28-Feb-2006 1 Rayleigh, Mie, and Optical Scattering Note: There is a good explanation of Raleigh, Mie, and Optical scattering on the web at: http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html. Raleigh scattering occurs when the dimensions of the scatter is much smaller than the wavelength of the incident electromagnetic radiation. An example is when S-band radar waves are scattered by raindrops. Raleigh scattering exhibits a strong wavelength dependence. Mie scattering occurs when the dimensions of the scattered is much larger than the wavelength of the incident electromagnetic radiation. An example is when light is scattered by small water droplets in clouds. The intensity of the scattered radiation for Raleigh scattering is ()6222422022122cos1+−+=DnnRIIλπθ Where n is the refractive indeed of the material, D is the diameter, and λ is the wavelength, and θ is the scattering angle. Note that the forward scatter equals the backscatters and at θ = 90o scattering is half of the forward/back scatter. Integrating over a sphere surrounding the particle gives the Raleigh scattering cross section: 2224652132+−=nnDλπσ Question: what are the units? Note the strong dependence on wavelength and even stronger dependence on particle diameter.28-Feb-2006 2 Back scatter from raindrop 4625λκπσD= Where2κ is a parameter related to the complex index of refraction of the material. For water it is normally taken as 0.93, and for ice 0.197. Radar reflectivity (m2 m-3): zDVolumeUniti4256425λκπλκπση ===∑∑ Radar reflectivity factor (m3) Why do we need two factors? ∑=VolumeUnitDz6 z425λκπη
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