this could be implemented in 2 ways ( if my understanding of measuring rain is correct).
first way is to use metal probes at diferent heights, so that they successively gets conducting as the level of water increases. Any conventinal circuit could be used afterwards.
the second way is to measure the weight of the rain drops accumulated within a certain period of time.
the second is a little complex and needs to be tricky with ciruicts, but may prove to be the best.
Sajjad