WPEDIS – Wetting Pattern Estimator under Drip Irrigation Systems AAM. Al-Ogaidi1,a, W. Aimrun2, MK. Rowshon2, and AF. Abdullah2 1 Dams and Water Resources Eng. Dept., College of Eng., University of Mosul, Mosul, Iraq; 2 Biological and
Agricultural Eng. Dept., Faculty of Eng., Universiti Putra Malaysia, Selangor, Malaysia.
Abstract The dimensions of the wetted soil zone under drip irrigation systems are of considerable practical importance in designing these systems. The selection of proper spacing between emitters and suitable distance between laterals is mainly related to the wetting pattern dimensions. In this study, an empirical model was developed to predict the dimensions of the wetted soil zone under drip irrigation systems. The developed model includes empirical equations to estimate the main dimensions of the wetted soil zone as well as its ability to predict the full shape of the wetting pattern. Series of laboratory experiments were carried out under surface and subsurface emitters using two soil textures, two application rates, and two soil profiles. Application time, emitter discharge, initial moisture content, saturated hydraulic conductivity, bulk density, and the percentages of sand, silt, and clay of the soil are the main inputs of the proposed model. The performance of the model was assessed by comparing the measured and predicted results statistically by considering some statistical criteria such as mean error, root mean square error, and model efficiency. A good agreement between the observed and predicted wetting patterns was achieved which reflects the model suitability in design drip irrigation systems. Keywords: emitter, wetted soil zone, empirical model, wetted radius, wetted depth, homogeneous soil profile, layered soil profile INTRODUCTION More than 90% of worldwide consumptive water use is for irrigation requirements. In arid and semi-arid regions where there are water shortage, drip irrigation is considered as a compulsory rather than other optional choice due to its advantages in saving water, increasing yield, limiting evaporation and reducing weeds development. Designing an efficient drip irrigation system requires thorough knowledge and information on wetting patterns under a single emitter. These patterns are resulted from water infiltration from emitters to form a wetted zone of truncated sphere or ellipsoid under surface emitter or of spherical or ellipsoidal shape under subsurface emitter. The main parameters of the wetted soil zone are the wetted radius and depth (Dasberg and Or, 1999), as can be seen in Figure 1. R Emitter Soil surface R Du
D
Wetting pattern
Emitter
Dd
b a Figure 1. Schematic drawing of the wetting pattern under: (a) surface emitter, (b) subsurface emitter a E‐mail:
[email protected]
Where R: is the wetted radius, D: is the wetted depth under surface emitter, Du and Dd: are the upward and downward wetted depths, respectively under subsurface emitter. The wetting pattern dimensions should be well-defined in order to attain good matching between these dimensions and the spacing between emitters and laterals as well as the rooting depth (Yao et al., 2011). Many studies have been conducted during last decades to evaluate these patterns. Some of these studies have focused on the factors affecting on these patterns such as soil texture, bulk density, saturated hydraulic conductivity, initial moisture content, application time, emitter discharge and emitter position (Li et al., 2005; Lazarovitch et al., 2005; Elmaloglou and Diamantopoulos 2010; and Naglič et al. 2014). Other studies have concentrated on developing models to simulate the wetting patterns numerically (Šejna et al., 2014; Elmaloglou et al., 2013; Arbat et al., 2013), analytically (Cook et al., 2003; b; Hammami and Zayani, 2016) or empirically (Schwartzman and Zur, 1986; Amin and Ekhmaj, 2006; Malek and Peters, 2011; Al-Ogaidi et al., 2015). In addition to the former mentioned models, other models have been developed but they are less common. For instance, moment analysis model suggested by Lavarovitch et al., (2007), using artificial intelligence techniques like