Geoscience Reference
In-Depth Information
Thermal Balance at the Ice / Ocean Interface
d
T
d
z
Ice
Thermal conduction into ice
Water
w
=
w
0
+
w
p
T
0
,
S
0
Latent heat source or sink
ρ
ice
ρ
w
--------
·
w
0
=
-
w
'
T
'
0
=
Turbulent heat f lux
α
h
u
*0
(
T
w
-
T
0
)
Fig. 6.2
Schematic of vertical exchanges at the ice/ocean interface in a small control volume (de-
tail)following the ice/ocean interface
Thekinematicice conductiontermis
=
−
K
ice
T
z
ρ
w
c
p
q
(6.2)
where
T
z
isthethermalgradientnearthebaseoftheicecolumn,and
K
ice
isthermal
conductivity of sea ice there. The latter is a fairly complicated function of brine
volume and temperature,but here we use a simplified approximationsuggested by
Untersteiner(1961):
T
ice
where
S
ice
and
T
ice
are ice salinity (practical salinity scale) and tempera-
ture
K
ice
≈
K
fresh
+
β
S
ice
/
(
◦
C
averaged over that part of the ice column spanned by
T
z
;
K
fresh
is
thermal conductivity for fresh ice
)
04Jm
−
1
K
−
1
s
−
1
(
2
.
)
and
β
is a constant
117Jm
−
1
K
−
1
s
−
1
psu
−
1
◦
C
(
0
.
)
.
Theeffective(apparent)latentheatofseaiceisalsostronglyaffectedbyvariation
inbrinevolumeandtemperature.Fortherangeoficetemperaturesnearthebaseof
theicecolumn,aroughapproximationtheformulasforthebrinevolumeandlatent
heatgivenbyMaykut(1985,hisequations(6.13)and(19)is
L
ice
c
p
=
L
fresh
c
p
Q
L
=
(
1
−
0
.
03
S
ice
)
where
Q
L
is a “latent heat temperature” with units kelvins, and
L
fresh
=
333
5kJkg
−
1
islatentheatforfreshice.Bothapproximationsfortheiceproperties
arecrude,butshouldbeconsideredinlightof largeuncertaintiesin icesalinity and
brinevolumeneartheinterface,particularlyifice isfreezing.
.
