Theoretical expression for the autoconversion rate of the cloud droplet number concentration

Abstract

[1] Accurate parameterization of the autoconversion rate of the cloud droplet concentration (number autoconversion rate in cm À3 s À1 ) is critical for evaluating aerosol indirect effects using climate models; however, existing parameterizations are empirical at best. A theoretical expression is presented in this contribution that analytically relates the number autoconversion rate to the liquid water content, droplet concentration and relative dispersion of the cloud droplet size distribution. The analytical expression is theoretically derived by generalizing the analytical formulation previously developed for the autoconversion rate of the cloud liquid water content (mass autoconversion rate in g cm À3 s À1 ). Further examination of the theoretical number and mass autoconversion rates reveals that the former is not linearly proportional to the latter as commonly assumed in existing parameterizations. The formulation forms a solid theoretical basis for developing multi-moment representation of the autoconversion process in atmospheric models in general.

Sensitivity study of cloud parameterizations with relative dispersion in CAM5.1: impacts on aerosol indirect effects

“…It is well established that effective radius (Martin et al;1994;Liu and Daum, 2002) and autoconversion rate (Liu and Daum, 2004;Liu et al, 2007;Li et al, 2008;Xie and Liu, 2009;Chuang et al, 2012;Wang et al, 2013;Michibata and Takemura, 2015) are both related to the relative dispersion of cloud droplet size distribution ε (which is defined as the ratio of the standard deviation to the mean value of droplet size distribution) in addition to droplet number concentration and cloud liquid water content. Liu and Daum (2002) suggested that ε is increased by anthropogenic aerosols under similar dynamical conditions in clouds, because more numerous small droplets formed in polluted clouds compete for water vapor and broaden the droplet size distribution compared with clean clouds having fewer droplets and less competition.…”

“…This explicit relationship permits a direct investigation of the dispersion influence on the first aerosol indirect effect. According to the generalized mean value theorem for integrals (Liu and Daum, 2004;Liu et al, 2007), the twomoment parameterizations of Au can be easily derived based upon the equation of the gamma droplet size distribution from the results of Xie and Liu (2009):…”

“…P N and P L are the increasing functions of L c and ε, as well as the decreasing functions of N c (Liu et al, 2007;Xie and Liu, 2009). This two-moment parameterization of Au that explicitly accounts for ε is used to replace the Khairoutdinov-Kogan parameterization in the original CAM5.1 (Khairoutdinov and Kogan, 2000) to investigate the impact of ε on the second aerosol indirect effect.…”

Measurements of the relation between aerosol properties and microphysics and chemistry of low level liquid water clouds in Northern Finland

“…The essential cloud microphysical parameters in studying aerosol-cloud-climate interactions are the total number concentration and effective radius of cloud droplets, cloud liquid water content and the relative dispersion of a cloud droplet population (e.g. Lu and Seinfeld, 2006;Ekman et al, 2007;Liu et al, 2007;Bulgin et al, 2008).…”

Aerosols and Clouds in Chemical Transport Models and Climate Models

“…One promising scheme that has been derived from theoretical considerations (Liu et al, 2007, and earlier papers referenced therein) represents the autoconversion of any integral moment quantity Y of a cloud drop size distribution as…”