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) in the upper troposphere and lowermost stratosphere we set up the frequency distribution of path lengths flown by MOZAIC aircraft within ISSRs. The mean path length is about 150 km with a standard deviation of 250 km. We analyse 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 distribution to the underlying size distribution of ISSRs, assuming that they have circular shape. We solve the equation (by trial and error) and test the result 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 relevance of the result is discussed and dedicated research flights to measure the true extension of ISSRs are recommended.