Geoscience Reference
In-Depth Information
Fig. 3.17
Schematic picture of
radiation concepts in the
transfer through ice cover
Incoming
Reflection
Backscatter
Snow
Scattering
(by gas bubbles)
Ice
Absorption
Water
Transmission
Radiation is absorbed and scattered in ice and water, described with the absorption
coef
cient a(
ʻ
) and scattering function, assuming isotropic medium,
ʲ
(
ˈ
,
ʻ
), where
ˈ
is
the angle of the scattered beam from the unscattered beam (0
≤ ˈ ≤ ˀ
). The absorption
cient and the scattering function are inherent
6
coef
optical properties (Fig.
3.17
).
Absorption follows the Beer
-
Lambert law:
dL
ds
¼
aL
ð
3
:
15
Þ
where s is the direction of light propagation. The scattering function is usually integrated
over forward and backward hemispheres for forward scattering and backscattering coef-
), respectively. By diffusing the radiation, scattering reduces the
radiance level in the direction of propagation, as speci
ficients bf(λ)
f
(
ʻ
) and b
b
(
ʻ
ed by the total scattering coeffi-
-
cient b(
ʻ
)=b
f
(
ʻ
)+b
b
(
ʻ
). For this reduction, an attenuation law similar to the Beer
-
-
Lambert law is employed. Additivity is assumed for the in
fl
uences of absorption and
scattering, and the total beam attenuation coef
cient becomes c = a + b.
'
s surface directly from the Sun and as diffuse radiation
from the whole sky due to scattering in the atmosphere. The contributions of the direct and
diffuse radiation depend on the solar zenith angle and cloudiness. To obtain the amount of
incoming radiation at the surface and at different depths in ice-covered lakes, radiance
needs to be integrated over all directions. This leads to the concept of irradiance. Take the
vertical, z-coordinate zero at the lake surface and positive downward (the top surface may
Solar radiation comes to Earth
6
Inherent optical properties depend on the properties of the medium only, while apparent optical
properties depend also on the directional distribution of the incoming light.
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