From Glossary of Meteorology
(Also called extinction coefficient, especially in reference to optical frequencies.) For radiation propagating through a medium, the fractional depletion of radiance per unit pathlength, or in radar usage, of the power density of plane-wave radiation per unit pathlength.
The attenuation coefficient is defined through Bouguer's law as
where L is the monochromatic radiance at a given wavelength, γ is the attenuation coefficient, and ds is a differential increment of pathlength. So defined, the attenuation coefficient is the same as the volume extinction coefficient and has dimensions of inverse length. In radar, the usual convention is to measure the depletion of power on a decibel scale in terms of the specific attenuation Y, which is related to attenuation coefficient by
where Y is in decibels per kilometer when γ is in inverse kilometers. The numerical factor in this equation is 10 log10e.