Well, if you're in a drought, the ground under your pool will likely lose some moisture, what happens depends a lot on the makeup of your soil.
How deep are your canyons? If they're pretty shallow, I doubt it's moles since when their tunnels collapse, they leave about 4-6" deep canyons, 4-8 inches wide.
Moles like to create tunnels near the edge of a water source (pond/stream), working their way inland sometimes up to 100 feet, if your pool is close to a pond or such it could well be.
Likely, it is due to the earth drying and shrinking under the pool, your sand should not wash out from rain unless you have a hill coming down to the side of your pool that allows tons of water to rush at the pool, some of this water could work it's way under and do some damage, but it would not create mini streams from one side to the other (too much weight pushing down from above).