I don't know the exact math but trying to equate the volume of water being moved to the volume of air on a 1:1 basis is incorrect. It may be proportional but it is more dependent on the bubble size and not just the air volume. Otherwise you wouldn't need a diffuser and could just stick the end of the hose in the pond.
In my case I have tubular ring diffusers. I too asked the supplier about lift rates and, not surprisingly, they didn't have an answer. Just a generic reply that it all depends on the exact situation. Based on the size of the upwelling when running they have to be moving at least several hundred GPM, if not more.
When I measured the temperature differences yesterday morning after running from 3am-7am they were within 1 degree at virtually all depths. With the system off at mid-day there was a 7 degree difference from the surface to 4 feet down.
This is all anecdotal of course (other than the temperatures) as I've no way to actually measure the volume of water being moved. I guess one could use a large diameter column and build a makeshift airlift and capture the water but that sounds like too much work.
