Agriculture Reference
In-Depth Information
Transport and Consumption of O
2
in the Roots and Losses to the Soil
To avoid unduly complicating the model, radial diffusion within the root is not
allowed for. Equation (6.1) therefore reduces to:
D
G
θ
G
f
G
d[O
2
]
G
d
r
d
d
r
−
R
root
−
R
soil
=
0
(
6
.
5
)
where
r
is the distance from the root bases (not the radial distance across the
root as in Equation 6.1).
R
root
at a particular distance along the root is the sum of
the respiration in the primary root and in any laterals emerging from it. Hence,
if the rate of respiration per unit root mass is
Q
,
ρ(
1
−
θ
G2
)Qπa
L
π(x
2
−
a
P
)L
VL
R
root
=
ρ(
1
−
θ
G
)Q
+
(
6
.
6
)
πa
P
Likewise
R
soil
at a particular distance is the sum of the rates of loss from the pri-
mary root and from the laterals. Hence, if
F
O
2
is the flux across unit root surface,
2
πa
L
F
O
2
π(x
2
−
a
P
)L
VL
2
πa
P
F
O
2
πa
P
R
soil
=
+
(
6
.
7
)
πa
P
It is assumed that the primary root wall is completely impermeable to O
2
in the
zone covered with laterals. In fact the root wall is not completely impermeable
in this zone but the resulting flux is small compared with that from the rest of
the root system and no serious error arises from ignoring it.
It is also assumed that the flux from the laterals and the primary root in the
zone beyond the laterals is constant. In fact the sink for O
2
in the surrounding
soil will vary in a complicated way with soil conditions and time, and there will
be differences along the root length. However to some extent these differences
cancel each other (Kirk, 2003) and the additional complexity involved in allowing
for them is unjustified.
The same boundary conditions apply as for Armstrong and Beckett's model,
and the equations are solved numerically.
Model Calculations
Figure 6.6 shows results for a realistic set of standard parameter values. The
maximum primary root length is 27.3 cm declining to 17.7 dm as the coverage
with laterals increases from
<
5 to 80% of the root length. Although the maximum
root length decreases as the coverage with laterals increases, the absorbing root
surface per unit root mass increases more than two-fold as the coverage with
