Geoscience Reference
In-Depth Information
and emits no visible radiation; thus, its visible radiation
intensity (
I
)atpoint
x
0
is zero, and it appears black.
As a viewer backs away from the object, background
white light of intensity
I
B
scatters into the field of view,
increasing the intensity of light in the viewer's line of
sight. Although some of the added background light
is scattered out of or absorbed along the field of view
by gases and aerosol particles, at some distance away
from the object, so much background light has entered
the path between the viewer and the object that the
viewer can barely discern the black object against the
background light.
The
along the path due to scattering out of the path and
absorption along the path. A total extinction coefficient
is the sum of extinction coefficients due to scattering
and absorption by gases and particles. Thus,
σ
t
=
σ
a
,
g
+
σ
s
,
g
+
σ
a
,
p
+
σ
s
,
p
(7.10)
Integrating Equation 7.9 from
I
=
0atpoint
x
0
=
0to
I
at point
x
with constant
σ
t
yields the equation for the
contrast ratio:
I
B
−
I
e
−
σ
t
x
C
ratio
=
=
(7.11)
I
meteorological
range
is
a
function
of
the
When
C
ratio
m, the
resulting distance
x
is the meteorological range (also
called the
Koschmieder equation
).
=
0.02 at a wavelength of 0.55
contrast ratio
, defined as
I
B
−
I
C
ratio
=
(7.8)
I
B
3
.
912
σ
t
x
=
(7.12)
The contrast ratio gives the difference between the
background intensity and the intensity in the viewer's
line of sight, all relative to the background intensity.
If the contrast ratio is unity, the contrast is clear and
an object is perfectly distinguishable from background
light, whereas if it is zero, the object cannot be distin-
guished from background light.
The meteorological range is the distance from an
object at which the contrast ratio equals the liminal con-
trast ratio of 0.02 (2 percent). The
liminal
or
threshold
contrast ratio
is the lowest visually perceptible bright-
ness contrast a person can see. It varies from individual
to individual. Koschmieder (1924) selected a value of
0.02. Middleton (1952) tested 1,000 people and found a
threshold contrast ratio range of between 0.01 and 0.20,
with the mode of the sample between 0.02 and 0.03.
Campbell and Maffel (1974) found a liminal contrast
of 0.003 in laboratory studies of monocular vision. Nev-
ertheless, 0.02 has become an accepted liminal contrast
value for meteorological range calculations. In sum, the
meteorological range is the distance from an ideal dark
object at which the object has a 0.02 liminal contrast
ratio against a white background.
The meteorological range can be derived from the
equation for the change in object intensity along the
path described in Figure 7.22. This equation is
In polluted tropospheric air, the only important gas-
phase visible light attenuation processes are Rayleigh
scattering and absorption by NO
2
(g). Table 7.3 shows
the meteorological ranges derived from calculated
extinction coefficients, resulting from these two pro-
cesses in isolation. For NO
2
(g), Table 7.3 shows values
at two mixing ratios, representing clean and polluted
air, respectively. For Rayleigh scattering, one meteoro-
logical range is shown because Rayleigh scattering is
dominated by molecular nitrogen and oxygen, whose
mixing ratios do not change much between clean and
polluted air.
At a wavelength of 0.55
m, the meteorological
range due to Rayleigh scattering alone in Table 7.3 is
334 km, indicating that,
in the absence of all pollutants,
the furthest one can see along the horizon, assuming a
liminal contrast ratio of 2 percent, is near 350 km
.Wag-
goner et al. (1981) reported a total extinction coefficient
Table 7.3.
Meteorological ranges (km) resulting from
Rayleigh scattering and NO
2
(g) absorption at
selected wavelengths (
)
NO
2
(g) absorption
Rayleigh
0.01 ppmv
0.25 ppmv
(
m)
scattering
NO
2
(g)
NO
2
(g)
d
I
d
x
=
σ
t
(
I
B
−
I
)
(7.9)
0.42
112
296
11.8
where all wavelength subscripts have been removed,
σ
t
is the
total extinction coefficient
,
0.50
227
641
25.6
σ
t
I
B
accounts for
the scattering of background light radiation into the
path, and -
0.55
334
1,590
63.6
0.65
664
13,000
520
σ
t
I
accounts for the attenuation of radiation
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