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| Proc Natl Acad Sci U S A. 2001 February 27; 98(5): 2154–2157. doi: 10.1073/pnas.051511598. | PMCID: PMC30108 |
Copyright © 2001, The National Academy of Sciences Geophysics Keeping Mars warm with new super greenhouse gases M. F. Gerstell, * J. S. Francisco, † Y. L. Yung, *‡ C. Boxe, * and E. T. Aaltonee †*Division of Geological and Planetary Sciences, MS 150-21,
California Institute of Technology, Pasadena, CA 91125; and
†Department of Chemistry and Department of Earth and
Atmospheric Sciences, Purdue University, West Lafayette, IN 47907 Received October 26, 2000. |
Abstract Our selection of new super greenhouse gases to fill a putative
“window” in a future Martian atmosphere relies on
quantum-mechanical calculations. Our study indicates that if Mars could
somehow acquire an Earth-like atmospheric composition and surface
pressure, then an Earth-like temperature could be sustained by a
mixture of five to seven fluorine compounds. Martian mining
requirements for replenishing the fluorine could be comparable to
current terrestrial extraction. |
Greenhouse gases may be
of some use in making Mars habitable, or at least in sustaining its
habitability if otherwise achieved. Previously suggested gases include
the chlorofluorocarbons (CFCs; refs. 1 and 2),
SF 6 ( 2), and
C nF 2n+2 ( 2, 3). Recent
detailed calculations for
C 2F 6 and the CFCs ( 3) have
led to optimism about terraforming. Probably some means other than
greenhouse gases must be used for the initial warming, even though a
few heavy gases may absorb strongly ( 4) at current Martian pressure
(600 Pa). They are unlikely to cover the low-frequency half of the
emission spectrum. We introduce some new candidate gases, and we frame
our inquiry by asking what mixture of trace gases could sustain an
Earth-like temperature if Mars were endowed somehow with an Earth-like
atmospheric composition and surface pressure. We suggest that a 70-K
greenhouse effect might be maintainable with as little as 5 ×
10 22 m −2 column amount of
a mixture of “designer” greenhouse molecules. This molecular
column corresponds to about 240 parts per billion by volume in Earth's
atmosphere. Our argument begins with a simple energy balance
( 5) arising from a two-stream approximation.
Here, σ is the Stefan–Boltzmann constant,
θ g is the temperature at the planet's surface,
Fs is the downward solar flux, and τ
is the gray optical thickness. To obtain τ directly from θ, we must
assume no absorption of incoming solar radiation, but our assumption
about a window implies the presence of much water, hence of some
absorption in the interval 1 to 3 μm, and also the presence of water
clouds. The cooling or warming effect of clouds depends in a complex
way on their distribution in altitude and latitude ( 6), so we prefer
not to address it. If we ignore absorption of incoming solar radiation, a fractional
increase in θ g is a simple function of τ.
Taking the present gray opacity on Mars to be nearly zero, Eq.
1 implies that a gray opacity near τ = 3 should
increase the surface temperature to 280 K from the current 210 K. If
Mars can acquire an Earth-like atmosphere somehow, the transmission of
outgoing radiation at frequencies below 700 cm −1
and above 1,400 cm −1 will be just a few
percentage points as on Earth. We therefore direct our attention to
filling the window. In the interval between 700 and 1,400 cm −1, we
approximate the spectral transmission of the Earth's atmosphere at a
crude resolution ( 7). We then double the spectral optical thicknesses,
because the lower gravity of Mars requires 2.6 times Earth's column
airmass to achieve 100 kPa pressure at the surface. Next, we seek to
add a mixture of greenhouse gases that will lower the overall
transmission through the window to 5% (=
e−3). We considered 21 fluorine compounds, some of which were not previously
synthesized, observed, or documented. Fluorine in the bulk composition
of Mars has been estimated at 32 ppm by mass vs. 19.4 ppm for the Earth
( 8). Abundances of the other elements are more than sufficient for our
purposes. We performed ab initio calculations to find
vibrational fundamental frequencies and band intensities. After
estimating bandwidth and selecting five of the candidate molecules, we
stepped along the window spectrum at intervals of 1
cm −1 to calculate spectral transmission and
derive gray opacity. Then we iterated with the aim of minimizing the
required number of molecules of manufactured gas. Finally, we will demonstrate that Earth-like ozone and oxygen, if
present, would shield all of the selected molecules effectively against
rapid photolysis, such that their continuous replenishment by synthesis
on Mars then might be feasible. |
Infrared Quantum-Mechanical Calculations Gases considered for the special purpose of maintaining
warmth on Mars are shown in Table 1. To
determine the structure and vibrational spectra of each gas, all
calculations were performed by using the GAUSSIAN 98
suite of programs ( 9). All geometries were optimized fully with no
constraints to better then 0.1 pm (for bond lengths) and 0.1° (for
angles). The calculations were done with two kinds of basis sets:
( i) the medium size double ζ-split valence basis set,
6–31G(d); and ( ii) the large 6–311 ++G(3df,3pd) basis set.
