1. 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?

2. 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 ?

3. Scattering by clear air
Lord Rayleigh
John William Strutt
(third Baron Rayleigh)
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

4. 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

5. 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)

6. 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?

7. Phase diagram for Rayleigh scattering

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

11. 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

12. Phase diagrams for aerosols

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

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

15. Blue Moon
May happen after volcanic eruptions, very rare

16. 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

17. 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?