I’ll throw in something a little different that caught me off guard the first time it happened.
Sometimes it’s not that the rain “caused” algae, it just exposed that you were already riding the edge. I had my free chlorine sitting at what I thought was fine for my CYA, but I was basically at the bare minimum on the FC/CYA ratio. Water looked perfect. Then we got a hard storm, pool temp dropped about 5 degrees overnight, a bunch of fine dirt blew in, and boom, faint green haze the next day.
What I learned was that rain does three things at once. It dilutes chlorine and CYA a bit, it adds organics, and it can shift pH. If your stabilizer drops even 5 to 10 ppm and you were already dosing to the low end, your effective protection margin shrinks fast. Add extra demand from debris and algae gets a tiny head start.
Now before big storms I bump chlorine slightly above my normal target, not crazy high, just a cushion. After the rain I test CYA and free chlorine, brush everything, and make sure circulation runs longer than usual. I also keep an eye on filter pressure because storms tend to load it up with fine junk, and reduced flow doesn’t help when you’re trying to clear something up.
If you can, check what your CYA and free chlorine are the day after a storm compared to a dry week. A lot of times the pattern shows you were just barely hanging on before the rain hit.