Geoscience Reference
In-Depth Information
The saturation vapor pressure
e
s
is the highest pressure of water vapor that can
exist in equilibrium with a plane, free water surface at a given temperature. It can be
approximated by the Tetens formula:
a
∗
exp
b
∗
T
T
e
s
=
(12.33)
+
c
∗
◦
C. For temperatures above freezing,
where
T
is the water temperature in
the
237.3
◦
C. The air vapor
pressure
e
air
can be calculated using Eq. (12.33) by substituting
T
with the dew point
temperature.
coefficients are
a
∗
=
6.108 mb,
b
∗
=
17.27, and
c
∗
=
Sensible heat flux
Sensible heat flux is due to conduction and convection. It can be in either direction,
depending on the temperature difference between air and water. Edinger
et al
. (1974)
determined the sensible heat flux as
J
Ts
=
C
b
f
(
U
wind
)(
T
air
−
T
water
)
(12.34)
·
◦
K
−
1
), and
f
(
U
wind
)
where
C
b
is the Bowen coefficient (0.62 mb
is the wind speed
function defined in Eq. (12.32).
An alternative formula for the sensible heat flux is (Imberger and Patterson, 1981)
J
Ts
=
C
h
c
p
,
air
ρ
air
U
wind
(
T
air
−
T
water
)
(12.35)
10
−
3
; and
c
p
,
air
is
the specific heat capacity at constant pressure, approximately 1003 J
where
C
h
is the bulk coefficient of sensible heat flux, about 1.4
×
kg
−
1
·
◦
C
−
1
for
·
typical air temperatures in the near surface region.
Net heat flux in water column
It is generally presumed that the long-wave radiation (
J
Tlw
), latent heat flux (
J
Te
),
and sensible heat flux (
J
Ts
) are non-penetrative; thus, they would appropriately be
modeled by the surface boundary condition:
T
∂
T
1
ρ
ε
=
c
P
(
J
Tlw
+
J
Te
+
J
Ts
)
(12.36)
∂
z
The short-wave radiation is penetrative and has an exponential decay distribution
along the flow depth:
e
−
λ(
z
s
−
z
)
J
Tsw
(
z
)
=
J
Tsw
(
z
s
)
(12.37)
where
J
Tsw
(
z
)
is the short-wave radiation absorbed at height
z
,
J
Tsw
(
z
s
)
is the net
short-wave radiation penetrating the water surface, and
is the bulk extinction
coefficient determined by Eqs. (12.69) and (12.70) in Section 12.2.2.
λ
