It will probably lower your pH (all rain is acid despite what you hear on the news; some is just more acidic ). It may introduce dirt and organics that need to get oxidized by your chlorine thus increasing chlorine demand.
Your test results will tell the tale. Post a full set of numbers and the experts here will help you interpret. Post free and combined chlorine, pH, alkalinity, CYA, and calcium hardness. A chlorine test tonight and one tomorrow morning before the sun hits the water would be especially instructive.