Geoscience Reference
In-Depth Information
by Fischer
et al
. (1979), Imberger and Patterson (1981), Jacquet (1983), and TVA
(1972) as
T
air
(
0.17
C
cloud
)(
T
water
J
Tlw
=
ε
σ
1
+
1
−
R
tlw
)
−
ε
σ
(12.28)
water
air
10
−
8
W
m
−
2
·
◦
K
−
4
);
T
air
is the
where
σ
is the Stefan-Boltzman constant (5.669
×
·
air temperature in Kelvins (
◦
K
◦
C
273.15), measured two meters above the
water surface;
T
water
is the water surface temperature in
◦
K;
R
tlw
is the reflectivity
of the water surface for long-wave radiation, which is generally small and
=
+
≈
0.03
(TVA, 1972; Brown and Barwell, 1987; Chapra, 1997);
water
is the emissivity of
water, which is between 0.95 and 0.963 corresponding to the temperature range of
0
◦
and 100
◦
C (Reynolds and Perkins, 1977), but is given 0.97 by TVA; and
ε
ε
air
is the
emissivity of air, determined by (Swinbank, 1963)
10
−
5
T
air
ε
=
0.938
×
(12.29)
air
Latent heat flux
The latent heat flux per unit surface area (W
m
−
2
) due to evaporation and conden-
·
sation can be modeled as
J
Te
=
LE
(12.30)
kg
−
1
), which is related to temperature
(TVA, 1972; Jacquet, 1983; Blanc, 1985), but given a constant value of 2.5
where
L
is the latent heat of evaporation (J
·
10
6
×
kg
−
1
by Gill (1982); and
E
is the water vapor flux (kg
s
−
1
m
−
2
), determined by
·
·
J
(Imberger and Patterson, 1981)
E
=
C
W
U
wind
ρ
(
q
air
−
q
surface
)
(12.31)
air
where
U
wind
is the wind speed;
C
W
is the dimensionless bulk transfer coefficient for
evaporation (primarily due to wind), given as 1.4
10
−
3
;
ρ
air
is the density of air at
the surface;
q
air
is the specific humidity in the air (unitless); and
q
surface
is the specific
humidity at the water surface (unitless). Note that 1 W
×
s
−
1
.
Edinger
et al
. (1974) determined the latent heat flux as a function of wind speed
and water vapor:
=
1J
·
J
Te
=
f
(
U
wind
)(
e
air
−
e
s
)
(12.32)
where
e
s
is the saturation vapor pressure (mb) at the water surface temperature,
e
air
is the air vapor pressure (mb), and
f
is a function of wind speed. Var-
ious formulations were examined by Edinger
et al
. (1974), and one choice was
f
(
U
wind
)
0.345
U
wind
,7
m
−
2
mb
−
1
) with
U
wind
,7
being the wind speed
(
U
wind
)
=
6.9
+
(W
·
s
−
1
) measured 7 m above the water surface.
(m
·
