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ZANCO Journal of Pure and Applied Sciences
The official scientific journal of Salahaddin University-Erbil
https://zancojournals.su.edu.krd/index.php/JPAS
ISSN (print ):2218-0230, ISSN (online): 2412-3986, DOI: http://dx.doi.org/10.21271/zjpas
RESEARCH
PAPER
Multivariate Models for Predicting the Maximal Diameter of the
Wetted Area under Surface Drip Irrigation System
Ismael O. I smael1, Triq H. Karim2
1,2Department of Soil and Water, College of Agricultural Engineering Science, Salahaddin University-Erbil, Kurdistan Region,
Iraq
A B S T R A C T:
Water shortage has been and will continue to be a key global-scale threat to agricultural production. One approach to
mitigate the intensity this problem is the efficient use of water and this necessitates introduction of high efficient irrigation
systems like drip irrigation. Reliable information about the dimensions of wetted soil under drip irrigation enables designers to
find out optimal emitter flow rates and spacing to offer efficient use of irrigation water. Accordingly, the current study was
initiated and the main objectives were to predict the ultimate diameter of wetting area under emitters from dripper discharge and
other properties of the dominant soils in Erbil plain. To achieve the above objective 24 sites were selected over the indicated plain
keeping in mind covering a wide spectrum of soil properties. At each site the soil moisture distribution in horizontal and vertical
directions were monitored under three drip discharges of 1.2, 2.5 and 3.5 l hr-1 such that each line represented a discharge level.
The results indicated that among a host of input variable, emitter discharge, soil clay content and saturated hydraulic conductivity
were the most influential factor affecting the maximal diameter of the wetted area (D). A linear and a nonlinear model were also
derived for predicting the maximal diameter of the wetted area (D). The mean absolute percentage errors were 10.37 and 8.57 %
respectively. Similarly, a linear model was proposed for predicting the wetting depth with a reasonable accuracy. Additionally, the
results also confirmed that the model proposed by Schwartzman and Zur, (1986) had poor predictability for estimating D in the
area under study.
KEY
WO
R
D
S:
Wetting Pattern, empirical models, Erbil Plain, Drip Spacing.
DOI: http://dx.doi.org/10.21271/ZJPAS.32.4.16
ZJPAS (2020) , 32(4);135-143 .
1.INTRODUCTION
Water scarcity can be considered as a
threat to agricultural production on the globe. The
water shortage can be mitigated by increasing
irrigation efficiency through the adoption of
modern technologies, such as drip irrigation,
which leads to substantial water savings, releasing
the saved water to other uses (Perry et al., 2017).
Drip irrigation can be defined as the
application of water via point or line source above
or under the soil surface at small operating
pressure ranging between 0.02 and 0.2 MPa and at
discharge rates of 1-30 l hr-1, giving rise to partial
of the soil surface (Dasberg and Or, 1999).
Information on moisture distribution patterns
under point source trickle emitters is a pre-
requisite for the design and operation of trickle
irrigation systems (Subbauah and Mashru, 2013).
The distance that water spreads
horizontally from a drip line and the volume of
* Corresponding Author:
Ismael O. I smael
E-mail: esmahel_2008@yahoo.com
Article History:
Received: 23/12/2019
Accepted: 27/02/2020
Published: 08/09 /2020
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ZANCO Journal of Pure and Applied Sciences 2020
soil wetted are limiting factors that determine the
spacing and number of drip lines and emitters, the
frequency of irrigation, and thus the cost of
irrigation (Skaggs et al., 2010).
The general objective of drip irrigation
system design is to select proper layout and
components to achieve suitable distribution of
irrigation water throughout the field to meet the
crop water requirement and deliver water
efficiently (Naglič et al., 2014). Proper design and
installation are essential to provide a drip
irrigation system that can be managed with
minimal inputs and maximum profit (Clark and
Smajstrla, 1996). The dimensions of the wetting
pattern are imperative in selecting the right
spacing between emitters and the suitable distance
between laterals (Al-Ogaidi et al., 2016). The
spacing between emitters can be determined on
the basis of form of wetting pattern and area
which is occupied with per emitter (Neshat and
Nasiri, 2012). The shape of the wetted soil volume
under single drip emitter is affected by a host of
factors including soil hydraulic properties, soil
structure, soil texture, impermeable layers in the
soil profile and anisotropy. (Gärdenäs et al., 2005,
Skaggs et al., 2010).
