Examining impacts of mass-diameter (m-D) and area-diameter (A-D) relationships of ice particles on retrievals of effective radius and ice water content from radar and lidar measurements

Mass-diameter (m-D) and projected area-diameter (A-D) relations are often used to describe the shape of nonspherical ice particles. This study analytically investigates how retrieved effective radius (reff) and ice water content (IWC) from radar and lidar measurements depend on the assumption of m-D [m(D) = a Db] and A-D [A(D) = γ Dδ] relationships. We assume that unattenuated reflectivity factor (Z) and visible extinction coefficient (kext) by cloud particles are available from the radar and lidar measurements, respectively. A sensitivity test shows that reff increases with increasing a, decreasing b, decreasing γ, and increasing δ. It also shows that a 10% variation of a, b, γ, and δ induces more than a 100% change of reff. In addition, we consider both gamma and lognormal particle size distributions (PSDs) and examine the sensitivity of reff to the assumption of PSD. It is shown that reff increases by up to 10% with increasing dispersion (μ) of the gamma PSD by 2, when large ice particles are predominant. Moreover, reff decreases by up to 20% with increasing the width parameter (ω) of the lognormal PSD by 0.1. We also derive an analytic conversion equation between two effective radii when different particle shapes and PSD assumptions are used. When applying the conversion equation to nine types of m-D and A-D relationships, reff easily changes up to 30%. The proposed reff conversion method can be used to eliminate the inconsistency of assumptions that made in a cloud retrieval algorithm and a forward radiative transfer model.