Atmosphere models

Clearly the design of heatshields and parachute systems requires assumptions on the density structure of the atmosphere to be encountered. Thus atmospheric models must be constructed as a design basis - these models must provide the extreme range of conditions likely to be encountered, since extremes in any direction may drive the design.

Where in situ data from prior missions is available (e.g. at Mars and Venus) this of course adds considerable confidence to the model. More generally, as for the first missions to Mars, Titan, Jupiter, etc., the major source of guidance is an atmospheric refractivity profile derived from radio-occultations by prior flyby or orbiter missions. The refractivity may be converted into a mass-density profile with some assumptions on composition. However, the altitudes probed by radio occultations are generally lower than those at which peak aerodynamic heating and deceleration occur, so some assumptions must be made in propagating those measurements upward. Some of these assumptions are rather robust, such as hydrostatic equilibrium, while others are less so.

There is in model development an inherent tension, just as in the development of a mission as a whole. The engineer designing the heat shield will just want a definitive answer to the question 'what is the density at 500 km?' (or whatever), while the scientist developing a model will wish to acknowledge the widest range of uncertainty - there may be intrinsic measurement errors in a refractivity profile, there are uncertainties in the assumed composition or other factors, there may be diurnal and seasonal variations, and variations with solar activity. Thus the range between 'minimum' and 'maximum' atmospheres may be rather large, which is problematic for engineering design. Furthermore, this range alone offers little insight into the probability of the extremes or the values between them.

These uncertainties can be accommodated better with improved models, wherein the deterministic variability (e.g. the seasonal variation of pressure on Mars) are modelled explicitly, whereas stochastic variations such as 'weather' and measurement errors are modelled statistically. These models, such as the Titan-GRAM model or the Mars Climate Database, can be used in Monte-Carlo studies to determine engineering parameters such as the 3-c loads. The 3-c is a typical design criterion, with the expectation that the chances of exceeding such loads is less than 0.5%, a modest risk compared with the probability of other failures such as launch failure. The association of 'sigma' (i.e. a standard deviation) with a certain probability assumes, strictly speaking, Gaussian statistics, which are not always appropriate; for example, windspeeds have a much more skewed distribution, with a long high-end tail. The 'sigma' terminology is widespread, however.

These statistical models may provide more comfort than they should, in that real data is rarely available to give meaningful confidence in the statistical parameterizations used, but inasmuch as available information is folded into the estimates, unnecessary margins can be reduced. It is sobering that even with two spacecraft in orbit around Mars to provide fresh information, day-to-day variations in dust opacity and thus the temperature and density structure in the atmosphere exceeded 'worst-case' model predictions, and were nearly enough to cause failure in the Mars Exploration Rover entry and descent (and may have caused the loss of Beagle 2). The prudent designer will therefore apply as much margin as he or she can.

For Mars, the atmosphere is subject to dramatic seasonal changes (the surface pressure dropping by 30%, for example) and there are more data available. Accordingly models are more sophisticated, being based on output from numerical models as in the Martian Climate Database developed under ESA sponsorship by Laboratoire de Meteorologie Dynamique in Paris and Oxford University, or being derived from statistical descriptions of the variations in a more empirical way, as in the Mars Global Reference Atmospheric Model (MARS-GRAM) developed at NASA Marshall Research Center: Justus, C.G. and Johnson, D.L., Mars global reference atmospheric model 2001 version (Mars-GRAM 2001) User's Guide NASA/TM-210961.

For Venus and Titan at present only limited engineering models are published from the handful of measurements available. One may expect this situation to change for at least the latter two as more data arrive, and statistical models (e.g. Titan-GRAM) are under development. Papers describing the limited knowledge of the wind fields can usually be found adjacent to relevant publications in the temperature/density papers.

A.J. Kliore et al. (1985) Venus international reference atmosphere Advances in Space Research, 5, 1-305.

R. V. Yelle, D. F. Strobell, E. Lellouch and D. Gautier (1997) Engineering models for Titan's atmosphere ESA SP-1177, 243-256.

For Jupiter, in-situ measurements are available from Galileo:

A. Seiff et al. (1998) Thermal structure of Jupiter's atmosphere near the edge of a 5-mm hot spot in the north equatorial belt. Journal of Geophysical Research, 103, 22857-22890.

For the other outer planets and Triton, no in-situ measurements are available, and in the absence of an imminent mission, no engineering models have been developed. A literature search (e.g. for results from the Voyager radio-occultation experiment will yield the relevant information.

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