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\title{An empirical parameterization of the subgrid-scale distribution of water
vapor in the UTLS for atmospheric general circulation models}



\author[1]{Audran Borella}%
\author[2]{Étienne VIGNON}%
\author[1]{Olivier Boucher}%
\author[3]{Susanne Rohs}%
\affil[1]{Institut Pierre-Simon Laplace}%
\affil[2]{Laboratoire de Météorologie Dynamique}%
\affil[3]{Forschungszentrum Juelich}%


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  \date{May 25, 2024}


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\begin{abstract}
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 IAGOS (In-service Aircraft for a Global Observing
System) are used to parameterize the distribution of water vapor in the
upper troposphere and lower stratosphere (UTLS). 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 hundreds 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
simulates the observed distributions with a determination coefficient
always greater than 0.917, with a mean value of 0.997. Moreover, the ice
supersaturation fraction in a model gridbox is well simulated with a
determination coefficient of 0.983. The parameterization is robust to a
selection of various geographical subsets of data and to gridbox sizes
varying between 25 to 300 km.%
\end{abstract}%



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