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\begin{document}

\title{Northern Preference for Terrestrial Electromagnetic Energy Input from
Space Weather}



\author[1]{Ivan Pakhotin}%
\author[1]{I R Mann}%
\author[1]{K Xie}%
\author[2]{J Burchill}%
\author[2]{D Knudsen}%
\affil[1]{University of Alberta}%
\affil[2]{University of Calgary}%


\vspace{-1em}



  
  \date{May 24, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Terrestrial space weather involves the transfer of energy and momentum
from the solar wind into geospace. Despite recently discovered seasonal
asymmetries between auroral forms and the intensity of emissions between
northern and southern hemispheres, seasonally averaged energy input into
the ionosphere is still generally considered to be symmetric. Here we
use Swarm satellite data to show an unexpected preference for
electromagnetic energy input at 450 km altitude into the northern
hemisphere, on both the dayside and the nightside, when averaged over
season. We propose that this is explained by the offset of the magnetic
dipole away from Earth's center. This introduces a larger separation
between the magnetic pole and rotation axis in the south, creating
different relative solar illumination of northern and southern auroral
zones, resulting in changes to the strength of reflection of incident
Alfv\selectlanguage{ngerman}én waves from the ionosphere. Our study reveals an important
asymmetry in seasonally averaged electromagnetic energy input to the
atmosphere. Based on observed lower Poynting flux on the nightside this
asymmetry may also exist for auroral emissions. Similar offsets may
drive asymmetric energy input, and potentially aurora, on other planets.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


Northern Preference for Terrestrial Electromagnetic Energy Input from
Space Weather

I. P. Pakhotin*, I. R. Mann, K. Xie, J. Burchill, D. Knudsen

Terrestrial space weather involves the transfer of energy and momentum
from the solar wind into geospace. Despite recently discovered seasonal
asymmetries between auroral forms and the intensity of emissions between
northern and southern hemispheres, seasonally averaged energy input into
the ionosphere is still generally considered to be symmetric. Here we
use Swarm satellite data to show an unexpected preference for
electromagnetic energy input at 450 km altitude into the northern
hemisphere, on both the dayside and the nightside, when averaged over
season. We propose that this is explained by the offset of the magnetic
dipole away from Earth's center. This introduces a larger separation
between the magnetic pole and rotation axis in the south, creating
different relative solar illumination of northern and southern auroral
zones, resulting in changes to the strength of reflection of incident
Alfv\selectlanguage{ngerman}én waves from the ionosphere. Our study reveals an important
asymmetry in seasonally averaged electromagnetic energy input to the
atmosphere. Based on observed lower Poynting flux on the nightside this
asymmetry may also exist for auroral emissions. Similar offsets may
drive asymmetric energy input, and potentially aurora, on other planets.

\textbf{Main}

Solar-terrestrial coupling involves energy transfer from the
magnetosphere into the ionosphere and atmosphere below. A critical
component of this magnetosphere-ionosphere coupling (MIC) involves large
scale field-aligned currents (FACs) which flow in patterns of upwards
and downwards sheets in response to solar wind forcing {[}1{]}{[}2{]},
and which are related to convection plasma flows in the magnetosphere
arising from coupling to the solar wind through magnetic reconnection
{[}3{]}. Such FACs are established and change dynamically as a result of
the field-aligned propagation of Alfvén waves {[}4{]}. Such waves are
also linked with the formation of some types of auroral features
{[}5{]}{[}6{]}.

Recent research has addressed the question of whether the aurora are
symmetric between the northern and southern hemispheres. For example,
the aurora in each hemisphere can be differentially distorted as due to
non-zero dawn-dusk component of the interplanetary magnetic field (IMF)
{[}7{]}. Evidence for a seasonal dependence in the aurora was also
presented by {[}8{]}{[}9{]}. Asymmetries in the aurora may also occur as
a result of differential solar illumination {[}10{]}, from potential
interhemispheric differences in ionosphere-thermosphere coupling as due
to the offset of the magnetic dipole from the Earth's centre, as well as
from higher-order multipole terms {[}11{]}.

These studies demonstrate that the auroral forms and their intensities
in the two hemispheres can be asymmetric. However, a systematic study of
asymmetries in the incoming Poynting flux from electromagnetic plasma
waves has not been completed. Interestingly, recent work found that FACs
in the auroral zone tend to be stronger in the north {[}12{]}. The
ionospheric conductance is known to have a strong influence on the
strength of the FACs {[}12{]}. However, in order to assess in-situ
electromagnetic energy transfer one requires both electric and magnetic
field measurements in order to compute the Poynting vector and this has
heretofore not been analysed in detail. Under common assumptions the
magnetic-field-aligned component of the Poynting vector is equal to the
height-integrated Joule dissipation below the satellite {[}13{]}.

