Chapter 2: SEA SURFACE MICROLAYER
2 2
3 3
0
4
8
0,
2
1 2
exp 2
,
2
6
c
c
rs
c
c
T
r
r
t
S
t
PS
r
r
N S
§
·
/
/
'
/
/
¨
¸
©
¹
and
2
1 / 2
0
1
1
0,
exp
1 1
L
l r
rV
l
l
l
l
T
l
a
S
t
PS
erf
9
G
G
S G
N
\
ª
º
ª
º
'
¬
¼
¬
¼
/
¦
.
The first term on the right side of (2.108) is related to the surface flux of
rainwater, while the second term is related to the volume source of
rainwater.
The salinity difference should be averaged over time by weighting with
probability density
p t of the surface renewals:
0
0,
mr
S
p t S
t dt
f
'
'
³
(2.109)
where
^
`
0
2 2
3 3
0
2
2
2
1 / 2
1
1
0,
4
8
4
1 2
exp 2
3
2
1
exp
1
1 2
1
4
,
3
mr
c
c
c
T
L
l r
l
l
l
l
l
T
l
L
l
l
T
S
t
PS
r
r
t
r
r
a
erf
t
N S
9
G
G
G
S G
N
\
9 SN
'
u
§
·
/
/
/
/
®
¨
¸
¯
©
¹
ª
º
¬
¼
/
½ °
¾
° ¿
¦
¦
(2.110)
Solutions (2.110) holds for the linear case only under an assumption that
w
S S
|
(i.e.,
w
S
S
' ) and physical properties of seawater do not change
substantially because of the salinity dependence. The properties that could be
affected by the rain-caused changes in sea surface salinity are the thermal
expansion coefficient, kinematic viscosity, density, specific heat, and latent
heat of vaporization. The large salinity differences arising from substantial
freshwater influx and relatively long renewal times would require a
nonlinear solution to (2.105)-(2.106). However, as shown in the next section,
under moderate and heavy rain conditions the renewal time is restricted to
125
2 2
3 3
0
4
8
0,
2
1 2
exp 2
,
2
6
c
c
rs
c
c
T
r
r
t
S
t
PS
r
r
N S
§
·
/
/
'
/
/
¨
¸
©
¹
and
2
1 / 2
0
1
1
0,
exp
1 1
L
l r
rV
l
l
l
l
T
l
a
S
t
PS
erf
9
G
G
S G
N
\
ª
º
ª
º
'
¬
¼
¬
¼
/
¦
.
The first term on the right side of (2.108) is related to the surface flux of
rainwater, while the second term is related to the volume source of
rainwater.
The salinity difference should be averaged over time by weighting with
probability density
p t of the surface renewals:
0
0,
mr
S
p t S
t dt
f
'
'
³
(2.109)
where
^
`
0
2 2
3 3
0
2
2
2
1 / 2
1
1
0,
4
8
4
1 2
exp 2
3
2
1
exp
1
1 2
1
4
,
3
mr
c
c
c
T
L
l r
l
l
l
l
l
T
l
L
l
l
T
S
t
PS
r
r
t
r
r
a
erf
t
N S
9
G
G
G
S G
N
\
9 SN
'
u
§
·
/
/
/
/
®
¨
¸
¯
©
¹
ª
º
¬
¼
/
½ °
¾
° ¿
¦
¦
(2.110)
Solutions (2.110) holds for the linear case only under an assumption that
w
S S
|
(i.e.,
w
S
S
' ) and physical properties of seawater do not change
substantially because of the salinity dependence. The properties that could be
affected by the rain-caused changes in sea surface salinity are the thermal
expansion coefficient, kinematic viscosity, density, specific heat, and latent
heat of vaporization. The large salinity differences arising from substantial
freshwater influx and relatively long renewal times would require a
nonlinear solution to (2.105)-(2.106). However, as shown in the next section,
under moderate and heavy rain conditions the renewal time is restricted to
125