Is a Sandstorm copy?
Googling around it says it has something to do with Wave analytics but couldn't find much info about it.
What does this option do?
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If you look at some older release notes, it becomes slightly clearer what exactly Sandstorm may be:
We’ve rebuilt our sandbox copy engine to optimize performance, scalability, and customer success. The new engine impacts Full sandboxes as they are created and existing Full sandboxes as they are refreshed.
Several enhancements to the copy engine make sandbox creation and refresh faster and minimize sandbox inconsistencies. These improvements are available on a rolling basis during the Summer ’15 release.
New Data Copy Framework
New Post-Copy Framework
My guess, based on this and the two subsequent release notes is that SFDC built a great new way to make Sandboxes better and quicker, but it failed to work properly for Analytics Cloud, so they gave users an override. Now, it seems like they've fixed it, but they forgot to remove the checkbox from the layout (or maybe kept it intentionally for some reason).
Anyway, based on that history, I'd say, "Ignore the field - it's default and you should just keep it unless your support rep gives you a way to override it for some reason."
As for the name, my guess is that "Sandstorm" is a pun on "Sandbox." And it just sounds cool. I'd assume it has nothing to do with the hash function mentioned in the earlier answer.
When you use the Sandbox to test Wave Analytics functionality, sandbox copy now uses the new Sandstorm algorithm.
Although I have have not been able to find any information directly related to what the "Sandstorm algorithm" actually is.
Unless this is it:
The SANDstorm hash is a cryptographic hash function designed in 2008 by Mark Torgerson, Richard Schroeppel, Tim Draelos, Nathan Dautenhahn, Sean Malone, Andrea Walker, Michael Collins, and Hilarie Orman for the NIST SHA-3 competition.
The SANDstorm hash was accepted into the first round of the NIST hash function competition, but was not accepted into the second round.
The SANDstorm hash family is designed for maximal cryptographic strength and high speed on most common architectures