Geoscience Reference
In-Depth Information
K
c
(stage 3)
1.0
K
c
K
c
(stage 4)
Figure 23.2
Simplified seasonal
pattern used by FAO to specify
the time dependence of
K
c
values for agricultural crops in
terms of four growth stages with
period lengths defined for each
crop, and with crop-specific
values of
K
c
defined to apply
during a stage, or as limiting
values with linear interpolation
during the stage.
0.5
K
c
(stage 1)
Crop
development
Initial
Mid-season
Late-season
0
Stage 1
Stage 2
Stage 3
Stage 4
Time
Total growing season
Planting date
The resulting method is called the Matt-Shuttleworth approach.
To address the need to allow readily available climate data measured at 2 m to be
realistically applied to calculate aerodynamic resistance from tall crops when
using the Penman-Monteith equation, Shuttleworth derived a version of the
equation that is indexed to a common blending height arbitrarily selected to be at
50 m. This means the reference height and value of
D
are the same when calculat-
ing both the evaporation rate for any well-watered crop and reference crop
evapotranspiration rates. With
A
in units of W m
−2
, this version of the Penman-
Monteith equation has the form:
r
cuD
D
⎛
⎞
ap
22
Δ+
A
50
⎜
⎟
50
R
⎝
D
⎠
ET
=
c
2
RC
⎛
⎞
u
Δ+
g
1()
+
r
2
50
⎜
⎟
sc
R
⎝
⎠
(23.30)
c
where (
r
s
)
c
is the crop-specific surface resistance,
D
50
and
D
2
are the vapor pressure
deficit at 50 m and 2 m, respectively. The ratio of these two values, (
D
50
/
D
2
) is
given by:
⎡
⎤
⎛
D
⎞
⎛
(
Δ+
g
)302
+
70
g
u
⎞
⎛
(
Δ+
g
)302
+
70
g
u
⎞ ⎛
⎞
1
208
302
50
=
2
+
2
−
⎢
⎥
⎜
⎟
⎜
⎟
⎜
⎟ ⎜
⎟
⎝
D
⎠
⎝
(
Δ+
g
)208
+
70
g
u
⎠
r
⎝
(
Δ+
g
)208
+
70
g
u
⎠ ⎝
u
⎠
u
⎢
⎥
⎣
⎦
(23.31)
2
2
clim
2
2
2
and
R
c
50
the aerodynamic coefficient for a crop of height
h
c
given by:
