The pH of rain is generally acidic due to the dissolved carbon dioxide (carbonic acid) from the air as well as from other acidic sources (nitric and sulfuric acids). However, the TA (pH buffering) of rain is fairly low so the effect of rain on pool pH is minimal from the rain itself (unless it is very, very acidic). Generally, rain increases aeration of the pool water so will raise the pH of the water as a result.
If you dilute the pool with a lot of rain water, but don't have it splash into the pool, then the pH will likely drop slowly. If you let the raindrops splash into the pool, then the pH may go up at first and then slowly drop if there is enough dilution of the water.
If you dilute the pool with a lot of rain water, but don't have it splash into the pool, then the pH will likely drop slowly. If you let the raindrops splash into the pool, then the pH may go up at first and then slowly drop if there is enough dilution of the water.