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Theoretical expression for the autoconversion rate of the cloud droplet number concentration
Author(s) -
Liu Yangang,
Daum Peter H.,
McGraw Robert L.,
Miller Mark A.,
Niu Shengjie
Publication year - 2007
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2007gl030389
Subject(s) - mathematics , liquid water content , expression (computer science) , representation (politics) , growth rate , statistical physics , mechanics , environmental science , atmospheric sciences , physics , cloud computing , computer science , geometry , politics , political science , law , programming language , operating system
Accurate parameterization of the autoconversion rate of the cloud droplet concentration (number autoconversion rate in cm −3 s −1 ) 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 −3 s −1 ). 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.