I believe I heard during the race coverage last year that the wet tires "pump" 400 gallons a minute of water at some RPM's. Never really thought of tires as pumps before but it makes sense; They move water from the center of the contact patch to the outside to prevent hydroplaning.
Looking into street tires I have seen water "pumping" numbers around 30-50 gallons. So F1 rain tires move roughly 10 times the water of a street tire...
Imagine F1 snow tires!