Geoscience Reference
In-Depth Information
4.1
Heat Budget of Lakes
4.1.1 Total Heat Budget
The heat content of a lake consists of sensible and latent heat. It is convenient to take the
reference level as the heat content of liquid water at the temperature of 0
C. Thus the heat
content per unit area can be expressed as U = U
0
+ E, where U
0
is the heat content at the
reference level and
°
Z
h
b
Z
h
0
dz
E ¼
q
w
c
w
Tdz
þ
q
i
1
m
ð
Þ
L
f
þ
c
i
T
ð
4
:
1
Þ
h
B
h
b
is the
liquid water content of ice, and the temperature is in degrees centigrade (Fig.
4.1
). The
integrals on the right-hand side represent the heat in the water body and ice sheet,
respectively. Snow layer is considered as a part of the ice sheet. The evolution of the heat
content is given by
Here h
0
, h
b
, and h
B
are the altitudes of ice surface, ice bottom and lake bottom,
ν
z¼h
B
þ
Q
A
þ
Q
M
Z
h
0
dE
dt
¼ Q
0
þ
k
Q
s
dz
j
@
T
@
z
ð
4
:
2
Þ
h
B
where Q
0
is the surface heat balance or the net surface heat
fl
ux, Q
s
is solar radiation,
ʺ
is
thermal conductivity, Q
A
is the advective heat
fl
ux, and Q
M
is the heat brought in by mass
fl
ned positive into the lake. The surface heat balance is always
important, while penetration of solar radiation has a key role in the melting season. Heat
fl
uxes. The
fl
uxes are de
cant in the early ice season. Solid precipitation
decreases the heat content but liquid precipitation with temperature above 0
flux from the lake bottom is often signi
C increases
it. The distribution of heating between ice and water body depends on the internal
properties of the system. At the ice
°
water interface, heat can be transferred from water to
ice, and latent heat is released or taken when ice grows or melts, respectively.
The surface heat balance is written as
-
Q
0
¼
Q
s0
þ e
0
Q
La
þ
Q
L0
þ
Q
H
q
w
L
ES
E
þ
p
ð
v
;
T
Þ
P
ð
:
Þ
4
3
where Q
s0
is the surface absorption of solar radiation, Q
La
is the atmospheric thermal
radiation, Q
L0
is the thermal radiation from the surface, Q
H
is the turbulent sensible heat
fl
flux, and p is the heat transfer function for precipitation. The last term depends on the
liquid water content
ν
and temperature T, given as:
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