THE NEAR-SURFACE LAYER OF THE OCEAN
0
0
T
E
L
r s
z
Q Q
Q Q I Q
o
,
(1.26)
where 0
Q is the net surface heat flux; T
Q and E
Q are the sensible and latent
heat fluxes respectively; L
I is the net longwave radiative flux; rs
Q is the
surface component of the rain-induced heat flux (see Section 1.5.4). Solar
radiation does not enter the surface boundary condition because it is treated
as a volume source of heat.
The surface boundary condition for the salinity transport equation (1.11)
is associated with freshwater fluxes at the air-sea interface. A vertical
balance of freshwater flux across the ocean surface is as follows (Mellor,
1996):
0
0
1
0
E P m
S
˜
,
(1.27)
where 0
S is the sea surface salinity; E is the evaporation rate, which is
related to the latent heat flux as
E
Q
LE ,
(1.28)
L is the specific heat of vaporization for water; P is the precipitation rate,
and 0
m is the flux of seawater to the sea surface in units of volume of water
per unit area per unit time. The factor
0
1 S
accounts for the exclusion of
salt from seawater. The salt flux at the waterside of the air-sea interface in
units of mass of water per unit area per unit time is
0
00
0
z
J
J
Sm
U
o
.
(1.29)
Combining (1.27) and (1.29) leads to the following boundary condition
on the salt flux at the ocean surface:
0
0
0
0
0
/ 1
/
E
J
E P S
S
E P S
Q L P S
|
.
(1.30)
Note that 0 35
S | psu = 0.035; therefore, factor (
0
1 S
) is replaced with
unity in (1.30).
The salinity increases towards the ocean surface when evaporation
exceeds precipitation (E > P) or decreases when precipitation exceeds
evaporation (E < P) because of freshwater flux subtracted from or added to
the surface water, respectively. Vertical salinity gradients developing in the
near-surface layer of the ocean due to surface forcing are considered in
12