“… in the absence of rain on Mars, these channels are probably the main mechanism by which the water can spread on the dry surface of the planet.
Giovanni Schiaparelli 1877
SATURATION VAPOR PRESSURE
Consider the air in a covered fish tank. If it is undisturbed, the water vapor will be at the saturation vapor pressure. This parameter depends on temperature; there is generally no condensation on the glass with a temperature change since vapor will simply transfer to the liquid surface. There are a number of formulas which match experimental values depending on the temperature range. If there is no cover on the fish tank, these concepts can be extended to a (simple) atmosphere.
If there is about 500 meters of saturated air, at night, this water vapor will condense on the surface, which can be any depth. However, the surface temperature stays the same as long as there is vapor to condense on that surface. The latent heat of condensation is 2.2 million joules per liter of water and the only question is whether there is enough saturated atmosphere to maintain the surface temperature for 12 hours.
Our planet can have a temperature of 25 degrees C. at the equator so that there will be about 23 grams of water per cubic meter of air. (see reference) If the daytime sun heats the water for a 12 hour day at 450 watts per square meter. The total energy will be:
12 x 60 x 60 x 450 = 19.44 MJ
The saturated atmosphere will have to be about 400 meters high:
0.023 x 2.2 x 10^6 x 400 = 20.24 MJ
Reference:
Saturated vapor density (not to be confused with pressure) tables are here:
http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/watvap.html#c1
Why is Venus so Hot?
If the temperature of the Earth is 60 degrees C. and there is a depth of one meter of water, then this water will evaporate. The saturation vapor density is 130.5 grams per cubic meter.
Hot air rises, from the now dry surface, and forms a cloud deck at a few kilometers. in elevation. Say that 50 grams per cubic meter per second of water vapor condenses into a mist. The heat generated will be,
0.05 x 2.2 x 10^6 = 110 kilowatts.
If 10% of this heat is radiated to the surface, the temperature (black body radiation formula) will be 390 degrees C.
How high are the clouds?
https://en.m.wikipedia.org/wiki/Lifted_condensation_level
Multiply the difference of surface and dew point temperature by 125:
125 ( 390 – 100) = 36.25 km. This compares to 48 km. for Venus.
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