Here we use data from the European Space Agency (ESA) Swarm mission
{[}14{]} to assess the seasonal dependence of the electromagnetic energy
input associated with MIC at Swarm altitudes, and thereby assess the
response of space weather in geospace to solar wind forcing. Preliminary
statistics {[}15{]} demonstrated a northern preference for
electromagnetic energy input during the northern summer. As that study
only considered northern summer months, they were unable to assess
whether such asymmetry would reverse six month later, nor whether there
was any systematic seasonably averaged interhemispheric asymmetry.

In contrast to the standard paradigm of interhemispheric symmetry, we
demonstrate using data from the Swarm satellite, in polar low-Earth
orbit (LEO) at an altitude of around 450 km, that there is persistently
higher electromagnetic energy input in the northern hemisphere even when
averaged over season. This preference for stronger northern
electromagnetic energy input is observed in both the dayside and
nightside. Indeed, on the nightside there is a dominance of energy
transfer into the north in both near-summer and near-winter solstice
seasons.

\emph{Ionospheric Electromagnetic Energy Input}

Here we examine the electromagnetic energy input into the ionosphere by
assessing the Poynting vector associated with perturbations along the
satellite world-line, calculated using\(S=\ \frac{1}{u_{0}}E\ \times B\) where
\(u_{0}\) is the magnetic constant, and \emph{E} and \emph{B}
denote the electric and magnetic field vectors of the perturbation
fields, respectively. By applying band-pass filters it is possible to
remove the influence of large-scale variations of the Earth's main field
as measured along the trajectory of the moving satellite, and to focus
on the Poynting flux contributions arising from perturbations at various
scales of interest. With a single satellite it is impossible to uniquely
separate the impacts arising from spatial and temporal variations along
the satellite world-line. However, as shown for example by
{[}16{]}{[}17{]}, analysis of the wave impedance as a function of
frequency in the Swarm frame provides strong evidence for the importance
of Alfvén waves in MIC.

Figure 1 shows the statistical Poynting flux over two separate one
month-long time periods, one in the northern near-summer solstice
conditions (1-31 July, 2016\emph{;} panels (a) and (b)) and the other in
the northern near-winter solstice conditions (15 November-15 December,
2016; panels (c) and (d)), for both the dayside (left column) and the
nightside (right column) as determined by magnetic local time (MLT).
These two intervals were chosen to reflect periods where the Swarm A
orbits were in similar noon-midnight local time orientations. In this
Figure, the error bars show the median spanned by the upper and lower
quartiles in the statistics, with the scale dependence of the Poynting
flux as a function of frequency derived by the application of a
time-domain Savitzky-Golay low-pass filter of varying width along the
x-axis (see Methods for details). It can be seen that on the dayside
during near-summer solstice, there is a clear statistical preference for
more electromagnetic energy to be driven into the northern hemisphere
than the southern hemisphere at Swarm altitudes. On the dayside during
near-winter solstice, the preferential direction of the energy transfer
does reverse such that there is more Poynting flux directed into the
southern hemisphere. However, and very significantly, the asymmetry in
the interhemispheric energy transfer is much smaller than in the
near-summer solstice period. As a result, there is a clear preference
for more energy transfer into the north. Indeed, if the results from
these two months approximating the near-summer and near-winter solstice
periods are summed, the implied summer-winter seasonally-averaged
Poynting flux will have a clear net northern preference.

On the nightside (panels (b) and (d)), the northern preference for
electromagnetic energy transfer is even more stark. During the
near-winter solstice on the nightside (panel (d)), there is a reduction
in the northern preference, but remarkably the direction of the
electromagnetic energy transfer does not reverse as compared to the
near-summer solstice such that the median direction of energy transfer
remains slightly northwards even in the near-winter solstice at night.

