INTRODUCTION
The last decade has seen major advances in the design, technology and
management of trickle irrigation system. This is due, in the large part,
to a better understanding of the movement of water in soil in response
to a surface point source like the trickle emitter. One of the important
aspects of planning and management of drip irrigation system is soil moisture
movement pattern under it.
In trickle irrigation, the soil serves less as a reservoir for water than for
conventional irrigation because the water that is withdrawn from the root zone
is continually replenished. As a result, soil type does not play much role in
irrigation scheduling in trickle irrigation (Lubana et
al., 2002). However, the soil type and the application rate of water,
both influence the pattern of water movement in the soil. The distances between
emitters would determine the degree of overlap between neighboring wetted circles.
In addition, the cost of a unit length of a lateral is influenced by the number
of emitters on it. The volume of soil wetted from a point source is primarily
a function of the soil texture, soil structure, application rate and the total
volume of water applied (Ekhmaj et al., 2005;
Lubana et al., 2002).
Present design procedures recommend the use of empirical coefficients to calculate
optimal emitter spacing. These coefficients vary with emitter discharge and
soil texture. Clearly, the volume of water applied per irrigation also affects
the width and depth of the wetted soil volume and therefore influences the optimal
emitter spacing. Wetting pattern can be obtained by either direct measurement
of soil wetting in field, which is sitespecific, or by simulation using some
numerical or analytical models. In most of models, the Richards equation governing
water flow under unsaturated flow conditions have been used to simulate soil
water matrix potential or water content distribution in wetted soil. Also, the
hydraulic conductivity in unsaturated flow equations is highly nonlinear and
show high spatial variable (Warrick and Nielson, 1980).
Numerical and analytical methods have been used to solve unsaturated flow equations.
These methods call for detailed information on the physical properties of the
soil and for an access to computers (Battam et al.,
2003).
Schwartzman and Zur (1986) developed a simplified semiempirical
method for determining the geometry of wetted soil zone under line sources of
water application placed on surface. They assumed that the geometry of wetted
soil, the width and depth of wetting at the end of irrigation depends on the
soil type, emitter discharge per unit length of laterals and total amount of
water in the soil. The objectives of the present study were to develop and test
the simplified semiempirical method of Schwartzman and Zur
(1986) for determining the geometry of the wetted soil volume under point
sources in three type soil.
DESCRIPTION OF MODEL
Schwartzman and Zur (1986) model can be applied for
use under surface drip irrigation from point source. The geometry of wetted
soil volume, width (W) and depth (Z) under this method of water application
at the end of an irrigation event was assumed to depend on emitter discharge
(q), total amount of water (V), saturated hydraulic conductivity of soil (Ks).
Therefore, the functional relationships among these parameters may be written
as:
Using dimensional analysis method, three dimensional independent terms
were developed which are represented as follows:
The relationships between dimensionless parameters; Z*, W* and V* in
Eq. 2 could be extracted either from experimental or
simulated results. The following relationships exist between dimensionless
parameters:
In Eq. 3 and 4, n_{1} and
n_{2} are exponents and A_{1} and A_{2} are constants
of equation, respectively. Now putting values of W* and V* in Eq.
3, the following relationship for wetted width was obtained:
Similarly putting values of Z* and V* in Eq. 4, yielded
value for wetted depth as below:
MATERIALS AND METHODS
Measurement of soil wetted front: The experiments were conducted in
Physical Modeling Laboratory, Water Engineering Faculty, Shahid Chamran University,
Ahwaz, Iran.

