ENGINEERING-LEVEL MODEL ATMOSPHERES FOR TITAN AND MARS
C. G. Justus(1), Aleta Duvall(1), Vernon W. Keller(2)
(1)
Computer Sciences Corporation, P.O.Box 240005, Huntsville, AL 35824 (USA),
Jere.Justus@msfc.nasa.gov, Aleta.Duvall@msfc.nasa.gov
(2)
NASA Marshall Space Flight Center, ED44, Marshall Space Flight Center, AL 35812 (USA),
Vernon.W.Keller@nasa.gov
ABSTRACT
An engineering-level atmospheric model for Titan has
been developed for use in NASA’s systems analysis
studies of aerocapture and entry, descent and landing
(EDL) applications in potential missions to Titan.
Analogous to highly successful Global Reference
Atmospheric Models for Earth (GRAM) and Mars
(Mars-GRAM), the new model is called Titan-GRAM.
Like GRAM and Mars-GRAM, an important feature
of Titan-GRAM is its ability to simulate quasi-random
perturbations for Monte Carlo analyses in developing
guidance, navigation and control algorithms, and for
thermal systems design. Titan-GRAM capabilities
and sample results are presented. Capabilities of
Mars-GRAM especially related to EDL applications
are also presented and illustrated.
Fig. 1 compares density-height profiles for Earth,
Mars, Titan, and Neptune. Relatively low scale
heights (~10 km) make densities for Earth and Mars
drop rather rapidly with altitude. Significantly higher
scale height values for Titan and Neptune (~40 km)
make these atmospheres considerably “thicker”.
Titan’s large density scale height is due to its low
gravity (~0.14 times Earth gravity), while that for
Neptune is due to its low atmospheric mean molecular
weight (~2.6 versus ~29 for Earth). Vertical dotted
lines in Fig. 1 show density values and altitudes at
which aerocapture or aerobraking maneuvers would
occur on these planets.
1. INTRODUCTION
Similar to the Global Reference Atmospheric Model
(GRAM) for Earth [1], Mars Global Reference
Atmospheric Model (Mars-GRAM 2001) is an
engineering-level atmospheric model, widely used for
diverse mission applications [2, 3]. From 0-80 km
altitude, Mars-GRAM is based on NASA Ames Mars
General Circulation Model (MGCM) [4], while above
80 km it is based on Mars Thermospheric General
Circulation Model [5].
Mars-GRAM 2001 and
MGCM use surface topography from Mars Global
Surveyor Mars Orbiting Laser Altimeter (MOLA) [6].
Recently, engineering-level atmospheric models for
Titan and Neptune have been developed [7] for use in
NASA’s systems analysis studies of aerocapture
applications in missions to outer planets. These new
models are called Titan-GRAM and Neptune-GRAM
(Neptune-GRAM is not discussed here in detail).
Like GRAM and Mars-GRAM, an important feature
of Titan-GRAM is its ability to simulate quasi-random
perturbations for Monte Carlo analyses in developing
guidance, navigation, and control algorithms,
especially for entry, descent, and landing (EDL) and
precision landing.
Fig. 1. Typical density versus height above surface or
pressure reference (1 bar) for Earth, Mars, Titan, and
Neptune.
2.
BASIS FOR MARS-GRAM AND TITANGRAM
In Mars-GRAM, input values for date, time, latitude,
longitude etc. are used to calculate planetary position
and solar position, so that effects of latitude variation,
and seasonal and time-of-day variations can be
computed explicitly.
A simplified approach is
adopted in Titan-GRAM whereby these effects (as
well as effects of relatively large measurement
uncertainties for Titan) are represented within a
prescribed envelope of minimum-average-maximum
density versus altitude. Fig. 2 shows this envelope for
Titan, for which engineering atmospheric profiles of
Yelle et al. [8] are used.
GRAM/RS comparisons versus height and latitude.
Except for heights above ~30 km and latitudes above
~45 N, Mars-GRAM/RS density differences are
generally within about 6%.
A single model input parameter (Fminmax) allows
users of Titan-GRAM to select where within the minmax envelope a particular simulation will fall.
Fminmax = -1, 0, or 1 selects minimum, average, or
maximum conditions, respectively, with intermediate
values determined by interpolation (i.e. Fminmax
between 0 and 1 produces values between average and
maximum). Effects such as variation with latitude
along a given trajectory path can be computed by
representations of variation of Fminmax with latitude.
Fig. 3. Percentage density (daily averaged) difference,
Mars-GRAM minus Radio Science observations.