In all cases the error bars plotted in this Figure, and which refer to
the 25\% and 75\% quartiles in Poynting flux, appear be a significant
fraction of the median. However, we emphasise that this feature should
not be interpreted as a low statistical significance of our result
demonstrating northern preference for electromagnetic energy transfer
seen at Swarm. Instead, the large range of average Poynting flux
magnitudes represented by the quartiles simply reflects the expected
large variability in the magnitudes of energy flux from hour to hour and
day to day in response to non-steady solar wind forcing. Supplementary
Material Figures 1 and 4, for the northern near-winter and near-summer
solstice periods, respectively, show this effect clearly. It can be seen
that during more intense geomagnetic activity, the magnitude of the
Poynting flux increases in both hemispheres. This can be seen
particularly during conjugate observations from adjacent northern and
southern hemisphere passes, where the Poynting flux is seen to increase
and decrease in tandem in both hemispheres in response to varying levels
of driving. In particular for the near-summer solstice period it can be
seen that the northern Poynting flux dominates over the conjugate
southern hemisphere counterpart, both on the dayside and on the
nightside, in the time domain across the whole interval despite it
spanning a wide range of intensities of solar wind driving conditions.
Therefore the northern preference for electromagnetic energy input
persists in the time domain from event to event, and not just when
combined statistically as in Figure 1.

Figure 1 further shows that in general the electromagnetic Poynting flux
observed at Swarm appears to be smaller on the nightside than on the
dayside. This is evident both in the near-summer and near-winter
solstice periods and appears to be a general characteristic of the
magnitude of the observed electromagnetic energy input arising from
electromagnetic fluctuations at this altitude. A likely explanation for
this is that a significant fraction of the incoming electromagnetic
energy is converted to the kinetic energy of downgoing auroral electrons
as a result of coupling at higher altitudes above Swarm in the nightside
auroral acceleration region (AAR) located around 4000-12000 km in
altitude {[}18{]}. This inference is consistent with the concept whereby
the ionospheric feedback instability {[}19{]} can produce discrete arcs
which convert incoming electromagnetic energy into field-aligned
electron acceleration in the AAR. This feedback process happens
preferentially at night where the background conductivity is low, and
where in the absence of dayside EUV illumination strong conductivity
gradients can be formed {[}20{]}. In such a paradigm, the reduction in
nightside Poynting flux observed at Swarm, located below the AAR, is
explained as a result of significant energy removed in association with
discrete arc auroral electron acceleration above.

Interestingly, in the data shown in Figure 1, the interhemispheric
energy fraction appears to be independent of scale. This suggests that
the processes responsible for the observed asymmetry are most likely
self-similarly active at and/or self-similarly impact all transverse
scales considered.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\emph{Figure 1: Average Poynting flux observed by Swarm A satellite
crossings of the northern and southern auroral zones. Dayside (left
column) and nightside (right column) auroral zone crossings for northern
near-summer solstice (1-31 July, 2016; top row, panels (a) and (b)) and
northern near-winter solstice (15 November-15 December, 2016; bottom
row, panels (c) and (d)), during periods where the orbits are confined
to the noon-midnight local time sector (see also Supplementary Figure
5). The panels compare Poynting flux as a function of transverse spatial
scale, derived using a time-domain Savitzky-Golay filter, in the
northern and southern hemispheres (blue and red, respectively) and plot
the median Poynting flux power values (solid line) and the 25\% and 75\%
quartiles (error bars). Three regions separating small-scale (10-150
km), mesoscale (150-250 km) and large-scale (\textgreater{}250 km)
phenomena as observed along the Swarm orbit, as per the definitions in
{[}21{]} are denoted by pink, green, and blue backgrounds,
respectively.}

\emph{Seasonal and Scale-Dependence of Electromagnetic Energy Input}

The time periods around the equinoxes also show similar behaviour in
terms of the northern preference for electromagnetic energy transport at
Swarm altitudes, with the time periods closer to the equinoxes
exhibiting behaviour that falls between the dynamics seen near the
solstices (see Figure 2). The median and quartile Poynting fluxes at
small, medium and large spatial scales shown in Figure 2 continue to
show the northern preference, and how this preference evolves with
season from the peak interhemispheric asymmetry in the northern
near-summer solstice, through the equinoxes, to the northern near-winter
solstice. Significantly, the behaviour of the interhemispheric asymmetry
in electromagnetic energy flux is self-similar at small, medium and
large scales, suggesting that most likely the same physical processes
are active in magnetosphere-ionosphere coupling across the entire range
of spatial and temporal scales shown in Figures 1 and 2, and during all
seasons. It is also possible that energy is transferred between scales
within this system via a cascade {[}22{]}. It can be seen that the sum
totals of Poynting fluxes (north hemisphere flux plus south hemisphere
flux) remain relatively similar across the seasons on the dayside,
suggesting a relatively constant average total energy input is then
re-distributed differentially into the two hemispheres -- but with a
seasonally averaged northern preference which is especially strong near
the summer solstice. On the nightside, the same conclusion applies --
except that the northern preference is even stronger than on the
dayside. Indeed, on the nightside the northern preference is so
pronounced that the median Poynting flux at Swarm altitudes is always
much larger in the north, and at all scales, independent of season --
even near winter solstice.

