Sean, Fishman & others - Many of the popular windmills being sold today ($500-$800) produce a VERY SMALL(0.1-0.2cfm)amount of air at 5mph; watch a windmill produce bubbles in a low wind. Very small surface boil. Very few bubbles at that wind speed (depending on depth & type of diffuser)! Air flow is somewhat proportional to the wind speed. The windmill works at 5mph but barely. It also depends on the depth and water head pressure on the diffuser as to the minimal wind speed necessary for the windmill compressor to "generate" air. The 1 cfm produced at even a 20-25 mph wind is really not very much air when compared to a 1/4-1/3 hp ROTARY VANE compressor which produces 4-4.5cfm of air! That's 5.8-6.6 five-gallon buckets (29-33gal) of air every 1 minute (7.48 gal/cu.ft.)! This results in about 8-10 times larger and stronger boil than what the windmill can produce in the best wind. With 4X more air the diffuser can be LARGER and many more bubbles generated over the larger area which results in more water being entrained in the cylindrical-conical upward flow.
Diaphragm and piston compressors produce less air flow per hp than rotary vanes.
You can push air with the compressor 200-400 ft thru 1/2" pipe and farther 400-700ft thru 3/4" pipe and not have a lot of pressure drop. Larger pipe dia. is necesary for longer pipe "runs".

However, 1 cfm and less air volume delivered to a good membrane diffuser with very small holes is a LOT BETTER than nothing at circulating your pond' bottom water during summer stagnation.
Circulation moves low oxygen water out of the bottom and oxygenated water to the bottom where decomposers process the organic sediments; plus water with diss. oxygen prevents anoxic or septic conditions from forming on top of the bottom sediments & in deep water. Fish do not live where the Diss. oxygen is less than 3 parts per million they are uncomfortable at 4 ppm.
Any questions? I try to educate without bias.

aka Pond Doctor & Dr. Perca Read Pond Boss Magazine -
America's Journal of Pond Management