Geoscience Reference
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where the subscript
'
refers to the different layers, h '
are the layer thicknesses, and
h =
ʣ ' h ' is the total thickness. This equation actually presents an inversion formula to
estimate the attenuation coef
cients of the individual layers by linear regression based on
measurements of irradiance above and below the ice sheet and thicknesses of the layers
(see Lepp
ranta et al. 2010). The number of layers to be included is limited by the number
of degrees of freedom in the observational data set.
The transmittance of light is about the same for congelation ice and for liquid lake
water but snow and snow-ice are much more opaque. The optical thickness of congelation
ice and snow/snow-ice are 100
ä
ranta et al.
2003a; Arst et al. 2006), while in lake waters it ranges from 10 to 500 cm depending on
the water quality (Arst 2003; Arst et al. 2008). Thus the amount of snow and snow-ice is a
critical factor for the light transfer. In spring, when the snow has melted, the solar
radiation level is high and sunlight penetrates through the ice cover well. The optical
properties of saline ice are in
200 cm and 5
20 cm, respectively (e.g., Lepp
ä
-
-
uenced also by the salt content (Perovich 1998). The brine
pockets absorb light and salt crystals scatter light, but the amount of salt crystals becomes
signi
fl
cant only at very low temperatures. Especially in warm ice, chlorophyll in the brine
pockets absorbs light strongly in the bands 430
440 nm and 660
690 nm.
-
-
3.5
Ice Mass Balance
The ice sheet consists of ice and snow layers. The mass per unit area, expressed in
thickness of an equivalent water layer, is h =(
ρ i h i +
ρ s h s )/
ρ w . The density of ice can be
ρ i = 910 kg m 3 ) but snow density changes signi
taken as a constant (
cantly in time and
space. The mass of ice sheet changes at the lower boundary by freezing and melting, and
at the upper boundary by precipitation (P) and sublimation (E). The mass balance is
dS 1
dt ¼
q w dh i
q i
dt þ f þ P E
A
ð
3
:
25
Þ
where S 1 = hA and f stands for the
fl
flooding of lake water onto the top of ice sheet. The
growth rate of ice thickness,
flooding and precipitation can be of the order of 1 cm per
day, while submission is less than that. Precipitation is purely external factor, while
sublimation depends on the difference between the absolute humidity in the lake surface
and air (see Sect. 2.3 ). The mass budget is taken just as a vertical process, and the in
fl
fl
ow
and out
ow of ice from the lake are ignored. In dry regions, the ice budget is simple since
precipitation and slush are absent and f = P = 0 (Fig. 3.20 ).
The lake water storage can be expressed as S =(h + H)A, with S 2 = HA as the liquid
water part. Equation ( 3.25 ) represents the conservation of ice, and the conservation of
liquid water is
fl
 
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