Environmental Engineering Reference
In-Depth Information
where:
accordance with Eq. 6.27. The water vapor pressure in the
air,
u
ai
v
, is defined as follows:
thermal flux into soil ground, J/(m
2
/day),
R
g
=
u
air
v
u
air
=
v
0
h
r
(6.67)
net radiation, J/m
2
/day
R
n
=
sensible heat flux, J/m
2
/day
R
h
=
where:
latent heat flux, J/m
2
/day, where
R
l
=
R
l
=
(L
v
)(
AE
)/
1000 (1000
=
unit conversion factor, where 1mm
h
r
=
relative humidity of the air above the soil surface.
=
1/1000 m),
volumetric latent heat of vaporization, J/m
3
, and
L
v
=
The daily air temperature
T
a
and daily relative humidity
h
r
of the air above the ground surface are usually measured
at a weather station. Minimum and maximum daily temper-
ature and relative humidity values are generally recorded on
a daily basis. Sometimes the hourly values of temperature
and relative humidity are also recorded. The amount of data
becomes quite excessive when hourly values are recorded.
When minimum and maximum values are given for tem-
perature and relative humidity, then an assumption can be
made regarding the distribution of these variables throughout
each day.
Figures 6.38 and 6.39 show two possible assumptions that
can be made regarding the daily patterns of air tempera-
ture and relative humidity based on minimum and maximum
daily readings. Figure 6.38 illustrates an asymmetric vari-
ation of air temperature and relative humidity throughout
each day. Figure 6.39 illustrates a symmetrical variation of
air temperature and relative humidity throughout each day.
In the asymmetric daily patterns shown in Fig. 6.38, the
relative humidity is assumed to have a maximum value at
night and a minimum value at about noon. The daily distri-
butions of temperature and relative humidity are known to
have some effect on the calculation of AE.
The symmetric patterns shown in Fig. 6.39 have a max-
imum value of relative humidity at about midnight and a
minimum value of relative humidity occurring near noon.
The daily changing pattern of air temperature is in general
opposite to the pattern for relative humidity.
AE
=
actual evaporation, mm/day.
Boundary Condition for Moisture Flow.
The atmo-
spheric moisture flux at the ground surface,
q
y
surface
,must
satisfy the water balance equation (Eq. 6.7):
q
y
surface
=
P
−
AE
−
R
(6.65)
where:
q
y
=
moisture flow rate at soil surface, mm/day,
P
=
precipitation flux (i.e.,
rainfall plus
snowmelt
water), mm/day,
R
=
water runoff, mm/day, and
AE
=
actual evaporation, mm/day.
The net
infiltration flux at
the ground surface,
q
y
,is
defined in terms of
k∂h/∂y
.
Actual Evaporation.
The Wilson-Penman equation
(Wilson et al., 1994), provides one procedure for
the
calculation of AE:
Q
n
+
ηE
a
AE
=
(6.66)
+
η/h
s
where:
flux associated with “mixing”;
f(u)C
f
u
air
E
a
=
(
1
/h
r
v
−
1
/h
s
)
, mm/day,
h
r
=
relative humidity in the air above the ground (i.e.,
h
r
u
air
v
/u
air
=
v
0
),
80
30
h
s
=
relative humidity at the soil surface (i.e.,
h
s
=
/
u
soil
Relative humidity
Air temperature
u
soil
v
v
0
),
76
28
u
air
v
=
water vapor pressure in the air above ground
surface, kPa,
72
26
68
24
u
air
v
0
=
saturated vapor pressure at the mean air tempera-
ture, kPa,
64
22
60
20
u
soil
v
0
=
saturated vapor pressure in the soil at ground
surface, kPa,
56
18
52
16
=
slope of saturation vapor pressure versus temper-
ature curve, kPa/
◦
C,
48
14
44
12
6:00 AM 13:00
Q
n
=
net radiation at the water surface, mm/day, and
40
10
constant, kPa/
◦
C,
η
=
psychrometric
η
=
0
.
06733
0
0.5
1.0
1.5
2.0
2.5
3.0
kPa/
◦
C.
Time, day
Figure 6.38
Asymmetric distributions of daily changing pattern
of air temperature and relative humidity based on maximum and
minimum values.
The saturated vapor pressure for the air,
u
air
v
0
,inEq.
6.66 can be calculated based on air mean temperature, in
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