Li et al., (2004) reported that as the time
increased, the radius of saturated water entry zone
becomes larger and after around 3.5 h approached
to a constant size. The ultimate surface saturated
wetted radius was reached faster under a higher
emitter discharge. Furthermore, the findings of
Abu-Awwad et al., (2017) revealed that soil
surface wetted area would increase in decreasing
rates as application time increased until the
application rate became in equilibrium with soil
infiltration rate. Roth (1974) elucidated that matric
potential is dominant compared to gravitational
potential in dry soils. As soil gets wetter,
gravitational potential dominates the matric
potential. The higher the application rate, the
larger is the influence of gravity and, as a result,
the smaller will be the wetted area.
Naglič et al., (2014) has shown that a number
of models exist for wetting pattern prediction. The
proposed models vary from relatively simple to
more complex codes. They can be categorized
empirical, analytical or numerical models. On the
other hand, Alshammary and Salim (2016)
demonstrated that several models have been
developed to predict wetting front dimensions,
which are important for the optimal design of drip
irrigation system, using some of the variables such
as emitter discharge, water application rate and
soil hydraulic properties.
It is commendable to mention that the area
under drip irrigation is expanding over the region
under study. In this region, a wide spectrum of
soils with various properties is existing. Site
specific information is required on the wetting
pattern and hydraulic properties of these soils.
Reliable information about the dimensions of
wetted soil under drip irrigation enables designers
to find out optimal emitter flow rates and spacing
to lessen system equipment cost and offer better
soil water conditions for the most efficient use of
irrigation water (Malek and Peters, 2010).
Unfortunately, there is lack of information on such
study in the area under study, therefore the current
study was initiated to: 1) develop empirical
models for predicting ultimate diameter of the
wetting area of the dominant soil in Erbil plain
under drip irrigation and 2) evaluate the
Schwartzman and Zur (1986) model for predicting
the maximum diameter for these soils under drip
irrigation.
1. MATERIALS AND METHODS
2.1. Study Sites Description
The selected sites are located within the
outskirts of Erbil city, mostly lying at 400 m
a.m.s.l. It is bounded approximately by parallels
N 36o 00 00 and N 36o 20 00 and meridians E
43o 45 00 and E 44o 15 00. The study area
experience Mediterranean climate type, being cold
and rainy winters and hot and dry summers. Mean
annual temperature amounts to about 20 oC with a
maximum in July (44oC) and a minimum in
January (5oC). Mean annual precipitation across
the study ranges between about 180 and 750 mm
distributed over rainy months. It has a unimodal
distribution with an average value of about 400
mm. Further, the annual distribution shows a dry
season lasting from June to September and a wet
season from October to April.
On the basis of aridity index defined as the
ratio of mean annual precipitation to potential
evapotranspiration, the climate regime can be
classified as semiarid ( 0.2 > AI < 0.5 ) (Unesco,
1979). There is no mountain vegetation over most
of the area, even the smaller woody shrublets have
been eradicated by plough, wood cutter and fuel
gatherer and most of the palatable perennials have
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ZANCO Journal of Pure and Applied Sciences 2020
been greatly reduced or eliminated by
overgrazing. It includes mostly agricultural and
grazinglands, but also residential areas and
marginal spots. The spring aspect of the
uncultivated lands is luxuriant grasslands
dominated by Poa sp and Hordium sp (Guest and
Al-Rawi, 1966). According to soil taxonomy Staff
(1999), the majority of the soils are categorized
as: Fine Loamy, Active, Mixed, Thermic, Typic
Chromoxerets. The soil textures are
predominantly silty clay loam followed by silt
loam and silty clay. Soil reaction is basic and
organic matter content is generally low, with
values of less than 2%. With no exception, all the
existing soils are non-saline and calcareous. The
equivalent CaCO3 content ranges from about 20%
to more than 40%. There are narrows strips of
sandy loam to silt loam or loam along the Tigris
tributaries.