genetic programing (Samadianfard et al., 2012) and artificial neural networks (Ekhmaj et al., 2007) were introduced. Subbaiah (2013) presented a review paper including detailed information on most of the developed models of drip irrigation systems. As numerical and analytical models require considerable computing power and high skills to be used, it is impractical to use them for design purposes. Therefore, empirical models can be an ideal alternative to be used in design due to their simplicity. However, the previous empirical model can be used to predict the main parameters of the wetting patterns. Thus, the objective of this study was to develop an empirical model for estimating the main parameters of the wetting patterns as well as the ability to predict the full shape of the wetting pattern. MATERIALS AND METHODS Experimental setup Series of laboratory experiments were performed at Irrigation and Drainage Laboratory, Faculty of Engineering, Universiti Putra Malaysia. The experiments were conducted using a soil container of internal dimensions (50 cm length, 50 cm width, and 70 cm depth). To observe the wetting front movement, two sides of the container were fabricated from plexiglass sheets while the others were from metal plates. The water was applied at the corner of the container where the plexiglass sheets intersected, so this container represents one part of four parts of complete cylinder. Therefore, quarter of the wetted soil zone was simulated so the actual emitter discharges were multiplied by 4 and displayed here (Li et al., 2003; 2004; 2005; 2007; Zhang et al., 2015). The water application system consists of two tanks installed on a stand where the upper tank was fixed and supplies water to the lower tank which is movable to adjust the hydraulic head and set the required emitter discharges. A tap water was used in experiments after passing through a domestic water filter of two stages to remove any particles that may lead to emitter clogging. The average laboratory temperature was 25±0.5˚C. Two soils were used in the experiments, sandy soil (94.02% sand, 4.11% silt, and 1.87% clay) and clayey soil (29.28% sand, 10.57% silt, and 60.15% clay). An adequate amount of each soil was collected, spread, air dried, passed through a 2 mm sieve, mixed carefully, and kept in plastic bags. The soil profile was prepared by packing the soil in the container gradually until reaching 65 cm depth. During the packing and compacting processes, some soil samples were taken to determine the average initial moisture content for each experiment. In total, 16 experiments were carried out under surface and buried emitter using two application rates (3 and 4.5 l/h, in average), two homogeneous profiles (sandy and clayey profiles), two layered-textural profiles (sandy layer over clayey layer and vice versa), two positions for emitter (surface and subsurface installed 15 cm below soil surface) with one application time for all experiments (430 min). Table 1 shows a summary of experiments.
Table 1. Summary of the laboratory experiments.
E11
4.57 2.88
HP-Sand
E12 E13 E14 E15 E16
4.18 2.75 4.62 2.82 3.98
LP-20S/45C LP-20C/45S
Surface
Emitter position
Subsurface (15 cm below the soil surface)
Emitter discharge (l/h) 2.79 4.50 3.00 4.69 3.23 4.46 3.00 4.46 2.72
Experiment Soil profile no. E1 1HP-Clay E2 E3 HP-Sand E4 E5 2LP-20S/45C E6 E7 LP-20C/45S E8 E9 HP-Clay E10
Initial moisture Bulk density (cm3/cm3) (g/cm3) 0.0578 1.2102 0.0567 1.2111 0.0113 1.6095 0.0138 1.6070 30.0122/0.0530 31.6086/1.2150 0.0119/0.0559 1.6089/1.2121 0.0540/0.0145 1.2148/1.6063 0.0556/0.0149 1.2124/1.6059 0.0443 1.2237
4Saturated
hydraulic conductivity (cm/h) 1.1379 1.1333 23.1729 23.3258 323.3683/1.1183 23.2067/1.1300 1.1192/23.3683 1.1292/23.3921 1.0846
0.0480
1.2200
1.0988
0.0097
1.6111
23.0679
0.01 0.0090/0.0460 0.0091/0.0479 0.0437/0.01 0.0493/0.0112
1.6108 1.6118/1.2220 1.6117/1.2201 1.2243/1.6108 1.2187/1.6096
23.0867 23.0263/1.0913 23.0329/1.0983 1.0817/23.0913 1.1042/23.1625
1HP-Clay:
Homogeneous Profile, 2LP-20S/45C: Layered Profile of 20 cm sand over 45 cm clay, 3value of upper/lower layer, 4Determined using ROSETTA software (Schaap et al., 2001).
