Just a quick idea, if the tarp could potentially have some sort of gutter system on the edges, I would suggest drilling a small hole through the snowpack and funneling the water down through it (with a sleeve in the snow of course) so that all the water that lands on a whale will go right under the snow and into the ground causing the least amount of damage possible. I would suggest a long inflatable tube on the edge of the tarp. When inflated it would cause a little gully between the edge of the tarp and it, giving the water somewhere to pool and then drain.
Kinda makes me want to draw something up but I've got wayyy too many lab reports to take the time.