Fig. 2. Minimum, average, and maximum density
versus altitude for Titan-GRAM, from [8].
3. MARS-GRAM VALIDATION
Validation studies [9-11] have been conducted
comparing Mars-GRAM with Mars Global Surveyor
(MGS) Radio Science (RS) [12] and Thermal
Emission Spectrometer (TES) [13] data. RS data from
2480 profiles were used, covering latitudes 75 S to
72 N, from surface to ~40 km, for seasons ranging
over areocentric longitude of Sun (Ls) = 70-160 and
265-310. RS data spanned a range of local times,
mostly 0-9 hours and 18-24 hours. For interests in
aerocapture and precision landing, comparisons
concentrated on atmospheric density. TES data were
used covering surface to ~40 km, over more than a full
Mars year (February, 1999 – June, 2001, just before
start of a Mars global dust storm). Depending on
season, TES data covered latitudes 85 S to 85 N.
Most TES data were concentrated near local times 2
hours and 14 hours. Fig. 3 shows results of Mars-
Results of Mars-GRAM validation versus the
European Mars Climate Database (MCD) [14-16] are
shown in Fig. 4 through Fig. 7. The dotted box in
these figures denotes the approximate height-latitude
area of comparison with RS data in Fig. 3. Dust
optical depth in MCD was simulated using the
latitudinally- and seasonally-varying “MGS Scenario”
[15]. In Mars-GRAM, spatially uniform, seasonally
varying dust optical depth was used, ranging between
0.1 (at Ls = 90) and 0.5 (at Ls = 270). Although
Mars-GRAM-vs-MCD density comparisons are
generally good, large differences exist for Ls = 0, 90
and 270, above ~35 km altitude, and poleward of
~70N. These modeling uncertainties at high northern
latitudes could have significant impact on planning
Mars Phoenix mission EDL scenarios and systems.
Candidate Phoenix landing sites are between 65 N
and 75 N. Present RS and TES data do little to
resolve these MCD/Mars-GRAM discrepancies, since
most on the model differences are at higher altitudes
and latitudes than covered by the observations.
However, comparison of Fig. 3 with Fig. 4 and Fig. 5
indicates that at these high latitudes and altitudes,
Mars-GRAM tends to over-estimate the observations,
while MCD tends to underestimate them by a like or
larger amount.
Table 1 gives quantitative statistics for comparisons of
both Mars-GRAM and Mars Climate Database with
TES (over essentially the same height/latitude area as
for the RS comparison shown in Fig. 3). Average and
standard deviation of model-minus-observed density
difference (in percent) are given for local times 2 hr
and 14 hr. Average density differences in Table 1 are
indicative of model bias error, while standard
deviations indicate random error. Larger magnitude
values (between the two models) are shown in bold.
For the sixteen statistics given, Mars-GRAM had the
larger density difference from observed in five cases,
while Mars Climate Database had larger density
deviations from observed in 11 cases. However, all
values of average and standard deviation were
generally less than 10% in magnitude, indicating good
agreement of both models with TES observations (in
the latitude and height range for which TES data are
available).
Fig. 4. Percentage density (daily averaged) difference,
Mars-GRAM minus Mars Climate Database, Ls = 0.
Fig. 7. Percentage density (daily averaged) difference,
Mars-GRAM minus Mars Climate Database, Ls =
270.
Fig. 5. Percentage density (daily averaged) difference,
Mars-GRAM minus Mars Climate Database, Ls = 90.
Fig. 6. Percentage density (daily averaged) difference,
Mars-GRAM minus Mars Climate Database, Ls =
180.
Table 1. Comparison of Mars-GRAM (MG) versus
Thermal Emission Spectrometer (TES) observed
density and Mars Climate Database (MCD) vs. TES.
Avg (Hrx),% and Sig (Hrx),% are average and
standard deviation of model-minus-observed density
difference (in percent) at local time x = 2 hr or 14 hr.
Model
Ls,
deg
Avg,
Hr2,%
Sig,
Hr2,%
Avg,
Hr14,%
Sig,
Hr14,%
MG
0
-2.8
7.8
1.0
5.7
MG
90
-5.5
6.8
-4.2
5.6
MG
180
-6.5
7.0
-1.8
5.8
MG
270
2.7
9.9
6.0
8.9
MCD
0
1.8
8.3
4.6
7.6
MCD
90
-7.4
7.2
-1.7
7.6
MCD
180
2.2
8.5
3.4
8.7
MCD
270
3.4
9.1
10.4
7.3
Plans are underway to do additional Mars-GRAM
validation against TES limb sounding data, which
extends to higher altitudes than the nadir-view TES
data used here.
