Engineering-Level Model Atmospheres For Titan and Mars C. G. Justus(1), Aleta Duvall



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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.
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 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.


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 TITAN-GRAM
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.
A single model input parameter (Fminmax) allows users of Titan-GRAM to select where within the min-max 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. 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-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%.

Fig. 3. Percentage density (daily averaged) difference, Mars-GRAM minus Radio Science observations.

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

Fig. 4. Percentage density (daily averaged) difference, Mars-GRAM minus Mars Climate Database, Ls = 0.



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.

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. 7. Percentage density (daily averaged) difference, Mars-GRAM minus Mars Climate Database, Ls = 270.

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-mean-square (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 Mars-GRAM.

Fig. 8. Comparison of Earth-observed root-mean-square (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 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. 10. Sample Monte Carlo simulations with Titan-GRAM for minimum, average, and maximum density profiles.



5. CONCLUSIONS
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, Mars-GRAM 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.

Fig. 11. Height versus latitude for simulated Mars Smart Lander (MSL) EDL profile.



Fig. 12. Height profile of Mars-GRAM simulated density perturbations along MSL EDL trajectory, with envelope of expected one-standard-deviation density perturbations.



6. ACKNOWLEDGMENTS
The authors gratefully acknowledge support from the NASA/Marshall Space Flight Center (MSFC) In-Space 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.
7. REFERENCES
1. Justus, C. G., et al. New Global Reference Atmospheric Model (GRAM-99) and Future Plans, C4.2-0003, COSPAR 33rd General Assembly, Warsaw, Poland, 16-23 July, 2000.
2. Justus, C.G. and Johnson, D.L., Mars Global Reference Atmospheric Model 2001 Version (Mars-GRAM 2001) Users Guide, NASA/TM-2001-210961, April, 2001.
3. Justus, C.G., et al. Mars-GRAM 2000: A Mars Atmospheric Model for Engineering Applications, Advances in Space Research, Vol. 29, 193-202, 2002.
4. Haberle, R.M., et al. Mars atmospheric dynamics as simulated by the NASA Ames general circulation model 1. The Zonal-Mean Circulation, Journal of Geophysical Research, Vol. 98(E2), 3093-3123, 1993.
5. Bougher, S.W., et al. The Mars thermosphere: 2. general circulation with coupled dynamics and composition, Journal of Geophysical Research, Vol. 95(B9), 14,811-14,827, 1990.
6. Smith, D.E. and Zuber, M.T., The relationship between MOLA northern hemisphere topography and the 6.1-mbar atmospheric pressure surface of Mars, Geophysical Research Letters, Vol. 25, 4397-4400, 1998.

7. Justus, C.G., Duvall, A.L., and Johnson, D.L., Engineering-Level Model Atmospheres for Titan and Neptune, AIAA-2003-4803, 39th AIAA/ASME/ SAE/ASEE Joint Propulsion Conference, Huntsville, Alabama, July 20-23, 2003.



    8. Yelle, R.V., et al. Engineering Models for Titan’s Atmosphere, in Huygens Science, Payload and Mission, ESA SP-1177, August, 1997.

    9. Justus, C.G., Duvall, A.L., and Johnson, D.L., Mars-GRAM validation with Mars Global Surveyor data, COSPAR 02-A-00128, 34th COSPAR Scientific Assembly, Houston, TX, October, 2002.

    10. Justus, C.G., Duvall, A.L. and Johnson, D.L., Global Summary MGS TES Data and Mars-GRAM Validation, COSPAR 02-A-02047, 34th COSPAR Scientific Assembly, Houston, TX, October, 2002.

    11. Justus, C.G., Duvall, A.L., and Johnson, D.L., Mars Global Reference Atmospheric Model (Mars-GRAM) and Database for Mission Design, International Workshop: Mars Atmosphere Modeling and Observations, Granada, Spain, January 13-15, 2003.

    12. Hinson, D.P., et al. Initial Results from Radio Occultation Measurements with Mars Global Surveyor, Journal of Geophysical Research, Vol. 104(E11), 26,997-7012, 1999.

    13. Smith, M.D., et al., One Martian Year of Atmospheric Observations by the Thermal Emission Spectrometer, Geophysical Research Letters, Vol. 28, 4263-6, 2001.





    14. Lewis, S. R., et al. A climate database for Mars, Journal of Geophysical Research, Vol. 104(E10), 24,177-194, 1999.

15. Forget, F., et al. Modeling of the General Circulation with the LMD-AOPP GCM: Update on Model Design and Comparison with Observations, Mars Atmosphere Modeling and Observations, Granada, Spain, January 13-15, 2003.




    16. Bingham, S.J., et al. The Mars Climate Database, Mars Atmosphere Modeling and Observations, Granada, Spain, January 13-15, 2003.



17. Keating, G.M., et al. The structure of the upper atmosphere of Mars: in situ accelerometer measurements from Mars Global Surveyor, Science, Vol. 279, 1672-6, 1998.


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