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albedo to decrease it leads to increased melting and further decrease of the albedo, and so
on. Since the conduction of heat within the ice sheet is slow, the positive feedback system
produces a patchy lake ice cover as can be well observed. This mechanism also increases
the irradiance beneath the lake ice and can produce patchiness there as well.
Dry,
fine-grained snow has albedo as high as 0.9, and for wet snow it is typically
around 0.5 (see Sect.
3.4.3
). Snow-ice has higher albedo than congelation ice due to
scattering. Bare, dry ice has albedo of 0.5, and with increasing surface wetness and
formation of melt ponds, the albedo decreases to 0.2
0.3. Thin (10 cm) bare ice has an
-
albedo of 0.2
0.3. According to Perovich and Polashenski (2012), the albedo of Arctic
Ocean seasonal sea ice is 0.85 in winter (dry snow-covered ice), and it decreases down to
0.2 in August. Most of the time the ponded ice cover has albedo within 0.4
-
0.6.
-
are apparent optical properties, i.e., in addition to the
properties of the medium, they depend on the directional distribution of the incoming
radiation and, consequently, on the solar altitude and cloudiness. They also depend on the
spectral distribution of solar radiation. On the surface of the Earth, the shape of solar
radiation spectrum can be taken
Albedo and the fraction
ʳ
xed (see Sect.
3.4
) but inside snow, ice and water the
spectral distribution changes. Snow and ice cover act as a diffusive
filter for the solar
radiation transfer but short and long wavelengths attenuate faster and the spectral band of
radiation becomes narrower with depth.
To determine the distribution of solar power with depth, the attenuation should be
determined from the spectral distribution since this in
uences the penetration depth.
Attenuation of irradiance is modelled with a linear model shown by Eq. (
3.18
). The total
power is obtained by integration:
fl
2
4
3
5
d
k
Z
1
Z
z
Þ
E 0
; k
Kz
0
; k
Þ
dz
0
Q
s
ðÞ
¼
ð
1
a
ð
Þ
exp
ð
ð
4
:
6
Þ
0
0
In practice, integration needs to take a few spectral bands only when using Eq. (
4.6
) for
lakes. With the spectral approach also the division of solar radiation into the surface
absorption and transmission can be properly treated and with desirable vertical resolution.
The mean light attenuation coef
5m
−
1
for lake water,
1m
−
1
for
cient is
ʺ
*
0.1
ʺ
*
-
10 m
−
1
for snow and snow-ice. Thus snow accumulation has a major
role in the light conditions in ice-covered lakes (see Sect.
3.4
).
congelation ice,
ʺ
*
4.1.3 Terrestrial Radiation
Lake surface
—
whether liquid water, ice or snow
—
radiates as a grey body with emissivity
very close to one (0.96 <
ʵ
0
< 0.98):
Q
L0
¼
e
0
r
T
0
ð
4
:
7a
Þ
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