Development of empirical model The empirical model was derived based on relating the main parameters of the wetting pattern (R, D, Du, Dd, cm) with some factors affecting wetting pattern dimensions. These factors include application time (t, min), emitter discharge (q, l/h), bulk density (ρ b, g/cm3), initial moisture content (θi, cm3/cm3), saturated hydraulic conductivity (Ks, cm/h), and percentages of sand, silt, and clay (S, Si, and C, respectively, %). The considered cases in Table 1 can be categorized into four categories: (HP-S): homogeneous profile under surface emitter (E1-E4), (LP-S): layered profile under surface emitter (E5-E8), (HP-SS): homogeneous profile under subsurface emitter (E9-E12), and (LP-SS): layered profile under subsurface emitter (E13-E16). Each category has different empirical model. The general form of the proposed models for estimating any wetted parameter for homogeneous profiles under surface or subsurface emitter is illustrated in Eq. 1: 𝑎
𝑎
𝑎
(1)
𝑊𝑃 = 𝑎𝑡 𝑎1 𝑞 𝑎2 𝜌𝑏 3 𝜃𝑖 4 𝐾𝑠 5 𝑆 𝑎6 𝑆𝑖 𝑎7 𝐶 𝑎8
Where WP: any wetted parameter (cm), and a to a8: are empirical coefficients. While the general form of the suggested models for predicting any wetted parameter for layered profiles under surface or subsurface emitter (Eq. 2): 𝜌𝑏1 𝑏3 𝜃𝑖1 𝑏4 𝐾𝑠1 𝑏5 ) ( ) ( ) 𝜌𝑏2 𝜃𝑖2 𝐾𝑠2
𝑊𝑃 = 𝑏𝑡 𝑏1 𝑞 𝑏2 (
𝑆 𝑏6 𝑆𝑖1 𝑏7 𝐶1 𝑏8 ) ( ) 𝑆2 𝑆𝑖2 𝐶2
( 1) (
(2)
Where b to b8: are empirical coefficients, numbers 1 and 2 refer to factors of upper and lower layer, respectively. Moreover, the full shape of the wetting pattern can be predicted by estimating the wetted radius at multiple depths under the soil surface using the following equations (Eqs. 3 and 4): 𝛽
𝛽
𝛽
(3)
𝑅 ′ = 𝛽𝑡𝛽1 𝑞 𝛽2 𝜌𝑏 3 𝜃𝑖 4 𝐾𝑠 5 𝑆𝛽6 𝑆𝑖 𝛽7 𝐶𝛽8 + 𝛽9 𝑅 ′′ =
𝛾3 𝜃 𝛾4 𝐾 𝛾5 𝑆 𝛾6 𝑆𝑖 𝛾7 𝐶 𝛾8 𝜌 𝛾𝑡 𝛾1 𝑞𝛾2 (𝜌𝑏1 ) (𝜃𝑖1 ) (𝐾𝑠1 ) (𝑆1 ) (𝑆𝑖1 ) (𝐶1 ) 𝑏2 𝑖2 𝑠2 2 2 2 ′ ′′
+ 𝛾9
(4)
Where 𝑅 and 𝑅 : are the wetted radius under the soil surface for homogeneous and layered profiles, respectively, β to β9, and γ to γ9: are empirical coefficients. Eqs. 3 and 4 were derived
for each 1 cm below the soil surface. The coefficient for all the proposed models were estimated based on the nonlinear regression analysis using Microsoft Excel Solver. In order to evaluate the performance of the suggested models, some statistical criteria such as mean error (ME), root mean square error (RMSE), and model efficiency (EF) were used. These criteria can be calculated from Eqs. 5, 6, and 7, respectively (Willmott et al., 2012): 1 𝑀𝐸 = |∑𝑁 (5) 𝑖=1(𝑃𝑖 − 𝑂𝑖 )| 𝑁
1
2 𝑅𝑀𝑆𝐸 = [𝑁 ∑𝑁 𝑖=1(𝑃𝑖 − 𝑂𝑖 ) ]
𝐸𝐹 = 1 −
0.5
(6)
2 ∑𝑁 𝑖=1(𝑃𝑖 −𝑂𝑖 ) 2 ̅ (𝑂 ) ∑𝑁 −𝑂 𝑖=1 𝑖
(7)
Where N is the total number of data, P and O are referred to the predicted and observed data, respectively, and 𝑂̅ is the mean value of observed data. RESULTS AND DISCUSSION Based on the results of the laboratory experiments and the nonlinear regression analysis, the coefficients of all the proposed models were predicted and listed in Table 2 with values of statistical criteria. Table 2. The coefficients of the proposed models with statistical criteria. Category 1 HP-S 2 LP-S 3 HP-SS 4 LP-SS
Statistical criteria Wetted Empirical coefficients parameter ME RMSE EF 6.7314 0.2615 0.2309 2.2494 -0.0138 -0.3028 -0.1165 0.0836 -0.1571 0.385 0.499 0.9941 R D
R D R Du Dd R Du Dd
0.2956 4.1267 1.5750 2.0629 1.5418 0.0942 2.6335 1.4830 1.3688
0.4246 0.2784 0.4496 0.3155 0.2782 0.4302 0.3266 0.3020 0.4707
0.4309 0.2663 0.3399 0.4222 0.9930 0.3584 0.4003 0.3472 0.2113
2.8931 -1.1652 -0.2720 9.7930 -1.2467 0.3688 -0.8848 0.0609 0.0513
-0.1581 0.0272 0.1064 0.6122 0.0626 0.9552 0.0200 -0.2529 -0.1001
0.0010 0.0813 1.2076 -0.5122 0.0010 0.5555 0.7981 -0.0343 0.0013
-0.1443 -0.1314 -0.1675 0.0322 -0.0410 0.9321 -0.0356 0.0390 0.0382
0.2997 0.0940 0.3128 -0.0288 0.2007 0.7718 0.1628 0.0602 0.0596
0.0764 -0.1193 0.8556 -0.0123 -0.1920 0.1066 0.5261 0.0955 0.0852
0.515 0.329 1.628 0.343 0.345 0.468 0.488 0.448 0.866
0.648 0.418 1.892 0.461 0.458 0.590 0.585 0.559 1.058
0.9965 0.9964 0.9636 0.9960 0.9809 0.9956 0.9950 0.9736 0.9854
