Environmental Engineering Reference
In-Depth Information
Here
) denotes the wavelength-dependent absorption cross section of the
constituent of interest. The column density
S
of a gaseous constituent is related
to its concent
ra
tion
c
(
x
)(
x
denoting the position inside the plume), or mean
concentration
c
, and the extension of the plume
L
:
σ
(
λ
ð
L
S
¼
c
ð
x
Þ
d
x
¼
c
L
ð
8
:
11
Þ
0
More generally, the optical density
D
(
λ
) is given as:
ð
L
c
ð
x
Þ
d
x
¼ σðλÞ
S
ð
:
Þ
D
ðλÞ¼σðλÞ
8
12
0
Thus, in principle, gas column densities
S
can be determined by solving
Equations
(8.10)
and
(8.12)
for
S
(and thus the average gas concentration, if the plume
diameter
L
is known, can be estimated):
D
ðλÞ
σðλÞ
¼
I
0
ðλÞ
IðλÞ
1
σðλÞ
S
¼
ln
ð
8
:
13
Þ
In practice, this simple approach outlined above will not work very well, since
processes other than absorption by the gas of interest (such as aerosol extinction
and absorption by other gases) will also occur and may cause significant errors.
The well-known solution to this problem is to use the
differential absorption
'
approach, where differences in optical densities rather than absolute absorptions
and optical densities are analysed. In other words, differential optical absorption
spectroscopy (DOAS, see Platt and Stutz,
2008
) makes use of the fact that
'
σ
(
λ
) for
a given gas (and only gases which ful
l this condition are measurable by DOAS),
and thus
D
(
λ
) (see
Equation (8.12)
) are frequently a strong function of the
wavelength
ed in volcanic
plumes (e.g. Bobrowski
et al
.,
2003
; Galle
et al
.,
2010
; Hörmann
et al
.,
2013
).
Effectively, the trace-gas abundance is derived from the intensity
I
(
λ
. In particular, SO
2
, BrO, OClO were thus identi
) of (UV,
visible and IR) radiation originating from an external light source (e.g. scattered
sunlight) after traversing the plume as shown in
Figure 8.2a
,
b
.
An alternative approach is the recording of the thermal emission (in the mid-IR
around 8
λ
m) originating from the gas of interest itself, as shown in
Figure 8.2c
. Neglecting external light sources, the spectral distribution of the
intensity radiated by a gas is given by:
-
20
μ
exp
ðλÞ
I
ðλÞ¼
B
ðλ
,
T
Þ
D
ð
8
:
14
Þ
2
h
c
2
λ
5
B
ðλ
,
T
Þ¼
ð
8
:
15
Þ
e
hc
1
λ
kT
