The comparisons are summarized. The quantities compared include Bayesian weighted least squares differential correction statistics and orbit solution consistency and accuracy

Cappellari, J. O., Jr.

Kuseski, R. A.

Lee, T.

Mallick, M. K.

Shanklin, R. E., Jr.

English

NASA Technical Reports Server

A COMPARATIVE STUDY OF THE HARRIS-PRIESTER,
JACCHIA-ROBERTS, AND MSIS ATMOSPHERIC DENSITY
MODELS IN THE CONTEXT OF SATELLITE ORBIT
DETERMINATION*
R. E. Shanklin, Jr., T. Lee, M. K. Mallick, R. A. Kuseski,
and J. O. Cappellari, Jr.
Computer Sciences Corporation
ABSTRACT
Extensive comparlsons of the Harris-Priester, Jacchia-
Roberts, and MSIS (Mass Spectrometer/Incoherent Scatter)
atmospheric density models as used in satellite orbit deter-
mination are summarized. The quantities compared include
Bayesian weighted least squares differential correction sta-
tistics and orbit solution consistency and accuracy.
*This work was supported by the Operations Analysis Section,
Operational Orbit Support Branch, Goddard Space Flight
Center, National Aeronautics and Space Administration,
under Contract NAS 5-24300.
i-i
https://ntrs.nasa.gov/search.jsp?R=19820002192 2020-03-21T11:58:29+00:00Z
SECTION i - INTRODUCTION
Atmospheric drag is a significant perturbation of Earth sat-
ellite orbits with perigee heights of less than i000 kilom-
eters. The acceleration of a spherical satellite due to
atmospheric drag is given by the equation
i
Adrag 2 m
where D = atmospheric density at the position of the satel-
lite
V = satellite velocity relative to the atmosphere
A = satellite reference cross-sectional area
C D = satellite drag coefficient
m = satellite mass
Therefore, calculation of the drag acceleration requires
knowledge of the atmospheric density as a function of posi-
tion and time.
This paper presents the results of a comparative study of
three different global atmospheric density models in the
context of orbit determination. The three models compared
are the Harris-Priester (H-P) model, the Jacchia-Roberts
(J-R) model, and the Mass Spectrometer!Incoherent Scatter
(MSIS) model.
The Harris-Priester model is based on theoretical tempera-
ture profile solutions of the heat conduction equation under
hydrostatic equilibrium conditions. The model assumes two
heat sources: solar extreme ultraviolet (EUV) heating and
an artificial heat source that produces the diurnal varia-
tion deduced from satellite drag calculations. In the mod-
ified Harrls-Priester model used for this study, the EUV
1-2
heating level is selected by choosing among i0 different
altitude-density profile tables representing i0 different
levels of solar flux, and the diurnal variation is modeled
by a correction calculated using a power of a cosine
(References 1 and 2).
The Jacchia-Roberts model is based on empirical temperature
profiles scaled by an upper boundary exospheric temperature
(T). Analytic density calculation is accomplished through
integration of thermodynamic equations. The modeling in-
cludes corrections for EUV heating, solar particle flux
(so-called geomagnetic) heating, semiannual variations, sea-
sonal variations, and the diurnal variation (References 2
and 3).
The MSIS model is based on fitting spherical surface har-
monic expansions to match the angular dependence exhibited
by mass spectrometer and incoherent scatter measurements.
The MSIS formulation includes sections that model EUV heat-
ing, solar particle flux heating, annual variations, semian-
nual variations, diurnal variations, semidiurnal variations,
terdiurnal variations, and departures from diffusive equi-
librium. MSIS modeling has been implemented in a special
GTDS load module. Dr. Hedin and his associates at the
Goddard Space Flight Center, who developed the model {Ref-
