The Collaborative International Dictionary of English v.0.48:

Udometer \U*dom"e*ter\, n. [L. udus wet, moist + -meter.]
   (Meteor.)
   A rain gauge.
   [1913 Webster]

WordNet (r) 3.0 (2006):

udometer
    n 1: gauge consisting of an instrument to measure the quantity
         of precipitation [syn: rain gauge, rain gage,
         pluviometer, udometer]