Optimizations were performed with the Becke nonlocal
three-parameter exchange ( 10) and correlation functional was
performed with the Lee-Yang-Parr method (B3LYP) with these basis sets
( 11). In all cases, harmonic vibrational frequency calculations were
done with the optimized geometries. Structures giving rise to imaginary
vibrational frequencies were rejected, because these structures are not
global minimum structures. To determine the reliability of the various
methods for predicting the vibrational frequencies for the super
greenhouse gases, 10 other gases were selected as calibrants, because
the fundamental vibrational modes are experimentally well
characterized. These gases are CO 2,
CFCl 3,
CF 2Cl 2,
CF 2CFOCF 3,
CH 3OCH 3,
CHF 2OCF 3,
CHF 2OCHF 2,
CH 3OCF 3,
SF 6, and NF 3. Usually,
vibrational frequencies calculated with lower levels of theory are
found to overestimate experimental frequencies by 5–10%, so a popular
approach has been to use scale factors ( 12). However, in the
present work no scaling factors were applied. A comparison of observed
and calculated frequencies for our calibration set of gases
showed that calculations performed at the B3LYP/6–311 +
+G(3df,3pd) level of theory produced frequencies within an rms error of
3% of experimental vibrational frequencies. Recent studies have
found that the B3LYP method offers the best performance in computing
intensities ( 13). As a further test of the reliability of the
calculations, the infrared spectra from the ab initio
frequencies were simulated and compared with the experimental spectra.
We found that the simulated spectra showed reasonable agreement with
the experimental spectra of each calibrant gas.
| Table 1 The 21 fluorine compounds considered for super greenhouse
warming |
|
Required Greenhouse Columns After examining the calculated spectra, we selected five gases in
an attempt to minimize remaining windows. These five gases' strong
vibrational bands in the range of 670–1,400
cm −1 are listed in Table
2. Although some of these gases have been
synthesized or observed elsewhere (e.g., SF 6 in
ref. 4 and SF 5CF 3 in ref.
14), we use B3LYP outputs for all of them to work with a consistent set
of statistics.
| Table 2 Strong bands in the spectral region of interest, for the
selected super greenhouse
gases |
Based on various analogs such as fluorinated ethers ( 15), the Earth's
9.6-μm band of ozone, or the calibrations described above, we
estimate bandwidths for the super greenhouse gases to have full-width
half-max between 16 and 30 cm −1. Rather than use
Lorentzian band shapes and give ourselves the benefit of far wings that
may not exist, we model all bands as triangles. We do not increase
bandwidths with gas amount, so that the equivalent width of any given
band has an upper-limit independent of concentration. In this way we
hope to avoid crediting a saturated band with filling in nearby
windows. For a first guess at column amounts, we identified a constraining
band of each gas not overlapping strong absorptions of any of the other
gases. Because the band intensities are calculated at standard
temperature and pressure (STP), we are not accounting for the reduction
of pressure in the Martian upper troposphere and stratosphere properly;
however, we note that the 9.6-μm ozone band in the Earth's
atmosphere contributes an optical thickness comparable to the product
of its STP band intensity and its column density divided by its
bandwidth, even though most of Earth's ozone is not in the
troposphere. We doubled the spectral optical thickness of terrestrial
gases, because Mars's lower surface gravity (0.38 that of Earth)
requires increased airmass to achieve 100 kPa at the surface. We added
spectral optical thicknesses of the five selected super greenhouse
gases to the spectral opacity of the doubled terrestrial gases. Without
regard to the variation of the Planck function, we then stepped through
the spectrum 700 to 1,400 cm−1 at
1-cm−1 intervals adding optical thicknesses and
calculating spectral transmission. We iterated with the intent of
minimizing the total number of special greenhouse molecules within the
constraint that the gray optical thickness be at least 3. The minimum column amounts resulting when bandwidth (full-width
half-max) is estimated as 30 cm −1 are given as
the second column in Table 3. The total
molecular column density of the mixture is less than 5 ×
10 22 m −2, which would be
about 240 parts per billion by volume (ppbv) of Earth's atmosphere. If
the bandwidth is estimated as 16 cm −1, achieving
τ = 3 would require the addition of some
NF 3 and
CF 3NF 2 to the five gases in
Table 2 and a total molecular column of 1.7 ×
10 23 m −2 (about 810 ppbv
of Earth's atmosphere).
