Rain does change the chemistry of the pool water but, keep in mind that minor amounts of rain aren’t going to change the pH that drastically 😁 Rain is acidic 😎 It is at a pH lower than the one we sete set for our pool 😁 Our pool pH should remain between 7.4- 7.6. This is because the pH in our pool should be between 7.4 and 7.6. Major fluctuations can result in severe discomfort. Many people say that the chlorine levels are too high and their eyes burn. If your eyes feel uncomfortable swimming, chlorine is rarely an issue. Most likely, the pH of your water is either low or high. Rainwater is normally around pH 5.0. Depending on the amount of rainfall, it may lower the pH. 
The acidity and alkalinity The pH scale is used to measure the acidity and alkalinity of liquids. It ranges between 0 and 14, where 7 is neutral. This means it’s neither alkaline nor acidic. An acidic pH value is one that is between 0 and 7, meaning the liquid is more acidic than the other. Alkaline is a pH value higher than 7 or 14 — the further away from 14, the better. You can calculate pH by taking the same measurement in alkaline or acidic liquids. Low pH liquids have high levels of hydrogen ions (also known as hydrogen atoms). High pH liquids have fewer hydrogen ions. 
Blog.hayward-pool.com It is possible for rainwater to fall directly onto your pool. This, however, does not make it a good thing. You now have another source of water when rainwater falls on your landscaping or deck. When rainwater and ‘run off’ enter the pool, they can change your water’s pH, calcium hardness, total dissolved solids (TDS), alkalinity and other chemical levels as well as bring contaminants (e.g. Rainwater is generally acidic (see map showing pH of rainwater across U.S.), so debris, dirt and other contaminants can enter the pool. Your pool water may become acidic due to rainwater (see map showing pH across U.S.). Damage to the plaster and metal parts You can also add to your pool. 
Mywaterearth.com Continued to explain how there’s an innovative product that appears like a pool covering. This is called SMOPS Leave Net Cover for 12-foot by-24-Foot Rectangle Above-Ground Pools. Keeps leaves and other debris off your winter pool cover.| Keeps Leaves and Other Debris Off Your Winter Pool Cover It is a large net mesh cover that will cover the pool cover in the winter but you can also stretch it over your pool and catch leaves and trash that will blow into the pool during a storm – I checked it out it folds up nicely and is light enough to put on and take off with 2 people. This cover may be well worth it! This was revised by Margaret Howard, Sanliurfa (Turkey), January 14, 2020.