erence 4), contributed advice and some of their program sub-
routines during the GTDS implementation.
Table 1 shows sample density profiles for the three atmos-
pheric models with two different solar EUV levels and one
geomagnetic activity level. Figure 1 shows the Jacchia-
Roberts and MSIS densities, relative to the Harris-Priester
density, as a function of altitude. The figure shows max-
imum ratios as high as 2.0 but, as is apparent from the
table, the three profiles are quite similar in overall shape.
1-3
TABLE 1. ATMOSPHERIC DENSITIES COMPUTED USING HARRIS_°RIESTER,
JACCHIA-ROBERTS, AND MSlS MODELS
DENSITY (kg/km 3)
ALTITUDE HARRIS°PRIESTER JACCHIA-ROBERTS MSIS
(kin) F10.7 = 116.2 F10.7 = 140.0 F10.7 = 116.2 F10.7 = 140.0
F10.7 = 125.0 F10.7 = 150.0 --F10.7 = 135.1 F10.7 = 165.3 F10.7 = 135.1 F10.7 = 165.3
150 .205 E + 1 .206 E + 1 .193 E + 1 .210 E + 1 .203 E + 1 .204 E + 1
200 .224E 0 .255E 0 .228E 0 .270E 0 ;274E 0 .313E 0
250 .459 E - 1 .583 E -- 1 .559 E -- 1 .721 E - 1 .636 E -- 1 .802 E - 1
300 .129 E - 1 .178 E -- 1 .177 E -- 1 .249 E - 1 .187 E- 1 .255 E -- 1
350 A25 E -- 2 .631 E -- 2 .637 E - 2 .977 E - 2 .633 E -- 2 .926 E -- 2
400 .155 E -2 .247 E -- 2 .246 E -- 2 .4i3 E -- 2 .236 E -- 2 .368 E - 2
450 .521 E -- 3 .879 E -- 3 .835 E -- 3 .157 E -- 2 .780 E -- 3 .131 E - 2
500 .218 E -- 3 .392 E -- 3 .353 E -- 3 .724 E - 3 .324 E - 3 .582 E - 3
550 .963 E - 4 .182 E -- 3 .155 E - 3 .344 E- 3 .139 E 3 .266 E - 3
600 .451 E - 4 .851 E -- 4 .706 E - 4 .169 E - 3 .619 E --4 .125 E -- 3
650 .227 E - 4 .451 E -- 4 .339 E - 4 .851 E - 4 .285 E -- 4 .600 E -- 4
700 .112E-4 .217 E--4 .154E--4 .394E-4 .120E-4 .259E-4
750 .691 E - 5 .127 E --4 .878 E - 5 .219 E -4 .623 E -5 .134 E -4
800 .464 E - 5 .804 E --5 .548 E - 5 .128 E -4 .352 E -5 .728 E -5
850 .316 E -- 5 .462 E -- 5 .348 E - 5 .737 E - 5 .200 E - 5 .378 E - 5
900 .245 E 5 .301 E -- 5 .258 E -- 5 .500 E - 5 .137 E 5 .236 E - 5
950 .198 E-- 5 .201 E-- 5 .201 E - 5 .361 E - 5 .102 E - 5 .158 E - 5
1000 .163E 5 .141 E--5 .155E--5 .262E-5 .761E--6 .107 E-5
co
NOTES: 1. Kp = 3.3 FOR JACCHIA-ROBERTS DENSITY AND Ap = 33 FOR MSIS DENSITY ARE USED.
2. THESE PROFILES ARE FOR AUGUST 30, 1978, AT A LATITUDE OF 46 ° N, AN EAST LONGITUDE OF 205 °,
AND A LOCAL SOLAR TIME OF 1:40 P.M.
2.0 m
F10.7 _, 120
1.8-
1.6- • • • •
X _ X X X X •
"_ 1.4- X • X •
CL
"_ 1.2 X •
X
o_ •
; • J--RXr_ •
_. 1.0 X • =-
X
Z
,,, 0.8
a X
0.6 X
X X
0.4 MSlS X
0.2 I 1 I I /
200 400 600 800 1000
ALTITUDE (kilometer=)
2.0 •
F10.7 _- 145 • •
• J-R •
1.8 • • •
1.6 • •
X X X X X X
"_ 1.4-
_: x 1_
_ x
0 1.2 X •
- X
<
cc • X
>- 1.0I.-
XZ
LM
a 0.8 X
x x x
MSIS
0.6
0.4-
q_
O
0.2 I
200 4_0 6{_]0 L800 10_0 ==
ALTITUDE (kilometers)
FIGURE 1. ATMOSPHERIC MODEL DENSITY RATIOS
1-5
SECTION 2 - COMPARATIVE STUDY STRUCTURE
All the results presented in Section 3 of this paper are
based on Goddard Tra3ectory Determination System (GTDS)
Bayeslan weighted least squares differential correction so-
lutions. Nine different series of six GTDS Differential
Correction (DC) Program runs were made for each of the three
atmospheric models. Three different satellites, with per-
igee heights between 310 and 560 kilometers, were studied;
other orbital parameters for these satellites are given in
Table 2. The nine series of orbit determination arcs are
listed in Table 3.
Each series contains six 30-hour-arc solutions. The solu-
tions are used to generate 30-hour ephemerides that overlap
adjacent ephemerides by 6 hours. The ephemerides are then
compared in order to determine the maximum position differ-
ences (in the orbital reference frame) during the overlap
periods. The 162 DC Program solutions produce 135 maximum
overlap position differences. These differences are used to
