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The ‘1/3’ power law between effective radius and liquid‐water content
Author(s) -
Liu Yangang,
Hallett John
Publication year - 1997
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49712354220
Subject(s) - power law , radius , entrainment (biomusicology) , liquid water content , entropy (arrow of time) , radiative transfer , physics , statistical physics , thermodynamics , mechanics , law , cloud computing , mathematics , optics , computer science , statistics , computer security , rhythm , acoustics , political science
Radiative properties of water clouds are parametrized in terms of the effective radius, liquid‐water content and total droplet concentration. A new general ‘1/3’ power law between effective radius and the ratio of liquid‐water content to total droplet concentration is formulated theoretically. The prefactor in the ‘1/3’ power law depends upon, and relates, cloud droplet size distributions to physical mechanisms such as entrainment and mixing. It shows that the ‘1/3’ power law holds in general for non‐precipitating water clouds with any entrainment and mixing, including clouds with monodispersed cloud droplet size distributions as special cases. The formulation builds upon a system theory that is based on Shannon's maximum entropy principle. The theoretical ‘1/3’ power law is further demonstrated using observational data. The existence of such a ‘1/3’ power law indirectly justifies the system theory generalized in this paper.