IDW is a weighted average: closer gauges get more say. With a power of 2 the centre of our three gauges reads 30.9 mm, not the plain 20.7.

Inverse distance weighted interpolation guesses the value between samples by averaging the neighbors, each weighted by one over its distance raised to a power. It is exact at the gauges, never leaves the range of the data, and gives no error estimate, so you test it with cross validation.