Yes what he said is correct, after researching this issue I think I'll go with an all
natural swimming pool, this is where a pond is used adjacent to the pool with plants that do the bio break down.
This has been used in Europe for years and is just now gaining traction here in the US.
The water is circulated between the pond and pool, the standard sand or cartridge filter is used along with a UV filter or Ozone, one or the other not both.
THis pond will also add warm water back to the pool because it would be shallow 6-12"
Here's rough idea the pond is at the upper part of the pic, the pond would be located outside the birdcage