tonecold,

Since your case is the only one I have ever seen where keeping sufficiently high chlorine levels would not keep away green algae, I've been thinking more about it and I believe I may know what is happening in your situation. I suspect that in your above-ground pool that you do not have a floor drain, but only have a skimmer (and a return, of course). So perhaps the circulation is very poor in the depths so that chlorine concentrations are low there, especially when the algae wasn't completely killed (as Janet pointed out as a possibility). Though keeping a higher concentration overall will increase even the concentration at depths, an easier solution would be to improve circulation through pointing the return down and to the side to try and get a spiraling effect. Also, using a pool sweep regularly to mix up the water might help. Manual solutions include regular brushing to mix up the water -- or just using the pool every day including deep diving!

Anyway, I could be wrong about this, but wanted to offer some suggestions. You might try inverting a container and with a grabber tool take it to the depths not far from the algae, then invert the container and bring it up to measure the chlorine level down there. That would help confirm or dispute my assertion. Janet's recommendation for shocking is still appropriate since getting rid of the chlorine demand from nascent algae should help.

Richard