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Last night I was looking at NASA's equations for pressure and temperature of the atmosphere of Mars.

P (in kiloPascals) = $0.699 \exp^{-0.00009 h}$

The Valles Marineris is 11 kilometers deep at it's lowest point.

$P = 0.699 \exp^{(-0.00009) (-11000)} = $ 1.99 KPa = 0.28 psi

Correction: a commenter informed that Valles Marineries is 4.5 kilometers beneath "sea level" at it's lowest point. $P = 0.699 \exp^{(-0.00009) (-4500)} = $ 1.048 KPa = 0.15 psi

Then I looked up this chart of water boiling temperatures at low pressures, and saw that the boiling temperature of water in this pressure is a very reasonable, if slightly chilly $60^{o} F / 15^{o}C$

Correction: $45^{o} F / 7^{o}C$

I wonder if it's possible for surface water (rivers, lakes) on Mars at the bottom of the Valles Marineris?

Have we completely ruled it out with satellites surveying the region?

Would the relative dryness of the rest of the planet generally transport any water-bearing air in the region somewhere else (eventually drying the place out), or since it's at the bottom of a chasm, might the humidity remain?

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There's been a lot of talk in recent years about transient features known as dark slope streaks and recurrent slope lineae. They're known to be quite common in parts of the Valles Marineris, moreso than in other locations.

Whilst more recent research suggests that many of the features are more likely to be sand than water, the possibility doesn't seem to have been entirely ruled out. One suggestion is that surface deposits of hygroscopic salts can sometimes pull enough water vapour out of the air to briefly form liquid brine. It may be that the frequency of RSLs in the canyons is due to slightly increased humidity there.

What does seem to have been ruled out at this time is the unambiguous appearance of surface water in the canyons, even temporarily, given that people are actively looking at those areas and have been for a good few years.

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