The ‘1/3’ power law between effective radius and liquid‐water content

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.