Tarp blew off and pool cover pump dropped water level

[Stic2it]

I have a 40x20 in ground pool that was just finished in Oct/Nov. We were decided to hold off on the pool cover until next year and now I’m messing with a tarp. We have had some of the windiest days lately and the tarp blew off a bit. One of the edges blew free and dragged the cover into the pool, letting pool water on top and the pump quickly got to work emptying the pool. The pool is now 8 inches under the skimmer. I’ve got the tarp secured better but the question is do I need to add more water? If so I’d assume I have to add some winter chemicals also? There is plenty of water in the pool and the tarp seems to fit better with it dropping into a bowl shape. Add water or leave it? Will this hurt my new plaster that’s exposed?
Thanks

 

[ajw22]

That is around the amount the water level is lowered when closed. I would just leave it. The pool will fill from the winter precipitation.

 

[bmoreswim]

You mention perhaps adding winter chemicals if you add water. Am I understanding correctly that the pool was not winterized? I'm not familiar with folks leaving the water at operating level with a plaster pool with waterline tile which is subject to damage/popping from freezing. Weather will be below freezing for roughly a week starting tonight.