Physics of Climate In-Class Discussion: Radiation & Mars

Properties of Martian Atmosphere This web site, by a student in Finland, appears to have reliable data on Mars: Let's assume it is, and use it as a starting point for "planetary engineering".

Compare radiative temperature computed in Problem Set 1 with the radiative surface temperature on the web site. How do they compare? Surface Temperature

Suppose we wanted to make the planet more habitable (by human standards). What optical depth would we need for radiative equilibrium surface temperature of 0˚C? Surface Temperature

For this optical depth … … what lapse rate does this give? (What is a relevant depth to use?) Surface Temperature

Assume this optical depth is produced by carbon dioxide. How would the mass and hence surface pressure of the atmosphere change? Surface Temperature

Assume this optical depth is produced instead by water vapor. How much would be needed? Is the surface amount consistent with the radiative equillibrium surface temperature? Surface Temperature

Ice  Vapor 3 x kg needs to become gas (out of a total ice mass of ~ 8 x 10**17 kg) How long to melt this? How far equatorward is the ice line? Solar flux ~ 250 W/m**2 Area of 50N = 1.7 x 10**7 km**2 = 1.7 x 10**13 m**2 Ice volume to melt: 3 x 10**15 kg/ 917 kg/m**3 = 3.3 x 10**12 m**3 Ave thickness to melt = V/A ~ 0.2 m

Ice  Vapor How long to melt this? Solar flux ~ 250 W/m**2 Ave thickness to melt = V/A ~ 0.2 m Latent heat of sublimation? 2834 kJ/kg Mass to melt = 917 kg/m**3 x 0.2 m = 183 kg/m**2 577 hr. = 24 days (if albedo = 0)

Ice  Vapor Moist convection? Moist adiabatic lapse rate = ?? Need mass of vapor near surface.

Increase CO2? Current optical depth: ~ 0.1 (Harvard study of Viking results) Target depth ~ 2 What CO2 mass is needed? (Or what CO2 pressure?) Ratio: original tau/target tau = 0.1/2 Or want CO2 to increase by factor of 20 The ps = 6-8 mb  new ps = 120 – 160 mb  Density = ps/Rd Ts = 140 hPa/(192*273) = 0.27 kg/m**3  Mass of CO2 for whole atmosphere? Scale height for CO2 atmos on 273 K = 14 km M= integral from 0 to infinity of (surface rho) exp{-z/H} = H * rhos = 14,000 * 0.27 = 3739 kg/m**2 M total = 1.441e14 m**2 X 3739 kg/m**2 = 5.4 e17 kg

Increase CO2? Is there enough mass in the ice caps? 9,500 – 12,500 km**3 (in southern ice cap) Mass of CO2 there is then ~ 2e16 kg Using a density of solid CO2 = 1562 kg/m**3 But needed 5e17 kg. Not enough.

In-Class Discussion ~ End ~