On the size distribution of ice-supersaturated regions in the upper troposphere and lowermost stratosphere

In order to determine typical sizes of ice-supersaturated regions (ISSRs) i n the upper troposphere and lowermost stratosphere we set up the frequency distribution of path lengths flown by MOZAIC aircraft within ISSRs. The mea n path length is about 150 km with a standard deviation of 250 km. We analy se the influence of a selection bias (viz. that large ISSRs are more often crossed by aircraft than small ones) on the obtained path length statistics and derive a mathematical equation that relates the path length distributi on to the underlying size distribution of ISSRs, assuming that they have ci rcular shape. We solve the equation (by trial and error) and test the resul t using numerical simulations. Surprisingly, we find that there may be many more very small ISSRs than apparent from the data such that the true mean diameter of the ISSRs may be of the order a few kilometres only. The releva nce of the result is discussed and dedicated research flights to measure th e true extension of ISSRs are recommended.