A model for the horizontal exchange between ice-supersaturated regions and their surrounding area

A simple model is devised to simulate the turbulent exchange of humidity between ice-supersaturated regions in the upper troposphere and their subsaturated environment. The model works as a random version of a 2-dimensional cellular automaton, and does not contain dynamics nor microphysics, In spite of its simplicity the model helps to interpret certain stochastic properties of ice-supersaturated regions. namely the exponential distribution of the degree of supersaturation and the Weibull distribution of path-lengths through these regions. In particular, the exponential distribution of the degree of supersaturation evolves from permanent humidity exchange in spite of a rather peculiar initial distribution of supersaturation, that is, two Dirac delta functions. Such a robust feature is advantageous for future parameterisations of ISSRs for large-scale models.