| Table 3 Column amounts to raise grey opacity of a doubled
terrestrial atmosphere to 3; lifetimes in present terrestrial
atmosphere |
Fig. 1 shows spectral absorption through
the 700–1,400 cm −1 window when the gas mixture
of Tables 2 and 3 is added (solid curve) to the spectrally doubled
terrestrial gases. The dotted curve represents absorption by the super
greenhouse gases only. The three humps just to the left of the deepest
trough may be identified roughly with bands of
SF 4(CF 3) 2,
SF 5CF 3, and
SF 6 seen in Table 2. The contribution of ozone
accounts for the difference between the two curves in the interval
between 1,000 and 1,080 cm −1. Other humps are
hybrid absorptions of several gases. It's worth noting that
experiments on SF 6 ( 4) show its peak absorption
between 940 and 950 cm −1, which would make our
problem a little easier to solve.
| Figure 1The solid curve is fractional absorption by the gas mixture of Table 3
when added to a spectrally doubled terrestrial atmosphere. The dotted
curve is the absorption of the super greenhouse gases by themselves
(but at standard temperature and pressure). (more ...) |
|
Photolysis For four of the five selected gases, we computed photolytic
lifetimes in the Earth's present atmosphere. For
SF 6, we use the lifetime reported in ref. 16.
Because the super greenhouse gases have no multiple bonds or hydrogen
atoms that would make them readily susceptible to atmospheric
degradation, the primary loss mechanism for these gases will, in
general, be photolysis. Chemical losses by reactions with
O( 1D) in the atmosphere will probably be less
important than photolysis ( 16), and OH is not expected to attack this
class of molecules. To estimate the UV-excited state spectra for the super greenhouse
gases, vertical excitation energies were calculated by using the
configuration interaction singles method ( 17). This method allows for
systems with a large number of atoms and large number of basis
functions to be investigated with reliability. The success of this
method in predicting excited states depends on the choice of basis set,
so we used the large 6–311 ++G(3dp,3pd) basis set. The UV absorption
cross sections then were estimated, assuming that they have the same
spectral shape as that of
CF 2Cl 2, shifted to the
proper wavelengths, and scaled by the oscillator strengths. The
resulting spectra then were used to generate photolytic lifetimes by
using the one-dimensional Caltech/Jet Propulsion Laboratory
photochemical model for the terrestrial mesosphere and lower
thermosphere ( 18, 19). The times for
e−1 folding are shown in Table 3.
Given the crude way the lifetimes were computed, they must be regarded
as order-of-magnitude results. The lifetime of the reference molecule
CF 2Cl 2 computed by our
model is 96 years. |
Discussion The initial warming of Mars and volatilizing its polar caps
remains a major problem. Investigators have suggested engineering
solutions such as a large reflecting solar sail over the Martian north
pole (see reviews in refs. 1 and 2). Relative to the difficulty of increasing the volatiles on the Martian
surface, the task of maintaining them at an Earth-like temperature
would seem easy. Our work should be refined with a multilayered
radiative-transfer model, and specific absorption line-spacings and
-strengths used. If we have overestimated bandwidths, the strategy of
choice would not be to increase column amounts but to include another
gas with a strong vibrational fundamental near 10.25 μm (the clearest
spectral region in the presence of a terrestrial atmosphere and
“our” gas mixture). Although the lifetimes in Table 3 look long, they imply that the
greenhouse gases considered here would require replenishment at a rate
of nearly 400 kilotons per year to offset photolysis. Because the
lifetimes in Table 3 were modeled at 1 astronomical unit from the sun,
it would be plausible to multiply those lifetimes by 2.3, reducing the
annual requirement to 170 kilotons. In either case, the rate compares
very favorably with the 3-teraton annual rate of CFC production
mentioned in ref. 1, which was based on a recognition that CFCs would
destroy any ozone layer. Fluorine on Mars would have to be mined locally. For comparison, South
African export of acid-grade fluorspar was 470 kilotons in 1980 but
then receded somewhat because of weak commodity markets ( 20). It takes
2.2 tons of acid-grade fluorspar to produce a ton of HF, and the
majority of the weight of the gases we are discussing is the fluorine
weight. Even though the bulk composition of Mars may be richer in
fluorine than that of Earth's ( 8), whether the element can be found
there in sufficient concentrations is unknown. Considering the likely 3% rms error in band-center frequencies, our
solution is presented as an example, not a prescription. During the
course of our own calculations, we had selected some other gases at
various times as members of our optimal subset
(CF3SCF3,
CF3OCF2OCF3,
CF3SCF2SCF3,
CF3OCF2NFCF3).