Fig. 1: The location map for the sampling and experimental sites
2.2 Field Tests
Before initiating field tests, several tours
were made in the outskirts of Erbil city to select
24 sites to cover a wide spectrum of soil
properties. Fig.1 shows the location map for
experimental sites.
At each site, a representative bare area
with negligible slope was selected. Small
obstacles like stones and twigs were removed.
Trampling was avoided over the location of
measurements. Three laterals were installed at
each site and provisions were made to install three
emitters at a spacing of 2 m on each lateral. A
regulating valve was installed ahead of each
lateral to regulate the emitters discharge. The
emitters were connected to a portable water
reservoir by polyethylene tubes (main and lateral)
with diameters 50 and 16 mm, respectively. The
water reservoir was a cylindrical metal tank with
1000 L capacity. Three discharge rates of 1.2, 2.5
and 3.5 l hr-1 were applied such
that each line represented a discharge level. The
three installed emitters had equal discharges of
(1.2 or 2.5 or 3.5 l hr-1) and represented a unit or a
replicate for a given discharge level. After
operation of drip irrigation system until the
wetting radius became constant by using a meter
scale. The observations were taken until a steady
state was reached which took a period in between
24 and 48 hours.
To monitor soil moisture distribution in
horizontal and vertical directions, soil samples
were also obtained on two orthogonal lines
passing through the center of the wetting area at 5
positions on each line and at several depths below
each position using a small auger 2 cm in
diameter. The obtained samples were oven dried
for measuring soil water content.
After termination of the experiment,
composite disturbed soil samples were obtained
from three depths (0.0-0.20; 0.20–0.4 and 0.4-0.6
m) for performing soil physical and chemical
analysis. Three undisturbed soil samples were
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ZANCO Journal of Pure and Applied Sciences 2020
obtained from each site for measuring insitu soil
bulk density by core method as outlined by (Blake
and Hartge, 1986). In the meantime infiltration
rate was measured at each site by using double
infiltrometer according to the method outlined by
(Michael, 1978). Additionally, the soil around the
emitter was excavated to expose a vertical soil
profile, to monitor the water distribution in the
vertical direction.
2.3. Soil and Water Analyses
Particle size distribution was carried out by
using both hydrometer and sieving methods
according to the procedures described by (Klute,
1986). The soil bulk density was measured by
core method as outlined by (Blake and Hartge,
1986). The soil infiltration rate was measured by
double ring infiltrometer method as described by
(Michael, 1978). Additionally, the well water
which was used as the source of irrigation was
analyzed for some chemical analysis following
standard procedures as outlined by (Richards,
1954) ( EC =0.44 dSm-1, pH= 7.51 ).
3.RESULTS AND DISCUSSION
3.1.General Aspects of the Soil Properties
Table 1 depicts the database of the current
study. It compasses particle size distribution, soil
hydraulic properties, soil bulk density, maximal
diameter of wetted area and wetted depth from 24
sites surrounding Erbil city. It can be noticed from
Table 1 that the database covers a wide spectrum
of soil properties. For instance the clay content
ranged from 4.18% at site to as high as 43.97% at
site, with a mean value of 28.44%. On the other
hand sand content ranged from as low as 17.7% to
as high as 77.39% with an average value of
33.72%. Overall, the soil texture, ranged from
loamy sand at Eski-Kalak site to clay at several
sites and most of them fell in the clay loam and
silty clay loam classes. Additionally, the insitu
soil bulk density obtained by core method for the
upper 60 cm varied between 1.17 to 1.70 Mgm-3
while the saturated hydraulic conductivity ranged
from as low as 0.22 cm hr-1 to as high as 4.42 cm
hr-1. It is also of note to mention that that
among the study variables, the saturated hydraulic
conductivity exhibited by the highest spatial
variability (CV = 61.07%), followed by sand
content (CV = 46.54%) and clay content (CV=
37.55%). The result is in tune in the findings of,
who observed that the soil infiltration rate was
characterized by a high spatial variability. It can
also be noticed the remaining variables were
characterized by intermediate or degree of
variability.
