Normalized particle size distribution for remote sensing application

The ice particle size distribution (PSD) is fundamental to the quantitative description of a cloud. It is also crucial in the development of remote sensing retrieval techniques using radar and/or lidar measurements. The PSD allows one to link characteristics of individual particles (area, mass, and scattering properties) to characteristics of an ensemble of particles in a sampling volume (e.g., visible extinction (σ), ice water content (IWC), and radar reflectivity (Z)). The aim of this study is to describe a normalization technique to represent the PSD. We update an earlier study by including recent in situ measurements covering a large variety of ice clouds spanning temperatures ranging between -80°C and 0°C. This new data set also includes direct measurements of IWC. We demonstrate that it is possible to scale the PSD in size space by the volume-weighted diameter Dm and in the concentration space by the intercept parameter inline image and obtain the intrinsic shape of the PSD. Therefore, by combining inline image, Dm, and a modified gamma function representing the normalized PSD shape, we are able to approximate key cloud variables (such as IWC) as well as cloud properties which can be remotely observed (such as Z) with an absolute mean relative error smaller than 20%. The underlying idea is to be able to retrieve the PSD using two independent measurements. We also propose parameterizations for ice cloud key parameters derived from the normalized PSD. We also investigate the effects of uncertainty present in the ice crystal mass-size relationships on the parameterizations and the normalized PSD approach.