Available Energy: Net Radiation and Soil Heat Flux - Transport in the Atmosphere-Vegetation-Soil Continuum - page 15

a) d p =0.0001 µm b) d p =0.5 µm

c) d p =5µm d) d p = 1000 µm

Figure 2.1 Pattern of radiation scattered by spherical particles of various sizes. The
logarithm of the normalized intensity is given (with a minimum of 10 -4 and 10 -8
for parts a - c , and d , respectively). Wavelength of the radiation is 0.5 μm, refractive
index of the particle is 1.33 and the particle is nonabsorbing. Dashed lines are lines
of equal intensity (lines are one order of magnitude apart). Diameters are representa-
tive of ( a ) gas molecule (Rayleigh scattering), ( b ) large aerosol (Mie scattering), ( c )
cloud droplets (Mie scattering), and ( d ) cloud droplet (geometric optics).

• d p << λ : Rayleigh scattering. The theory of Rayleigh scattering assumes that the par-
ticles are spherical, do not inluence each other and are smaller than 0.2 λ . For the wave-
lengths considered here, this size requirement implies that Rayleigh scattering is relevant
for gas molecules. In the case of Rayleigh scattering, the amount of scattering is equal for
the forward and the backward directions (see Figure 2.1a ). The extinction for Rayleigh
scattering is proportional to λ -4 , that is, the shorter the wavelength, the more scattering.
One of the consequences of this wavelength dependence is that the sky is blue. Blue light
has a short wavelength and hence is scattered more than visible radiation with longer
wavelengths. Owing to the direction independence of Rayleigh scattering, the blue light
appears to come from the entire hemisphere.
• d p ≈ λ : Mie scattering. Mie scattering occurs due to interaction of radiation with aerosols.
Aerosols are suspensions of small solid and/or liquid particles (e.g., from anthropogenic
sources such as industry, biomass burning, or from natural sources as cloud particles, sea
spray, desert dust). Although aerosols occur with a large range of diameters, only those with
diameters of the order of 0.1-100 μm give rise to Mie scattering in the short wave and long-
wave wavelength range. The amount of scattering is only a weak function of wavelength, but
the direction in which light is scattered is complex, with various side lobes. Most radiation
is scattered in the forward direction, and the proportion of forward scattering increases with
increasing particle size. Examples of the angular dependence of scattering by an aerosol and
a cloud droplet are given in Figures 2.1b and c .
• d p >> λ : Geometric optics. Raindrops, ice crystals, snowlakes and hailstones have a size
that is much larger than visible (and infrared) wavelengths. Then scattering is determined
by classical optics, such as Snell's law. The scattered (or better, refracted) radiation can
have a strong directional dependence. Figure 2.1d shows the scattering pattern for a rain-
drop. Strong scattering is present in the forward and backward direction. Four distinct
peaks (two on each side) are present in the backward direction. Those correspond to the
primary and secondary rainbow (at 137° and 130°) respectively (Petty, 2004 ).