Based on the obtained values of skewness
and kurtosis, it can be that most the study
variables are slightly deviated from normal
distribution like saturated hydraulic conductivity
(Jackson, 1958) and depth of wetting (Z), while
the reverse may be true for sand (S), bulk density
and the maximal diameter of the wetted area (D).
Table (1) Some statistics of the studied variables during the current study
Variable
Unit
Sample
size
Minimum
value
Maximum
value
Range
Average
Value
Standard
error
Standard
deviation
CV
(%)
Skewness
Kurtosis
S
%
24.00
17.70
77.39
59.69
33.72
3.20
15.69
46.54
1.50
1.82
Si
%
24.00
18.42
50.00
31.58
37.83
1.69
8.30
21.93
-0.87
0.79
C
%
24.00
4.18
43.97
39.79
28.44
2.18
10.68
37.55
-0.68
-0.33
Ks
cm3 hr-1
24.00
0.22
4.42
4.20
2.33
0.29
1.42
61.07
0.08
-1.42
BD
Mgm-3
24.00
1.17
1.70
0.73
1.34
0.04
0.17
12.90
1.82
3.86
i
%
24.00
3.00
12.78
9.78
6.84
0.45
2.20
32.14
1.54
3.17
D
Cm
24.00
47.00
109.00
62.00
60.21
2.52
12.33
20.48
2.84
10.67
Z
Cm
24.00
32.20
45.40
13.20
39.31
0.75
3.69
9.39
0.05
-0.75
3.2. Sensitivity Analysis
Prior to models calibration, a simple
sensitivity analysis based on correlation analysis
was conducted without considering interaction
into account to identify non-influential variables
that can be omitted from the calibration. Table 2
presents the correlation matrix using all possible
cases procedure. The regressors
encompassed sand (S), silt(Si), clay(C), saturated
hydraulic conductivity (Jackson, 1958), bulk
density (Al-Ogaidi et al., 2016), initial soil water
content (i), the maximal diameter of the wetted
area (D), and the wetted depth (Z). As can be
noticed in Table 2, the all correlation coefficients
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ZANCO Journal of Pure and Applied Sciences 2020
among the regressors were far below 0.9. This is
indication of the fact the developed models with
these variables will not be suffered from
multicollinearity.
It also observed that the clay content
offered the highest correlation coefficient with
wetted diameter (r =0.547) followed by saturated
hydraulic conductivity. By contrast, silt content
offered the least correlation coefficient followed
by initial soil water content further, the results
indicated that wetted diameter was negatively
correlated with each of Si, C, Ks and Ɵi, while it
was positively correlated with remaining
variables. It was also noticed that the soil bulk
density is the most initial factors affecting depth
of wetted (Z). It appears from the above analysis
that each of discharge, clay content and saturated
hydraulic conductivity are the best candidate for
predicting wetted diameter of the area under the
emitters.
Table (2) Pearson's correlation matrix among the studied variables during the current study.
S
Si
C
Ks
BD
Ɵi
D
Z
S
1
-0.772**
-0.869**
-0.095
0.346
-0.347
0.435*
-0.045
Si
1
0.357
0.058
-0.188
0.121
-0.119
0.266
C
1
0.095
-0.363
0.417*
-0.547**
-0.141
Ks
1
-0.023
0.007
-0.461*
-0.137
BD
1
-0.448*
0.321
-0.473*
Ɵi
1
-0.127
0.059
D
1
0.204
Z
1
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).