Note that in our analysis we have taken care to exclude the possibility
that the northern preference we report could occur as a result of
sampling bias, for example as a result of the inclination of the Swarm
orbit generating impacts from differentially sampling auroral zone
crossings at different angles of attack with respect to the auroral
oval. For example, the orbits of Swarm A for all four seasonal time
periods were chosen to be confined in the noon-midnight meridian (see
Supplementary Material Figure 5). Moreover, exploration of limited
subsets of the two time periods in Figure 1, focusing on only MLT times
one hour before or after 00 or 12 MLT (i.e., more strictly confined to
the noon-midnight local time meridian) also produced similar results
further confirming the characteristics reported in Figure 1 are real
(see e.g., Supplementary Material Figure 6). Note that although the
electromagnetic fields are derived in local coordinates, both
perpendicular polarisations of E and B fields are used to derive the
parallel component of the Poynting flux. As such the reported northern
preference for electromagnetic energy transfer appears to be geophysical
in origin, and not the result of sampling bias or orbital orientation
effects.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\emph{Figure 2: Median values of electromagnetic power at small, medium
and large scales for near-solstice and near-equinox periods in the
noon-midnight local time meridian. Electromagnetic energy in northern
and southern dayside (blue, red, respectively; left column) and
nightside (black, pink, respectively; right column) passes are shown at
three spatial scales. Band-pass filtering was done using the
Savitzky-Golay filter, with small scales (top row, panels (a) and (b))
derived using time domain filters characteristic of 75 km along track
scales; medium scales (middle row, panels (c) and (d)) characteristic of
200 km along track scales; and large scales (bottom row, panels (e) and
(f)) characteristic of 350 km along track scales. Dashed lines connect
the median values (marked with crosses), while the error bars show the
lower and upper quartiles in terms of magnitude. The positions of the
medians and error bars for different MLT and hemisphere sectors during
the same time periods have been slightly shifted on the x-axis for
visual effect and to enable the reader to better differentiate between
the error bars. Note as explained in Methods that all electromagnetic
power values are derived by integrating in time along the spacecraft
world-line during an event, and dividing by the duration of the event.}

\emph{Asymmetric Seasonal Auroral Zone Illumination}

Here we advance a paradigm which can explain the observed persistent
asymmetry and northern preference for incoming Poynting flux at Swarm
altitudes based on the known offset of the magnetic dipole moment from
the center of the Earth towards the northwest Pacific {[}23{]}. This
offset generates different relative effective solar illumination of the
auroral ovals in the northern and southern hemispheres arising from the
rotation of the Earth. The offset can also introduce asymmetries in the
magnetic fields in the auroral zones as well (cf. {[}10{]}). A model of
the north and south auroral ovals at two particular instants, shown in
blue and red, respectively, is shown in the left and right hand panels
of Figure 3. In each panel, the two ovals are over-plotted in a two
dimensional projection of a polar view of the Earth in the geocentric
solar ecliptic (GSE) x-y plane, and where the x=0 line marks the
terminator and with the nightside beyond the terminator shaded in grey.
As the Earth rotates, the offset of the dipole axis from the rotation
axis sweeps the auroral ovals, whose location is defined by the magnetic
field, further into and out of the sunlight; the offset of the dipole
from the Earths centre making the excursions into and away from the
sunlight significantly more pronounced in the southern hemisphere than
the north. This also changes with season. To illustrate this effect, the
left panel (a) in Figure 3 shows an example from the northern summer
solstice, while the right hand panel (b) shows the northern winter
solstice, at the same UT.

The offset of the magnetic dipole from the Earths center means that in
the south the magnetic pole at the Earth's surface is further from the
Earth's rotation axis than the north magnetic pole {[}10{]}{[}11{]}. As
a result, the southern auroral oval experiences more diurnal variation
in its motion both across the terminator into the nightside, and across
the terminator into the dayside 12 hours later, than its northern
counterpart as a result of the rotation of the Earth. This means that at
certain times the southern oval spends fractionally more time in
darkness than the northern oval, and at others fractionally more time in
daylight. To illustrate the impacts of the Earth's rotation on the
extent of the ovals in the x-y plane through one Earth rotation, the
dashed lines show the circles which mark out 65\selectlanguage{ngerman}° MLAT while the solid
circles show the 75° MLAT. This MLAT range may be taken to be roughly
representative of an auroral oval. Meanwhile the bold line traces
circles which show the locus of the geomagnetic poles (90° MLAT).

