Geoscience Reference
In-Depth Information
Q
w
¼ k
w
@
T
@
z
ð
4
:
63
Þ
In the case of laminar
fl
flow, molecular conductivity of water is used, k
w
= 0.6 W/
(m
turbulent transition regime, molecular conductivity
is replaced by effective thermal conductivity (Petrov et al. 2006; Shirasawa et al. 2006).
An other way to express the heat
°
C). If the
fl
flow is in the laminar
—
fl
flux is the bulk formula Q
w
=
ˁ
w
c
w
C
Hw
(T
w
−
T
b
)U
w
,
where C
Hw
is the heat exchange coef
cient, and T
w
and T
b
are water temperature and ice
bottom temperature.
As an example, a numerical modelling study of the ice cover in Lake Vanajavesi,
southern Finland, is presented (Yang et al. 2012). The thermodynamics model HIGHTSI
(Cheng 2002) was used for an individual ice season 2008
2009 and for the climatological
-
period 1971
2000 with good calibration data. The novel model features were advanced
treatment of superimposed ice and turbulent heat
-
fl
fluxes, coupling of snow and ice layers,
and snow modelled from precipitation.
The model solves the surface temperature T
0
from a detailed surface heat balance. Solar
radiation is strongly attenuated along the vertical depth immediately below the surface
(Grenfell and Maykut 1977), and part of the radiation is taken to contribute to the surface
heat balance. The level of this contribution depends on the quality of the surface layer, i.e. the
first layer of snow or ice in model (Launiainen and Cheng 1998; Cheng 2002; Cheng et al.
2008). The albedo is critical for snow and ice heat balance. A parameterization suitable for
the Baltic Sea coastal snow and land-fast ice was selected (Pirazzini et al. 2006):
a
¼ 0
:
15
;
h
i
\
0
:
1cm
h
i
0
:
1cm
ða
i
þ a
s
Þ
a
¼ min
a
s
;
;
h
i
0
:
1 cm and h
s
10 cm
ð
4
:
64
Þ
a
¼
a
s
;
h
i
0
:
1 cm and h
s
[
10 cm
where
ʱ
s
and
ʱ
i
are
the
snow and
ice
albedo,
respectively,
taken
as
. The surface turbulent heat
a
s
¼ 0
:
75
; a
i
¼ min 0
:
55
;
0
:
85h
1
:
i
cm
1
:
5
þ
0
:
15
fl
uxes were
parameterized using the Monin
Obukhov similarity theory, and snow cover evolution was
modelled as discussed above. The temperature criterion of T
a
< 0.5
-
°
C was set to decide
when the precipitation is assumed solid.
The integral interpolation method was applied to build up the numerical scheme
(Cheng 2002). A high spatial resolution (10 layers in snow and 20 layers in ice) ensures
that the high frequency response of the snow and ice temperature to forcing and the
distribution of the absorption of solar radiation near the surface are correctly resolved. The
model parameters for this study are summarized in Table
4.3
. The freezing date is pro-
vided as the initial condition by a thin ice layer (2 cm). The
first day when the ice starts to
grow successively is de
ned as the freezing date. This is a crude approximation, as the
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