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I have a large plateau, and roughly in the center are mile-high cliffs surrounding a valley.

Inside the valley is a green sandy desert. The sand is composed of olivine. Unfortunately for the inhabitants of the green desert, a hostile power has resolved to remove all the sand out of the valley, off of the plateau, and into the lowlands below it via a huge ramp/shaft that they dug and some vague (and very classified) magic trickery.

What does this do to the local climate? Is a desert in a closed-off valley even entirely possible?

Of equal interest: what happens to the lowlands? This particular area of them where the sand is being drained is a region of badlands. Keep in mind that it isn't all of the sand being dumped at once, but rather a steady (albeit massive) flow of the stuff.

And what would happen to the flora and fauna on both ends?

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    $\begingroup$ FYI: Angle of repose. For dry sand, its 34 degrees. Sand will not flow down if its slope is less than 34 degrees. $\endgroup$ – Alexander Aug 2 '18 at 0:12
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    $\begingroup$ @RonJohn It is made of olivine. The hostile power's motivations are hardly relevant to the question, but suffice it to say that it's a brute-force and roundabout way of committing genocide for a variety of reasons. As for your last question, I'm not a climate scientist, even by armchair qualifications. That's why I'm asking. $\endgroup$ – Classified Angel Aug 2 '18 at 0:17
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    $\begingroup$ @RonJohn Again, not relevant to the question, but these aren't humans they're committing genocide against. They're a species entirely dependent upon the existence of their desert without much ability to live in other climates. $\endgroup$ – Classified Angel Aug 2 '18 at 0:25
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    $\begingroup$ @RonJohn Except I'm not asking about the inhabitants, I'm asking about the natural world around them. I couldn't care less what happens to the inhabitants for the purposes of this question; I'll do some handwavium in my story regarding that. $\endgroup$ – Classified Angel Aug 2 '18 at 0:30
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    $\begingroup$ @ronjohn This is purely a question about ecological effects. None of that other stuff matters. It's not nearly that complicated, and the presence of predictable environmental effects makes this not opinion based. $\endgroup$ – user49466 Aug 2 '18 at 1:09