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In 2016 a large ice deposit was found within the Utopia Planitia region on Mars by the SHARAD instrument on board of the Mars Reconnaissance Orbiter.
The thickness of the deposit ranges from about 80 to 170 meters with a composition of 50% to 85% water ice, mixed with dust or rocky particles.
It is shielded from the atmosphere by a soil covering estimated to be about 1 to 10 meters thick.
The volume of the ice is estimated to be about 14,300 cubic km, so the mass will be more than 13 teratonnes, the mass of the atmosphere being 25 teratonnes.

If bulldozers could remove a part of the soil covering in summertime, round midday the ice would sublimate into the atmosphere, where at a certain height the water vapour could become cold enough to crystallize.

But would this really happen with such a low atmospheric pressure and could the crystals become large enough to fall down on the surface like snow ?

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Actually it already snows on Mars. The snow, made of carbon dioxide, has been observed and studied by orbiting spacecraft. Aside from the different chemical composition from the stuff we shovel on Earth, Martian $\text{CO}_2$ snow also is very finely divided, microscopic in size in fact; likely this is related to the low density of available material and the very fine nature of the dust on which the snowflakes nucleate. In fact studying the snow could provide clues about the atmospheric Martian dust on which it nucleates.

Details are published in the Journal of Geophysical Research.

NASA has also reported evidence of snow clouds and accumulation on Mars from observations by the Mars Reconnaisssance Orbiter in 2012.

Indirect evidence for water ice snow has also been found. According to an article published in Nature, mixing layers have been identified from orbiting spacecraft and water-ice precipitation signatures have been found by the Phoenix lander. Simulations show that such signatures are consistent with snow formation, with the water-ice snow expected to fall at night (as temperatures cool and the atmosphere can retain less water vapor). The arcticle does not claim any direct detection of water-ice snow.

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    $\begingroup$ Water ice snow may also be possible: nature.com/articles/ngeo3008 $\endgroup$
    – ceejayoz
    Commented Sep 27, 2019 at 15:40
  • $\begingroup$ Can what has been actually observed be characterized as snow, or simply very tiny ice crystals suspended at high altitude? Has it been shown in any way that ices on the surface are at least in part accumulations of fallen snow and not simply depositions of CO2 and H2O directly from gas phase from the atmosphere (i.e. frost)? I read through the article briefly but I don't see how the spectroscopic data demonstrates a preference of fallen snow versus frost, is it possible to highlight the sections or passages that do so? Are there any observations inconsistent with frost? Thanks! $\endgroup$
    – uhoh
    Commented Dec 3, 2020 at 22:57
  • $\begingroup$ The article implies they found the snow aboveground, whence it would settle: "They also analyzed measurements from MGS' laser altimeter, which gauged the topography of Mars by timing how long laser pulses took to bounce back from the planet's surface. Occasionally, the laser beam returned faster than anticipated, after ricocheting off cloud particles in the Martian atmosphere." $\endgroup$
    – Oscar Lanzi
    Commented Dec 4, 2020 at 0:32

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