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In-Depth Information
ice, scattering is strong and therefore also albedo is large, while in open water conditions
the volume backscatter is at most 10 % of the surface re
ection.
Since natural ice and snow are scattering media, a two-stream approach is often
employed in modelling the irradiance. This model considers both downwelling and
upwelling irradiance (Dunkie and Bevans 1956; Perovich 1990):
fl
dE
d
dz
¼
aE
d
bE
d
þ
bE
u
ð
3
:
19a
Þ
dE
u
dz
¼ aE
u
þ
bE
u
bE
d
ð
3
:
19b
Þ
This system has the general solution
b
z
þ
B
ð
1
þ jÞ
e
b
z
E
d
¼ A 1
j
ð
Þ
e
ð
3
:
20a
Þ
b
z
þ
B
ð
1
þ jÞ
e
b
z
E
u
¼ A 1
j
ð
Þ
e
ð
3
:
20b
Þ
p
a
=ð
a
þ
2b
Þ
p
a
ð
a
þ
2b
Þ
where
j
¼
;
b
¼
, and A and B are constants determined by the
boundary conditions.
3.4.3 Light Transfer in Ice-Covered Lakes
Snow and ice cover act as a diffusive
filter for the solar radiation transfer from the
atmosphere to the lake water body. The level of radiation decreases, but usually only small
modi
cations are seen in the spectrum when passing through snow and ice layers
(Fig.
3.18
). Solar radiation provides heat and causes internal deterioration of the ice. It is
the key factor in lake heat balance in the ice melting season. Also sunlight heats the water
beneath the ice, triggers spring convection, and provides photons for primary production
in snow, ice and water. Due to the strong scattering in ice and snow, radiation is diffuse
beneath the ice (Lepp
ranta et al. 2003a; Arst et al. 2006). In clear sky, open water
conditions, radiation becomes diffuse only at a distance from the surface.
Light transfer in ice and snow is in
ä
uenced by the crystal structure of ice and optically
active substances (OAS). Ice crystals are optically uniaxial, with c-axis as the optical axis.
In extreme cases, in small ponds the crystals may grow with vertical c-axes and then it is
possible to see through ice as through glass. Absorption of light in pure ice is much as in
pure liquid water (Fig.
3.17
), but there are no published results how much ice absorption
depends on the crystal structure. Liquid water layers in the ice sheet reduce long wave-
lengths by absorption; in lake ice such layers may occur all winter in the ice
fl
snow
-
interface and across the whole sheet in the melting season.
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