poster - International Conference of Agricultural Engineering

2. Material and Methods
After the surface irrigation practice, soil water content was measured every 2 hours, using a
TRIME-FM time domain reflectometry (TDR) probe in 12 glass fiber tubes around the apple
tree.
Considering the vertical and radial variations of the root distribution, soil samples were taken
from around the tree, and the position of each sample was recorded including radial distance
from the trunk and depth to the midpoint of each sample, at the end of the experiment. The
root-length density (cm cm -3 ) of each sample was determined by dividing the total root length
by the sample volume. The 2D depth- and radial-wise distribution of roots was determined
from the average the root-length density of the same sample within the root zone.
The model (SWMRUM) was obtained based on the observation of root density in field and
the root density distribution was fitted to deduce the root density function as follow:
r
z
( ( r / rm
(t )) (z
/ zm
(t )))
(r,z, t) Cir
(1 )(1 ) 0e
(1)
rm
(t) z
m
(t)
where â(r, z, t) is the root density function [LL -3 ], C ir is a coefficient used to show growing
power of root that is evaluated with a penetrometer tool [-], t is the certain time, r is the
distance in radial direction [L], z is the distance vertical direction [L], r m (t) is the maximum root
development radius [L] in the radial direction at time t, z m (t) is the maximum root depth [L] in
the vertical direction at time t, and â 0 , ñ, and are the empirical parameters. Values of the
coefficient C ir in different soil, evaluated for root distribution ability, have given in Table 1.
These values were calculated by using a Penetrometer tool (Rimik CP20), which measures
the resistance against penetration in soil. The instrument consists of a data logger, load cell,
a cone attached to a shaft and GPS. The data logger records the cone index value of the
load required for insertion of the cone through the soil as well as time, date, and GPS
coordinates. The logger plots these cone index values against the depth.
The root water uptake rate at (r,z) can be calculated by following equation:
S(r,z,t,h)
(r,z,h)S
(r,z,t)
(2)
max
where S(r,z,t,h) is the proposed root water uptake in r-direction and z-direction for spatial soil
water pressure head (h) at time t, (r,z,h)
is adjusted water stress function.
As the potential cumulative root water uptake must equal the potential transpiration rate
(T pot ), the maximum root water uptake distribution, S max [T -1 ], may be computed from
(Simunek et al. 2006):
S
max
(r,z, t)
2
R
z m r m
(r,z,
t)T
2
r
0 0
pot
(r,z, t)drdz
where S max (r,z,t) denotes the maximum root water uptake rate [T -1 ] and R is the size of the
flow domain in the r-direction[L].
(3)
3. Results
The presented two dimensional models of root water uptake were evaluated using measured
soil water content values, around the apple tree during the irrigation period. For simulating
water movement in soil, the two-dimensional root water uptake model was developed, which
was linked to a soil water dynamic model. The spatial two-dimensional maps of simulated
and measured water content values (m 3 m -3 ) involving the effects of root water uptake after
irrigation at three different days are shown in Fig 1. During experiment the soil volumetric