In Figure 3 it can be seen that the maximum area of the northern auroral
oval which is in shadow during (northern) summer solstice (left panel)
is approximately one quarter of the total oval area, whereas the maximum
shadow of the southern oval during winter solstice is larger, reaching
as much as approximately one third of its total area. According to the
hypothesis described above, discrete auroral acceleration would occur
preferentially in dark background ionospheric conductivity conditions.
This would make the southern oval more susceptible to losing energy to
nightside discrete auroral electron acceleration processes, consistent
with the geometrical aspects of shown in Figure 3 and with the nightside
reduction in electromagnetic energy transfer observed at Swarm altitudes
shown in Figures 1 and 2.

Meanwhile on the dayside the southern oval also similarly experiences
more variation in solar illumination than the north, potentially
traversing further into and dwelling longer in sunlit dayside regions
where there is expected to be a greater mismatch between the Pedersen
and Alfvén impedances as a result of increased background Pedersen
conductance due to dayside solar EUV illumination. This would be
expected to lead to greater average Alfvén wave ionospheric reflection
coefficients in the south, as per the ionospherically reflecting Alfvén
wave paradigm {[}16{]}{[}17{]}{[}24{]}{[}25{]}. In turn this could lead
to a stronger reflection of Poynting flux from the southern ionosphere
back towards the equator than in the north. This may lead to an overall
redirection of a fixed equatorial energy source on the dayside away from
the southern hemisphere and into the northern hemisphere, in line with
the observations presented in Figure 2 (panels (a), (c), and (e)). These
two dayside and nightside Alfvén wave processes may therefore generate a
different MIC response as a result of different ambient dayside and
nightside ionospheric conductivity conditions. Nonetheless, they could
occur in tandem and could collectively be responsible for the observed
northern Poynting flux preference both on the dayside and on the
nightside. In both cases, the effect would be to create the observed
northern preference for incoming Poynting flux when observed at Swarm
altitudes.

\emph{Implications for Magnetosphere-Ionosphere-Atmosphere Energy
Transfer in the Auroral Zone}

The seasonally averaged northern preference for electromagnetic energy
input at Swarm altitudes seems to exist in both the dayside and
nightside auroral zones. On the nightside, it implies stronger average
discrete arc auroral precipitation in the south, as residual Poynting
flux there is lower and as discrete arcs are expected to be the primary
absorber of electromagnetic energy incident from above. This conclusion
is also consistent with some previous conjugate auroral observations at
specific instants in time {[}8{]} but which has not been examined
statistically in terms of electromagnetic energy input. Meanwhile on the
dayside, our results appear to complement the statistics of {[}26{]} who
used DMSP data to observe auroral electron energy flux as a function of
season and hemisphere (note however that {[}26{]} did not explicitly
look at north-south seasonal asymmetries as we do here).

For example, {[}26{]} reported that all types of aurora maximised on the
nightside in local winter. Meanwhile, they observed that the electron
fluxes were higher on the dayside in local summer. The former
observation is consistent with our hypothesis that the electromagnetic
energy we observe on the nightside is lower during local winter than
summer, which we propose occurs as a result of preferential discrete
auroral electron acceleration in the AAR above Swarm. The fact that we
also observe higher Poynting fluxes in the dayside summer hemisphere
suggests that both auroral acceleration and the residual Poynting flux
penetrating to Swarm altitudes under the AAR are both higher in local
summer than local winter on the dayside. Based on our results we hence
suggest that dayside discrete aurora might also be more pronounced
during the northern summer than southern summer, an assertion that could
be verified by a future study looking for this potential seasonal
interhemispheric asymmetry using DMSP particle data. Similar asymmetries
in seasonal interhemispheric nightside discrete auroral electron flux
could also be investigated using DMSP data in the same way.

On the dayside we also observe that the sum of northern and southern
Poynting flux appears to be almost constant across seasons. Certainly
there is a preference for more energy input into the summer hemisphere,
but the northern preference means that this is more pronounced in the
northern summer rather than the southern summer on the dayside. Overall,
this suggests that the total dayside electromagnetic energy which
reaches Swarm altitudes might be rather constant with season, but that
ionospheric conductivity effects and asymmetric Alfvén wave reflections
result in a redistribution of the incoming energy flux from one
hemisphere to the other. This favours the summer hemisphere, with a more
pronounced interhemispheric asymmetry occurring during the northern
summer.

