Describing the DSD Shape with the Mass Spectrum Standard Deviation

The raindrop size distribution (DSD) can be described as a Gamma function with three parameters (e.g., N_w, D_m and µ). Previous studies have shown that these three parameters are correlated. But there is controversy in the research literature over why the three parameters are correlated. Some studies suggest that the correlation is a statistical artifact due to correlation between the raindrop spectrum moments. Other studies suggest that the correlation is not a statistical artifact and have developed slope-shape (µ-Λ) relationships so that the three parameter Gamma function can be described as a constrained two parameter function.

Analysis of vertical profiles of DSD estimates and surface disdrometer observations from the Mid-Continental Convective Cloud Experiment (MC3E) and other field campaigns suggests a relationship between the mass-weighted mean diameter (D_m) and the mass spectrum standard deviation (σ_m). This relationship is not a statistical artifact due to correlations between spectrum moments and suggests a physical relationship between the two DSD parameters.

There are mathematical relationships that relate σ_m , D_m and µ. These relationships imply that data can be analyzed in σ_m – D_m space and then converted into µ – D_m space (if needed) avoiding the statistical artifact controversy of directly estimating µ from spectrum moments. The DSD parameter retrievals and the relationships between retrieved DSD parameters will be presented at the conference.