Geoscience Reference
In-Depth Information
Numerical analysis showed that
a
z
has a relatively constant value of 0.53. Substituting
M
a
and
r
a
into Eq. (
6.11
), and incorporating Eq. (
6.12
) yields:
−=
−
r
2
ar
2
2
ar
r
MM
S
+
( )
0
,
z
z
m
,
z
z
m
,
z
z
r
2
r
2
ln
(6.13)
a
,
z
0
,
z
m
,
z
0
,
z
2
2
0
,
z
Rewriting Eq. (
6.13
) results in a general root water extraction formulation that is valid
for both the constant and falling rate phase and that can be applied at any depth in the
root zone:
(
)
4
MM
−
a
,
z
0
,
z
S
=
(6.14)
z
ar
r
+
( )
r
2
−
ar
2
2
+
2
r
2
r
2
ln
z
m
,
z
0
,
z
z
m
,
z
0
,
z
m
,
z
0
,
z
Integration of Eq. (
6.14
) over the root zone yields the total actual transpiration. The
input data for this methodology consists of potential transpiration rate
,
plant wilting
point, root length density proile and the soil hydraulic functions (retention func-
tion and conductivity function). The approach may include layers with different soil
hydraulic properties and root densities. Most soil water will be extracted at locations
with high root density and soil water pressure head. When at certain locations in the
root zone soil water extraction is limited, other locations will automatically extract
more soil water.
Question 6.1:
The discussed microscopic approach can be used to quantify the effect
of atmosphere, plant and soil on root water uptake. Which input parameters in Eq. (
6.14
)
relate to atmosphere, which to plant and which to soil?
De Jong van Lier et al. (
2006
,
2008
) applied the methodology to various soil types
and atmospheric conditions.
Figure 6.5
depicts results for a clay soil during a dry-
ing period with three root densities and two transpiration rates. In all cases both the
constant and falling rate phases are clearly visible. In the case of higher transpiration
rates and lower root densities, the falling rate phase starts earlier. The pressure head
at the root surface,
h
root
, shows a diurnal luctuation (lower values during day time),
especially in case of low root densities.
In the above approach no hydraulic resistances inside the roots are considered.
Noordwijk et al. (2000) and Heinen (
2001
) followed a similar approach in the soil, but
included the radial hydraulic resistance within the roots. Such an approach no longer
can be solved directly, but requires numerical iteration. Even more detailed, Javaux
et al. (
2008
) and Schröder et al. (
2009
) use a three-dimensional numerical model in
which all the hydraulic resistances in the root and soil system are made explicit. Their
research model can be used to explore the complex feedback mechanisms between
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