I've done it, but I followed David Pagan Butler's idea using bubble pumps. I kept the sand filter that came with the above ground pool, but swapped the sand for scoria. It certainly wasn't enough filtration, according to DPB, so I also included a number of plant beds, made out of stacked milk crates, lined with shade cloth and using perforated pvc running through the middle of these, to filter the water using DPB style bubble pumps. Once it became established, the water was lovely and clear all year round, although too cold to swim over winter. It did get some algae settle on the bottom of the pool over winter, but I just used a pool scoop on spring to tidy it up and emptied the algae onto the permaculture style gardens.
Nobody ever got earaches or eye infections, no mosquitoes etc, and the water was so soft to swim in. I miss it, now I've moved...
