Agriculture Reference
In-Depth Information
the plants and the space above the bare soil fraction. Therefore,
K
s
inside a sparse canopy,
denoted
K
, can be represented by some combination of turbulent transfer coefficients in that
space. If, as a working hypothesis, we assume a linear combination weighted by the fractional
vegetation cover,
σ
f
(a measure of how sparse the tall grass is), then we can define
s
s
K
as
(
)
z
s
s
K
=
σ
σ
u
+
ku
1
−
σ
,
(32)
f
*
f
where
u
*
is the friction velocity above the bare soil fraction. In the case of dense vegetation
(
σ
f
= 1), Eq. (32) reduces to Eq. (17). Otherwise, when
σ
f
= 0, Eq. (32) represents the
turbulent transfer coefficient over bare soil. We can use Eq. (32) in calculating the wind speed
inside a sparse tall grass canopy. For that purpose we have to slightly modify Eq. (11) to take
into account
σ
f
(
)
2
C
L
H
−
h
d
⎛
du
⎞
s
s
d
d
K
=
σ
u
(33)
⎝
⎠
f
dz
dz
H
Replacing the expression for
s
K
given by Eq. (32) in Eq. (33) produces
(
)
2
[
]
d
⎧
(
)
du
⎫
C
L
H
−
h
d
d
σ
σ
u
+
ku
1
−
σ
z
=
σ
u
.
(34)
f
*
f
dz
dz
H
After differentiation and grouping, the terms we reach are
2
2
d
u
du
du
⎛
⎞
2
a
(
u
,
z
)
+
b
(
z
)
+
c
=
gu
,
(35)
⎝
⎠
2
dz
dz
dz
where
( )
(
)
z
a
u
,
z
=
σ
σ
u
+
ku
1
−
σ
c
=
σ
f
σ
f
*
f
(
)
C
L
H
−
h
()
(
)
z
b
z
=
ku
1
−
σ
g
= σ
d
d
*
f
H
To get the wind profile inside the sparse canopy, we can solve Eq. (35) numerically,
using the fourth-order Runge-Kutte method [40].
2.4. Surface Resistances
The resistances to the transport of water vapor from within the crop and up
per
soil layer
to the adjacent exterior air are defined as the bulk crop stomatal resistance,
r
, and soil
surface resistance,
r
surf
, respectively. Combining dependence of
r
on solar radiation, air
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