With our final set, a judicious shift of just two strong band centers
by 30 cm−1 in opposite directions increases the
manufacturing requirement by almost 15%. Here again, the best response
to an unexpected window in the true spectrum of the gases, when all
have been synthesized, would be to identify an additional gas to fill
the window. A secondary implication of our findings is a reminder that the current
terrestrial warming scare or controversy may be too fixated on the
likelihood of CO 2 doubling, when the greater
danger may be from new trace gases with strong absorption bands in the
window such as SF 5CF 3,
which is observed in the Earth's atmosphere ( 14). A more speculative corollary is that advanced extrasolar civilizations,
if they exist, already may have engineered planetary environments in
zones we would consider inhospitably cold. Therefore, searches for
extraterrestrial intelligence, which now mainly seek radio waves,
should perhaps include looking for spectra of manufacturable molecules
such as those mentioned here. Speculations on planetary environmental engineering have considered
most often materials found in nature or materials already engineered
for some terrestrial purpose. We have taken the next step by including
consideration of some materials not found in nature and not previously
manufactured. Our methods of investigating these materials are not in
themselves novel; nor would we want them to be, preferring to build our
argument on accepted foundations. |
Acknowledgments We thank J. Blamont, A. Haldemann, and K. Nealson for
stimulating discussions on climate modifications by using
greenhouse gases and G. Blake for a conversation on
bandwidths. We thank M. Marinova for a thoughtful reading and for
pointing out a reference we had neglected. We thank the National
Academy of Science's Member Editor and two anonymous referees for
their comments. This research is supported in part by the National
Aeronautics and Space Administration Grant NAG5-4022 and National
Science Foundation Grant AST-9816409. |
Abbreviations CFC | chlorofluorocarbons | B3LYP | Lee-Yang-Parr method |
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References 1. McKay, C P; Toon, O B; Kasting, J F. Nature (London). 1991;352:489–496. [PubMed]2. Fogg, M J. Terraforming: Engineering Planetary Environments. Warrensdale, PA: Soc. Auto. Eng.; 1995. 3. Marinova, M; McKay, C P; Hashimoto, H. J Br Interplanetary Soc. 2000;53:235–240. 4. Ko, M; Sze, N D; Wang, W C; Shia, G; Goldman, A; Murcray, F; Murcray, D G; Rinsland, C P. J Geophys Res Space Phys. 1993;98:10499–10507. 5. Goody, R M; Yung, Y L. Atmospheric Radiation. New York: Oxford Univ. Press; 1989. p. 392. 6. Ramanathan, V; Cess, R D; Harrison, E F; Minnis, P; Barkstrom, B R; Ahmad, E; Hartmann, D. Science. 1989;243:57–63. 7. Goody, R M; Yung, Y L. Atmospheric Radiation. New York: Oxford Univ. Press; 1989. , figure 1.1, p. 4. 8. Wanke, H; Dreibus, G. Phil Trans R Soc London A. 1988;235:545–557. 9. Frisch, M J; Trucks, G W; Schlegel, H B; Scuseria, G E; Robb, M A; Cheeseman, J R; Zakrzewski, V G; Petersson, G A; Montgomery, S A, Jr; Stratman, R E, et al. GAUSSIAN 98, Version G. Inc., Pittsburgh, PA: Gaussian; 1998. 10. Becke, A D. Phys Rev A At Mol Opt Phys. 1988;38:3098–3100. 11. Lee, C; Yang, W; Parr, R G. Phys Rev B Condens Matter. 1988;37:785–789. [PubMed]12. Pople, J A; Scott, A P; Wong, M W; Radon, L. Isr J Chem. 1993;33:345–350. 13. Halls, M D; Schlegel, H B. J Chem Phys. 1998;109:10587–10593. 14. Sturges, W T; Wallington, T J; Hurley, M D; Shine, K P; Sihra, K; Engel, A; Oram, D E; Penkett, S A; Mulvaney, R; Brenninkmeijer, C A M. Science. 2000;289:611–613. [PubMed]15. Good, D A; Francisco, J S. J Phys Chem. 1999;102:1854–1864. 16. Ravishankara, A R; Solomon, S; Turnipspeed, A A; Warren, R F. Science. 1993;259:9194–9199. 17. Foresman, J B; Head-Gordon, M; Pople, J A; Frisch, M J. J Phys Chem. 1992;96:135–149. 18. Allen, M; Yung, Y L; Waters, J. J Geophys Res Space Phys. 1981;86:3617–3627. 19. Yung, Y L; DeMore, W D. Photochemistry of Atmospheres. New York: Oxford Univ. Press; 1999. 20. Crocker, I T; Martini, J E J; Sohnge, A P G. The Fluorspar Deposits of the Republics of South Africa and Bophuthatswana. Pretoria, South Africa: S. African Govt.; 1988. |
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