Mars
Water Vapor in the Martian Atmosphere
0.021% or 210 ppm, presumably by weight.
Atmosphere is 64 Pa. About 20 g/m³ (Earth is 1290 g/m³ at sea level. Equatorial wind speed up to 150 m/s, which produces a dynamic pressure equivalent to a 19 m/s (42 mph) wind on Earth. Scale height 11 km, Total mass 25e15 kg.
Air stripped away (about 200 g/s) by solar wind. Sun less energetic (but with more UV) billions of years ago. At current loss rates, atmosphere would last 4 billion Earth years.
Five million cubic kilometers of ice is claimed. At 9.2e11 kg/km³, that is 4.6e18 kg of frozen water. About 5e12 kg in the atmosphere, perhaps 0.01 Pa vapor pressure.
Mars global average temperature is 60C or 210 K (surface?) kT = 0.018 eV or 2.9e21 J. 3.71 m/s² surface gravity, escape velocity 5.03 km/s.
Viking lander temperature (at 22°N) ranges from 89C to 31C, average 60C. Corresponding ice/water vapor pressures of 0.1 Pa, 34 Pa, and 1 Pa.

CO₂ 
H₂O 
CH₄ 
H₂ 
Molecular Weight, daltons 
44 
18 
16 
2 
Molecular Weight, kg 
7.3e26 
3.0e26 
2.7e26 
3.3e27 
Escape energy, joules 
9.2e19 
3.8e19 
3.3e19 
4.2e20 
Escape energy, eV 
5.74 
2.3 
2.1 
0.26 
So, the big question: if belowsurface ice is 60C, and has a vapor pressure of 1.08 Pa, and the atmosphere above is 0.01 Pa, what keeps the ice from sublimating quickly, the vapor seeping to the surface, and raising the vapor pressure? There must be a cap layer of rock that is impermeable to water vapor, but how can that be, over an entire planet with significant surface topology?
The heat of fusion of ice is 330 J/g. Ice density at 60C is 922.4 kg/m^{3}. Average Mars insolation is 586 W/m² (493 to 717), averaged over a day on the equator that is about 185 W/m². If 0.1% of that power made it down to the ice, it would evaporate at the rate of 1 meter per 1.65e9 seconds (52 Earth years). After billions of years, why is there any ice left at all?
Perhaps silly question: Could the water vapor be due to comet impacts? Seems unlikely, I expect the flux of water molecules from the Oort to be way too small.
At higher latitudes, the average insolation is lower and temperatures are colder. Ice will be a lot more stable near the poles; perhaps the temperatures are low enough for the ice to condense from a 0.01 Pa concentration in the atmosphere.
Other stats

Ratio 
Mars 
Earth 

Radius km 
0.532 
3390 
6371 

Gravity m/s^{2} 
0.379 
3.71 
9.80 
weakened bones, muscles, cardiovascular and lymphatic system 
Escape Velocity km/s 
0.450 
5.03 
11.19 

Escape Energy MJ/kg 
0.202 
12.65 
62.61 
light gases escape more quickly 
Surface area Tm^{2} 
0.283 
144 
510 

Insolation MW/km^{2} 
0.431 
586 
1361 

Total Insolation PW 
0.122 
21.2 
173.5 
Rotational Stability
What (if anything) stabilizes the rotational axis of Mars? How fast do the poles shift?