Cloud droplet effective radius ($r_e=⟨r^3⟩/⟨r^2⟩$)

The ratio of the third to the second radius moment determines projected extinction area per liquid mass. For size-independent extinction efficiency $Q$, the local particle extinction coefficient is $3Qw/(4{\rho }_w{r}_e)$. It is not generally the mean radius or the mean-volume radius. In adiabatic cloud droplet moments, the shape factor gives $r_e=r_v/k^{1/3}$.