## Appendix C

A Terraforming Simulator Model for Mars

Equation (5.1) describes the direct surface-heating effect due to solar radiation. To account for the greenhouse-heating effect, however, the composition of the atmosphere must be specified. The key greenhouse gases we shall consider are carbon dioxide (CO2), water vapor (H2O), methane (CH4), ammonia (NH3), CFCs, CF4, and C3F8. Without going into the details behind the calculations, we will simply present a set of approximation equations that describe the opacity terms (r) as determined and/or published by Martyn Fogg, Christopher McKay, Robert Zubrin, and Margarita Marinova. The opacity of a gas is essentially a measure of how effective it is at trapping the outflowing infrared radiation—the larger the opacity term the greater is the greenhouse-heating effect. The key opacity terms we have are r —10 P 0.45 p 0.11 rCO2 — 1 .2 P total P CO2

rmo - 3,PH2O, where Phoo — Rh Po exp(-L/R Ta) and Rh = 0.7 is the relative humidity, P0= 1.4 x 106 is a reference pressure, L = 43655 J/ mol is the latent heat, and R = 8.314 J / K/ mol is the gas constant.

The units for the partial pressure terms are given in bars, where 1 bar = 105 Pa. The partial pressures of CH4, NH3, CFCs, CF4, and

C3F8 will typically be expressed in microbars (1 mbar = 10—6 bar = 0.1 Pa), while the CO2 partial pressure is usually expressed in millibars (1 mbar = 10—3 bar = 100 Pa). An important point to note at this stage is that the water-vapor pressure PH2O varies according to the surface temperature TA. Dalton's law dictates that the total atmospheric pressure is the sum of partial pressures: Ptotal = Png + Pco2 + PH2O + Pch4 + Pnh3 + Pcfc + Pcf4 + Pc3F8, where Png corresponds to the partial pressure of nongreenhouse gases such as N2and O2. The model calculation proceeds by first setting values for the individual pressure terms; some characteristic values for these terms are provided in Chapter 6. Note that we need not specify the water-vapor pressure term PH2O, since it is evaluated in terms of the surface temperature TA.

In total, there are eight parameters that can be varied in this model Martian atmosphere, and they are: the albedo A, the insolation term S / S0 = L©(at time t) / L©(now), and the partial pressure terms for the CO2, CH4, NH3, CFC, CF4, and C3F8 components. The mean surface temperature is now expressed through the equation:

Ta = Tp S1/4(1 + |[TcO2 + TH2O + TCH4 + TNH3 + TCFC + TcFA + Tc3F8})1=4

where Tp is determined according to Equation (5.1) with the orbital distance being that of Mars (D = 1.52 AU = 2.2739 a 1011 m). Once all the constant and input parameter terms have been specified, then the procedure for calculating TA is illustrated in Figure C.1. Having found the mean surface temperature, the approximate temperatures at the Martian equator and poles can be calculated as Tequator = 1.1 Ta, and Tpole = TA — 75/( 1 + 5 Ptotal). The latitude extent (above and below the equator) to which the temperature might be above 273 K (that is, the freezing point) is determined through the equation: Xhabitabie = arcsin{[(273 — Teqilator) / (Tequator — Tpofe)}2/3}. Most computers/calculators will return the ''arcsin'' quantity in units of radians, so the number needs to be multiplied by 180 / p « 57.2958 to convert the result to the more familiar units of degrees. For example calculations see the various graphs presented in Chapter 6. Figure C.1. Pseudo computer-code flowchart for the evaluation of TA. The need for an iteration loop comes about because PH20 varies according to the mean temperature TA; the iteration should continue until the difference TA(n) — TA(n— 1) < 10—5. Convergence is fairly rapid, and typically only four or five iterations are required to determine the final value for TA.

Figure C.1. Pseudo computer-code flowchart for the evaluation of TA. The need for an iteration loop comes about because PH20 varies according to the mean temperature TA; the iteration should continue until the difference TA(n) — TA(n— 1) < 10—5. Convergence is fairly rapid, and typically only four or five iterations are required to determine the final value for TA.

Once the polar ice caps of Mars have been warmed by about 20 K, the runaway degassing of CO2 will begin to occur (recall Figure 6.15). Under these circumstances the input conditions for the model will require modification in order to take into account the increased atmospheric CO2 abundance and its associated partial pressure. Exactly how much CO2 might be liberated from the fully degassed Martian polar caps and regolith is presently unclear, but it is estimated to be equivalent to an additional 100-400 mbar of atmospheric pressure. The procedure described in Figure C.1 is not capable of following the time evolution of CO2 during the runaway stage, so this quantity will have to be ''added in'' as an increment to PC02.