Short of draining, drying, and washing with bleach . . . you usually can't remove it. Black algae tends to penetrate INTO crevices in the plaster, and go dormant when you kill the visible parts. Then, it just waits till you slack off on pool maintenance again, to regrow.
But to CONTROL it, you need to do the following:
#1 - Get a Taylor K2006 (Amazon link below) test kit or OTHER FAS-DPD drops based test kit, so you can accurately determine your pH, chlorine and stabilizer level. And no, even the best dealer-used 'stupid' strips are NOT an adequate substitute. They are almost useless at measuring stabilizer.
#2 - Once you have the kit, and have your pH between 7.2 and 7.8, your alkalinity below 140ppm, and know what your stabilizer is, use the "Best Guess" chart (again, link in my signature below) to determine the CORRECT chlorine levels for your pool.
#3 - Once you've done all that, adjust chlorine to shock levels AND use your brush. Continue doing so (chlorine AND brushing) for 1 week AFTER all visible algae is gone.
#4 - Then, make sure you MAINTAIN adequate chlorine levels for your stabilizer level.
Meanwhile, if you can get some calcium hypochlorite shock, and then BRUSH the spots, followed by sprinkling them with cal hypo, that will help.
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