As shown in Figures 1 and 2, these same dayside and nightside
interhemispheric seasonal asymmetries occur across a wide range of
spatial scales, and in general the same behaviour is maintained across
small (10-150 km), medium (150-250 km), and large (\textgreater{}250 km)
spatial scales. Previous work has shown that to some degree, similar
behaviour can be inferred in terms of field-aligned currents (FACs)
{[}12{]} which must logically be associated with these electromagnetic
perturbations as well -- especially since they are related to Alfvén
wave dynamics. For example, previous observational studies have made the
link between Alfvénic disturbances and FACs, and have suggested that
both may be explained as part of the same physical framework which can
explain the characteristics of magnetosphere-ionosphere coupling at
these scales {[}17{]}{[}25{]}{[}27{]}{[}28{]}. This study is the first
to demonstrate that, when seasonally averaged, the high-latitude
electromagnetic Poynting flux observed across a wide range of scales has
a definitive northern preference both on the dayside and on the
nightside. The incoming electromagnetic energy, and indeed likely the
incoming discrete auroral electrons, are expected to additionally play a
role in driving ionosphere-thermosphere-atmosphere (I-T-A) coupling
below, perhaps including effects from gravity waves and other
atmospheric phenomena, driven from above (see e.g. {[}29{]}). Therefore
the northern preference for electromagnetic energy input which we report
here could also be very important in relation to impacting the dynamics
of the global atmosphere, perhaps having implications for an
interhemispheric asymmetry in the long-term atmospheric climate
response.

Overall, we propose that, for electromagnetic energy input at Swarm
altitudes, northern preference can likely be explained by the relative
displacement of the north and south auroral ovals with respect to the
Earth's rotation axis, causing effective interhemispheric differential
solar illumination of the two auroral ovals. This effect may also be
present on other magnetized planets or moons where the magnetic dipole
is offset from the planet's center, asymmetries in MIC occurring as a
result of the impacts of differential ionospheric conductivity.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\emph{Figure 3: Asymmetric interhemispheric auroral zone solar
illumination. The figure shows the two-dimensional projection in GSE x-y
coordinates of the traces of the north (blue) and south (red) auroral
ovals, each assumed here to lie between lines of constant altitude
adjusted corrected geomagnetic (AACGM) latitude from 65-75 degrees
during matching UT times for northern summer (left; June 21 2016) and
northern winter (21st December, 2016) solstices. The solid and dashed
black lines denote the loci of the edges of the ovals in the northern
and southern hemispheres as a result of diurnal rotation during the
northern summer (left, panel (a)) and winter (right, panel (b))
solstices. The bold solid black circle at high latitudes denotes the
locus of the geomagnetic poles. The solid vertical line denotes GSE x=0
mark/the terminator. The area in Earth's shadow is shown in grey.}

\textbf{Methods}

The ESA Swarm mission, launched in late 2013, comprises three identical
spacecraft equipped for making simultaneous, high accuracy and high
cadence magnetic and electric field measurements. This study uses data
from the Swarm A satellite, in a \textasciitilde{}450 km polar orbit,
equipped with the fluxgate magnetometer instrument {[}14{]} measuring
magnetic field vectors at 50 samples/sec and the Electric Field
Instrument {[}30{]} measuring ion velocity vectors at 16 samples/sec
based on observed ion distributions from two sensors, which are
converted into a 2 Hz E-field data product. Under the assumption of
frozen flux of the observed ions based on ideal Ohm's Law where E = -v x
B the inferred velocity vectors can be converted into electric field
vectors in the plane perpendicular to the magnetic field.

The automatic event identification algorithm used here has been designed
to extract useful scientific data from synchronous magnetic and electric
field measurements while addressing known caveats in the electric field
data (e.g. uncertainties regarding offsets and magnitudes of the
electric field instrument data {[}31{]}, {[}32{]}). It is based on the
methodology employed by {[}33{]}. Only magnetic latitudes of between +-
60 and +- 80 degrees magnetic latitude (MLAT) are considered for the
analysis. This avoids low-latitude phenomena such as plasma bubbles
{[}34{]} and localised extreme high latitude phenomena such as polar cap
traversals {[}35{]}. The magnetic and electric field data is rotated
into the mean-field aligned (MFA) frame, where z points along the
direction of the mean magnetic field, x points towards the geomagnetic
North Pole, and y completes the triad facing eastwards. A sliding
3-minute window is used for mean field calculation.

