Atmospheric Transmission Beer's Law

3/31/10Optical thickness and transmittance of cloudsCan you see the sun through a cloud? a (absorptance)r (reflectance or albedo)Liquid water cloudsDroplet radii: 5-15 µmN = 10 2 -10 3 cm -3t dir + t diff + r + a = 1t + r + a = 1t = t dir + t difft diff (diffuse transmittance)t dir (direct transmittance)r = reflected to spacet = available for surface heatinga = heats atmosphere locallyOptical thickness and transmittance of clouds• t dir , t diff , r and a depend on the cloud optical thickness (τ*), single-scatteralbedo (ω) and how radiation is scattered by the cloud droplets• Values of t diff , r and a depend on multiple scattering of radiation by thecloud droplets• Consider a monodisperse cloud composed of droplets of identical radius(r) with a concentration N m -3• Volume extinction coefficient:β e= NQ eπr 2€27