
^{1}Centre for Atmospheric Science, Department of Chemistry, University of Cambridge, Cambridge, UK ^{2}Deutsches Zentrum für Luft und Raumfahrt, Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany Abstract. The global observation, assimilation and prediction in numerical models of ice supersaturated (ISS) regions (ISSR) are crucial if the climate impact of aircraft condensations trails (contrails) is to be fully understood, and if, for example, contrail formation is to be avoided through aircraft operational measures. A robust assessment of the global distribution of ISSR will further this debate, and ISS event occurrence, frequency and spatial scales have recently attracted significant attention. The mean horizontal path length through ISSR as observed by MOZAIC aircraft is 150 km (±250 km). The average vertical thickness of ISS layers is 600–800 m (±575 m) but layers ranging from 25 m to 3000 m have been observed, with up to one third of ISS layers thought to be less than 100 m deep. 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. 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. Specifically each radiosonde profile is divided into 50 and 100hPa 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 sshaped curve describing the ISS fraction in any average relative humidity pressure layer. An empirical investigation has shown that this one curve is statistically valid for midlatitude locations, irrespective of season and altitude, however, pressure layer depth is an important variable. Using this empirical understanding of the sshaped relationship a mathematical model was developed to represent the ISS fraction within any arbitrary thick pressure layer. Here the statistical distributions of actual high resolution RHi observations in any thick pressure layer, along with an error function, are used to mathematically describe the sshape. Two models were developed to represent both 50 and 100hPa pressure layers with each reconstructing their respective sshapes 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 supersaturation. Citation: Dickson, N. C., Gierens, K. M., Rogers, H. L., and Jones, R. L.: Probabilistic description of icesupersaturated layers in low resolution profiles of relative humidity, Atmos. Chem. Phys. Discuss., 10, 23572395, doi:10.5194/acpd1023572010, 2010. 
