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 (r eff ) and ice water content (IWC) from radar and lidar measurements depend on the assumption of m-D [m(D) = a D b ] and A-D [A(D) = γD s ] relationships. We assume that unattenuated reflectivity factor (Z) and visible extinction coefficient (k ext ) by cloud particles are available from the radar and lidar measurements, respectively. A sensitivity test shows that r eff 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 r eff . In addition, we consider both gamma and lognormal particle size distributions (PSDs), and examine the sensitivity of r eff to the assumption of PSD. It is shown that r eff increases by up to 10% with increasing dispersion (μ) of the gamma PSD by 2, when large ice particles are predominant. Moreover, r eff 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, r eff easily changes up to 30%. The proposed r eff -convertion method can be used to eliminate the inconsistency of assumptions that made in a cloud retrieval algorithm and a forward radiative transfer model.