Skip to main content
SpringerLink
Log in

A method for solving relative dispersion of the cloud droplet spectra

  • Research Paper
  • Published:
Science China Earth Sciences Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Cohard J M, Pinty J P. 2000. A comprehensive two-moment warm microphysical bulk scheme. I: Description and tests. Q J R Meteorol Soc, 126: 1815–1842

    Article  Google Scholar 

  • Cotton W R, Anthes R A. 1989. Storm and Cloud Dynamics. London: Academic Press. 883

    Google Scholar 

  • Curry J A, Hobbs P V, King M D, et al. 2000. FIRE arctic clouds experiment. Bull Amer Meteorol Soc, 81: 5–29

    Article  Google Scholar 

  • Ferrier B S. 1994. A double-moment multiple-phase four-class bulk ice scheme. Part I: Description. J Atmos Sci, 51: 249–280

    Article  Google Scholar 

  • IPCC. 2007. Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. In: Solomon S, Qin D, Manning M, et al, eds. New York: Cambridge University Press.

    Google Scholar 

  • Jiang H L, Cotton W R, Pinto J O, et al. 2000. Cloud resolving simulations of mixed-phase arctic stratus observed during BASE: Sensitivity to concentration of ice crystals and large-scale heat and moisture advection. J Atmos Sci, 57: 2105–2117

    Article  Google Scholar 

  • Jiang H L, Feingold G, Cotton W R, et al. 2001. Large-eddy simulation of entrainment of cloud condensation nuclei into the arctic boundary layer: May 18, 1998 FIRE/SHEBA case study. J Geophys Res, 106: 15113–15122

    Article  Google Scholar 

  • Khairoutdinov M F, Kogan Y L. 2000. A new cloud physics parameterization for large-eddy simulation models of marine stratocumulus. Mon Weather Rev, 128: 229–243

    Article  Google Scholar 

  • Khvorostyanov V I, Curry J A. 1999a. Towards the theory of stochastic condensation in clouds. Part I: A general kinetic equation. J Atmos Sci, 56: 3985–3996

    Article  Google Scholar 

  • Khvorostyanov V I, Curry J A. 1999b. Towards the theory of stochastic condensation in clouds. Part II: Analytical solutions of the gamma distribution type. J Atmos Sci, 56: 3997–4013

    Article  Google Scholar 

  • Kogan Y L, Martin W J. 1994. Parameterization of bulk condensation in numerical cloud modeles. J Atmos Sci, 51: 1728–1739

    Article  Google Scholar 

  • Kogan Y L, Belochitski A, 2012. Parameterization of cloud microphysics based on full integral moments. J Atmos Sci, 69: 2229–2242

    Article  Google Scholar 

  • Liu Y G, Daum P H. 2002. Indirect warming effect from dispersion forcing. Nature, 419: 580–581

    Article  Google Scholar 

  • Liu Y G, Daum P H, McGraw R, et al. 2006a. Parameterization of the autoconversion process. Part II: Generalization of Sundqvist-type parameterizations. J Atmos Sci, 63: 1103–1109

    Article  Google Scholar 

  • Liu Y G, Daum P H, McGraw R, et al. 2006b. Generalized threshold function accounting for effect of relative dispersion on threshold behavior of autoconversion process. Geophys Res Lett, 33: L11804, doi: 10.1029/2005GL025500

    Article  Google Scholar 

  • Lohmann U, McFarlane N, Levkov L, et al. 1999. Comparing different cloud schemes of a single column model by using mesoscale forcing and nudging technique. J Clim, 12: 438–461

    Article  Google Scholar 

  • Lu M L, Conant W C, Jonsson H H, et al. 2007. The marine stratus/stratocumulus experiment (MASE): Aerosol-cloud relationship in marine stratocumulus. J Geophys Res, 112: D10209, doi: 10.1029/2006JD07985

    Article  Google Scholar 

  • Ma J Z, Chen Y, Wang W, et al. 2010. Strong air pollution causes widespread haze-cloud over China. J Geophys Res, 115: D18204, doi: 10.1029/2009JD013065

    Article  Google Scholar 

  • Martin G M, Johnson D W, Spice A, 1994. The measurement and parameterization of effective radius of droplets in the warm stratocumulus clouds. J Atmos Sci, 51: 1823–1842

    Article  Google Scholar 

  • Mason B J. 1971. Physics of Clouds. Oxford: Clarendon Press. 481

    Google Scholar 

  • Meyers M P, Walko R L, Harrington J Y, et al. 1997. New RAMS cloud microphysics parameterization. Part II: The two-moment scheme. Atmos Res, 45: 3–39

    Article  Google Scholar 

  • Milbrandt J A, Yau M K. 2005a. A multimoment bulk microphysics parameterization. Part I: Analysis of the role of the spectral shape parameter. J Atmos Sci, 62: 3051–3064

    Article  Google Scholar 

  • Milbrandt J A, Yau M K. 2005b. A multimoment bulk microphysics parameterization. Part II: A proposed three-moment closure and scheme description. J Atmos Sci, 62: 3065–3081

    Article  Google Scholar 

  • Morrison H, Curry J A, Khvorostyanov V I. 2005. A new double-moment microphysics parameterization for application in cloud and climate models Part I: Description. J Atmos Sci, 62: 1665–1677

    Article  Google Scholar 

  • Morrison H, Thompson G, Tatarskii V. 2009. Impact of cloud microphysics on the development of trailing stratiform precipitation in a simulated squall line: Comparison of one- and two-moment schemes. Mon Weather Rev, 137: 991–1007

    Article  Google Scholar 

  • Pruppacher H R, Klett J D. 1997. Microphysics of Clouds and Precipitation. Heidelberg: Springer. 954

    Google Scholar 

  • Pontikis C, Hicks E. 1992. Contribution to the cloud droplet effective radius parameterization. Geophys Res Lett, 19: 2227–2230, doi: 10.1029/92GL02283

    Article  Google Scholar 

  • Reisner J, Rasmussen R M, Bruintjes T. 1998. Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Q J R Meteorol Soc, 124: 1071–1107

    Article  Google Scholar 

  • Sedunov Y S. 1974. Physics of Drop Formation in the Atmosphere. New York: Wiley. 234

    Google Scholar 

  • Straka J M. 2009. Cloud and Precipitation Microphysics. New York: Cambridge University Press. 392

    Book  Google Scholar 

  • Twomey S. 1977. The influence of pollution on the shortwave albedo of clouds. J Atmos Sci, 34: 1149–1152

    Article  Google Scholar 

  • Xie X N, Liu X D, Peng Y R, et al. 2013. Numerical simulation of clouds and precipitation depending on different relationships between aerosol and cloud droplet spectral dispersion. Tellus Ser B-Chem Phys Meteorol, 65: 19054

    Article  Google Scholar 

  • Xu K M, Randall D A. 1996. Explicit simulation of cumulus ensembles with the GATE Phase III data: Comparison with observations. J Atmos Sci, 53: 3710–3736

    Article  Google Scholar 

  • Zhao C S, Tie X X, Brasseur G, et al. 2006. Aircraft measurements of cloud droplet spectral dispersion and implications for indirect aerosol radiative forcing. Geophys Res Lett, 33: L16809, doi: 10.1029/2006GL026653

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chinese Academy of Meteorological Sciences, Beijing, 100081, China

    Yu Liu & WeiLiang Li

Authors
  1. Yu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. WeiLiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Li, W. A method for solving relative dispersion of the cloud droplet spectra. Sci. China Earth Sci. 58, 929–938 (2015). https://doi.org/10.1007/s11430-015-5059-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11430-015-5059-9

Keywords

Search

Navigation