In celebration of @NASAPersevere's landing in two days (and the press release on my Mars Dust Activity Database, MDAD), let's review the chances Percy will encounter a dust storm on landing and after.
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Let's start with the timing of landing. We just entered Mars Year 36, Ls=0 (Happy New Year) (Ls is a measure of time of year, with 0 being northern spring equinox.) While on average it's clearer in the first half of the year, there are still plenty of individual dust storms.
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This is why landing now is important. There are lots of small storms (black and blue circles), but importantly, there are no "major" dust events during this time of year (gold circles). (There was an odd event at the beginning of last year in MY 35, but that is the exception.)
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Major events are the problem events. They're >10million sq km in size and are the ones big enough to impact their surrounding environment. Again, landing now avoids those. The smaller events are generally <1million sq km.

So the chances of Percy landing into one of them given the surface area of Mars ~150million sq km is really, really tiny even if storms were distributed evenly over the surface. But they aren't. Jezero crater (Percy's landing site) is at about 20N.
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At Ls~5 and 20N, there are almost no dust storms in any year. There are a couple, plenty at 20 N for other times of year, but during landing, they are rather scarce this near the equator. Percy should have no problem with landing.
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In the future, Percy may (probably) have to deal with large dust events like the one that killed Oppy. Fortunately, Percy isn't solar powered so will be just fine. However, Percy may get to see some of these events first hand given it is further north than @MarsCuriosity
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Here's how often a given spot gets a dust storm of any kind. The red circles show landers. About ~3% ish of days there is some sort of dust for Percy. That may not sound like a lot, but it's 20 sols per year.
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This is a lot more than any other recent lander except Phoenix, which by design had a short mission and didn't deal with dust. @NASA, of course, partly chooses locations based on lack of dust storms, excepting global dust events, which you know, by definition you can't avoid.
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Here's the interesting thing about Jezero though; it's on the edge of one of the N-S dust storm tracks, or flushing tracks as we call them. Dust originates along the edge of the ice cap because the strong thermal contrasts generate a lot of winds.
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Atmospheric waves can sometimes push that dust south in specific channels. Percy will be at the edge of the Utopia storm track. Over the 8 MY of the MDAD, there were ~50 flushing storms at Jezero. These start in the north and move south, and we might be able to image them.
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Here's an example of one. The arrows show the winds pushing the dust over Jezero from the north from the EMARS dataset. It will be extremely hard to get the timing right, but I think it is possible with enough (ahem) perseverance and time to image this from the surface.
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At least, that's what I tried unsuccessfully to convince NASA of. I'll have to wait for the next scientist call to propose again. Regardless, here is the full evolution of the dust event in the last tweet. Again, they start off the polar ice cap and are pushed south.
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They travel through three regions, and Utopia is second only to Acidalia in dust activity. Once in the southern hemisphere they sometimes get a second life and make large regional events, but that's a discussion for another time.
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They're exceedingly beautiful. The really fun part is, we don't exactly know why some push south and most don't. We have some ideas, but we aren't sure. The excellent pressure and wind measurements we get from Percy may help with that. Stay tuned over the next few years.
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Again, the dataset is free to download:
https://doi.org/10.7910/DVN/F8R2JX
Here's the (paywalled) paper:
https://doi.org/10.1016/j.icarus.2020.114059
Here's a copy on my website:
http://www.battalio.com/pdfs/MDAD.pdf 
Here's the @CenterForAstro press release:
https://www.cfa.harvard.edu/news/su202107 
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