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The question Most efficient method of storing energy with water on the moon? proposes a several hundred meeter tall subsurface cavern on the Moon. I added the following comment to an answer:

I keep thinking that there should be some way to use liquid/solid phase change as a way to store energy but I am bad at thermodynamics. Lunar subsurface temperatures are about 255 K near the surface and increase about 1.5 K per meter in depth (from here) so there are various temperatures above and below 273 K available in the walls of your 200 meter deep cavern if one did a little drilling. Who knows, it might be liquid at the bottom, and assuming the cavern is sealed and with evaporation there could even be rain!

Assuming the following:

  1. the cavern was sealed so that an equilibrium vapor pressure were established
  2. the floor was deep enough to expose the water to temperatures above the freezing point of water (273 K)
  3. the ceiling was high enough to expose the water vapor to temperatures well below the freezing point of water

Question: Would there be continuous rainfall or snowfall inside? Would there be fog or clouds?

uhoh
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    Presumably the energy for such a water cycle would have to come from sunlight heating the surrounding rock. Which in turn would repeat every lunar day (1 month). So even though you would be underground, you could perhaps tell the day of the month by the amount of fog in the cavern. Fascinating. – DrSheldon Jun 26 '20 at 04:47
  • @DrSheldon for solid rock with low heat conductivity the "daily" oscillations die out within the first 100 cm of depth per the material in my link. https://i.stack.imgur.com/8aZ27.png – uhoh Jun 26 '20 at 11:43
  • Well then, I suppose the best use of such an underground space would be for keeping a prisoner. As you left me -- as you left her -- in the middle of a cold, dead planet. Buried alive, buried alive! – DrSheldon Jun 26 '20 at 11:57
  • I think snow, fog and clouds would require a gaseous atmosphere with different temperatures and humidity with a height of several kilometers. – Uwe Jun 26 '20 at 16:05
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    relevant: https://worldbuilding.stackexchange.com/a/6951/65769 – Dragongeek Jun 26 '20 at 16:57
  • @Uwe the walls of the cavern may enforce a large geological thermal gradient, why would a large height then be necessary? – uhoh Jun 27 '20 at 01:49
  • The thermal gradient you mention is only valid for the very upper part of the regolith, A better number for the deeper moon is 1 degree per kilometer. You are very unlikely to find liquid water anywhere under the surface. Maybe closer to the crust/mantle boundary. Also, it's highly unlikely any underground lunar chamber is completely sealed. Lunar rock is largely porous and broken up by billions of years of impacts. Unlike Earth, the moon has no forces resurfacing the crust. – Dan Hanson Jun 29 '20 at 21:19
  • @DanHanson in the first few hundred meters the gradient changes by three orders of magnitude? Is it possible to find a source for that? – uhoh Jun 29 '20 at 21:53
  • The first few meters are dominated by the sun heating the surface. You dan get extreme gradients that way, which is what the Apollo measurements found. But once you get beyond this region, the temperature is dominated by internal heat fliw ffom the core. The core/mantle boundary has been found to be about 1350-1400 degrees, and the mantle us on average 1350 km thick. Therefore, since the temp goes from -21 near the surface to 1350-1400 degrees at the core/mantle interface, the gradient is on average 1 degree/km. – Dan Hanson Jul 01 '20 at 20:25
  • For example, lava tubes on the moon have been found to have an internal temperature of around -21c, despite being at least 70m below ground. That said, the Moon's interior is heterogenous with respect to radioactives, composition, melting, etc. No doubt there are hot spots due to radioactives in the KREEP regions, for example. MASCONS below the surface may also affect heat flows and distribution of volatiles. There's also no reason to assume the thermal gradient is linear - it might not change much at all in the upper mantle. We really don't know much about the lunar interior. – Dan Hanson Jul 01 '20 at 20:42
  • But even in the first few meters the temperature still increases with depth, meaning that it is coldest at the surface, so the gradient can not be due to "heating from the Sun". However, come to think about it, the steeper slope near the surface may be due to lower thermal conductivity of loose regolith compared to solid rock below. After all, the Apollo astronauts probably did not have the capability to drill through a meter plus of solid rock. – uhoh Jul 01 '20 at 23:50

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In Earth's atmosphere, fog and clouds form when saturated warm air flows into a mass of colder air. Condensation into droplets is also believed to be helped by the presence of fine dust particles.

In an enclosed cavern, the most likely place for condensation to form would be as dew and frost on the walls and ceiling, rather than as airborne droplets. Just slightly colder spots in the walls will collect the excess water vapor as condensation, as the warm air rises, before it can hit a cold front of air. If there are heat exchanger elements at the top (e.g. to collect the geothermal energy), they will be the most likely spot for ice to form, just as tends to happen inside a fridge.

Even in a truly massive cavern, the circulation of air will follow the geometry of the walls, so to create fog conditions (warm mass of air mixing with a cold mass of air) requires special design or luck. Of course, with special design it is also possible to shape the ceiling so that condensation "rains" down from it, instead of just running in rivulets down the walls. (Designs without occasionally dropping icicles may be harder to achieve.)

As I understand it, the force that makes warm air rise and cold air fall down in a pressurized container is based on gravity. This is also the basis of fractionation columns, which may not work as well on the Moon as they do on Earth (even if they are built six times taller). Because of the weaker gravity, the "lift" produced by geothermal heating is also weaker. On the other hand, separation of the fluids into cold and warm layers takes longer for the same reason. A lot depends on the shape of the hypothetical cavern, and the heat conducting properties of the walls. When water condenses, some ambient heat will be absorbed, which can serve to cool nearby air.

Miles Mutka
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    There is at least one building with its own weather on earth : the vehicle assembly building at cape Canaveral. https://en.m.wikipedia.org/wiki/Vehicle_Assembly_Building – planetmaker Jun 26 '20 at 23:54
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    Is it possible to explain why NASA's Vehicle Assembly Building can have clouds but our cavern can not? – uhoh Jun 27 '20 at 01:51
  • @planetmaker cool! I've just asked What did NASA Vehicle Assembly Building's "weather" look like? Did it really have clouds? Did it rain? – uhoh Jun 27 '20 at 01:56
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    A couple of other things: First, the saturation pressure of water vapor declines with air pressure, so when you reach saturation in a former vacuum the absolute amount of water in saturation will be small. Also, the ambient temperature in any realistic natural dome under the moon will be well below zero. So I think what you'd see is that ice at the bottom would sublimate then collect on the cold walls as hoar frost. Once equilibrium was reached, you'd just have a never-ending process of sublimation and re-freezing on all surfaces. At least, that's my guess. – Dan Hanson Jun 29 '20 at 21:40
  • @DanHanson, I did use words like "design" and "hypothetical" in my answer, not to suggest that this kind of situation would occur naturally, or be stable for a very long period. For example, too tight seal together with heating from below might cause the whole thing to explode outwards from the gas pressure, like happens in permafrost in Siberia. (Identifying a gas explosion crater on the Moon might be a cool discovery though.) – Miles Mutka Jun 30 '20 at 18:29