Environmental Engineering Reference
In-Depth Information
Q
n
=
net radiation at the water (or saturated ground) sur-
face, mm/day,
factors. The Penman-Monteith equation (Penman, 1965) bet-
ter represents evapotranspiration from a vegetated surface by
incorporationg canopy conductance.
The Penman-Monteith equation appears to be an enhance-
ment of the original Penman equation and has become
widely used in agriculture-related disciplines. However, the
Penman (1948) equation appears to still be widely used
for geotechnical engineering applications. The Penman-
Monteith equation is
psychrometric constant, kPa/
◦
C,
η
=
0
.
146
W
w
)(u
air
u
air
v
E
a
=
2
.
625
(
1
+
−
)
, mm/day,
v
0
W
w
=
wind speed, km/h,
u
air
v
=
vapor pressure in the air above the water (or satu-
rated ground), surface, kPa, and
u
air
v
0
=
saturated vapor pressure at the mean air tempera-
ture, kPa.
R
n
−
G
+
ρ
a
C
a
u
air
u
ai
v
g
a
v
0
−
86
.
4
10
6
The Penman (1948) equation shows that the vapor pres-
sure gradient between the water surface and the air above
the water becomes the primary driving mechanism for evap-
oration. There are two terms in the numerator of Eq. 6.20.
The first term involves net radiation and characterizes the
power of the sun to evaporate water. Net radiation quanti-
fies the net effect of short- and long-wave radiation from the
sun, surface reflectance (i.e., albedo), and surface tempera-
ture. The second term involves “mixing” of the air above
the water or the drying power associated with air movement.
The Penman (1948) equation assumes there is no heat
exchange with the ground, no advective energy within the
water and no exchange of heat energy. The Penman equation
is applicable to free-water surfaces. The Penman equation
has been shown to produce comparable results to pan evap-
oration and evaporation from lake surfaces. The air tem-
perature above the water surface is used in the calculation
of PE.
η
1
g
s
/g
a
Lρ
w
PE
=
×
+
+
(6.22)
where:
L
=
latent heat of vaporization or the energy
required to evaporate a unit mass of water
(i.e.,
10
6
∼
2
.
42
×
J/kg),
=
slope of the saturation vapor pressure versus
air temperature, kPa
◦
C
−
1
,
net radiation (J/m
2
/day), from the external
source of energy,
R
n
=
soil heat flux, J/m
2
/day,
G
=
specific heat capacity of air, MJ kg
−
1
C
−
1
,
C
a
=
dry air density, kg m
−
3
,
ρ
a
=
water density, kg m
−
3
,
ρ
w
=
u
air
v
=
vapor pressure in the air above the saturated
ground surface, kPa,
u
air
v
0
=
saturated vapor pressure at the mean air tem-
perature, kPa
,
6.3.8.3 Blaney and Criddle (1950) Equation
Blaney and Criddle (1950) used the variables of mean daily
air temperature and the fraction of the day in sunlight to
compute potential evaporation:
atmospheric conductance, m s
−
1
,
g
a
=
surface conductance, m s
−
1
,
g
s
=
0
.
066 kPa
◦
C
−
1
)
,
η
=
psychrometric constant
(η
≈
and
PE
=
p(
0
.
46
T
mean
+
8
)
(6.21)
10
6
86
.
4
×
=
conversion of m/s to mm/day.
where:
The soil heat flux can be assumed to be close to zero in
some cases.
PE
=
potential evaporation, mm/day,
p
=
percentage of daylight hours each day, and
mean daily temperature,
◦
C, calculated as
T
mean
=
(T
max
+
T
mean
=
6.3.8.5 Priestley-Taylor (1972) Equation
The Priestley-Taylor (1972) equation is quite similar to the
Penman equation but contains some different variables:
T
min
)/
2.
Jensen and Haise (1963) used air temperature and incident
solar radiation to predict potential evaporation from a water
surface.
η
Q
n
−
G
PE
=
α
3
(6.23)
+
where:
6.3.8.4 Monteith (1965) Equation
Monteith (1965) made modifications to the Penman (1948)
equation and the subsequent equation became known as the
Penman-Monteith equation (Monteith, 1965). The Penman-
Monteith equation contained the main variables from the
Penman (1948) equation but added variables such as air vol-
umetric heat capacity, vapor pressure deficit, fraction of the
day in sunlight as well as canopy and aerodynamic resistance
α
3
=
a constant taken as 1.26 for open and well-
watered surfaces,
=
slope of saturation vapor pressure versus tem-
perature curve, kPa
◦
C
−
1
,
Q
n
=
net radiation, mm/day,
psychrometric constant, kPa
◦
C
−
1
, and
η
=
G
=
soil heat flux, mm/day.
Search WWH ::
Custom Search