Environmental Engineering Reference
In-Depth Information
Penman (
1948
) derived this equation for open water evaporation. Evaporation
from bare soil, wet soil and grasses is obtained as a fraction of
E
. Bulk surface
resistances from the soil and crop is not explicitly accounted for, but are incorpo-
rated in the wind function. Resistance factors are incorporated in Penman-based
equations to include the resistance of vapour flow through stomata openings, total
leaf area and the soil surface (the surface resistance,
r
s
), and the resistance from
the vegetation upwards involving friction from air flowing over vegetative surfaces
(aerodynamic resistance,
r
a
) (Allen et al.
1998
). The Penman-Monteith equation
(Monteith
1965
) for evaporation from bare soil, wet soil and grasses,
ET
,isgivenin
the ASCE standard form (Allen et al.
1998
)as:
⎛
⎝
⎞
K
time
ρ
a
c
p
(
e
s
−
e
a
)
(
R
n
−
G
)
+
1
λ
r
a
⎠
=
1
r
a
(18.17)
ET
r
s
+
γ
+
ρ
a
is the mean air density at constant pressure (kg m
−
3
),
c
p
is the specific heat
of air (MJ kg
−
1
◦
C
−
1
),
r
a
and
r
s
are the aerodynamic and (bulk) surface resistances,
respectively (s m
−
1
), and
K
time
is a units conversion factor (86400 s d
−
1
when
ET
is
expressed in mm d
−
1
). For a more detailed definition and discussion of Eq. (
18.17
)
and its parameters the reader is referred to Allen et al. (
1998
).
where
18.2.6 FAO56 Reference Evapotranspiration
Allen et al. (
1998
) calculated the reference evapotranspiration,
ET
0
, using the ASCE
Penman-Monteith equation (Eq. (
18.17
)) for a hypothetical reference surface or ref-
erence crop defined as “a cropped soil with an assumed crop height of 0.12 m, a fixed
surface resistance of 70 s m
−
1
and an albedo of 0.23”, with climatological parame-
ters measured at a reference level of 2 m above the soil surface. The popularly used
FAO56 Penman-Monteith equation is defined as (Allen et al.
1998
):
900
0.408
(
R
n
−
G
)
+
γ
273
u
2
(
e
s
−
e
a
)
T
+
ET
0
=
(18.18)
+
γ (
1
+
0.34
u
2
)
To calculate
ET
0
using the FAO56 Penman-Monteith equation on a daily basis,
such as implemented for instance in the ET-REF program (Allen
2001
), site-specific
data (altitude above sea level and latitude) and climatological data (temperature,
humidity, radiation, and wind speed) are required. The altitude above sea level deter-
mines the local average value of atmospheric pressure. The latitude is needed to
compute extraterrestrial radiation.
The potential evapotranspiration of a particular crop or vegetation,
ET
c
, is then
obtained by multiplying
ET
0
with a crop coefficient,
K
c
.
ET
c
is divided between
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