A 

Semi-Annual Status ReDOrt 

IMPROVEMENTS IN THE GLOBAL REFERENCE ATMOSPHERIC 

MODEL AND COMPARISONS WITH A GLOBAL 3-D NUMERICAL MODEL 

C. G. Justus, Principal Investigator 

School of Geophysical Sciences 

Atlanta, Georgia 30332-0340 

F. N. Alyea, D. M. Cunnold and George Chimonas, Co-Investigators 

April, 1989 

Report Period: September 23, 1988 - March 22, 1989 

Prepared for the 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

MARSHALL SPACE FLIGHT CENTER 

Under Grant No. NAG8-078 

Georgia Tech Project G-35-685 

(NASA-CR-184947) IHPBOVEHENTS IN THE GLOBAL N89-247 55 

REFERENCE ATHOSPHEBIC HODEL AND COllPA EISONS 

WITH B GLOBAL 3-D NUHERICAL HODEL Semiannual 

Status Report, 23 Sep, 1988 - 22 Xar, 1989 Unclas 

(Georgia Xnst, of Tech.) 19 p CSCL OUA G3/46 0201507 
lSTATUS OF THE GLOBAL REFERENCE ATMOSPHERIC MODEL (GRAM) 

All of the data from a variety of sources has been analyzed and new 

"SCIDAT" data file listings for the revised zonal mean values, stationary 

perturbation values, and random perturbation values have been sent to Marshall 

Space Flight Center for review and comment. Barring any recommended changes, 

these data will become the new "SCIDAT" data (along with previous, unchanged 

values for the NMC grid point locations, the annual fractional variances in 

the large scale perturbations, the velocity-density correlation values, and 

the quasi-biennial parameter values). 

During the coming period the programming modifications to GRAM will be 

implemented and tested. These changes, along with the revised "SCIDAT" data 

will become the new, revised GRAM-90 model. The programming changes required 

are mostly to accommodate the new, higher resolution, stationary perturbation 

values, and the new zonal mean and stationary perturbations for mean wind 

components (to replace the spherical harmonic wind model in the middle 

atmosphere altitude range). 

Following the program modifications, height-latitude cross-sectional 

contour plots will be generated, to compare with comparable cross-sections 

evaluated from the stratospheric global circulation model of Drs. Alyea and 

Cunnold. The equivalent contours from the current GRAM (GRAM-88), have 

previously been evaluated and will be compared to demonstrate changes and 

improvements between the GRAM-88 and GRAM-90 model versions. 

STATUS OF THE MARS GLOBAL REFERENCE ATMOSPHERIC MODEL (MARS-GRAM) 

Following a long history of development and improvement of the Global 

Reference Atmospheric Model (GRAM) for the atmosphere of Earth (Justus, et 

al., 1975, 1976; Justus and Roper 1987; Justus, 1988), NASA, under grant 

monitorship by Marshall Spaceflight Center, has commissioned Georgia Tech to 

develop a similar model, the Mars Global Reference Atmosphere Model (MARSGRAM) for the atmosphere of that planet. MARS-GRAM, is based on 

parameterizations to approximate, as realistically as possible, the 

temperature, pressure, density and winds of the Martian atmosphere, and their 

latitudinal, longitudinal, diurnal, seasonal and altitude variation, from the 

surface through thermospheric altitudes. Pararneterizations are also included 

for the effects of global-scale dust storms on the variations of the 

thermodynamic and wind properties of the Martian atmosphere, Recently, David 

Kaplan, compiler of the definitive report "Environment of Mars, 1988" (Kaplan, 

1988), has decided to propose MARS-GRAM as the reference model atmosphere for 

use by engineers on upcoming equipment design contracts for NASA's Mars Rover 

and Sample Return Mission (Kaplan, private communication). 

The near-surface air temperature on Mars is parameterized in the MARSGRAM program by computing an approximate value for the geographically and 

seasonally-dependent daily total absorbed radiation flux. The daily average, 

maximum and minimum near-surface air temperatures are then calculated from a 

simple regression relationship assumed between the daily absorbed flux and the 

temperature parameters. The absorbed flux estimates include the variations in 

insolation due to the orbital position of Mars, the latitudinal variation of 

surface albedo (Pollack, et al. 198l), and seasonally-dependent 

parameterizations for the polar caps (Martin and James, 1986a, 1986b; Iwasaki, 

1986; Paige and Ingersoll, 1985; Philip, 1986) and polar hood clouds (James et 

al., 1987). The resultant seasonally and latitudinally dependent daily 

1 
average, maximum and minimum temperatures from the MARS-GRAM model are shown 

in Figures 1-3. These agree well with the surface temperature maps of Kieffer 

et al. (1977), with more realistic variations in the polar regions, as 

suggested by the observations of Kieffer (1979). Seasonal variations of the 

daily maximum, minimum and average temperature at the latitudes of the Viking 

1 and Viking 2 landers, as evaluated by MARS-GRAM, are shown in Figures 4a and 

5a. These plots agree nicely with the Viking 1 and Viking 2 observational 

data reported by Ryan and Henry (1979), shown for comparison in Figures 4b and 

5b. 

