Parameterizations of different hydrometeor spectral relative dispersion in the convective clouds

Spectral relative dispersion of different hydrometeors is vital to accurately describe sedimentation.Here,the Weather Research and Forecasting model with spectral bin microphysics is used to simulate convective clouds in Shouxian of Anhui province in China to study the spectral relative dispersion of different hydrometeors.Firstly,regardless of clean or polluted conditions,the relative dispersion of ice crystal spectra and its volume-mean diameter are negatively correlated,while the relative dispersion of other hydrometeor spectra is positively related to their respective volume-mean diameter.The correlations for cloud droplets and raindrops are affected by the process of collision-coalescence;the correlations for ice crystals,graupel particles,and snow particles could be affected by the deposition,riming,and aggregation processes,respectively.Secondly,relative dispersion parameterizations are developed based on a comprehensive consideration of the relationships between the relative dispersion and volume-mean diameter under both polluted and clean conditions.Finally,the relative dispersion parameterizations are applied to terminal velocity parameterizations.The results show that for cloud droplets,ice crystals,graupel particles,and snow particles,assuming the shape parameter in the Gamma distribution is equal to 0 underestimates the shape parameter and overestimates the relative dispersion;and for raindrops,assuming the shape parameter is equal to 0 is close to the relative dispersion parameterizations.The most appropriate constant shape parameters are recommended for different hydrometeors.The relative dispersion parameterizations developed here shed new light for further optimizing the terminal velocity parameterizations in models.