Geoscience Reference
In-Depth Information
Appendix D
Microscopic Root Water Uptake
D.1 Mass Balance Equation
Microscopic models describe the radial low of soil water towards individual roots.
The roots are considered as linear tubes. The root system as a whole can then be
described as a set of such individual tubes, assumed to be regularly spaced in the soil
at deinable distances (
Figure D.1
). The density of the tubes may vary with depth,
similar to root density in a root zone.
In such a geometry, a radial low pattern towards the roots exists.
Figure D.2
depicts
this low pattern for a segment with angle d
α
(rad). The inlow
Q
in
(m
2
d
-1
) can be
written as:
Q r
in
= α
(D.1)
and the outlow
Q
out
(m
2
d
-1
) equals:
=+
∂
∂
q
r
rr r
+
( )
α
Qq
d
d d
(D.2)
out
where
q
(m d
-1
) is the soil water lux density and
r
(m) is the radial distance from the
root centre. Calculation of the terms of Eq. (
C.2
), and subsequently the difference
Q
in
-
Q
out
yields:
+
∂
∂
q
r
+
∂
q
r
∂
()
2
QQ
− −
dd
α
qr r
d
r
d
r
(D.3)
in
out
The segment area
A
(m
2
) between radial distances
r
and
r
+ d
r
(m) from the root
centre is equal to:
d
α
π
π
d
α
π
d
r
2
=
( )
−
2
Ar
π
d
r
r
= +
rdr
d
α
(D.4)
2
2
2
2
359
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