MARS-GRAM parameterizations for the geographical, seasonal and altitude 

dependence of non-dust storm, daily average temperatures above the surface 

come from a combination of observational and model values. The observational 

data include: Mariner 9 IRIS data from Conrath (1981), and Conrath data as 

reported by Leovy (1982) and Magalhaes (1987), Viking IRTM data (Martin et 

al., 1982), Mariner 9 radio occultation data from Kliore (1973), and Viking 1 

radio occultation data (Fjeldbo et al., 1977), Linda1 et al. (1979), and Davis 

et al. (1979). Model output used include results from Pollack et al. (1981), 

Haberle et al. (1982), and Pitts et al. (1988). An example of the altitude 

dependence of the non-dust storm daily average temperatures from MARS-GRAM is 

shown in Figure 6, for Northern Hemisphere winter solstice (areocentric 

longitude of sun, Ls - 270"). 

The parameterizations in MARS-GRAM for temperature variations during dust 

storm conditions were taken from observational data of Kliore et al. (1972), 

Jakosky and Martin (1987), Martin et al. (1982), Hanel et al. (1972), and 

Cornrath (1975). Model values for dust storm effects were taken from Haberle 

et al. (1982) and Pitts et al. (1988). An example of a MARS-GRAM dust-storm 

temperature cross section (at Ls - 270") is shown in Figure 7. 

Data for the MARS-GRAM parameterizations of the height variation of the 

diurnal (longitudinal) variations of temperature about the daily mean value 

were taken from Viking IRTM observations of Martin et al. (1982), Mariner 9 IR 

spectroscopy data of Hanel et al. (1972), and model results from Zurek, as 

reported in Pitts et al. (1988). Diurnal temperature variations (not shown 

here) are significantly larger during dust storm periods than during non-dust 

storm conditions. 

The new parameterizations for MARS-GRAM provide a simulation capability 

to altitudes reaching the base of the thermosphere. For simulations of the 

seasonal, geographical and solar-activity dependence of thermospheric 

conditions, the MARS-GRAM uses an adaption of the thermospheric model of 

Stewart (Culp and Stewart, 1983, 1984; Stewart and Hanson, 1982; Stewart, 

1987; see also the revised Stewart program code given in Pitts et al., 1988). 

The MARS-GRAM has numerous applications as a "poor man's global 

circulation model". For example, the computation of all of the data necessary 

to describe the complete seasonal variations at the surface (Figures 1-3) and 

all altitudes (e.g. Figure 8), takes at most a few minutes on an IBM-PC (with 

8087 co-processor; even faster on an IBM-AT or a 80386-based PC). Comparable 

data would take many hours of computation on a mainframe using a 3-D global 

circulation model for Mars. The diurnal (longitudinal) variability 

incorporated into the MARS-GRAM program is not even available in a 2-D version 

of a Mars global circulation model. 

In addition to the engineering applications envisioned for MARS-GRAM 

(e.g. aerocapture mission profile studies, Mars Rover Sample return mission 

planning and design), the MARS-GRAM has a number of potential scientific 

applications. One of these is its ability to provide a realistic, 

2 
geographically and seasonally-dependent background of temperatures and winds 

for studies of tides and the atmospheric propagation of other wave 

disturbances (e.g. gravity waves, mountain lee waves, etc.). Another 

application would be in providing realistic "first guess" profiles for the 

inversion processing for temperature retrievals from temperature sounders on 

upcoming Mars missions. 

Of course, being a parameterization model, rather than a first principles 

one such a global circulation model, MARS-GRAM is only as good as the 

parameterizations built into it. Also it cannot test the sensitivity to 

variation of parameters beyond those on which the parameterizations are based 

(e.g. it cannot estimate the effects of a dust storm of twice the optical 

depth previously observed). With continued analysis of additional 

observational data from the Viking and Mariner programs, analysis of new 

results from global circulation models, and with new data expected to be 

coming in from the Mars Observer program, MARS-GRAM should steadily improve in 

its realism and reliability in the future. 

