Snow patch and glacier size distributions

A simple theoretical model demonstrates that some amount of randomness in s now and ice mass balance is sufficient to reproduce empirically observed po wer law and exponential distributions of snow patch and glacier sizes. No o ther assumptions about the underlying topography or snow accumulation and a blation processes are necessary to extract this important spatial property. The inclusion of additional geometrical and physical processes can alter t he specific scaling constants of the size distributions, but the fundamenta l behavior remains unchanged. Specifically, for snow patch and glacier size s less than some correlation length the size distribution is a decreasing p ower law, and for sizes larger than the correlation length the distribution decreases rapidly as an exponential. The solution is based on a mapping to a relatively well explored class of problems in percolation theory.