For event detection and selection, the Poynting flux is calculated by
crossing the E- and B-field time series after applying a
2\textsuperscript{nd} order Savitzky-Golay filter with window size 60.5
seconds, to remove any residual mean field influences or large-scale
electric fields, as well as any uncertainties with the E-field baselines
which are a known artefact in the electric field data. The modulus of
this Poynting flux is then low-pass filtered with a 120.5 sec moving
average filter to obtain its magnitude envelope. Where the magnitude of
this Poynting flux envelope exceeds an empirically determined threshold,
the event is flagged and event duration defined both backwards and
forwards in time until the magnitude of the Poynting flux envelope drops
below a second, lower, empirically determined threshold. For the
analysis presented here, the thresholds are 25 and 8.75, respectively.
This time window then defines a single event. Only E-field data sets
flagged with the quality flags 1 (``use in consultation with EFI TII
team at University of Calgary'') {[}36{]} is used in the analysis.

The 2 Hz E-field estimates are provided for both the horizontal and the
vertical sensors. Based on the caveats described in {[}36{]} the outputs
from both TII sensors are averaged. Since the analysis in this study
used high-pass filtering to focus on relatively small scales, it is
deemed acceptable to use the full 3-D vector for Poynting flux
calculations. A separate test performed using only the along-track
component of the E-field, which is identical in both sensors, to
calculate the Poynting flux, also reproduced the observed northern
preference.

The selected events must all occur at locations between 60 and 80
degrees magnetic latitude (MLAT) and event length must be at least 150
seconds long. The time series are extended with zeros for 30 seconds at
the beginning and the end, which serves as padding to allow all filter
sizes to fully capture the energy content in each event without
edge-effect distortion. For the selected events, the electric and
magnetic field data are then passed through a Savitzky-Golay filter of
2\textsuperscript{nd} order and of various window sizes, from 1 (no
effective high-pass filter) to 60.5 seconds, at 0.5-second intervals.
The cross product of the two band-passed signals gives the Poynting flux
in that frequency band. The Poynting flux is integrated over time along
the spacecraft trajectory to obtain the integrated apparent energy flow
through the satellite world-line as it crosses the event region. This is
repeated for the entire range of low pass filter window sizes for each
event. Average Poynting fluxes for each event are obtained by dividing
the integrated Poynting flux values by the event duration. The median
and quartiles are obtained for these three quantities from all of the
events flagged by the algorithm.

A representative example of the analysis is shown in Figure 4 for an
auroral zone Swarm A crossing event from 05:11:30 to 05:15:00 UT on 17
Nov 2016, flagged by the algorithm. It can be seen that there is good
correspondence between B-field (panel (a)) and E-field (panel (b)) data,
suggesting mostly positive (downwards) Poynting flux throughout. This is
evidenced in panels (c) and (d) where the (parallel) Poynting flux
remains largely positive. The Poynting flux shown in panel (c) is
plotted for three Savitsky-Golay filter windows -- 9 sec (blue) for
small-scale phenomena, 27 sec (red) for mesoscales, and 47 sec (black)
for perturbations associated with larger-scales. It can be seen that the
Poynting flux reduces as progressively more low-pass filtering is
applied to the constituent E-field and B-field time series. Panel (d)
shows the time integrals of the fluxes in panel (c) demonstrating the
accumulation of Poynting flux on the satellite's world line as it
crosses the perturbation region. It can be seen that the cumulative
Poynting flux passing through the satellite during the event is
approximately half the value for large scales as for meso- and
small-scales, suggesting that large-scale perturbations associated with
global field aligned current systems carry only half of the
electromagnetic energy into the ionosphere during this particular event.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\emph{Figure 4: Example event selection during a Swarm A auroral zone
crossing. Magnetic and electric field and related field-aligned
electromagnetic energy from an event selected by the analysis algorithm
between 05:11:30-05:15:00 UT on 17 Nov 2016. From top to bottom, each
panel shows (a) magnetic field B\_y component, (b) electric field E\_x
component, (c), S\_z component Poynting flux low-pass filtered with
Savitsky-Golay filter of window sizes 9, 27 and 47 seconds (blue, red,
and black, respectively), capturing small-scale, mesoscale, and
large-scale perturbations, and (d) along-track integrated Poynting flux
using the three filtered time series from panel (c). Note that the event
is selected based implicitly on coherent electromagnetic fields, and
with its temporal extent defined from the local peak in the low-pass
filtered Poynting flux to a specified lower threshold (see text for
details). Please note that error estimates on the E-field are not
provided in the dataset. Please refer to {[}36{]} for a discussion of
the errors.}

\textbf{Data Availability Statement}

The ESA Swarm data can be obtained from the ESA server at
swarm-diss.eo.esa.int. The Swarm A 2 Hz E-field data is accessible at
swarm-diss.eo.esa.int/Advanced/Plasma\_Data/2Hz\_TII\_Cross-track\_Dataset/New\_baseline/Sat\_A.
Geomagnetic conditions and L1 information can be found at
https://omniweb.gsfc.nasa.gov.

