Geoscience Reference
In-Depth Information
Table 4.2
The monthly mean heat fluxes (W m
−
2
) in Lake P
ää
j
ä
rvi in ice season 2003
-
2004 (19
December 2003
-
28 April 2004); only ice days have been included in the budget
Winter 2003
-
2004
December
January
February
March
April
Surface heat balance (S)
Net solar radiation
0
0
3
10
38
Net terrestrial radiation
-
19
-
21
-
25
-
35
-
47
Sensible heat flux
-
10
-
4
-
4
-
1
2
Latent heat flux
-
8
-
3
-
4
-
3
-
2
Total
-
37
-
28
-
30
-
28
-
8
Inside the ice sheet (I)
Net solar radiation
0
1
3
11
39
Ice bottom (B)
Heat flux from the water
5
5
5
5
12
Freezing
30
17
19
6
0
Melting
0
0
0
0
-
41
Total
35
22
24
11
-
29
Residual (error)
Total (S + I + B)
-
5
-
3
-
6 2
Radiative heating of water 1 0 0 1 40
Budget residual is the sum of the heat fluxes from above and below and would be zero for a correct
flux estimates (Jakkila et al. 2009)
-
2
= 910 kg m
−
3
,
freshwater ice depend on the temperature and gas content, but
ˁ
c = 2.1 kJ kg
−
1
C
−
1
serve as convenient reference values. If they
are constant, we obtain the heat diffusion equation with constant diffusion coef
C
−
1
and k = 2.1 W m
−
1
°
°
cient D = k/
10
−
6
m
2
s
−
1
= 0.095 m
2
day
−
1
. This means that in one day the length scale of
(
ˁ
c) = 1.1
×
p
0
:
095
diffusion is
, e.g. one-day temperature cycle can penetrate 31 cm into
the ice. In the yearly time-scale, the diffusion length scale becomes 5.9 m. The temperature
must be below the freezing point; at there further heating leads to melting of ice.
The boundary conditions are determined by the heat
m
31 cm
fl
fluxes into the system. These
fl
fluxes produce phase changes, i.e. growth and melting of ice, and consequently the
boundaries of the ice sheet move:
z ¼ 0
:
T
\
T
f
:
dh
dt
¼
E
;
k
@
T
@
z
¼
Q
0
ð
4
:
25a
Þ
T ¼ T
f
:
dh
dt
¼
q
L
f
Max Q
0
;
0
Þ
E
;
k
@
T
ð
@
z
¼
Min
ð
Q
0
;
0
Þ
ð
4
:
25b
Þ
z ¼ h
:
T ¼ T
f
; q
L
f
dh
dt
þ
Q
w
¼
k
@
T
@
z
:
ð
:
Þ
4
25c
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