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The global observation, assimilation and prediction in numerical models of ice super-saturated (ISS) regions (ISSR) are crucial if the climate impact of aircraft condensation trails (contrails) is to be fully understood, and if, for example, contrail formation is to be avoided through aircraft operational measures. Given their small scales compared to typical atmospheric model grid sizes, statistical representations of the spatial scales of ISSR are required, in both horizontal and vertical dimensions, if global occurrence of ISSR is to be adequately represented in climate models. <br><br> This paper uses radiosonde launches made by the UK Meteorological Office, from the British Isles, Gibraltar, St. Helena and the Falkland Islands between January 2002 and December 2006, to investigate the probabilistic occurrence of ISSR. Each radiosonde profile is divided into 50- and 100-hPa pressure layers, to emulate the coarse vertical resolution of some atmospheric models. Then the high resolution observations contained within each thick pressure layer are used to calculate an average relative humidity and an ISS fraction for each individual thick pressure layer. These relative humidity pressure layer descriptions are then linked through a probability function to produce an s-shaped curve which empirically describes the ISS fraction in any average relative humidity pressure layer. Using this empirical understanding of the s-shaped relationship a mathematical model was developed to represent the ISS fraction within any arbitrary thick pressure layer. Two models were developed to represent both 50- and 100-hPa pressure layers with each reconstructing their respective s-shapes within 8–10% of the empirical curves. These new models can be used, to represent the small scale structures of ISS events, in modelled data where only low vertical resolution is available. This will be useful in understanding, and improving the global distribution, both observed and forecasted, of ice super-saturation.