Geoscience Reference
In-Depth Information
C
p
()
r
=
(23.24)
apan
11.35
+
u
2
where
u
2
is the wind speed (in m s
−1
) measured at 2 m,
C
p
has units of s m
−1
and the
factor 1.35 (implicitly) has units of s m
−1
. Rotstayn
et al
. (2006) prescribed the
effective value of surface resistance for a Class A evaporation pan when evapora-
tion is calculated using the Penman-Monteith Equation as:
()
r
=
1.4()
r
(23.25)
s pan
a pan
with the albedo of the pan set to 14%. Roderick
et al.
(2007) experimentally verified
the Penman equation against Class A pan data from pan sites in Australia where the
measured meteorological variables required in the equation were also available.
They showed that, on average, the equation gave a reasonable description of
monthly-average measured pan evaporation rate, albeit with systematic site-to-site
discrepancies in the order of 10-20% when
C
p
is set to an average value 224 s m
−1
.
Thus, both the Penpan equation and FAO's recommended equation for
calculating reference crop are implementations of the Penman-Monteith equation
with different values of aerodynamic and surface resistance, i.e., (208/
u
2
) and 70
for a reference crop and (
r
a
)
pan
1.4
r
a
for a pan, respec-
tively. By substituting these pairs of values into Equation (23.23) and taking the
ratio of the two calculated rates, it follows that:
=
C
p
/(1
+
1.35
u
2
) and (
r
s
)
pan
=
⎡
⎤
C
(
Δ+
2.4
g
) / (1
+
1.35
u
)
[
r
+
208/
u
]
⎣
⎦
p
2
K
=
c
lim
2
(23.26)
[
]
p
70
g
+Δ+
(
g
)208/
u
⎡
⎤
r CAA u
+
(
/
) / (1
+
1.35
)
⎣
⎦
2
c
lim
p
pan
rc
2
where (
A
pan
/
A
rc
) is the ratio of the energy available to support evaporation from a
reference crop to that available for an evaporation pan. Shuttleworth (2010) dem-
onstrated that the value of
K
p
is estimated to within an accuracy of a few percent
by setting (
A
pan
/
A
rc
)
1.15 for a wide range of short wave and longwave radiation
values, and recommended that in the absence of better information the value of
r
clim
in Equation (23.26) should be calculated from:
=
[
]
⎛
ag
Δ+
(1
+
0.377
u
)
⎞
208
2
r
=
−
1
⎜
⎟
clim
u
Δ+
g
⎝
⎠
2
(23.27)
where
u
2
, the wind speed measured at 2 m, is in m s
−1
and with
set to 1.26 and
1.74 at humid and arid sites, respectively. Shuttleworth also showed that the value
of
K
p
has limited sensitivity to temperature (via the value of
α
), but has a strong
sensitivity to wind speed. In the absence of measurements, he recommended that
a default temperature of 20
Δ
C and default wind speed of 2 m s
−1
are used in
Equation (23.26). When the temperature is 20
°
C and pressure is 100 kPa, in humid
conditions
K
p
has the wind speed dependent form:
°