The coefficients of Eqs. 3 and 4 were estimated for each 1 cm depth beneath the soil surface until reaching the last wetted depth for each category. Hence, 48, 43, 54, and 52 empirical formulas were derived for the four categories, respectively according to the highest wetted depth of each case. The performance of Eqs. 3 and 4 can be evaluated by considering the same statistical criteria as illustrated in Table 3. Table 3. The values of statistical criteria for the proposed models for predicting the full wetting pattern. Category ME RMSE EF 1 0.656 0.92933 0.98764 2 0.632 0.92161 0.98697 3 0.634 0.90731 0.98782 4 0.621 0.83559 0.98907 It is obvious from Tables 2 and 3 that the performance of the proposed models is good as the values of ME and RMSE are low as well as the values of EF are close to one. For more illustration on the performance of the developed models, it is possible to plot the estimated and observed wetting patterns. Figure 2 shows the estimated versus measured wetting patterns for a number of experiments. It can be seen from Figure 2 that there is an excellent
agreement between the measured and estimated wetting patterns. However, there are minor discrepancies in predicting the wetted depths which is also clearly seen from Table 2 where the values of ME and RMSE for downward vertical depth are higher than those for wetted radius. It can be concluded that including the effect of most of the factors affecting wetted zone geometry resulted in good performance of the developed models. It is worth mentioning that the merit of the proposed empirical model is its ability to predict the full shape of the wetting pattern unlike the previous empirical models such as the models of Schwartzman and Zur, (1986), Amin and Ekhmaj, (2006) and Malek and Peters, (2011). Wetted radius (cm) 20
0
30
-15 -20 -25 -30
-45
0
10
10
5
5
0
0
Wetted depth (cm)
15
15
-20
-30 -35
-5
-35
-20 -25 -30
-45
10
20
0
30
E11 HP-SS-Sand q=2.88 l/h
15
15
10
10
-5 -10 -15
-30
E7 LP-S-20C/45S q=3 l/h
Wetted radius (cm) 10 20 30
40
5
0
-25
-25
-45
Wetted radius (cm) 0
-15
-35
E5 LP-S-20S/45C q=3.23 l/h
-20
-25 -30
-15
5
-20
E9 HP-SS-Clay q=2.72 l/h
40
-10
-40
40
-15
-15
-25
Wetted radius (cm) 10 20 30
-10
-10
30
-5
-35
E3 HP-S-Sand q=3 l/h
-50
Wetted radius (cm) 0 10 20 30
-5
-30 -40
E1 HP-S-Clay q=2.79 l/h
-40
-20
Wetted depth (cm)
-35
20
0
Wetted depth (cm)
-10
10
-5
-10
Wetted depth (cm)
Wetted depth (cm)
-5
Wetted radius (cm) 0 10 20 30
Wetted radius (cm) 0
0
0
Wetted depth (cm)
Wetted radius (cm) 5 10 15 20 25 30 35 40
Wetted depth (cm)
10
Wetted depth (cm)
0
0 -5 -10 -15 -20 -25
E13 LP-SS-20S/45C q=2.75 l/h
-30 -35
E15 LP-SS-20C/45S q=2.82 l/h
Figure 2. Measured (solid lines) versus estimated (dashed lines) wetting pattern at different application times for number of experiments. CONCLUSIONS Series of laboratory experiments were performed under drip irrigation systems. The results were used to develop a new empirical model to predict the wetted zone dimensions as well as its capability to estimate the full shape of the wetting patterns. The inputs of this model include application time and rate, initial water content, bulk density, saturated hydraulic conductivity, and percentages of sand, silt, and clay of the soil. Based on statistical comparison using mean error, root mean square error, and model efficiency, good agreement was attained between the measured and estimated wetting patterns. The good performance of the proposed model reflects its appropriateness in designing drip irrigation systems. ACKNOWLEDGEMENTS Special thanks to academic and support staff at Irrigation and Drainage Lab., Department of Biological and Agricultural Engineering, Faculty of Engineering, Universiti Putra Malaysia for their support during conducting the experiments. The project was funded by Putra Grant, Vote No. 9447700. References Al-Ogaidi, A. A. M., Wayayok, A., Rowshon, M., and Abdullah, A. (2015). A Modified Empirical Model for Estimating the Wetted Zone Dimensions under Drip Irrigation. J. Teknol. 76, 69–73. Amin, M. S. M., and Ekhmaj, A. I. M. (2006). DIPAC- Drip Irrigation Water Distribution Pattern Calculator. In 7th Int.
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