IEEE - Aerospace and Electronic Systems - February 2022 - 13

Yang et al.
The F10.7 index correlates very well with, and is a
proxy for, solar UV flux and the number of sunspots.
Figure 4 and Table 3 reveal that the F10.7 flux is much
higher during solar maximum than solar minimum
(approximately double), reflecting well the increased
activity ofthe sun during this period. All the models investigated
have input for F10.7 (or a similar index in the case
of DTM2013). Therefore, any changes to F10.7 generally
led to appropriate changes in the predicted mass density.
Currents in the ionosphere and magnetosphere are
Figure 3.
Selected days ofCOSMIC data and average heights ofeach day in
periods of 2014-2015 and 2018-2019. The top subfigure shows
the data in 2014-2015 and the bottom subfigure shows the data in
2018-2019. The black star mark indicates the selected day and
the red circle indicates the average orbital height of the COSMIC
satellite during the day.
periods. The major contributor for this is likely to be the
drag effect.
An important consideration in the variation of the
mass density in the upper atmosphere is solar activity. The
sun varies over an approximately 11-year cycle between
periods of high and low solar activity (usually referred to
as solar maximum and solar minimum). Solar activity is
usually quantified by the number of sudden energetic
events such as solar flares and coronal mass ejections.
Both these events happen as a result of magnetic reconnection
and a conversion of the sun's surface magnetic
energy into light and/or kinetic energy.
The amount of energy absorbed by the atmosphere
from the sun leads to variations in its temperature. The
average solar radiation at high frequencies increases during
solar maximum periods and, therefore, produces
effects in the upper atmosphere. The highest-frequency
radiation such as X-ray, EUV, and UV light contains the
largest amount of energy per photon, therefore delivering
the greatest amount of energy for a given flux. With
increased flux and energy absorption in the upper atmosphere,
the atmosphere expands and the AMD at a given
altitude above the Earth increases. Satellite drag, as a
result, has a much larger effect on LEO satellites during
solar maximum. This is the reason that COSMIC data corresponding
to different periods of solar activity were chosen
(2014-2015 representing solar maximum and 2018-
2019 representing solar minimum) and four different periods
of the year to reveal the effect of different solar radiation
conditions on the AMD.
Figure 4 and Table 3 summarize the space weather
conditions for the days investigated in the two data sets.
The F10.7 averages are of the daily F10.7 values in solar
flux units (sfu), Ap are those determined by the Helmholtz
Institute in Potsdam, and the X-ray flux values are averages
of the background flux values at 1:0 to 8:0 in
W m2 from the GOES-15 satellite [45].
FEBRUARY 2022
enhanced from the injection of charged particles from the
solar wind, leading to variations in the magnetic field
measured at the Earth's surface. This can occur when the
magnetic field of the Earth and solar wind are antiparallel.
The Ap index is based on magnetometer data on
Earth and is a proxy for the amount of geomagnetic
activity in the Earth's ionosphere/magnetosphere.
Increased activity is usually caused by coronal mass ejections
(during solar maximum) or high-speed solar wind
from coronal holes (during solar minimum) interacting
with the Earth's magnetosphere leading to " geomagnetic
storms. " Due to coupling of atmospheric layers, this
increase in energy can also affect the temperature of
regions where LEO satellites orbit.
Solar X-ray radiation, although much higher in energy
than UV light has a much lower average flux and, therefore,
less of an effect on the atmospheric density. However,
short bursts of X-ray radiation from solar flares can
momentarily increase this flux by orders of magnitude
from the background value. Table 3 lists the average background
flux and the average number of daily C- and Mclass
flares (or flares offlux 106 W m2 to 105 W m2
and 105 W m2 to 104 W m2, respectively) across
the 10-day periods.
COMPARISON METHODOLOGY AND RESULTS
Four AMD models, i.e., MSISE90, MSISE00, JB2008, and
DTM2013, the proposed model, and the no-drag model are
assessed via comparing one-day OP results with COSMIC
precise ephemerides. The 3-D distance error of the final
epoch ofthe day is saved, as well as the in-track error ofthe
final epoch and the maximum in-track distance error during
the whole day. The average of these values over each 10day
window is plotted along with samples, shown in
Figure 5 for 2014-2015 and Figure 6 for 2018-2019,
respectively. For some specific Cd and Cr values, it happens
that some AMD models fail to output the effective
density values at some epochs during the day. As a result,
these samples are removed for comparison.
The final epoch 3-D distance errors in 2018-2019 are
smaller than those in 2014-2015 due to less mass density
interaction with satellites in the solar minimum period.
For example, the average one-day OP errors over last ten
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