The Importance of the Shape Parameter in a Bulk Parameterization Scheme to the Evolution of the Cloud Droplet Spectrum during Condensation

The shape parameter of the Gamma size distribution plays a key role in the evolution of the cloud droplet spectrum in the bulk parameterization schemes. However, due to the inaccurate specification of the shape parameter in the commonly used bulk double-moment schemes, the cloud droplet spectra cannot reasonably be described during the condensation process. Therefore, a newly-developed triple-parameter condensation scheme with the shape parameter diagnosed through the number concentration, cloud water content, and reflectivity factor of cloud droplets can be applied to improve the evolution of the cloud droplet spectrum. The simulation with the new parameterization scheme was compared to those with a high-resolution Lagrangian bin scheme, the double-moment schemes in a parcel model, and the observation in a 1.5D Eulerian model that consists of two cylinders. The new scheme with the shape parameter varying with time and space can accurately simulate the evolution of the cloud droplet spectrum. Furthermore, the volume-mean radius and cloud water content simulated with the new scheme match the Lagrangian analytical solutions well, and the errors are steady, within approximately 0.2%.

Sensitivity of the Grid-point Atmospheric Model of IAP LASG(GAMILI.I.0)Climate Simulations to Cloud Droplet Effective Radius and Liquid Water Path

This paper documents a study to examine the sensitivity to cloud droplet effective radius and liquid water path and the alleviation the energy imbalance at the top of the atmosphere and at the surface in the latest version of the Grid-point Atmospheric Model of the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics （LASG）, Institute of Atmospheric Physics （IAP） （GAMIL1.1.0）. Considerable negative biases in all flux components, and thus an energy imbalance, are found in GAMIL1.1.0. In order to alleviate the energy imbalance, two modifications, namely an increase in cloud droplet effective radius and a decrease in cloud liquid water path, have been made to the cloud properties used in GAMIL. With the increased cloud droplet effective radius, the single scattering albedo of clouds is reduced, and thus the reflection of solar radiation into space by clouds is reduced and the net solar radiation flux at the top of the atmosphere is increased. With the reduced cloud optical depth, the net surface shortwave radiation flux is increased, causing a net warming over the land surface. This results in an increase in both sensible and latent heat fluxes over the land regions, which is largely balanced by the increased terrestrial radiation fluxes. Consequently, the energy balance at the top of atmosphere and at the surface is achieved with energy flux components consistent with available satellite observations.

Broadening of cloud droplet size distributions and warm rain initiation associated with turbulence: an overview

In the study of warm clouds,there are many outstanding questions.Cloud droplet size distributions are much wider,and warm rain is initiated in a shorter time and with a shallower cloud depth than theoretical expectations.This review summarizes the studies related to the effects of turbulent fluctuations and turbulent entrainment-mixing on the broadening of droplet size distributions and warm rain initiation,including observational,laboratorial,numerical,and theoretical achievements.Particular attention is paid to studies by Chinese scientists since the 1950s,since most results have been published in Chinese.The review reveals that high-resolution observations and simulations,and laboratory experiments,are needed because knowledge of the detailed physical processes involved in the effects of turbulence and entrainment-mixing on cloud microphysics still remains elusive.The effects of turbulent fluctuations and entrainment-mixing processes have been unrealistically separated in most theoretical studies.They could be unified by further advancement of a systems theory into a predictive theory.Developing parameterizations for the effects of fluctuations and entrainment-mixing processes is still in its infancy,and more studies are warranted.

Spectral dispersion of cloud droplet size distributions and radar threshold reflectivity for drizzle

From first principles, we find that the radar threshold reflectivity between nonprecipitating clouds and precipitating clouds is strongly related to not only the cloud droplet number concentration but also the spectral dispersion of cloud droplet size distributions. The further investigation indicates that the threshold value is an increasing function of spectral dispersion and cloud droplet number concentration. These results may improve our understanding of the cloud-precipitation interaction and the aerosol indirect effect.

