A Statistical Model for Stationary Atmospheric Cloudiness, Liquid Water Content, and Rate of Precipitation

Abstract

A simple model is developed whereby we compute the men hydrological elements in the atmosphere including fractional cloudiness, liquid water content, rate of precipitation, and the water vapor field over a large area. The atmosphere is modeled by an ensemble of many air parcels moving randomly in the vertical direction. The adiabatic expansion of the air parcel generates the condensation of water vapor, which in turn forms cloud droplets and precipitates as rain or snow. These processes are formulated in a simple manner based on the assumption of stationary equilibrium between the growth of cloud droplets and the precipitation due to gravity. Also, a high statistical correlation between vertical velocities and the lengths of vertical displacement is assumed in order to calculate the mean thermodynamical changes for the ensemble of moist air parcels. The model computes all the hydrological components if the mean humidity, the mean vertical velocity and its standard deviation, together with two time-parameters that characterize the stationary state of the model, are given. The model was tested by using a set of global atmospheric data computed in a general circulation experiment, and the results of zonal mean cloudiness and precipitation compare favorably with climatological observations.