Snow patch and glacier size distributions

A simple theoretical model demonstrates that some amount of randomness in snow and ice mass balance is sufficient to reproduce empirically observed power law and exponential distributions of snow patch and glacier sizes. No other assumptions about the underlying topography or snow accumulation and ablation processes are necessary to extract this important spatial property. The inclusion of additional geometrical and physical processes can alter the specific scaling constants of the size distributions, but the fundamental behavior remains unchanged. Specifically, for snow patch and glacier sizes less than some correlation length the size distribution is a decreasing power 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.