evaluate the consistency and accuracy obtained when each of
the three atmospheric models isused.
Each differential correction solution is made up of seven
numbers: three position coordinates, three velocity coor-
dinates, and the drag variation parameter (pl), which is
a scaling factor in the drag acceleration equation, i.e.,
-_d - i CD --_-_rag 2 m A pll + 01) IVl V
This scaling factor is applied during generation of the
ephemeris that uses the differential correction solution.
1-6
TABLE 2. SATELLITE ORBITAL ELEMENTS
PERIGEE APOGEE INCLINAT)ONSATELLITE DATE HEIGHT HEIGHT
• (kilometers) (kilometers) (degrees)
AE-3 AUGUST1,1978 _1 341
MAGSATOCTOBER,1,•1979352 581 97
MARCH1,19_0 _2_ 471 97
SAGE FEBRUARY 19, 1979 560 655 " 55
o3
TABLE 3. COMPARATIVE STUDY SERIES
SERIES
NUMBER SATELLITE TIMESPAN
1 AUGUST 1-6, 1978
2 AE-3 AUGUST 14--19, 1978
3 SEPTEMBER2--8, 1978
4 OCTOBER31--NOVEMBER 5, 1979
5 DECEMBER1--6, 1979
6 MAGSAT JANUARY 1--6, 1980
7 FEBRUARY 1-6_ 1980
8 MARCH 1--6, 1980
9 SAGE FEBRUARY19--25, 1979
co
.].-7
Spacecraft attitude is not considered, since a spherical
model is employed. Furthermore, no aerodynamic forces
(e.g., lift) other than drag are modeled. The spherical
approximation is crude for all three satellites, and it is
possible that other aerodynamic forces are nonnegligible.
However, it is reasonable to expect that both assumptions
have a negligible effect on the results of this study,
because the results are obtained by applying each of the
three atmospheric models to the same arcs with the same ob-
servation sets. Simply stated, unmodeled aerodynamic forces
should perturb the solutions for all three atmospheric
models in a similar manner.
1-8
SECTION 3 - COMPARATIVE STUDY RESULTS
This section summarizes the results of this comparative
study of atmospheric density models In the context of
short-arc (30-hour) orbit determination. A detailed, run-
by-run presentation of these results is available in Ref-
erence 5. Two cautionary remarks are appropriate.
First, these results should not be interpreted as a compar-
ison of atmospheric models; conclusions about the relative
merits of the models must be limited to this highly spe-
cialized context--short-arc orbit determination in which an
average drag scaling factor is solved for.
Second, any series of orbit determination and ephemeris com-
parison runs may contain a few sporadic large overlap dif-
ferences and a few differential corrections with large RMS
residuals. Some of the runs included in this study show
such large differences and/or high RMSs.
The average weighted RMSs and the average maximum position
differences for the three AE-3 series are glven in Table 4.
The averages over all three series are also given, along
with the ranges of the EUV heating index (FI0.7) and the
solar particle flux index (Kp). The averages show that
the Jacchia-Roberts overlap differences are about 11.5 per-
cent (24 meters) smaller than the Harris-Priester averages
and that the MSIS averages are about 19 percent (38 meters)
larger than the Harris-Priester averages. The 62-meter dif-
ference between the Jacchia-Roberts and MSIS averages cannot
be considered either large or significant.
The same information is given for Magsat in Table 5. This
study includes five series of arcs. The Magsat results show
that both the Jacchia-Roberts and MSIS average differences
are about 9 percent larger than the Harris-Priester average
1-9
TABLE 4. COMPARATIVE ATMOSPHERIC DENSITY MODEL STUDY RESULTS
FOR AE-3 (AUGUST AND SEPTEMBER 1978)
HARRIS-PRI ESTER MODEL JACCHIA-ROBERTS MODEL MSIS MODEL
RANGE OF F10'7 RANGI_ OF MAXIMUM MAXIMUM MAXIMUMSERIES AVERAGE AVERAGE AVERAGE
I'_ (1 ) Kp POSITION POSITION POSITIONI 0 -22 watt/(m 2 -Hz) WEIGHTED WEIGHTED WEIGHTEDDIFFERENCE DIFFERENCE DIFFERENCEi._= RMS (meters) RMS (meters) RMS (meters)C)
