IEEE - Aerospace and Electronic Systems - February 2022 - 10

Comparison of Atmospheric Mass Density Models Using a New Data Source: COSMIC Satellite Ephemerides
The acceleration due to SRP is formulated as [27]
asrp ¼ gCr
SfAs
m
1AU2
Rs
ðr rsÞ
(7)
where g is the conical shadow function, with g ¼ 1 indicating
no eclipse, g ¼ 0 indicating no sunlight and 0 <
g < 1 indicating partial shadow. Cr
is the SRP coefficient.
Sf is the solar flux constant; As is the projected area
for SRP calculation; AU is the astronomical unit; rs and r
are position vector of the sun and satellite, respectively,
and Rs is the satellite-sun distance. The projected area As
lies in a plane orthogonal to the vector ðr rsÞ and is calculated
by assuming that solar panels are always facing
the sun and the main body of the satellite is subject to
line-of-sight changes of the sun
As ¼ Amain
vðrrsÞ
jvjjrrsj
þApanel:
(8)
Precise calculation of the atmospheric drag for
orbital perturbation analysis is still challenging due to
the uncertainties of the variables in (3), i.e., the drag
coefficient Cd and AMD r. The uncertainty of the Cd,
as well as for the SRP coefficient Cr, is quantified
using the Monte Carlo simulation in this work. Their
mean and standard deviation (STD) values, e.g., 2.12/
0.29 for Cd and 1.23/0.30 for Cr, can be obtained from
the precise orbit determination process [25]. Specifically,
Cr and Cd vary with a window of 1:5h.Therefore,
a set of 16 values are generated to cover a whole
day; and 200 sets of samples are used for each day.
Four AMD models, the proposed model and the nodrag
model will be assessed for their uncertainty analyses
by conducting OP.
AMD MODELS
The empirical AMD models represent the average climatology
of the Earth's atmosphere with parameterized functions
such as spherical harmonics and polynomials. He
et al. [13] investigated that the empirical models have a
low horizontal scale of several thousands of kilometers (or
30 to 45) at the altitudes from 250 to 800 km.
The most representative empirical models are the
MSIS series [14], [33], [34], the DTM series [7], and JB
series models [6], [35]. These empirical models are widely
used in various space missions due to their computational
efficiency.
MSISE00
The MSIS series models were first released in 1983 [33].
The MSISE90 is the first MSIS series model which covers
the lower atmosphere down to the Earth's surface [36]. As
10
a follow-on model, MSISE00 represents the atmosphere
from the ground to the altitude of 2500 km [14]. In
MSISE90 and MSISE00, spherical harmonic functions are
used for the modeling of atmospheric components at a reference
height, i.e., N2, O2, Ar, He, O, H, and N. One particular
update of MSISE00 is the modeling of " anomalous
oxygen " (ionized oxygen and hot atomic oxygen), which
potentially contributes to the atmospheric drag in the
upper thermosphere [14]. However, the anomalous oxygen
does not present a significant impact on the OP at 400
km [13].
The source code of MSISE00 is available at https://
ccmc.gsfc.nasa.gov/modelweb/atmos/nrlmsise00.html.
JACCHIA-BOWMAN 2008
The JB2008 model was updated from the previous JB2006
model [35]. Many new space weather indices were
adopted in 2008 for the modeling of thermosphric heating
due to UV radiation and geomagnetic storm. In addition to
F10:7, i.e., solar flux at the wavelength of 10.7 cm, three
new solar parameters are used in JB2008, i.e., S10:7,
M10:7, and Y10, which are, respectively, the extreme ultraviolet
(EUV) index (26 nm to 34 nm), Mg II index (280
nm), and a weighted index from both the Lyman-a and Xray
indices (see Table 2). Another new geomagnetic index
is Dst accounting for the geomagnetic storm effect on the
exospheric temperature [6]. More description of these
indices can be found in the review of [13].
This model and required indices are available at http://
sol.spacenvironment.net/jb2008/index.html.
DRAG TEMPERATURE MODEL 2013
The DTM2013 model is the latest DTM series model
developed in the framework the Advanced Thermosphere
Modelling for Orbit Prediction project [7]. DTM2013
and MSISE00 use similar spherical harmonics formulations
but with different space weather indices. F30
(30 nm) and Km (based on the am index) are used as
solar and geomagnetic drivers for higher fidelity. Note
that the F30 index used by DTM2013 is scaled to the
range of F10:7 so that both of these two indices can be
used to drive the model.
Due to the ingestion of four-year drag-derived AMD
data set from GOCE satellite at the height of250 km,
DTM2013 becomes the most accurate model in the altitude
range of 275 km to 170 km. DTM2013 is the least
biased and most accurate model on all time scales [37].
DTM2013 and its required space weather indices are
no longer updated. An online run of DTM2013 can be
requested at https://ccmc.gsfc.nasa.gov/requests/IT/DTM/
dtm_first.php.
IEEE A&E SYSTEMS MAGAZINE
FEBRUARY 2022

https://ccmc.gsfc.nasa.gov/modelweb/atmos/nrlmsise00.html https://ccmc.gsfc.nasa.gov/modelweb/atmos/nrlmsise00.html http://sol.spacenvironment.net/jb2008/index.html http://sol.spacenvironment.net/jb2008/index.html https://ccmc.gsfc.nasa.gov/requests/IT/DTM/dtm_first.php https://ccmc.gsfc.nasa.gov/requests/IT/DTM/dtm_first.php

IEEE - Aerospace and Electronic Systems - February 2022

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