Cloud drop effective radius

The cloud drop effective radius (alternatively cloud effective radius or effective radius) is a weighted mean of the size distribution of cloud droplets. The term was defined in 1974 by James E. Hansen and Larry Travis as the ratio of the third to the second moment of a droplet size distribution to aid in the inversion of remotely sensed data. Physically, it is an area weighted radius of the cloud drop particles.

Mathematically, this can be expressed as ${\displaystyle r_{e}={\dfrac {\int \limits _{0}^{\infty }\pi \cdot r^{3}\cdot n(r)\,dr}{\int \limits _{0}^{\infty }\pi \cdot r^{2}\cdot n(r)\,dr}}}$.

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