Atmospheric Transmission Beer's Law

3/31/10MODIS visible imageGreat LakesPolydisperse clouds• The assumption of a single droplet size (monodisperse) is not realistic• Real clouds are polydisperse and contain a range of droplet sizesdescribed by a drop size distribution n(r)• n(r) drNumber of droplets (per unit volume of air)whose radii fall in the range [r, r + dr]€€€• Dimensions are length -4 ; e.g., m -3 µm -1N =A sfc=β e=∞∫0∞∫0n(r) dr∞∫0n(r)[4πr 2 ]drn(r)[Q e(r)πr 2 ]drTotal number densityTotal surface areaExtinction coefficient€r eff=∞∫0∞∫0n(r)r 3 drn(r)r 2 dr‘Effective’ radius31