Geoscience Reference
In-Depth Information
In the melting period, a thin boundary-layer forms under the ice (surface layer), where
temperature and salinity increase from T 0 and S 0 at the ice bottom to the bulk upper layer
values T 1 and S 1 . The presence of ice keeps the surface temperature at the freezing point,
T 0 = T f (S 0 ) and beneath the surface the bulk temperature is T 1
T f (S 1 ). As long as the
salinity increases with depth, the temperature can reach T m (S) or even more in the surface
layer. In the lower layer the temperature is determined by the depth of convection and the
sediment heat
flux. Just above the sediment there can be a more saline, dense layer as
described above. In the temperatures below 6
fl
8
°
C very small salinity changes can
-
compensate for the in
uence of temperature on the water density.
Solar radiation penetrating the ice is a major factor to drive convection (Farmer 1975;
Mironov et al. 2002). It raises the temperature of the water beneath the ice suf
fl
ciently to
initiate convective mixing. Solar forcing is an internal source term while the heat
fl
ux
from sediments is a boundary
fl
flux. The solar heating extends to a surface layer with
thickness of 1
-
10 m depending on the optical thicknesses of the ice and lake water
ä
(Lepp
ranta et al. 2003a; Arst et al. 2006; Jakkila et al. 2009). The resulting convection
deepens and penetrates down to the lake bottom (or halocline if such exists) when the
water temperature increases. Then the vertical heat transport predominates over the lateral
exchange between shallow and deep parts of the lake.
Farmer (1975) performed the
first systematic observations of radiatively-driven con-
vection in the deep ice-covered freshwater Babine Lake (B.C., Canada) and presented an
analysis of the convective mixing ef
ciency. Mironov et al. (2002) presented a compre-
hensive review on this topic. The buoyancy is de
ned as the relative weight
q w q 0
q 0
b ¼ g
ð
7
:
28
Þ
where ρ 0 is a fixed reference density. In freshwater lakes, the buoyancy conservation law
is given by
@ b
@ t ¼ @
K b @ b
@ z
q w c w @ Q T
g a
ð
7
:
29
Þ
@ z
@ z
where K b is the diffusion coef
cient of buoyancy, and
ʱ
is the thermal expansion coef-
ficient. Mironov et al. (2002) also proposed an appropriate scaling for the convection
velocity w* based on the kinetic energy budget integrated over the convective mixing
layer:
3 p
H d
; B ¼ B ðÞþ B ðÞ 2
H d
Z H
d B ðÞ dz
w ¼
ð
Þ B
ð
7
:
30
Þ
B ¼ g a Q T
q w c w
Search WWH ::




Custom Search