A distribution law for relative humidity in the upper troposphere and lower stratosphere derived from three years of MOZAIC measurements

Data from three years of MOZAIC measurements made it possible to determine a distribution law for the relative humidity in the upper troposphere and lower stratosphere. Data amounting to 13.5% of the total were obtained in regions with ice supersaturation. Troposphere and stratosphere are distinguished by an ozone concentration of 130 ppbv as threshold. The probability of measuring a certain amount of ice supersaturation in the troposphere decreases exponentially with the degree of ice supersaturation. The probability of measuring a certain relative humidity in the stratosphere (both with respect to water and ice) decreases exponentially with the relative humidity. A stochastic model that naturally leads to the exponential distribution is provided. Mean supersaturation in the troposphere is about 15%, whereas ice nucleation requires 30% supersaturation on the average. This explains the frequency of regions in which aircraft induce persistent contrails but which are otherwise free of clouds. Ice supersaturated regions are 3-4 K colder and contain more than 50% more vapour than other regions in the upper troposphere. The stratospheric air masses sampled are dry, as expected, having mean relative humidity over water of 12% and over ice of 23%, respectively. However, 2% of the stratospheric data indicate ice supersaturation. As the MOZAIC measurements have been obtained on commercial flights mainly between Europe and North America, the data do not provide a complete global picture, but the exponential character of the distribution laws found is probably valid globally. Since water vapour is the most important greenhouse gas and since it might enhance the anthropogenic greenhouse effects via positive feedback mechanisms, it is important to represent its distribution correctly in climate models. The discovery of the distribution law of the relative humidity makes possible simple tests to show whether the hydrological cycle in climate models is represented in an adequate way or not.