Cloud drop effective radius

The cloud drop effective radius (alternatively cloud effective radius or simply effective radius when in context) is a weighted mean of the size distribution of cloud droplets.^[1] 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 inversionofremotely sensed data.^[2] Physically, it is an area weighted radius of the cloud drop particles. Mathematically, this can be expressed as $${\displaystyle r_{e}={\dfrac {\displaystyle \int _{0}^{\infty }\pi r^{3}\cdot n($$r)\,dr}{\displaystyle \int _{0}^{\infty }\pi r^{2}\cdot n(r)\,dr}}.}