Interaction Between Entrainment-Mixing Process And Cloud Droplet Size Relative Dispersion And Its Parameterization

Cloud is a critical component of earth system.The turbulent entrainment-mixing process between clouds and ambient dry air has a significant impact on the cloud macro/micro physical properties,the warm rain initiation and the evaluation of aerosol indirect effects.However,understanding of this process is still far from complete.Currently,the parameterization of entrainment-mixing mechanisms needs to be further improved.On the one hand,quantitative analysis on the effect of the mixing mechanisms on cloud droplet size relative dispersion is still lacking,and the physical mechanisms and key influencing factors of the relationship between relative dispersion and entrainment rate are unclear.On the other hand,the effect of relative dispersion on the entrainment-mixing mechanisms is not considered in the traditional quantitative description of mixing mechanisms.This paper focuses on the above issues,and the main conclusions are as follows:The Explicit Mixing Parcel Model(EMPM)is used to simulate around 23,000 cases with different initial conditions to enhance the representativeness of the simulation results.Based on approximately 12,000 undissipated cases,it is found that with the increase of height,the mixing mechanisms change from inhomogeneous to homogeneous.Because the lower height has smaller droplet size,and complete evaporation is more likely occurs.During mixing,the mixing mechanisms develop from homogeneous to inhomogeneous,and then to homogeneous.Based on the cloud microphysical parameters of the simulation results,the parameterization of entrainment-mixing mechanisms is established.There is a good consistency between droplet number concentration calculated by the parameterization and the actual number concentration in the EMPM,which proves the reliability of the parameterization.The EMPM is designed to study the entrainment-mixing process,not limited to specific regions,and a large number of simulations take into account different factors that affect entrainment-mixing mechanisms;therefore,the parameterization is general.In addition to droplet number concentration,the effects of entrainment-mixing mechanisms on relative dispersion are also analyzed.With the decrease of homogeneous mixing degree,relative dispersion first increases and then decreases.This corrects the one-sidedness of traditional qualitative analysis results that the more inhomogeneity of mixing causes larger relative dispersion,and has a theoretical support that relative dispersion decreases to be consistent with the adiabatic cloud when extreme inhomogeneous mixing occurs.The positive and negative correlations between relative dispersion and homogeneous mixing degree are related to the concentration of small droplets.Two new dimensionless quantities are proposed to quantitatively describe the effect of small droplets and the competition of partial and complete evaporation of droplets.When partial evaporation is stronger than complete evaporation,the number of small droplets increases.In this case,if complete evaporation is strong,relative dispersion is negatively correlated with homogeneous mixing degree.If complete evaporation is weak,they are positively correlated.Besides,when complete evaporation is stronger than partial evaporation,they are positively correlated.The positive and negative correlations are also affected by the relative humidity of entrained air,the proportion of entrained air and the turbulence dissipation rate.Besides the mixing mechanisms,entrainment rate is another important physical quantity.Previous observational studies have shown that the relationship between relative dispersion and entrainment rate is positive or negative,and the conclusions are inconsistent.This study reproduces the positive and negative correlations by using the EMPM,reveals the mechanisms leading to the positive and negative correlations,and develops a conceptual model.When the entrained environmental air contains cloud condensation nuclei,the activation of condensation nuclei is the main source of small droplets.If small droplets evaporation dominates and the environmental air can reach a new saturation,then relative dispersion is negatively correlated with entrainment rate;if the evaporation of small droplets is accompanied by significant evaporation of big droplets,then relative dispersion is positively correlated with entrainment rate.If entrained environmental air contains no condensation nuclei,the mixing process is dominated by the evaporation of big droplets,and there is a positive correlation between relative dispersion and entrainment rate.The correlation is also related to many factors: the negative correlation corresponds to the high vertical velocity,the high relative humidity of environmental air,the large number of entrained environmental air,the small number concentration of droplets,the moderate turbulence dissipation rate and the liquid water content.The above discussions include the effect of entrainment processes on relative dispersion.In turn,relative dispersion also affects entrainment-mixing mechanisms.In previous studies,relative dispersion of the initial spectrum is usually assumed to be small,or even equal to 0,when entrainment-mixing mechanisms are analyzed.During mixing process,the mean volume radius decreases,which is in line with the theoretical expectation.However,it is found that when relative dispersion of the initial spectrum is large,the mean volume radius gradually increases during the mixing and evaporation process,because the small droplets are easy to completely evaporate and thus the proportion of large droplets increases.Meanwhile,the mean volume radius is negatively correlated with liquid water content or number concentration,which may be mistaken as the process of inhomogeneous mixing with subsequent ascent.The traditional homogeneous mixing degree based on the above two microphysical relationships is negative,indicating the limitations of the traditional method.We propose a new method for quantifying the degree of homogeneous mixing by considering relative dispersion,called bin-weighted homogeneous mixing degree.Three arguments support the rationality of the new approach.First,the homogeneous mixing degree is always in the range of 0-1.0.When relative dispersion equals to 0,the new method is equivalent to the traditional one.Second,the bin-weighted homogeneous mixing degree is positively correlated with the reciprocal of Damk(?)hler number and transitional scale number,which is consistent with the theoretical expectation.Third,the homogeneous mixing degree decreases first and then increases,and has a clear physical explanation.Stability of the above results is verified by sensitivity tests on the droplet concentration,the liquid water content,the scale of entrained dry air,the weight functions,and the bin number of the initial spectrum.