3.3. Model Calibration
The results shown In Table 3 revealed than
among the one-, two-, three-, four- and five-
variable models M1, M2, M3, M4 and M5 offered
the best performance for predicting wetted
diameter (D) following all possible cases
regression analysis. The selection was based on
the criteria displayed in Table 3. For the sake of
clarity, it can be mentioned that among the three-
variable models, M3 offered the largest values for
R2, R2adj and the lowest values of the remaining
criteria. As can be noticed in Table 3 there is a
steady increase in for R2, R2adj values and a
steady decrease in Akaike information criterion
(AIC) and Amemiya prediction criterion (APC)
with an increase in number of regressors.
The results also indicated that there was a
slight change in the value of the criteria shown in
Table 3 with further increase in number of
regressors above three. Additionally, stepwise
linear multiple regression revealed the three
variable model was based only on Q, C and Ks.
On the other hand the Mallows’ Cp exhibited no
obvious trend.
As the variance inflation factor (VIF) is
less than 10 and the tolerance (T) is more than 0.1,
it means none of the five models in Table 4 has
the problem of multicollinearity. In spite of higher
accuracy of prediction of M4 and M5, Model 3 is
proposed as a linear model for predicting wetted
diameter. This decision was made to avoid the
problem of overfitting. This means Model 4 and 5
may perform well for training data (the data used
to develop the model), but they may not perform
well for any test set out of the training data set.
To further improve the prediction of the maximal
diameter of the wetted area, a multiple non-linear
model (M6) was also proposed. This non-linear
model took the following form:
f
i
edcb BDKsCQaD
(3.1)
Where a, b, c, d, e and f are fitting
parameters. Table 5 shows the parameters of
Model 3, 6 and 7.
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ZANCO Journal of Pure and Applied Sciences 2020
Table (3) Results of all possible cases showing the linear models along with the included variables which
scored best based on a host selection criteria
Table (4) Some multicollinearity statistics for the selected variables during the current study.
Model
code
Model name
Variables
Tolerance
Variance inflation Factor
Q
C
Ks
BD
i
Q
C
Ks
BD
i
M1
One –variable
Q
M2
Two-variable
Q, C
1.00
1.00
1.00
1.00
M3
Three-variable
Q, C, Ks
1.00
0.99
0.99
1.00
1.01
1.01
M4
Four Variable
Q, C, Ks, BD
1.00
0.76
0.99
0.76
1.00
0.76
0.99
0.76
M5
Five variable
Q, C, Ks ,BD, i
0.99
0.72
0.99
0.67
0.72
1.01
1.40
1.01
1.49
1.38
Table (5) Regression coefficients of the developed linear and nonlinear models for predicting maximal
wetted diameter and average wetted depth from emitter discharge and some selected soil properties.
Model
code
Model name
Variables
R2
R2adj
Selection Criteria
AIC
APC
MPC
SBC
M1
One –variable
Q
0.328
0.318
381.54
0.711
2.00
386.09
M2
Two-variable
Q, C
0.647
0.636
337.24
0.384
3.00
344.07
M3
Three-variable
Q, C, Ks
0.702
0.688
327.08
0.334
4.00
336.18
M4
Four Variable
Q, C, Ks, BD
0.718
0.701
325.11
0.325
5.00
336.49
M5
Five variable
Q,C, Ks, BD, i
0.729
0.709
324.05
0.320
6.00
337.71
Response
variable
Type of Model
Model Code
Constant
Slope or exponent
Emitter
discharge
(cm3 hr-1)
Clay content
(%)
Saturated
Hydraulic
conductivity,
Ks (cm hr-1 )
Bulk Density,
BD(Mgm-3)
Initial soil
moisture
content,
i(%)
Maximal wetted
diameter (cm)
Multiple linear with
three variables
M3
79.393
0.01
-0.871
-2.833
Multiple non-linear
with five variables
M6
8.361
0.313
-0.216
-0.064
0.483
0.177
Average Wetted
depth (cm)
Multiple linear with
three variables
M7
65.096
0.002
-0.199
-17.248
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3.4. Performance of the Proposed Models
It is apparent from the above results, a
linear model (Model 3) and a non- linear model
(Model 6) were proposed for predicting the
maximal wetted diameter under drip irrigation.
