Cloud albedo ($A$)

The fraction of incident radiation reflected by a cloud under a specified spectral and angular convention. For the approximate shortwave relation $A=\tau /(\tau +7)$, increasing optical depth raises albedo with diminishing sensitivity near $A=1$. Transmitted and absorbed radiation must also be accounted for in the energy budget.

A shallow liquid cloud with $w=c_{w}h$ has liquid-water path $W=c_w{H}^2/2$. If $N$, extinction efficiency $Q$ and shape factor $k$ are constant with height, integrating droplet extinction gives ${\tau }_c=(3/5)\pi Q{k}^{1/3}[3c_w/(4\pi {\rho }_w){]}^{2/3}{N}^{1/3}{H}^{5/3}$. Eliminating $H$ yields $N=[250\sqrt{2}/(243\pi Q^{3}k)]{\rho }_w^2{c}_w^{1/2}{\tau }_c^3/W^{5/2}$. Nonadiabatic water profiles and biased water paths strongly affect the retrieval.

For spherical liquid droplets in the geometric-optics regime, the extinction efficiency is approximately2. Comparing projected extinction area with liquid-water mass gives the displayed relation. At fixed liquid-water path, smaller effective radius means larger optical depth, the basis of the Twomey effect. Absorption spectra, phase and cloud adjustments can invalidate a simple inference from this optical-depth change to net climate forcing.