Observational study of the relationship between entrainment rate and relative dispersion in deep convective clouds

This study investigates the influence of entrainment rate (λ) on relative dispersion (ε) of cloud droplet size distributions (CDSD) in the 99 growing precipitating deep convective clouds during TOGA-COARE. The results show that entrainment suppresses ε, which is opposite to the traditional understanding that entrainment-mixing broadens CDSD. To examine how the relationship between ε and λ is affected by droplets with different sizes, CDSDs are divided into three portions with droplet radius < 3.75 μm (N1), radius in the range of 3.75-12.75 μm (N2) and 12.75-23.25 μm (N3), respectively. The results indicate that although the droplet concentration at different sizes generally decrease simultaneously as λ increases, the variation of standard deviation (σ) depends mainly on N3, while the mean radius (rm) decreases with decreasing N3, but increases with decreasing N1. So the influence of entrainment on CDSD causes a more dramatical decrease in σ than that in rm, and further leads to the decrease of ε as entrainment enhances. In addition, a conceptual model of CDSD evolution during entrainment-mixing processes is developed to illustrate the possible scenarios entailing different relationships between ε and λ. The number concentration of small droplets and the degree of evaporation of small droplets are found to be key factors that shift the sign (i.e., positive or negative) of the ε-λ relationship.