Vegetation: Transport Processes Inside and Outside of Plants - Transport in the Atmosphere-Vegetation-Soil Continuum - page 207

Table 6.1 Minimum air content in the top 25 cm of different soil textures needed
to have suficient aeration for potential root water uptake in a humid climate

Minimum volumetric air content (m 3 m -3 ) in top 25 cm

Crop Sand Loam Clay

Bulb crops 0.20 0.16 0.10

Beet crops 0.16 0.12 0.08

Grain crops 0.12 0.08 0.06

Grass 0.08 0.06 0.04

account for all these physical factors simultaneously. In macroscopic models fewer
factors are considered, which makes them easier to apply but requires calibration of
semi-empirical input parameters.

Microscopic Models
Microscopic models describe the convergent radial low of soil water toward and into
a representative individual root. The roots are considered as a line or narrow-tube sink
uniform along its length. The root system as a whole can then be described as a set of
such individual roots, assumed to be regularly spaced in the soil at deinable distances
that may vary within the soil proile (De Willigen et al., 2000 ). In such a geometry,
water extraction at the roots generates a radial low pattern. The water balance of a
radial low pattern results in the following continuity equation (Appendix D):

∂

∂ =− − ∂

θ
t

q
r

q
r

(6.1)

∂

where θ is soil water content (m 3 m -3 ), t is time (d), q is soil water lux density (m d -1 )
and r is radial distance from the centre of the root (m). The soil water lux itself can
be described by the Darcy equation in which the gravity component can be omitted
( Chapter 4 ):

qk h
r

=− ∂

∂

(6.2)

where k is hydraulic conductivity and h is soil water pressure head (cm).
When we solve Eq. ( 6.2 ) using realistic igures for extraction rates and soil hydrau-
lic properties, we get a very strong gradient ∂ h /∂ r near the root surface ( Figure 6.4 ).
This is caused by the rapid decline of the hydraulic conductivity at lower h values
and by the increasing lux density due to converging low lines. To solve Eq. ( 6.1 )
numerically, researchers had to use gross simpliications (Gardner, 1960 ; Herkel-
rath et al., 1977 ; Feddes and Raats, 2004 ). However, Eq. ( 6.1 ) can be solved more