Geoscience Reference
In-Depth Information
⎡
⎤
⎡
⎤
(50
−
0.67
h
)
(50
−
0.67
h
)
(2
−
0.08)
⎡
⎤
c
c
ln
ln
ln
⎢
⎥
⎢
⎥
⎢
⎥
(0.123
h
)
(0.0123
h
)
0.0148
⎣
⎦
⎣
⎦
⎣
⎦
50
c
c
R
=
(23.32)
c
⎡
(50
−
0.08)
⎤
2
(0.41) ln
⎢
⎥
0.0148
⎣
⎦
Shuttleworth (2006) also derived a method for converting the existing values of
K
c
into the required values of (
r
s
)
c
. This involves specifying 'preferred conditions' in
which the reference crop evapotranspiration rate calculated by the FAO method and
the equivalent rate calculated by the Priestley-Taylor equation are equal. The justifi-
cation for forcing this equivalence is that in the original FAO recommendations
(Doorenbos and Pruitt, 1977), the FAO crop coefficients were considered applicable
to a range of estimates of potential evapotranspiration based on different formulae,
including the Priestley-Taylor equation. Such preferred conditions are therefore
those described earlier as 'humid' conditions, and the corresponding 'preferred'
value of climatological resistance, (
r
clim
)
pref
, is therefore given by rearranging Equation
(23.20) and substituting
a
effective
2 m s
−1
is
because FAO states the wind speed for which their tabulated crop coefficients apply
best is 2 m s
−1
. The resulting equation for (
r
clim
)
pref
is then:
=
1.26 and
u
2
=
2 m s
−1
. Substitution of
u
2
=
⎛
pref
⎞
Δ+
1.67
g
r
pref
(
)
=
104
1.26
−
1
(23.33)
⎜
⎟
clim
Δ+
pref
g
⎝
⎠
where
calculated at the 'preferred' temperature
T
pref
.
In these preferred atmospheric conditions (
r
s
)
c
, the value of the surface resistance
for a well-watered crop that is equivalent to the FAO crop coefficient, can be
calculated (see Shuttleworth, 2006 for details) from:
Δ
pref
is the value of
Δ
r
1
r
s
r
2
()
K
=−
sc
s
(23.34)
c
where:
⎛
pref
⎞
50
R
⎛
D
⎞
pref
c
+
50
(
r
)
⎜
⎟
⎜
⎟
clim
2
D
⎝
⎠
⎛
151(
Δ++
pref
g
)
70
g
⎞
⎜
⎟
1
2
r
=
(23.35)
⎜
⎟
⎜
⎟
s
pref
⎝
g
⎠
⎛
D
⎞
⎜
⎟
151
+
⎜
50
(
r
)
pref
⎟
⎜
⎟
clim
⎝
D
⎠
⎝
⎠
2
and:
pref
50
(
Δ+
g
)
R
r
2
c
=
(23.36)
s
g
2
In Equation (23.35), (
D
50
/
D
2
)
pref
is given by Equation (23.31) with
Δ
=
Δ
pref
and
u
2
=
2 m s
−1
. The values of
r
s
1
and
r
s
2
are therefore solely functions of the crop height
