Comparative analysis of the atmospheres of early Earth and early Mars

Adv. Space Res. Vol. 9. No. 6. pp. (6)139—(6)142, 1989 Printed in Great Britain. All rights reserved.

0273—1177/89 $0.00 + .50 Copyright © 1989 COSPAR

COMPARATIVE ANALYSIS OF THE ATMOSPHERES OF EARLY EARTH AND EARLY MARS R. Durham,* R. B. Schmunk** and J. W. Chamberlain** *

Department of Physics, United States Air Force Academy, Colorado

Springs, CO 80840, U.S.A. *sDepartment of Space Physics and Astronomy, Rice University, Houston, TX 77251, U.S.A.

ABSTRACT A surface partial pressure of CO 2 of at least 1.3 bars is required in order to sustain liquid water on Mars. We assume that the primitive atmospheres of Mars and Earth were similar and that present differences are a result of their different distances from the Sun and their different masses. We then use a one-dimensional radiative—convective atmospheric model to determine if a 1.3 bar CO2 partial pressure on Mars is consistent with the climatic conditions thought to have existed on Earth four billion years ago. The Earth atmosphere was evidently then stable against a runaway greenhouse, so that huge amounts of liquid water could accumulate on the surface. We find that these terrestrial conditions are consistent with a high CO2 partial pressure on Mars, which produces liquid water at perihelion if not during the entire orbit. METHODOLOGY The radiative—convective model used in this study is a derivative of one described by Kasting et al. /1,2/ and by Kasting and Ackerman /3/. This one—dimensional model uses a broad band approach and detailed radiative transfer equation to determine the thermal structure of the atmosphere. The present model differs from that described by Kasting and Ackerman in several major respects. First, the solar energy deposition is calculated from a subroutine provided by T. P. Ackerman /~/, in which the solar spectrum is divided into 26 intervals in which Rayleigh scattering and absorption by CO2 and H20 are calculated in 2~l layers, each assumed to be homogeneous on optical properties. Second, our model does not yet include the updated absorption coefficients for CO2 and H20 employed by Kasting and Ackerman /3/. The necessary input parameters for either planet are the solar flux reaching its orbit and its gravitational acceleration, surface N2 partial pressure and CO2 volume mixing ratio. Regarding the solar flux and degassing of the terrestrial planets, we first assumed that Z4.O billion years before present, the solar luminosity was about 78% of its present value /5/. Second we accepted the conclusion of Pollack and Black /6/ that, during their first billion years, Earth and Mars had similar outgassing histories. Third, the surface albedo was fixed at 0.237 for all calculations. This value is higher than Earth’s present surface albedo because it partially accounts for the reflectivity of clouds, which we have otherwise not treated. Finally, we assume that both atmospheres were composed of N2, H20 and CO2 and that Earth had an initial surface N2 partial pressure of 1.0 bar. Since Mars and Earth were formed in the same manner at about the same time in the same region of the solar nebula, we assume that their primitive atmospheres were similar and that their present differences arise from their differing distances from the Sun and differing masses. To compare their early atmospheres, we scaled the surface pressure calculations to account for the smaller mass and surface area of Mars. For example, the mass of Mars is about one tenth that of Earth, so we assume that the amount of volatiles degassed was also about 10% that of Earth. However, the acceleration due to gravity and the surface area of Mars are smaller than those of Earth. To account for these effects, we relate the surface pressure on Mars (~m~ to that of Earth (Pe): —

(Mm/Me) (Ae/A.ji)

(g~/g~)~e’

(1)

where Mm and Me are the masses of Mars and Earth, respectively; A~and Ae are their surface areas; and gm and ~e are their gravitational accelerations. The scaled surface N2 partial pressure for Mars is then 0.1~4~1bars. (6)139

R. Durham er a!.

(6)140

Surface CO

2 partial pressure (bar)

Fig. 1.

Mean global surface temperature of early Mars for perihelion and for mean solar distance.

The variations in insolation caused by periodic fluctuations in the eccentricity of the Martian orbit were also considered. These effects are much greater for Mars than for Earth. The maximum eccentricity of O.1~I /7/ causes the insolation at perihelion to be 38% greater than that associated with the mean annual solar flux. RESULTS AND DISCUSSION The radiative-convective model gives the response of the early atmospheres to varying amounts of atmospheric CO2. Calculations of the mean global surface temperature of Earth were made for CO2 partial pressures up to 100 bars. Similar calculations were then made for Mars. Figure 1 shows the mean global surface temperature for early Mars for mean annual conditions and for perihelion. At perihelion, the mean surface temperature is above the melting point of water for surface CO2 partial pressures greater than 2.1 bars. From the scaling equation (1), this pressure is equivalent to about 1~4 bars of CO2 on Earth. The mean surface temperature is above 260 K for surface CO2 partial pressures greater than 1.3 bars, which is equivalent to about 9 bars on Earth. At this lower mean temperature, surface conditions would still be above freezing in the equatorial regions. The Mars pressures and Earth equivalent pressure for mean annual conditions are 3.6 bars and 25 bars for 273 K, and 5.6 bars and 39 bars for 260 K.

