Chapter 2: SEA SURFACE MICROLAYER
2 2
3 3
4
8
0,
2
1 2
exp 2
,
2
6
c
c
rs
r
w
c
c
T
r
r
t
T
t P T T
r
r
N S
§
·
/
/
'
/
/
¨
¸
©
¹
2
1 / 2
1
1
0,
exp
1 1
L
l r
rV
r
w
l
l
l
l
T
l
a
T
t P T T
erf
9
G
G
S G
N
\
ª
º
ª
º
'
¬
¼
¬
¼
/
¦
,
/ 4 T
z
t
[
N , and l
l
r
kt a
G \ /
. The first term on the right side of
(2.101) is related to the surface flux of rainwater, while the second term is
related to the volume source of rainwater.
In accordance with the renewal concept, this temperature difference
should be averaged over time by weighting with probability density
p t of
the surface renewals:
0
0,
wr
T
p t T
t dt
f
'
'
³
(2.102)
where
0
1
0,
0, ' '
t
wr
r
T
t
T
t dt
t
'
'
³
(2.103)
With (2.101), the solution to (2.103) is
^
`
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
wr
r
w
c
c
c
T
L
l r
l
l
l
l
l
T
l
L
l
l
T
T
t P T T
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
° ¿
¦
¦
(2.104)
which is used together with (2.102) and the log-normal probability density
function of the surface renewals similar to (2.88)-(2.89); this allows the
numerical integration that gives the modification of the cool skin caused by
the sensible heat flux related to the rain.
123