A Parameterization of the Visible Extinction Coefficient of Ice Clouds in Terms of the Ice/Water Content

Abstract

This article describes a parameterization of the visible extinction coefficient of cirrus and frontal ice cloud in terms of the ice/water content. The parameterization is based on the discovery that the ice cloud particle size spectra from a particular dataset tended to fall into three separate well-defined regions. These regions were a Marshall?Palmer distribution covering particles with dimensions larger than between 100 and 1400 ?m, depending on the cloud temperature; a Heymsfield?Platt type power-law distribution for the smaller particles (dimensions from 20 ?m to somewhere between 100 and 800 ?m); and a different spectrum of the smallest particles of sizes less than 20 ?m. The dataset chosen had been obtained from aircraft in situ observations of cloud particle size spectra in ice clouds and covered the entire spectral range from 2 to 3000 ?m, thus allowing a study of every important spectral region. Part of this dataset was used originally in a previous study by Heymsfield and Platt. The data used in the present study covered cirrus clouds overlying deep frontal clouds, together with a reanalysis of the Heymsfield?Platt set for ?dry? cirrus clouds. In the present study, the visible extinction coefficient σ was parameterized in terms of the ice/water content W. A model of cylindrical ice particles was used. It was found that the dependence of σ on W followed a power law of the form, σ = jWk, where k had a value that depended on the temperature range. The size spectra, although measured in certain cirrus and frontal ice clouds, were also used as surrogate spectra to estimate similar σ?W relations for water clouds. The σ?W relations for cirrus ice clouds were found to agree reasonably with those obtained recently by other workers. The relations also indicated, conversely, that the cloud ice/water content of cirrus could be retrieved from a measure of the cloud volume extinction coefficient to within an uncertainty of about 30%.