Scattering Extinction: scattering + absorption Types of scattering: Single vs. multiple Conservative vs. non-conservative Elastic vs. inelastic (e.g., Raman) This lecture discusses three aspects of scattering: How much radiation is affected? Is there absorption too? Into which direction does the scattered radiation go?

Question 1: How much radiation is affected? Equation of radiative transfer: , where d=dz Rearranging this gives: Scattering coefficient () given by: r = particle radius, n = number of particles Q = scattering efficiency Q depends on size parameter (x), given by  = wavelength How come Q > 1 ?

Scattering by clear air Lord Rayleigh John William Strutt (third Baron Rayleigh) 1842-1919 Essex, Cambridge Nobel Prize in Physics in 1904 "for his investigations of the densities of the most important gases and for his discovery of argon in connection with these studies" Air molecules scatter light as dipoles Dipole induced

Scattering Two types of scattering are considered – molecular scattering (Rayleigh) and scattering from aerosols (Mie) The equation for Rayleigh scattering can be written as Where α is the polarizability

Scattering by clear air 2 We know that In clean air, r remains constant, but  of interest may vary Consequences: (next slide) Which part of Q(x) curve applies? ≈ 0.2 in blue ≈ 0.03 in red Easy-to-calculate formulas available (will have code)

Rayleigh scattering , nm , cm2 , surface Exp(-) 300 6.00 E-26 1.2 0.301 400 1.90 E-26 0.38 0.684 600 3.80 E-27 0.075 0.928 1000 4.90 E-28 0.0097 0.990 10,000 4.85 E-32 9.70 E-7 0.999 Sky appears blue at noon, red at sunrise and sunset - why?

Phase diagram for Rayleigh scattering

Scattering by clear air 4 Red sky in the morning, sailors take warning. Red sky at night, sailors delight. Morning Evening

Mie-Debye scattering For particles which are not small compared with the wavelength one has to deal with multiple waves from different molecules/atoms within the particle Forward moving waves tend to be in phase and this gives a large resultant amplitude. Backward waves tend to be out of phase and this results in a small resultant amplitude Hence the scattering phase function for a particle has a much larger forward component (forward peak) than the backward component

Phase diagrams for aerosols

Aerosol size (indicates composition) Scattering by aerosol MODIS product Aerosol size (indicates composition)  is Angstrom exponent  ≈ 1.2 typical

Aerosol size determination from space Visible Near-infrared Fine particles from smoke Coarse dust particles Fine particles from smoke

Blue Moon May happen after volcanic eruptions, very rare

Question 2: Is there absorption too? c speed of light H magnetic field E electric field  permittivity µ permeability (=1 for non-ferromagnetic materials) Maxwell’s equations Instead of r, i, we use mr and mi Refractive index: m = mr + i mi Imaginary part (mi): If only absorption is considered:  = absorption coefficient;  = density; s = path, k = absorption coefficient) The value of mi depends on how easy it is to bounce electrons to higher energy levels so that they don’t fall back. Usually: small values + sharp peaks at a few wavelengths (though learned about widening of absorption spectra) Exception: metals: large  values (Why?) Meaning of real part later

Single scattering albedo (a) What portion of influenced radiation is scattered? (The rest is absorbed.) Upper bound: 1.0 (why?) Lower bound for large particles: 0.5 (why?) Typical values for droplets at visible wavelengths: just below 1.0 Some aerosols contain mix of water and carbon -> lower values Wavelength-dependence of a: why decrease with size?