.
Our method can supplement currently available instruments for ionospheric
plasma velocity measurements (e.g. SuperDARN and DMSP satellites), especially
in cases where these traditional instruments suffer from their inherent
limitations (e.g. along-track component of ion drift metres). Also, the
method can be generalized to other satellite constellations carrying similar
electron density probes.