Geoscience Reference
In-Depth Information
⎡
⎤
0.303
C
/ (1
+
1.35
u
)
[58+208/
u
]
⎣
⎦
p
2
K
=
2
p
[4.63
+
43.8/
u
]
⎡
⎤
58
+
1.15
C
/ (1
+
1.35
u
)
⎣
⎦
2
p
2
(23.28)
while in arid conditions, it has the form:
⎡
⎤
0.303
C
/ (1
+
1.35
u
)
[120+208/
u
]
⎣
⎦
p
2
K
2
=
p
[4.63
+
43.8/
u
]
120
⎡
+
1.15
C
/ (1
+
1.35
u
)
⎤
⎣
⎦
2
p
2
(23.29)
The implicit dimensions of the constants that appear in Equations (23.28) and
(23.29) require that
C
p
in s m
−1
and
u
2
in m s
−1
. Assuming
C
p
is the average value
224 s m
−1
found by Roderick
et al.
(2007), then, when
u
2
2 m s
−1
, the default values
of
K
p
are 0.88 and 0.82 in humid and arid conditions, respectively. Were a calibration
of
C
pan
at the pan site to be made (perhaps by temporarily deploying the sensors
needed to gather the weather data required by the Penpan equation), then the
subsequently sustained collection of wind speed measurement would give improved
accuracy for pan-based estimates of reference crop evaporation at the site.
Table 23.4 demonstrates example calculations of reference crop evaporation using
the Penman-Monteith-based FAO method and the less reliable radiation-based,
temperature-based and pan-based estimates described above for the three example
sites A, B, C. In the case of the radiation-based estimate, the value is calculated using
the most appropriate value, either 1.26 or 1.74, in Equation (23.21) depending on
whether the site is considered to have a generally humid or generally arid climate.
At the sites with humid climates A and C (sites near Oxford, England and Manaus,
Brazil), the radiation-based and temperature-based estimates of reference crop
evaporation give values that are roughly comparable to those given using the FAO
method. However, at site B near Tucson, Arizona, the radiation-based and tempera-
ture-based methods both give estimates of
E
RC
which are much lower than the values
given when using the FAO method, despite the fact that
a
effective
=
1.74 is selected
when making the radiation-based estimate of
E
RC
. Pan-based estimates are made
both using relevant default values of
K
p
and relevant wind speed dependent estimates,
i.e., using Equation (23.27) to calculate
r
clim
in humid and arid conditions as
appropriate, then calculating a wind-corrected value of
K
p
from Equation (23.26).
The default values of
K
p
give overestimates because in each case the wind speed is
significantly greater than 2 m s
−1
.
=
Evaporation from unstressed vegetation:
the Matt-Shuttleworth approach
Daily estimates of evaporation from vegetation cover that is plentifully supplied
with water are still usually made using Equation (23.12) with assumed values for
K
C
, taken from the tables provided by FAO (Allen
et al.
, 1998) for irrigated crops.
