To warm Mars above its present temperature or to maintain a N₂/O₂ atmosphere warm will require either lowering the surface albedo, increasing the energy deposition, or enhancing the greenhouse effect. To achieve any of these effects require production of the appropriate material on Mars. Various planetary engineering methods have been suggested to do this.

One of the features of the surface energy balance is that the rate of warming due to any single effect diminishes with increasing amount. For example the amount of warming that is produced by the first added 100 hPa (mbar) of CO₂ exceeds that warming resulting from the second 100 hPa of CO₂.

This has led to the observation that the best way to warm Mars is to use several effects together (Fogg, 1992). Each is pushed to the practical limit and a synergistic effect results.

In order to combine the effect of changes in the albedo, energy deposition, and greenhouse gases we need to have a physically based model of surface energy balance. We express the surface energy balance as

(Eq.1)

where s is the Stefan-Boltzman constant, T_s is the globally averaged surface temperature, a is the globally averaged surface albedo, S_m is the solar constant at Mars orbit, F_g is the flux incident on the surface due to the greenhouse effect of the atmosphere.

In principle one can solve Equation 1 for the surface temperature but the difficulty arises in computing the greenhouse flux, F_g. We wish to have an efficient method for computing F_g for a combination of possible greenhouse agents, including CO₂, H₂O, CH₄, NH₃ and CFCs. To approach this problem we note that the flux from each greenhouse gas is approximately independent of the flux from other gases. Thus we let

(Eq.2)

This allows us to combine expressions for the greenhouse effect of individual gases to obtain an estimate of the total resultant effect.

In obtaining expressions for the flux from each individual greenhouse agent we utilize the solution of the surface and atmospheric temperature profile for an atmosphere that absorbs uniformly at all wavelengths. In this case the greenhouse heating is given by

(Eq.3)

which in Equation 1 reduces to

(Eq.4)

where t is the equivalent grey opacity of the greenhouse gas. It is clear then that

(Eq.5)

where T_b is the effective temperature of the planet given by

(Eq.6)

and the t terms refer to the equivalent grey opacity of each individual greenhouse agent, S with no subscript refers to the energy deposited on Mars normalized to the present solar flux, S_m. (Artificially increasing the energy deposition on Mars involves increasing the S term, increasing the greenhouse effect involves increasing the t terms, and lowering the albedo involves reducing the a term.)

Pollack et al. (1987) have reported on detailed calculations for the surface temperature of Mars resulting from increases in CO₂ up to 1000 kPa (10 bars) and for values of the solar constant equal to 0.7, 1.0 and 1.3. McKay and Davis (1991) have fitted the results of Pollack et al. (1987) with the formula

(Eq.7)

where a and b are constants adjusted to give an optimum fit at 1.95 K kPa^-1/2 and 2.04 K kPa^-1/2 (a is not to be confused with albedo in this case) and P is the atmospheric pressure. This fit, while very accurate (see Figure 2 of McKay and Davis, 1991) is not suitable for our present purposes because it expresses the greenhouse effect as a change in surface temperature directly rather than a change in flux incident at the surface. From physical considerations the changes in temperature from various greenhouse agents are not expected to add simply. Therefore we have fit the Pollack et al. (1987) results to a parameterization of the form of Equation 3. A good fit is obtained if we let

(Eq.8)

where P_tot is the total atmospheric pressure, P_CO2 is the carbon dioxide partial pressure and both are in units of 100 kPa (bars). The resulting fit is shown in Figure 1 [not posted here].[This fit is as good for the S = 1 as that of McKay and Davis (1991) but is not as good for S = 0.7 and S = 1.3, systematically underestimating the effect of changes in S. Nevertheless the fit is suitable for our use here. (Statement only certain for V1.0)]

where R_h is the relative humidity (set here to 0.7), P₀ is the water vapour pressure at a reference temperature (set here to 1.4x10⁶), L is a latent heat term (43655), R is the gas constant for water (8.314) and T_s is the surface temperature. The opacity of water vapour is thus ultimately dependent on surface temperature and is not directly modifiable within the program. The warming effect of water vapour therefore acts as a bonus to the more direct methods of climate forcing involved in terraforming.

where PCH₄ is the methane partial pressure in bars. In the context of Martian terraforming it is only sensible to model methane as a trace atmospheric constituent (e.g. m bar to millibar pressures).

Turning now to the CFCs, McKay et al. (1991) have calculated the surface temperature that would result from an introduction of a mixture of CFCs into the Martian atmosphere. They treated the problem by assuming that the mixture would uniformly blanket the 8-12 m m ‘window’ region of the infrared spectrum. Their results were expressed as a function of the opacity of the CFC mixture in this spectral region. They considered the addition of CFCs to the present Mars atmosphere (6 hPa CO₂) and to a 100 kPa N₂/O₂ Earth-like atmosphere. They found that the resulting surface temperatures were similar for both cases depending only on the opacity of the CFCs in the window region. By considering these results we obtain a fit as follows

(Eq.13)

where W is the opacity of the CFC mixture in this 8-12 m m window region. Equation 13 represents a good approximation to the results of McKay et al. (1991) as shown in Figure 2 [not posted here].

To express this in terms of the pressure of CFCs in the atmosphere, we need to have a value for the warming due to a given amount of CFCs. We note from Equation 4 that if t _CFC is small then

(Eq.14)

Here we use the results of Ramanathan et al. (1985) indicating that a mixture of CFCs such as that suggested by McKay et al. (1991) – CF₃Br, C₂F₆, CF₃Cl, and CF₂Cl₂ – would have a warming effect of about 0.2 K from a column mass corresponding to 1 ppb in Earth’s atmosphere. This amount of mass would be 100 m Pa on Earth and 38 m Pa on Mars. If we assume that the window region opacity is proportional to the column mass for small mixing ratio then W = g PCFC. Approximating Equation 9 as t CFC = 1.1W/50 for small values of W and combining Equations 9 and 10 we obtain the following expression for g ,

M.J. Fogg, "A Synergic Approach to Terraforming Mars," JBIS, 45, 315-329, (1992).

C.P. McKay and W. Davis, "Duration of Liquid Water Habitats on Early Mars," Icarus, 90, 214-221 (1991).

C.P. McKay, O.B. Toon, and J.F. Kasting, "Making Mars Habitable," Nature, 352, 489-496 (1991).

J.B. Pollack et al., "The Case for a Wet, Warm Climate on Early Mars," Icarus, 71, 203-224 (1987).

V. Ramanathan et al. "Climate-Chemical Interactions and Effects of Changing Atmospheric Trace Gases," Rev. Geophys., 25, 1441-1482 (1987).

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