Geoscience Reference
In-Depth Information
7.1.5. Particle Scattering and Absorption
Extinction Coefficients
The quantification of particle scattering and absorp-
tion is more complex than is that of gas scattering or
absorption due to the variety of sizes and composi-
tions of aerosol particles. Aerosol particle absorption
and scattering extinction coefficients (cm 1 )atagiven
wavelength can be estimated with
2
2
Mie regime
Geometric
regime
1.5
1.5
Q s
1
1
Q a
0.5
0.5
Q f
0
0
0.01
0.1
1
10
100
1000
Particle diameter (µm)
N B
N B
r i Q a , i
r i Q s , i
σ a , p =
n i
σ s , p =
n i
(7.7)
Figure 7.20. Single-particle absorption ( Q a ), total
scattering ( Q s ), and forward scattering ( Q f )
efficiencies of black carbon particles of different sizes
at
i
=
1
i
=
1
respectively, where N B is the number of particle sizes;
n i is the number per cubic centimeter of air (number
concentration) of particles of radius r i (cm);
=
0.50
m( n
=
1.94,
=
0.66).
r i 2 is the
actual cross section of a particle, assuming it is spherical
(cm 2 per particle); and Q a,i and Q s,i are single-particle
absorption and scattering efficiencies (dimensionless),
respectively, for each size i .
A single-particle scattering efficiency is the ratio
of the effective scattering cross section of a particle to
its actual cross section. The scattering efficiency can
exceed unity because a portion of the radiation diffract-
ing around a particle can be intercepted and scattered by
the particle. Scattering efficiencies above unity account
for this additional scattering.
A single-particle absorption efficiency is the ratio
of the effective absorption cross section of a particle to
its actual cross section. The absorption efficiency can
exceed unity because a portion of the radiation diffract-
ing around a particle can be intercepted and absorbed
by the particle. Absorption efficiencies above unity
account for this additional absorption. The larger the
imaginary index of refraction of a particle, the greater
its absorption efficiency.
Single-particle absorption and scattering efficiencies
vary with particle size, radiation wavelength, and refrac-
tive indices. Figures 7.19 and 7.20 show Q a and Q s
for black carbon and liquid water, respectively, at a
wavelength of 0.5
When a particle's diameter (D) is much smaller
than the wavelength of light (
/ <
0.03)), the particle is in the Rayleigh regime and is
called a Tyndall absorber or scatterer. John Tyn-
dall (1820-1893) was an English experimental physi-
cist who demonstrated experimentally that the sky's
blue color results from scattering of visible light by gas
molecules and that a similar effect occurs with small
particles.
When a particle's diameter is near the wavelength
of light (0.03
)(e.g., when (D
32), the particle is in the Mie
regime .TheGerman physicist, Gustav Mie (1868-
1957), derived equations describing the scattering of
radiation by particles in this regime (Mie, 1908). When
a particle's diameter is much larger than the wavelength
of light (D/
D
/ <
32), the particle is in the geomet-
ric regime .Figures 7.19 and 7.20 show the diame-
ters corresponding to these regimes for a wavelength
of 0.5
m.
Figure 7.20 shows that visible light absorption effi-
ciencies of black carbon particles peak when the parti-
cles are 0.2 to 0.4
mindiameter. Figure 7.21 shows
that water particles 0.3 to 2.0
mindiameter scatter
visible light more efficiently than do smaller or larger
particles. Such particles in both figures are in the accu-
mulation mode with respect to particle size and in the
Mie regime with respect to the ratio of particle size to
the wavelength of light.
Because the accumulation mode contains a relatively
high particle number concentration, and because parti-
cles in this mode have high scattering efficiencies and,
in the presence of black carbon, high absorption effi-
ciencies, the accumulation mode almost always causes
more light reduction than do the nucleation or coarse
particle modes (Waggoner et al., 1981). In many urban
m. They also show the single-
particle forward scattering efficiency , Q f ,which is
the efficiency with which a particle scatters light in
the forward direction. The forward scattering effi-
ciency is always less than is the total scattering effi-
ciency. The proximity of Q f to Q s in Figures 7.19 and
7.20 indicates that aerosol particles scatter strongly
in the forward direction. The difference between Q s
and Q f equals the scattering efficiency in the backward
direction.
 
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