Additionally, a three –variable model (M7) was
proposed for predicting the depth of wetting with
reasonable accuracy. The influential variables of
this model are emitter discharge, clay content and
bulk density.
To further investigate the degree of
agreement between the observed and predicted
values, the predicted values from each of M3, M6
were plotted versus the observed values of the
maximal diameter of the wetted area in relation to
line 1:1 (Figs. 2 and 3) As can be seen from Fig. 2
and 3 that the majority of the plotted points falls
on or close to the line 1:1. It can also be noticed
from Fig.2 that the slope of the regression line is
close to unity. Overall, there is limited data
scattering over the lower and intermediate ranges
of the diameter of the wetted area.
Conversely, there is a wider scatter at the
upper D value ranges. Similar trend was obtained
for predicting the average depth of infiltrated
water as the predicted values were plotted versus
the measured values (Fig.4). Additionally, the plot
of residuals of predicted D from M3 and M6
indicated that the employed data were normally
distributed (Figs. 5 and 6). The same conclusion
was drawn as the residual of the predicted Z
values were plotted versus the observed Z values
(Fig.7).
Table 6 enlists some selected efficiency
criteria for evaluating the last three models.
Judging from Values of mean biased error (MBE)
and coefficient of residual mass (CRM), each of
these models neither overpredicted nor
underpredicted D and Z. It can be also observed
that the mean absolute error (MAE) of prediction
were 7.44, 6.12 and 2.41 for model M3, M6 and
M7 respectively. Based on CV, the simulation of
M3 and M6 is considered good (10% < CV <
20%), while that for Model 7 is excellent (CV <
10%). The closeness of the Willmott’s index (d)
suggests these models calibrated well enough to
simulate D and Z.
Judging from the mean absolute
percentage error (MAPE) and scheme proposed by
(Lewis, 2012), M3 was categorized under
potentially good class (10 %< MAPE<20%),
while M6 and M7 were categorized under very
potentially good class (MAPE<10%) according to
the above mentioned scheme.
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ZANCO Journal of Pure and Applied Sciences 2020
3.5. Evaluation of the Maximal Diameter of the
Wetted Area from Schwartzman and Zur
(1996) Model
Another trial was also made to evaluate the
model proposed by (Schwartzman and Zur, 1986)
to predict D from emitter discharge, wetting depth
and saturated hydraulic conductivity
33.0
Ks
QZ
1.32D
(3.2)
Where Q= the emitter discharge (cm3 hr-1),
Z= wetting depth (cm) and Ks= saturated
hydraulic conductivity (cm hr-1).
hydraulic conductivity (cm hr-1).
The results present in Fig.8 indicated that
the three variables (Q, Z and Ks) explained only
40% of variation in D. There is a wide scatter of
the points over the entire range of the observed D
values. The mean absolute percentage of error
exceeds 30%. This means this model has limited
application for predicting D. It was reported that
the regression models have usually restricted
application outside the region where they were
developed without testing their performance
(Hernando and Romana, 2015). Accordingly, the
two developed models (M3 and M6) are
recommended for use in the area under study.
These models will be beneficial for
predicting the maximal diameter of wetted area in
actual practice for designing emitter spacing. This
can be achieved by multiplying this parameter by
a factor of 0.8 to obtain the emitter spacing
(Hachem and Yaseen, 1992).
3. CONCLUSIONS
It can be concluded from the above results that
emitter discharge, clay content and saturated
hydraulic conductivity are the most influential
factors affecting the maximal diameter of wetted
area under drip irrigation system. Furthermore,
this parameter can be predicted by using linear
models and its accuracy can be improved by using
a non-linear model with six parameters.
These results are of vital importance in design
of emitter spacing under drip irrigation.
Additionally, it can be inferred from the results
the maximal diameter of the wetted area cannot be
predicted from Schwartzman and Zur (1986)
model with a reasonable accuracy in the area
under study.
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