50(

,,

~

40

,‘

\\/

= =

PCO2-O.1 bar PCO2—1.Obar

~

—

——

~

PCO2 2.0 bar PCO2 - 7.25 bar

.. I-,,-’

....

-‘

... ..

ILJ

.

•

.. S

100

200

.5’ ~.

300

Temperature (K) Fig. 2.

Temperature profiles for selected surface CO2 partial pressures on early Mars at perihelion.

Atmospheres of Early Earth and Mars

L

50

I

I

~

I

I

I

PCO

2 — 0.1 bar

•

40

(6)141

PCO2—1.0 bar

l\

—

E

PCO2 — 2.0 bar PCO2 — 7.25 bar

-

20 \

p... ‘5

10

‘:~\

‘....

I

I

~

I

I

I

Io~2 lO_lO ~Q8

10-14

\

I.~.

106

\

I

I0~ 10-2

100

H20 mixing ratio Fig. 3.

Water vapor profiles for selected surface CO2 partial pressures on early Mars at perihelion.

Vertical temperature profiles for selected surface CO2 partial pressures on early Mars at perihelion are shown in Figure 2. A well-defined tropopause appears in each profile, as does a definite cold trap (Figure 3) so that the volume mixing ratio of H20 never exceeds 10’. Hydrogen escape would have been diffusion-limited /8/ at the homopause, and the time to lose an Earth ocean of water would be much greater than the age of the solar system. Figures ~$and 5 show temperature and H2O volume mixing ratio profiles for early Earth. They are similar to those of’ early Mars in that they show a well-defined tropopause and a definite cold trap with very little water vapor reaching the upper regions of the atmosphere. For all surface CO2 partial pressures, the cold trap exists deep enough in the atmosphere to protect water vapor from solar ultraviolet radiation. These results indicate that a dense CO2 atmosphere on early Mars at perihelion is consistent with conditions expected to have existed four billion years ago on Earth. Earth would then have had a stable atmosphere with temperatures warm enough to support liquid water on the surface.

50 ci 40

PCO2

-

—

100 bar

PCO2 — 10.0 bar PCO2— 1.0 bar

~ 30

-

~

PCO2

-

0.1 bar

-

.1 .1

•5 5.5 5’. 5.. 5’. -

.. .5

5’. 55~ 5..

...

5’ 5,. 5’

I

100

200

-.

-

(.~

300

I

400

Temperature (K) Fig. 4.

Temperature profiles for selected surface CO2 partial pressures on early Earth.

R.

(6)142

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Durham et a!.

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I

50~

I

L.

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PC02—lOObar

I

40

——Pco2—io.obat

I

~3Q

:

..

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l0~~ 102

I

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i0~l0

I

108

L

10-s

I

I

iO~

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,~‘.

I

10-2

H20 mixing ratio Fig. 5.

Water vapor profiles for selected surface CO2 partial pressures on early Earth. ACKNOWLEDGMENTS

This paper is based on research supported by the National Science Foundation under Grant No. ATM-8~15118 and by the National Aeronautic and Space Administration under Grant No. NSG-7O~I3. REFERENCES 1.

J. F. Kasting, ,J. B. Pollack, and T. P. Ackerman, Response of Earth’s atmosphere to increases in solar flux and implications for loss of’ water from Venus, Icarus 57, 335 (198~l).

2.

J. F. Kasting, J. B. Pollack, and D. Crisp, Effects of’ high CO2 levels on surface temperature and atmospheric oxidation state of the earth Earth, J. Atmos. Chem. 1, 1403 (19814).

3.

J. F. Kasting and T. P.. Ackerman, Climatic consequences of very high carbon dioxide levels in the Earth’s early atmosphere, Science 23~I, 1383 (1986).

14.

R. M. Haberle, T. P. Ackerman, and 0. B. Toon, Global transport of’ atmospheric smoke following a major nuclear exchange, Geophys. Res. Lett. 12, #6, 1405 (1985).

5.

N. J. Newman and R. T. Rood, Implications of solar evolution for the Earth’s early atmosphere, Science 198, 1035 (1977).

6.

J. B. Pollack and D. C. Black, Noble gases in planetary atmospheres: for the origin and evolution of atmospheres, Icarus 51, 169 (1982).

7.

B. C. Murray, W. R. Ward, and S. C. Yeung, Periodic insolation variables on Mars, Science 180, 638 (1973).

8.

D. N. Hunten, The escape of’ light gases from planetary atmospheres, J. Atmos. Sci. 30, 11481 (1973).

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