(technically known as the relative aerosol optical depth) is the “extinctionper unit path length due to aerosols alone”…the typical means of computing this isto account for the extinction of as many of the other constituents as possible….(water vapor, ozone, mixed gases, and ‘equivalent extinction’ represented by Raylieghscattering of atmospheric molecules, and what is ‘left over’ is the aerosol extinction.The transmission T and “optical depth” t of an atmospheric constituent are related asfollows:
T = Exp(-t*m) , or t = – ln(T)/m,
where m is the airmass, or equivalent path length throughthe atmosphere.
In simplest terms, for Io = extraterrestrial radiation, and I = radiation at surface
I = Io * ( Tw*To*Tg*Tr*Ta)
where Tw=transmittance of water, To of ozone, Tg of gases, Tr Rayleigh effects, Ta aerosols
Strictly speaking, both extinction coefficients(see http://amsglossary.allenpress.com/glossary/search?id=extinction-coefficient1and transmission are a function ofwavelength, so optical depths are defined at specific wavelengths (spectral optical depth)or Total (integrated over all wavelengths). The total optical depth is sometimes called the”opacity”.