One would think that with barely 100th the atmosphere Earth has Mars would have pretty lame weather...if any. But it doesn't take much to whip up a good storm. Just look at the monster sand dunes that the winds on Mars manage to create. If they can do that, it's maybe less surprising that Mars' weather might be more interesting than you might at first suppose.
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Speaking of the wind on Mars, that's as good a place to begin as any. Winds on Mars can have speeds of up to 50 mph normally—-and up to 125 mph during a dust storm. But if you really want to experience what Mars can come up with, Mariner Valley would be a great place to start. The monster 3000-mile-wide canyon (rift valley, if want to be pedantic) is so long that one end will be well into the night side of Mars while the other end is still in full sunlight. The temperature difference can cause terrific winds to barrel down the canyon...at velocities reaching the speed of sound on the planet. Mars' winds might not knock you over, but they could probably have you sandblasted down to a nubbin in no time. More realistically, they might sandblast the face plate of your helmet to opacity. And then where will you be?
The tenuous atmosphere is perfectly capable of supporting a lot dust (which is probably talcum-like after 1.2 zillion years of erosion), evidenced by Mars' famous pink sky. Get some serious wind involved and you can get a fine dust storm. A dust storm so large, in fact, that the entire planet might be covered from pole to pole. This occurred during the first fly-by of Mars. When Mariner 4 arrived at Mars in 1964, scientists were appalled at the first photos sent back to earth. The planet looked like a cue ball. A monster dust storm had blanketed the planet: nothing was visible but for three or four dark spots. Fortunately, the storm cleared before the fly-by was over, revealing the dark spots to be the summits of gigantic volcanoes so high they protruded above the miles-deep cloud of dust.
Most of the dust in the Martian atmosphere is carried there by dust devils and dust tornadoes. These appear to dance over the Martian landscape by the hundreds...if not thousands, leaving a myriad of dark tracks traced over the surface, making Mars look like some sort of dune buggy convention site. Most of these are conventional dust devils, like those you might see whirling over a field on a hot Summer day. Others, however, may develop into full-fledged dust tornadoes no more to be messed around with than their Kansas cousins.
The Martian sky can be filled with regular clouds, too, made of water vapor or ice crystals just like on earth. At night, thin, icy, stratospheric clouds will glow eerily in the nearly black sky. They are high enough to be still illuminated by the sun even though the landscape around you is pitch dark. Glowing clouds like these are called "noctilucent clouds" and are a very pretty but fairly rare sight on earth.
Crystals of ice — water and carbon dioxide — fill the atmosphere, especially above the poles. These can create all sorts of interesting optical phenomena as sunlight passes through them. Haloes and sundogs are common sights in terrestrial skies (where they are all too often mistaken for UFOs). The same thing would occur as sunlight is refracted by the ice crystals in Mars' sky. But what you see might look unfamiliar. This is because most of the ice crystals would be carbon dioxide, and carbon dioxide crystals have a very different shape than water crystals. This would result in haloes and sundogs unlike those in terrestrial skies.
Maybe the most familiar and home-like weather you might experience on Mars would be a good old-fashioned snow storm. Even if that snow is mostly dry ice at -109 degrees F!