4. PERTURBATION MODELS AND SAMPLE
RESULTS
An important feature of the engineering-level
atmospheric models discussed here is their ability to
simulate quasi-random perturbations for Monte Carlo
analyses in developing guidance, navigation, and
control algorithms, for precision EDL and other
applications. Fig. 8 compares small-scale root-meansquare (rms) density perturbations observed for Earth
(GRAM climatology) [1] and modeled for Mars [2],
Titan, and Neptune [7]. Also shown is the range of
density variations observed during Mars aerobraking
operations [17]. Mars-GRAM perturbations, which
depend on surface terrain height, are also compared
with density perturbations from MCD in Fig. 9, which
shows that rate of increase of perturbation magnitude
with height is not as large for MCD as for MarsGRAM.
generate Monte Carlo perturbation profiles such as
those in Fig. 10 is a convenient way to estimate
various parameters of interest for precision EDL, such
as size of three-sigma landing ellipse, effectiveness of
various guidance algorithms, etc.
An example EDL application for Mars-GRAM in
planning for Mars Smart Lander (MSL) is provided in
Fig. 11 and Fig. 12. MSL trajectory positions for this
example were provided by Richard Powell of NASA
Langley Research Center (LaRC). Fig. 11 shows
MSL entry trajectory height versus longitude. The
simulated trajectory moves almost eastward, with very
little latitude change over the course of the EDL
maneuver.
Expected envelope of Mars-GRAM
density perturbations and one profile from a set of
simulated Monte Carlo density perturbations are
shown in Fig. 12.
Fig. 9. Comparison of density standard deviations
(percent of mean) for Mars-GRAM and Mars Climate
Database.
Fig. 8. Comparison of Earth-observed root-meansquare (rms) density perturbations (from GRAM
climatology) and model rms perturbation magnitudes
for Mars, Titan, and Neptune.
Fig. 10 shows samples of Monte Carlo simulations of
density variations with Titan-GRAM, for minimum
(Fminmax = -1), average (Fminmax = 0), and
maximum (Fminmax = +1) conditions. Although it
appears that the range of density variability is larger
for maximum conditions than for average conditions,
this is a plotting artifact due to the arithmetic of
percentages. For example, if a given perturbation is
25% larger than the mean of the Fminmax = 0 profile,
then the corresponding perturbation is also 25% larger
than the mean of the Fminmax = 1 profile. Ability to
Fig. 10. Sample Monte Carlo simulations with TitanGRAM for minimum, average, and maximum density
profiles.
5. CONCLUSIONS
6. ACKNOWLEDGMENTS
Mars-GRAM and Titan-GRAM are engineering-level
atmospheric models, suitable for a wide range of
mission design, systems analysis, and operations
tasks. For Mars or Titan lander missions, MarsGRAM and Titan-GRAM applications include
analysis for entry, descent and landing (EDL), and
guidance, navigation and control analysis for precision
landing.
Using
Mars-GRAM or Titan-GRAM
perturbation models in Monte Carlo mode make them
especially suited for design and testing of guidance,
navigation, and control algorithms.
The authors gratefully acknowledge support from the
NASA/Marshall Space Flight Center (MSFC) InSpace Propulsion Program and from the NASA Office
of Space Sciences Mars Data Analysis Program
(MDAP). Particular thanks go to Bonnie James
(MSFC), Manager of the Aerocapture Technology
Development Project, to Michelle M. Munk
(LaRC/MSFC), Lead Systems Engineer for
Aerocapture, and to Ann Trausch and Melody
Herrmann (MSFC), team leads and Mary Kae
Lockwood (LaRC), technical lead for the
Titan/Neptune Systems Analysis study. Mars-GRAM
user feedback and suggestions from the following are
also greatly appreciated: Dick Powell, Brett Starr, and
David Way (NASA LaRC), and Claude Graves and
Jim Masciarelli (NASA JSC). Mars Climate Database
Version 3.1 was provided on CD-ROM by Dr.
Francois Forget of the Laboratoire de Météorologie
Dynamique, Paris. Thermal Emission Spectrometer
data were provided on CD-ROM by Dr. John Pearl
and Ever Guandique at NASA Goddard Space Flight
Center.
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Fig. 11. Height versus latitude for simulated Mars
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