Physics of Climate

1
Physics of Climate

• In-Class Discussion
• Radiation Mars

2
Properties of Martian Atmosphere
This web site, by a student in Finland, appears
to have reliable data on Mars http//www.student.
oulu.fi/jkorteni/space/mars/properties.html Let's
assume it is, and use it as a starting point for
"planetary engineering".
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Surface Temperature
Compare radiative temperature computed in Problem
Set 1 with the radiative surface temperature on
the web site. How do they compare?
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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 0C?
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Surface Temperature
For this optical depth what lapse rate does
this give? (What is a relevant depth to use?)
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Surface Temperature
Assume this optical depth is produced by carbon
dioxide. How would the mass and hence surface
pressure of the atmosphere change?
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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?
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Ice ? Vapor
3 x 1015 kg needs to become gas (out of a total
ice mass of 8 x 1017 kg) How long to melt
this? How far equatorward is the ice line? Solar
flux 250 W/m2 Area of cap _at_ 50N 1.7 x
107 km2 1.7 x 1013 m2 Ice volume to
melt 3 x 1015 kg/ 917 kg/m3 3.3 x 1012
m3 Ave thickness to melt V/A 0.2 m
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Ice ? Vapor
How long to melt this? Solar flux 250
W/m2 Ave thickness to melt V/A 0.2
m Latent heat of sublimation? 2834 kJ/kg Mass to
melt 917 kg/m3 x 0.2 m 183 kg/m2 577 hr.
24 days (if albedo 0)
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Ice ? Vapor
Moist convection? Moist adiabatic lapse rate
?? Need mass of vapor near surface.
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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/(192273) 0.27
  kg/m3
• Mass of CO2 for whole atmosphere?
• Scale height for CO2 atmos on Mars _at_ 273 K 14
  km
• M integral from 0 to infinity of (surface rho)
  exp-z/H
• H rhos 14,000 0.27 3739 kg/m2
• M total 1.441e14 m2 X 3739 kg/m2 5.4 e17
  kg

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Increase CO2?
Is there enough mass in the ice caps? 9,500
12,500 km3 (in southern ice cap) Mass of CO2
there is then 2e16 kg Using a density of
solid CO2 1562 kg/m3 But needed 5e17 kg. Not
enough.
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In-Class Discussion End