# Cloud drop effective radius

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The cloud drop effective radius (alternatively cloud effective radius or effective radius) 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 inversion of remotely sensed data.[2] Physically, it is an area weighted radius of the cloud drop particles.

Mathematically, this can be expressed as $r_e = \dfrac{\int\limits_{0}^{\infty} \pi \cdot r^3 \cdot n(r)\,dr}{\int\limits_{0}^{\infty} \pi \cdot r^2 \cdot n(r)\,dr}$.

## References

1. ^ "Cloud Effective Radius". Goddard Earth Sciences Data and Information Services Center. Retrieved 3 August 2009.
2. ^ Hansen., J.E and L.D. Travis (1974). "Light scattering in planetary atmospheres". Space Science Reviews (Springer Netherlands) 16 (4): 527–610. Bibcode:1974SSRv...16..527H. doi:10.1007/BF00168069.