Relationships between Cloud Droplet Spectral Relative Dispersion and Entrainment Rate and Their Impacting Factors

Cloud microphysical properties are significantly affected by entrainment and mixing processes.However,it is unclear how the entrainment rate affects the relative dispersion of cloud droplet size distribution.Previously,the relationship between relative dispersion and entrainment rate was found to be positive or negative.To reconcile the contrasting relationships,the Explicit Mixing Parcel Model is used to determine the underlying mechanisms.When evaporation is dominated by small droplets,and the entrained environmental air is further saturated during mixing,the relationship is negative.However,when the evaporation of big droplets is dominant,the relationship is positive.Whether or not the cloud condensation nuclei are considered in the entrained environmental air is a key factor as condensation on the entrained condensation nuclei is the main source of small droplets.However,if cloud condensation nuclei are not entrained,the relationship is positive.If cloud condensation nuclei are entrained,the relationship is dependent on many other factors.High values of vertical velocity,relative humidity of environmental air,and liquid water content,and low values of droplet number concentration,are more likely to cause the negative relationship since new saturation is easier to achieve by evaporation of small droplets.Further,the signs of the relationship are not strongly affected by the turbulence dissipation rate,but the higher dissipation rate causes the positive relationship to be more significant for a larger entrainment rate.A conceptual model is proposed to reconcile the contrasting relationships.This work enhances the understanding of relative dispersion and lays a foundation for the quantification of entrainment-mixing mechanisms.

A Study of Shallow Cumulus Cloud Droplet Dispersion by Large Eddy Simulations

Cloud droplet dispersion is an important parameter in estimating aerosol indirect effect on climate in general circulation models（GCMs）.This study investigates droplet dispersion in shallow cumulus clouds under different aerosol conditions using three-dimensional large eddy simulations（LES）.It is found that cloud droplet mean radius,standard deviation,and relative dispersion generally decrease as aerosol mixing ratio increases from 25 mg-1（clean case） to 100 mg-1（moderate case）,and to 2000 mg-1（polluted case）.Under all the three simulated aerosol conditions,cloud droplet mean radius and standard deviation increase with height.However,droplet relative dispersion increases with height only in the polluted case,and does not vary with height in the clean and moderate cases.The mechanisms for cloud droplet dispersion are also investigated.An additional simulation without considering droplet collision-coalescence and sedimentation under the aerosol mixing ratio of 25 mg-1 shows smaller values of droplet mean radius,standard deviation,and relative dispersion as compared to the base clean case.This indicates that droplet collision-coalescence plays an important role in broadening droplet spectra.Results also suggest that the impact of homogeneous mixing on cumulus cloud droplet spectra is significant under all the three simulated aerosol conditions.In weak mixing（strong updraft） regions where clouds are closer to be adiabatic,cloud droplets tend to have larger mean radius,smaller standard deviation,and hence smaller relative dispersion than those in stronger mixing（downdraft or weak updraft） regions.The parameterized cloud optical depth in terms of cloud liquid water content,droplet number concentration,and relative dispersion is only slightly smaller than the result calculated from detailed droplet spectra,indicating that current parameterization of cloud optical depth as used in many GCMs is plausible for low clouds.

A method for solving relative dispersion of the cloud droplet spectra

The relative dispersion of the cloud droplet spectra or the shape parameter is usually assumed to be a constant in the two-parameter cloud microphysical scheme, or is derived through statistical analysis. However, observations have revealed that the use of such methods is not applicable for all actual cases. In this study, formulas were derived based on cloud microphysics and the properties of gamma function to solve the average cloud droplet radius and the cloud droplet spectral shape parameter. The gamma distribution shape parameter, relative dispersion, and cloud droplet spectral distribution can be derived through solving the droplet spectral shape parameter equation using the average droplet radius, volume radius, and their ratio, thereby deriving an analytic solution. We further examined the equation for the droplet spectral shape parameter using the observational droplet spectral data, and results revealed the feasibility of the method. In addition, when the method was applied to the two-parameter cloud microphysical scheme of the Weather Research and Forecast(WRF) model to further examine its feasibility, the modeling results showed that it improved precipitation simulation performance, thereby indicating that it can be utilized in two-parameter cloud microphysical schemes.