AUGUST 1-6 106.0-117.6 0-6 4.9 191 5.2 175 8.4 265
AUGUST 14-19 115.6-134.9 0-6 7.3 225 7.8 217 8.5 324
SEPTEMBER 2-8 159.8-181.1 0-6 7.3 209 8.4 163 7.2 164
AVERAGES - - 6.5 208 7.2 184 8.0 251
co
TABLE 5. COMPARATIVE ATMOSPHERIC DENSITY MODEL STUDY RESULTS FOR MAGSAT
(NOVEMBER AND DECEMBER 1979; JANUARY, FEBRUARY, AND MARCH 1980)
RANGE HARRIS PRIESTER RESULTS JACCHIA- ROBEHTS RESULTS MSIS RESULTS
OF F10.7 RANGE
PE HIO(_) VARIATION OF Kp MAXIMUM MAXIMUM MAXIMUM
(t0 " 22 watts m 2 Hz 1) VARIATION WEIGHTED POSITION WEIGHTED POSITION WEIGHTED POSITIONRMS DIFFERENCE RMS " DIFFERENCE RMS DIFFERENCE
(meters) (meters) (m_=urs)
t-'
I OCT. 31 NOV. 5, 1979 207.5-214.9 0.- 4 8.3 204 7.8 1 16 8.0 190
DEC. 1 -6, 1979 152.2- 223.4 0 -4 12.4 204 11.5 175 12.8 25b
JAN. 1 6, 19_0 181:1.9 212.4 1--.5 9.4 213 9.5 166 11.3 28S
FEB. 1 - 6, 1980 212,6 _ 231.7 0-4 12.7 326 12.5 298 13.8 313
MAR. 1 E, 1980 170.2 -176.7 O. 3 9.8 .161 13.4 396 10.0 159
AVEHAGES " - 30.6 222 10.9 242 11.2 243
i I "=
differences. As zn the case of AE-3, the Magsat results
demonstrate that the three atmospheric density models are
comparable in the context of this study.
The average RMSs and overlap position differences for the
serzes of SAGE arcs are given in Table 6. Both the RMSs and
the overlap differences agree to within 3 percent; all three
atmospheric models produce essentially equivalent errors.
TABLE 6. COMPARATIVE ATMOSPHERIC DENSITY MODEL STUDY RESULTS
FOR SAGE (FEBRUARY 19-25, 1979)
AVERAGE
ATMOSPHERIC AVERAGE MAXIMUMDENSITY
MODEL WEIGHTED POSITION
USED RMS DIFFERENCE(meters}
HARR IS--PR I ESTER 10.9 108
JACCHIA--ROBERTS 11.2 ! 14
• g
MSIS 11.0 112
o0
NOTE: DURING THIS PERIOD, F10.7 VARIED FROM196.0 TO
237.7 X 10-22WATTS METER -2 HERTZ -1 AND Kp
VARIED FROM 1 TO 7.
1-12
SECTION 4 - CONCLUSION
The results presented in this paper support the conclusion
that, for satellites above 300 kilometers, the Harris-
Priester, Jacchia-Roberts, and MSIS atmospheric density
models all produce roughly similar density profiles and es-
sentially comparable orbit determination results when the
drag variation parameter is solved for and orbit quality is
measured by adjacent arc overlap comparisons. It is impos-
sible to predict which of the three models will produce the
best fit or best predictions for any given orbit determina-
tion arc. However, for some problem arcs, switching atmos-
pheric models may result in marked solution improvements.
1-13
REFERENCES
i. I. Harris and W. Priester, "Atmospheric Structure and
Its Variations in the Region From 120 to 800 Km," COSPAR
International Reference Atmosphere (CIRA) 1965, Space
Research IV, North Holland Publishing Co., Amsterdam
2. Goddard Space Flight Center, X-582-76-77, Mathematical
Theory of the Goddard Trajectory Determination System,
J. O. Cappellari, Jr., C. E. Velez, and A. J. Fuchs
(editors), April 1976
3. L. G. Jacchia, Revised Static Models of the Thermosphere
and Exosphere With Empirical Temperature Profiles,
Smithsonian Astrophysical Observatory Special Report
No. 332, Cambridge, Massachusetts, May 1971
4. A. E. Hedin et al., "A Global Tropospheric Model Based
on Mass Spectrometer and Incoherent Scatter Data:
MSIS i. N 2 Density and Temperature," Journal of
Geophysical Research, 1977, vol. 82, pp. 2139-2147
5. Computer Sciences Corporation, CSC/TM-81/6166, Com-
parative Study of Atmospheric Density Models int_
Context of Spacecraft Orbit Determination, R. Kuseski,
T. Lee, M. Mallick, and R. Shanklin, Jr., September 1981
1-14


A comparative study of the Harris-Priester, Jacchia-Roberts, and MSIS atmospheric density models in the context of satellite orbit determination

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