= Cloud optical depth at fixed liquid-water path
{title2=$\tau\simeq3W/(2\rho_wr_{\rm eff})$}
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.
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