Theoretical Basis for Retrievals of Irregular-Particle Collections in the Atmosphere

The retrieval of water cloud microphysics involving ensembles of spherical droplets has been firmly established on a solid theoretical foundation by using liquid water content, effective radius, and effective variance as characterizing parameters for the scattering properties of these ensembles. However, there is no such solid theoretical foundation for the retrieval of non-spherical or irregular hydrometeors. Based on scattering calculations performed on realistic crystals generated from an innovative numerical crystal growth model, it is found that, under the constraint of a fixed particle volume distribution, the single-scattering properties derived from ensembles of irregular particles made up with the same set of crystal habits are nearly invariant, if they also have at the same time the same total volume-to-surface and total volume-to-mean-projected-area ratios. Therefore we suggest the use of two effective radii, i.e effective projected-area radius and effective surface area radius, together with ice water content and particle volume distribution, as characterizing parameters for the scattering properties of particulate ensembles composed of non-spherical or irregular ice crystals.