WAVES IN THE MARTIAN ATMOSPHERE 

Wave-like perturbations have been observed in the Viking 1 and Viking 2 

surface pressure data (Leovy, 1981), in the Mariner 9 IR spectroscopy data 

(Pirraglia and Cornrath, 1974; Cornrath, 1976, 1981), and in the Viking 1 and 

Viking 2 lander entry profiles (Seiff and Kirk, 1976, 1977). Most of the 

wave-like perturbations have been interpreted as atmospheric tides (Pirraglia 

and Cornrath, 1974; Cornrath, 1976; Seiff, 1982), or as planetary waves 

(Cornrath, 1981; Barnes and Hollingsworth, 1988). The theory of thermal tides 

in the Martian atmosphere has been well explored (Zurek, 1976, 1986; Zurek and 

Haberle, 1988). Compared to the detailed tidal analyses, relatively little 

attention has been paid to other forms of wave perturbations, such as gravity 

waves (Gadian and Green, 1983), Kelvin waves and normal modes (Zurek, 1988; 

Hamilton et al., 1986; Tilman, 1988), and lee waves (Pickersgill and Hunt, 

1979). The very strong influence of topography on the wave structure in the 

Martian atmosphere has been documented both by observational data (Cornrath, 

1976) and by theoretical analysis (Zurek, 1976). 

One of the best-known properties of gravity waves is that their 

amplitudes increase with height as the inverse square root of the mean 

atmospheric density. In this way, the kinetic energy of the wave is 

maintained even as the packet propagates upward into the rarer regions. The 

effect has been likened to the wave-kink that grows as it travels along a whip 

from the thick end near the handle to the thin region near the tip. The 

comparison is even more apt than first appears, for just as the wave traveling 

up the whip reaches an unsustainable amplitude and "cracks", the gravity wave 

may reach heights at which it becomes too large for smooth fluid behavior and 

it turns over into shocks and/or turbulence. 

One of the common sources of gravity waves is wind flow over mountains. 

As the atmospheric flow reaches the mountain, surface pressures deflect it up 

and over the mountain rise, and then restore it to level on the other side. 

However, the disturbance transmitted to the air flow is not confined to some 

surface region, as the pressure fields associated with the deflection have 

space and time scales that match the characteristics of gravity waves in the 

free atmosphere. Distorting any elastic medium in a way that matches its 

natural modes causes the excitation of waves that broadcast energy from the 

disturbance to the far reaches of the medium. So, around mountainous regions 

3 
the atmosphere normally contains a wealth of wave activity. Mountain waves, 

especially the resonant forms known as lee waves, are a familiar phenomenon of 

the Earth's atmosphere, and are expected to be of even more importance in the 

Martian atmosphere. 

Because erosion is much weaker in the rainless Martian environment, and 

because surface gravity is lower, surface features on Mars tend to be more 

severe than on Earth. Ridges and mountains are higher, while surface winds 

are comparable (and, at times, higher), so the Martian mountain waves provide 

stronger aerodynamic disturbances than are encountered on Earth. 

The waves of most interest for aerobraking or lander vehicles are readily 

modeled by the long-wave approximation. This component of the disturbance 

maps up through the atmosphere as a replica of the underlying terrain, and, in 

common with all gravity waves, the associated fractional density disturbances 

grow ever greater with altitude. Effectively the probing spacecraft will be 

"flying into the mountains", even when it is several tens of kilometers above 

the peaks. Limits may be imposed by wave saturation, absorption by critical 

layers, or by dissipation of the waves by molecular viscosity, but over the 

larger terrain features the tops of these ghost mountains may occur as shocks 

or wedges of turbulence. 

In the long-wave approximation, we assume that the wavenumber k satisfies 

the inequality 

where N is the Brunt-Vaisala frequency, and U is the mean wind speed. Under 

this assumption the governing differential equation for wave perturbations is 

d2y/dz2 + [N2/U2 - (d2U/dz2)/U - 1/4H2]y(z) - 0 , (2) 

where H is the atmospheric scale height. 

vertical velocity perturbations is, for example, given by 

The Fourier transform, Q(z), for the 

J (3) 

where p is 

and y(zp is 

the mean density, A(k) is presently an unknown Fourier amplitude, 

the solution obtained from equation (2). 

The assumption of purely tangential flow for the surface boundary 

condition determines the wave amplitude in terms of the slope dh/dx of the 

surface terrain and the mean wind qeed U(0) that must be deflected over the 

terrain undulation. The Fourier trmsform of this surface condition defines 

the component amplitudes A(k) of equation (3) through the Fourier components 

of the surface terrain shape, h(x). 

From this approach, the Fourier trznsform of the density variations can 

be obtained. Since there is no k dependtnce for the coefficients relating the 

Fourier transform of the density to the Fourier transform of the terrain 

surface, the Fourier inversion to obtain the vertical profile of density 

perturbations is straightforward, and yields 

4 
The implications of equation (4) are clear: 

(a) The horizontal structure of the density disturbance pw is an image of the 

terrain shape h(x). 

