An Empirical Parameterization of the Subgrid-Scale Distribution of Water Vapor in the UTLS for Atmospheric General Circulation Models

Temperature and water vapor are known to fluctuate on multiple scales. In this study 27 years of airborne measurements of temperature and relative humidity from In-service Aircraft for a Global Observing System (IAGOS) are used to parameterize the distribution of water vapor in the upper troposphere and lower stratosphere. The parameterization is designed to simulate water vapor fluctuations within gridboxes of atmospheric general circulation models (AGCMs) with typical size of a few tens to a few hundred kilometers. The distributions currently used in such models are often not supported by observations at high altitude. More sophisticated distributions are key to represent ice supersaturation, a physical phenomenon that plays a major role in the formation of natural cirrus and contrail cirrus. Here the observed distributions are fitted with a beta law whose parameters are adjusted from the gridbox mean variables. More specifically the standard deviation and skewness of the distributions are expressed as empirical functions of the average temperature and specific humidity, two typical prognostic variables of AGCMs. Thus, the distribution of water vapor is fully parameterized for a use in these models. The new parameterization reproduces the observed distributions with a determination coefficient always greater than 0.917 and with a mean value of 0.997. The parameterization is robust to a selection of various geographical subsets of data and to gridbox sizes varying between 25 and 300 km.