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On Earth (or another planet with an identical atmosphere), how high above sea level would a mountain have to rise so that its summit would no longer have any snow on it, not even temporary?

The highest "typical" clouds on Earth are the cirrus clouds around 40,000 ft altitude, but the tops of Cumulonimbus clouds can get higher than 55,000 ft above the equator. But even above 60,000 ft there still occur clouds called polar stratospheric clouds and then there are noctilucent clouds which can be as high as 53 miles - in outer space! Since these are made of ice crystals, could even those deposit on a mountain that is say 60,000 ft in elevation? So actually I don't ask on snow only, but on frost and ice as well. How high would a mountain have to be so that its summit would be bare rock (regardless of whether such mountain is physically possible to persist in the first place)?

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  • $\begingroup$ Welcome Giovani, interesting first post. Please take our tour and refer to the help center for guidance as to our ways. Enjoy Worldbuilding. $\endgroup$
    – Escaped dental patient.
    Nov 19, 2021 at 14:46

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The amount of ice in noctilucent clouds, or even cumulonimbus heads or typical cirrus, would take many centuries to deposit any depth on a peak above 50,000 feet -- and what you'd get wouldn't be "snow" so much as hoarfrost. Beyond that, direct sunlight would lead to rapid sublimation of deposited ice where it can reach, so you'd get significant deposits only in "cold trap" formations -- cracks in the rock that are (almost) permanently sheltered from direct sunlight.

For amusement, look up the annual snowfall in central Antarctica, near the pole -- and then realize this is land only a thousand meters or so above sea level. Now imagine how much less precipitation you'd get when the temperature is 15-20 °C cooler, never varies by more than a couple degrees, and the humidity is effectively zero 99% of the time.

If you specify "never" having even temporary snow, you'd need conditions in which any kind of deposit is impossible -- and mountains can't get that high on a planet the size of Earth (our gravity is high enough to prevent an Olympus Mons). Mountains can, in theory, reach 60,000 feet, which is high enough to be beyond any known phenomenon that can deposit ice on Earth (same would not be true with the kind of "atmosphere" the Moon has, BTW). Hawaii, measured from the deep ocean floor, is more than 33,000 feet to the peak of Mauna Kea (almost 14,000 above sea level), and there's no physical reason it couldn't be a bit higher -- but mountains that high form as "shield volcanoes", many times as wide as they are tall, not as towers taller than their width. This is partly due to the mechanics of vulcanism, and partly due to the compressive strength and weight of basaltic magmas.

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  • $\begingroup$ I know there can't be a 50-mi-mountain on Earth, hence my last sentence in brackets. My question is theoretical, but I think Eiffel-Tower-shaped mountains could indeed reach very extreme altitudes, even above 50,000 ft (9.5 mi). So your answer is about 50,000 ft (disregarding temporary deposits)? $\endgroup$
    – Giovanni
    Nov 19, 2021 at 14:53
  • $\begingroup$ If you're going to have not temporary deposits, you have to go high enough there's no ice in the air, or have a surface that's warm enough that the microcrystals sublimated immediately. Notice that Olympus Mons, even under only .38 G, has deformed a continent-sized piece of the Martian crust... $\endgroup$
    – Zeiss Ikon
    Nov 19, 2021 at 15:08
  • $\begingroup$ Why do you write same wouldn't be true with the Moon's exosphere? It's a hard vacuum. Do you just mean that on the Moon the elevation doesn't matter? $\endgroup$
    – Giovanni
    Nov 19, 2021 at 15:38
  • $\begingroup$ I mean that water vapor on the Moon (if it is released from a cold trap, for instance) doesn't depend on an atmosphere, it can go higher (not to mention, 1/6 G). Won't stay, though, unless in a cold trap. $\endgroup$
    – Zeiss Ikon
    Nov 19, 2021 at 15:39
  • $\begingroup$ Note that at its lowest elevation, the Martian atmosphere is equivalent to 22 miles/35 km, yet snow has been observed on Mars: livescience.com/61335-does-it-snow-in-space.html $\endgroup$
    – jamesqf
    Nov 19, 2021 at 17:34

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