(b) There is the standard vertical growth factor associated with gravity 

waves, proportional to the inverse square root of the mean density. 

(c) There is a vertical wave structure y(z)/y(O), which will usually be 

closely sinusoidal. 

(d) There is an excitation factor [U(O)N /U(z)g] relating surface conditions 

to the generated wave density field. 

2 

These results apply equally to an isolated surface feature, such as a 

mountain sitting alone in the plains region, or an extended complex area of 

severe terrain. If the surface shape is known, and one differential equation 

involving the meteorological functions U(z) and N(z) is solved, the density 

perturbation, pw(x,z), at any location above the surface is obtained. 

Although derived here for the two-dimensional case, the results of equation 

(4) can easily be generalized to a fully three-dimensional terrain 

description. 

It is proposed that a study of mountain waves in the Martian atmosphere 

be carried out, with the MARS-GRAM model providing the information on 

background profiles of U(z) and N(z). For these studies, terrain elevations 

relative to the reference ellipsoid of Cain et al. (1973), will be used (as 

revised from Viking measurements). As the wave amplitudes grow sufficiently 

large, wave "saturation" effects or wave breaking can occur. Although the 

linear theory considered here does not allow exact solutions under such 

circumstances, the theory, in conjunction with the MARS-GRAM profiles of U(z) 

and N(z), will allow the determination of the altitudes at which such 

saturation and breaking processes are likely to occur, and what magnitude of 

energy deposition is likely to be associated with these phenomena. 

If non-linear processes do not limit the growth of the wave, the high 

kinematic molecular viscosity of the upper atmosphere will. Because of lower 

density, the molecular viscosity effect will be felt at lower altitudes on 

Mars than on Earth. The treatment of Pitteway and Hines (1963), can be used 

to model this effect. 

MARS-GRAM PLANS FOR THE COMING PERIOD 

During the coming period, a version of the MARS-GRAM program, suitable 

for engineering use will be completed. It will include the temperature 

variations discussed here. Latitudinal and seasonal variations in surface 

pressure (including parameterized dust-storm perturbations, when desired) will 

be included. Surface pressure and temperature profile information will be 

5 
used in hydrostatic and perfect gas law relationships to construct profiles of 

pressure and density up to thermospheric altitudes, where the profiles will be 

smoothly merged into the latest version of the Stewart thermospheric model. 

Winds in the MARS-GRAM model will be evaluated with a thermal wind 

(areostrophic wind) approximation, with a modification to account for large 

values of kinematic molecular viscosity (as in the current MARS-GRAM). A 

simple version of the wave perturbation model of Dr. Chimonas, discussed 

above, will be implemented as a replacement model for the density perturbation 

magnitudes in the MARS-GRAM, at least up to thermospheric altitudes. 

6 
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Atmosphere. Icarus, 48: 246-255 

Culp, Robert D., A.I. Stewart, Chia-chuan Chow (1983). Time Dependent Model of 

the Martian Atmosphere for use in Orbit Lifetime and Sustenance Studies. JPL 

Contract #956446: Univ. of Colorado, 31 pp. 

Culp, Robert D., and A. Ian Stewart (1984). Time-Dependent Model of the 

Martian Atmosphere for Use in Orbit Lifetime and Sustenance Studies. J. 

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Davies, D. W. (1979). The Relative Humidity of Mars' Atmosphere. J. GeoDhvs. 

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Fjeldbo, Gunnar, Donald Sweetnam, Joseph Brenkle, Edward Christensen, David 

Farless, et a1 (1977). Viking Radio Occultation Measurements of the Martian 

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7 
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8 
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9 
Stewart, A.I., and W.B. Hanson (1982). Mars’ Upper Atmosphere: Mean and 

Variations. Adv. SDace Res,, 2: 87-101 

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Synchronized, Transient Normal-Mode Oscillations and the Triggering of Global 

Dust Storms. J. GeoDhvs. Res., 93(D8): 9433-9451 

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Sci., 33: 321-337 

Zurek, Richard W. (1986). Atmospheric Tidal Forcing of the Zonal-Mean 

Circulation: The Martian Dusty Atmosphere. J. Atmos. Sci., 43(7): 652-670 

Zurek, Richard W. (1988). Free and Forced Modes in the Martian Atmosphere. ?L, 

GeoDhvs. Res., 93(D8): 9452-9462 

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Atmospheric Tidal Forcing in the Dusty Martian Atmosphere. J. Atmos. Sci., 

- 45(18): 2469-2479 

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