There are measuring stations.
The most basic ones are just a tube in a field. It’s sufficiently wide to account for rain that isn’t falling straight down, and sufficiently clear on all sides to prevent wind currents around buildings from manipulating the readings. The amount of rainfall is recorded from them.
In older times, they would just be manually measured after a rain storm. There’s all sorts of tooling to automate it, but the premise is the same these days — just catch the rain while controlling for variables. Do it in many locations and average it for better results.
There are phydical measuring stations. Official government ones in the us are located at airports, unofficial sources like weather underground use volunteer stations get data from stations located more broadly in cities. Weather radar can also show amounts of precipitation in the air so they can see how much water is falling over larger areas.
Commercial weather providers also aggregate their own stations and official government sources to provide information to their subscribers.
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