Fig. 1: 
Physical model for wetting front observations 
The simulation experiments for the threedimension used in the
present study consisted of a Perspex transparent box 180 cm long, 150 cm wide
and 120 cm deep which a quarter of that was eliminated (Fig. 1).
The box was packed with a soil which was airdried and passed through a 2 mm
(No. 10) sieve. Uniform bulk density was assured by packing 5 cm layers of preweighed
soil. Three soil types were used in this study. A silty clay loam packed to
a bulk density of 1.36 g cm^{3} and a loam packed to a density of 1.6
g cm^{3} and a sandy packed to a density of 1.72 g cm^{3}.
The saturated hydraulic conductivity determined using Rosetta software (Version
1.0) (Schaap et al., 2001) was 32.1 cm day^{1} for the silty clay loam and 23.8 cm day^{1} for the loam and 99.52
cm day^{1} for the sand. Water was applied from a calibrated emitter
which was placed in the geometrical center at the top of the soil surface according
to Fig. 1. Three emitter discharges of 3.46, 2.17 and 1.38
l h^{1} with three replications were tested on each soil making a total
of 27 experimental runs.
The position of wetting front was marked on the transparent wall of the
box at fixed time intervals (1 h). These lines were then copied on transparent
drawing paper. The depth and width of the wetted soil volume at various
times during infiltration was determined from these results. Then the
results compared simulated values against observed values in field to
ensure model applicability under field conditions.
Steps for simulation: The following steps were followed for simulation
of wetted width, W and depth, Z of wetted soil zone around placed emitter
with point source of water application:
• 
Values of Z and W were observed under given q and V for given soil
of known value of K 
• 
Values of V*, W* and Z* were estimated using Eq. 2
for different simulated values 
• 
Values of W* and V* were presented graphically (Fig.
2) 
• 
The best fit equations and correlation coefficients relating simulated
V* to simulated W* was computed for each three soil types (Fig.
2) 
• 
Values of Z* and V* were presented graphically (Fig.
3) 
• 
The best fit equations and correlation coefficients relating simulated
V* to simulated Z* was computed for each three soil types (Fig.
3) 
Values of constant were put into Eq. 5 and 6.
It yielded relationships for wetted depth, Z and wetted width, W of soil
(Table 1).
The values of wetted widths and wetted depth of soil were simulated using
top equations for different discharge rates and duration of water application.
Performance of simulation model: Performance of model was tested
by comparing simulated values against observed values in field to ensure
model applicability under field conditions. For this purpose nullhypotheses
of equal variances and equal means at 0.05 significance level were tested
using ttest. These tests were performed for comparing simulated values
against observed values of wetted soil depth and width for given duration
of water application.
Calculated values of t were found less than critical values. Therefore,
nullhypotheses of equal variances and means, respectively, were accepted.
It was then concluded that simulated values followed distribution not
different than observed values at 0.05 significance level.
Table 1: 
Equations simulated and observed values 


Fig. 2: 
Relationship between simulated dimensionless wetted
soil width and simulated dimensionless wetted soil volume 

Fig. 3: 
Relationship between simulated dimensionless wetted
soil depth and simulated dimensionless wetted soil volume 
This indicated that model may be used for simulation of wetted soil depth
and width in duration of water application.
RESULTS AND DISCUSSIONS
The wetted width and depth was affected by discharge rates of emitters.
With increasing discharge rates of emitters depths and width of wetted
zone of soil increased. The reason was that, with increasing discharge
rate the volume of water supplied in a given duration increased which
created higher volume of wetted soil zone.
It was observed that wetted width and depth of was affected by duration
of water application. These increased with increased duration of water
application for given discharge rate. Because, with increased duration
of operation more volume of water is applied that was occupied by larger
wetted volume of soil (Fig. 4).
An increased in the value of K representing a shift to lighter soils results
in an increase in the ratio of the wetted soil depth to the wetted soil width
(Fig. 4). It should be stated, wetting pattern was affected
by soil structure (Peter et al., 2003). As expected,
more transmissive soil (silty clay loam, K = 32.1 cm day^{1}) have
greater values of Z and smaller values of W than more slowly permeable soil
(loam, K = 23.8 cm day^{1}). After extension application water value
of W changes little in sandy soil but are still increasing in silty clay loam
and loam soils.

Fig. 4: 
Change in vertical distance and change in radius of
the wetted volume of water applied for three contrasting soils 
Doubling the value of emitter discharge tends to increase the wetted
soil width more than to decrease the wetted depth.

Fig. 5: 
Relationship between the radius (W) and depth (Z) of
wetted volume 
Good agreement between simulated values and observed values strengthens
our confidence in the validity of the empirical equations developed for
the case of a point source. However, it is still of critical importance
to test these equations in the field.
There was a poor relationship between W and Z for sandy soil. Also, these
values were well correlated in loam and silty clay loam soils (R^{2}
= 0.99) (Fig. 5).