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\textbf{Acknowledgements}

IPP is supported by the European Space Agency Living Planet Fellowship
``Swarm Investigation of the Energetics of Magnetosphere-Ionosphere
Coupling (SIEMIC)''. The view expressed in this publication can in no
way be taken to reflect the official opinion of the European Space
Agency. IPP is also supported in part by the Canadian Space Agency Class
Grant ``What role do Alfven waves play in energy transfer in the
dynamical magnetosphere-ionosphere system?'' IRM is supported by a
Discovery Grant from Canadian Natural Sciences and Engineering Research
Council (NSERC). Swarm is a European Space Agency (ESA) mission with
contributions from the Canadian Space Agency (CSA) for scientific
analysis of Electric Field Instrument data. DJK and JKB are supported by
grants from the CSA and ESA.

\textbf{Author Information}

\textbf{Affiliations}

\emph{Department of Physics, University of Alberta, Edmonton, Alberta,
Canada}

Ivan P Pakhotin, Ian R Mann \& Kai Xie

\emph{Department of Physics and Astronomy, University of Calgary,
Calgary, Alberta, Canada}

Johnathan K Burchill \& David J Knudsen

\textbf{Contributions}

K.X. and I.P.P. developed the software algorithm for Poynting flux
analysis. I.R.M. provided overall research direction including
interpretation of the results, and assisted in software refinement.
J.K.B. and D.J.K. provided the electric field datasets and assisted with
the interpretation.

\textbf{Competing Interests}

The authors declare no competing interests

\textbf{Corresponding Author}

Correspondence to I. P. Pakhotin.

\textbf{Supplementary Material}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\emph{Supplementary Material Figure 1: Characteristics of the AE index
and IMF for the 15 November-15 December 2016 period. Panel (a) shows the
time series of the Auroral Electrojet (AE) index (b) IMF Bx, (c) IMF By,
(d) IMF Bz, all from OMNIWeb, with the times of Swarm events included in
the analysis being marked on (b), (c) and (d) with blue circles for the
corresponding IMF orientations. (e) shows the Poynting fluxes for
dayside events (marked with circles) for the northern and southern
hemispheres (blue and red, respectively); dashed lines represent linear
connections between individual events. Conjugate events in the
statistical event datasets, defined as those which occurred on conjugate
hemispheres within 30 minutes of each other, are marked with crosses.
These conjugate events are isolated and plotted in figure (g). Panels
(f) and (h) repeat figures (e) and (g) for the nightside. In panels (e)
to (h) the AE Index from (a) is plotted in the background in light gray
to give context to the variability of Poynting fluxes in response to
varying solar wind and geomagnetic driving conditions.}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\emph{Supplementary Material Figure 2: same format as Supplementary
Material Figure 1 but for the time period 20 February-25 March, 2016.}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

\emph{Supplementary Material Figure 3: same format as for Supplementary
Material Figure 1 but for the time period 20 March-20 April, 2017.}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

\emph{Supplementary Material Figure 4: same format as for Supplementary
Material Figure 1 but for the time period 1-31 July, 2016.}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

\emph{\textbf{Supplementary Material Figure 5}: NASA Satellite Situation
Center (SSC) 4D Orbit Viewer figure of the Swarm A satellite orbit for
the four seasonal time periods presented in Supplementary Material
Figures 1-4, showing the noon-midnight orientation of the orbit plane
for all examined seasons.}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

\emph{Supplementary Material Figure 6: Same as Figure 1 for one month of
noon-midnight orbits during northern near-summer solstice (Panels a-c)
and northern near-winter solstice (Panels d-f), but limited to local
times of auroral zone passes of only one hour either side of the 12 MLT
and 0 MLT sectors. Panels (a), (b), (d) and (e) use the same analysis as
(a)-(d) in Figure 1, while Panels (c) and (f) show the occurrence
distributions of individual events on a MLAT vs MLT map. The same
characteristic northern preference in Figure 1 is also verified here.}

\selectlanguage{english}
\FloatBarrier
\end{document}

