"increase of" vs. "increase in" in connection with abstract quantities

As a non-native speaker, I've had troubles with it too! The Academic Vocabulary in Use book (McCarthy and O'Dell, Cambridge, 2008) says on p. 62:

The nouns rise, growth, fall, drop and decline, like increase and decrease are followed by in (to explain what is rising) or of (to explain the size of the change), e.g. a rise of 10% in the number of cars.

I do not know whether the source quoted is reputable enough for you, though. In addition, I think that everything that you can increase automatically falls into the category of "abstract mathematical or physical quantities". You cannot really increase something concrete and tangible like "water" or "a cat", that'd be nonsensical. You can increase the amount of water or the weight of a cat - but these are the abstract quantities! The rainfall in your example isn't just water, but, as Merriam-Webster defines it, it is "the amount of precipitation...". Therefore, the next time you come out to the street, you may feel the increase in the rainfall... or you may not, depending on where you live)