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Rain gauges do not use the usual liquid level measurement as a rule. Instead they use what's called a tipping spoon counter.
Let me explain: You have a funnel of a certain area size for the large opening.
The small opening empties into a spoon which is mounted on a pivot axis underneath. On the handle side of the spoon is a small magnet (use a plastic spoon!) that keeps the spoon horizontal by getting attracted to a bracket from the case.
As the rain fills the spoon this end gets heavier until it breaks the magnetic force on the handle side and the spoon tips, emptying itself. The magnet side is now heavier and rotates back to the bracket rest.
The cycle repeats.
There is a optical sensor switch that gets triggered each tipping cycle or a reed switch could be used, triggered by the magnet wizzing past as the spoon tips.
The sensor switch output goes to a counter that counts the cycles.
If one has a funnel opening of 100 sq cm and 0.01litre of water (1mm rain) triggers the spoon to trip this would then measure the rain fall in millimetres.
If you live in a non metric country you do your own calculations :wink:
Have fun building one of these, there was a plan and good description of this type rain gauge in an Australian Electronics magazine many years back, from which I built my rain gauge.