Environmental Engineering Reference
In-Depth Information
18.2.5 Penman-Monteith Equation for Evapotranspiration
For evapotranspiration to occur, three conditions are needed in the soil-plant-
atmosphere system (Jensen et al.
1990
):
1. a supply of water must be available;
2. energy must be available to convert liquid water into vapour water;
3. a vapour pressure gradient must exist to create a flux from the evaporating surface
to the atmosphere.
Penman (
1948
) proposed a combination method by introducing an energy bal-
ance (condition 2) and a mass transfer term in an aerodynamic formula (condition
3) into a single equation to calculate
ET
. Penman's method was developed to cal-
culate
E
as open water evaporation. Written as the weighted sum of the rates
of evaporation due to net radiation,
E
r
(MJ m
−
2
d
−
1
), and turbulent mass trans-
fer,
E
a
(MJ m
−
2
d
−
1
), Penman's equation for the evaporative latent heat flux,
λ
E
(MJ m
−
2
d
−
1
), is:
+
γ
γ
+
γ
λ
E
=
E
r
+
E
a
(18.12)
is the latent heat of vaporization (MJ kg
−
1
),
where
λ
is the slope of the vapour
pressure curve (kPa
◦
C
−
1
) and
is the psychrometric constant (kPa
◦
C
−
1
).
E
r
is
γ
given by:
E
r
=
R
n
−
G
(18.13)
where
R
n
is the net radiation flux (MJ m
−
2
d
−
1
) and
G
is the sensible heat flux into
the soil (MJ m
−
2
d
−
1
), and
E
a
by:
E
a
=
W
f
(
e
s
−
e
a
)
(18.14)
where
e
s
and
e
a
are the saturation and actual vapour pressures, respectively (kPa),
(
e
s
-
e
a
) is the saturation vapour pressure deficit, and
W
f
is a wind function (MJ d
−
1
kPa
−
1
). A linear wind function was found to be adequate, defined as (Allen
2001
):
W
f
=
K
w
(
a
w
+
b
w
u
2
)
(18.15)
where
K
w
is a units conversion factor [6.43 for
ET
0
in mm d
−
1
], and
a
w
and
b
w
are
empirical wind function coefficients often obtained by regional or local calibration.
The Penman method to estimate the evaporation from open water is then:
e
a
)
+
γ
γ
1
λ
=
(
R
n
−
+
)
K
w
(
a
w
+
b
w
u
2
)(
e
s
−
E
G
)
(18.16)
(
+
γ
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