Soil wetting front in surface and subsurface drip irrigation for silty loam soil
Mohammad Sadegh Monjezi1, Hamed Ebrahimian2, Abdolmajid Liaghat3 and Mohammad Amin Moradi4
1
Graduate student of Irrigation and Drainage, Department of Irrigation and Reclamation Eng., College of
Agriculture and Natural Resources, University of Tehran, P. O. Box 4111, Karaj 31587-77871, Iran. Email:
[email protected] 2
Assistant professor, Department of Irrigation and Reclamation Eng., College of Agriculture and Natural
Resources, University of Tehran, P. O. Box 4111, Karaj 31587-77871, Iran (corresponding author). E-mail:
[email protected]
3
Professor, Department of Irrigation and Reclamation Eng., College of Agriculture and Natural
Resources, University of Tehran, P. O. Box 4111, Karaj 31587-77871, Iran. E-mail:
[email protected] 4
Graduate student of Irrigation and Drainage, Dept. of Irrigation and Drainage Eng., University of
Tehran, Pakdasht, Iran. Email:
[email protected]
Number of words: about 3500; Number of Tables: 5; Number of Figures: 9
Soil wetting front in surface and subsurface drip irrigation for silty loam soil Abstract Surface and subsurface drip irrigation systems have been applied to increase irrigation efficiency and uniformity, mainly in arid and semi arid regions. Determining soil wetting dimensions around a point source emitter is essential for better design of drip irrigation systems. In this paper, laboratory experiments were conducted to measure the soil wetting front for various arrangements of surface and subsurface drip irrigation in terms of emitter number, installation depth and flow rate. The two-dimensional numerical model HYDRUS-2D was used to simulate water movement around the emitter(s) in silty loam soil. The shapes of observed and simulated soil wetting front were almost ellipsoid and spherical for surface and subsurface drip irrigation, respectively. The HYDRUS-2D model proved better in estimating the dimensions of the soil wetting front when using one emitter than when using two emitters for irrigation. Both simulations and observations indicated that wetting velocity was greater during irrigation than during soil moisture redistribution. The model under- and overpredicted wetting area during irrigation and redistribution, respectively, but there were no significant differences between measured and predicted values of wetting area for surface and subsurface drip irrigation. The HYDRUS-2D model generally proved effective in simulating the soil water flow for various kinds of surface and subsurface drip irrigation systems in silty loam soils. Keywords: Drainage and irrigation; Models (physical); Water supply
1
Introduction Gravity subsurface drip irrigation is a modern irrigation system, where water is applied through tubes of 1 to 2 mm diameter (often known as spaghetti tubes), and the energy of the system is provided by the head of water arising from the level difference between the beginning and end of farm. The total energy needed for this method is normally one and three meters of water. Due to the internal diameter of the irrigation tubes (1 mm or more), the probability of physical clogging is minimal and there is no need for a central filtration plant to be introduced to the system. By setting the irrigation tubes under the surface, clogging will not occur through evaporation and salt accumulation and, therefore, low-quality waters (saline water) can be used. Understanding the soil wetting surface produced by a point source is a key aspect in drip irrigation design. A first step to ensure irrigation operations is to measure the wetting front in the soil profile. The wetting front shape depends on various factors such as soil texture and stratification, emitter discharge, initial soil moisture and slope. Surface drip irrigation (DI) is an irrigation method employed to increase the efficiency of water use and the distribution uniformity. Subsurface drip irrigation has been recently applied in agricultural lands and its advantages include fertilizer decrease, less deep percolation than in surface irrigation, higher efficiency and weed control. Its disadvantages are high initial installation cost and salt aggregation on top of installed drippers (Tampson et al., 2009). Clothier et al. (1985) conducted laboratory and field experiments to measure the soil wetting front under a point source on sandy soils. They expressed the view that the wetting front was limited by the horizontal movement of water. At the start of irrigation, the horizontal velocity of soil wetting was high and decrease with time, until it reached a negligible value. Oron et al. (1999) showed, whereas the wetting pattern shape in a subsurface drip irrigation (SDI) system was spherical, it is half- spherical in surface drip irrigation system. By 2
directing water to the root zone, a subsurface drip irrigation system minimizes evaporation, especially in arid areas (Suarez et al., 2000). Li et al. (2003) indicated that water movement through a point source (dripper) depends on soil infiltration rate and flow discharge. Peter et al. (2003) concluded that water and fertilizer application efficiency in trickle irrigation depends on factors relating to emitters distance, flow rate, soil moisture characteristics and irrigation time. Ruhi et al. (2006) declared drip irrigation system was good for scheduling irrigation of glasshouse gladiolus plant. However, they stated that knowing the soil wetting pattern is essential for that purpose. Metin et al. (2006) obtained similar results for pepper plants. HYDRUS-2D (Simunek et al., 1999), as a user-friendly simulation software, has been assessed for surface and subsurface drip irrigation systems to simulate water flow and solute transport. Cote et al. (2003) analyzed soil wetting and solute transport from a buried point source using HYDRUS-2D but the model was not verified due to lack of experimental data. Ben-Gal et al. (2004) showed a good agreement between observed field data and HYDRUS-2D simulation data in a situation when drip tube was installed in a gravel filled trench. Skaggs et al. (2004) simulated line source flow of subsurface trickle irrigation in sandy loam soil using HYDRUS-2D software. The results showed good agreement with field experiment data of a SDI system with fixed installation depth (6 cm) and three discharge rates. Provenzano (2007) indicated that the accuracy of HYDRUS-2D was satisfactory to simulate the matric potential for subsurface drip irrigation in a sandy loam soil with a 10 cm installation depth. Kandelous et al. (2010) simulated the distribution of water around the emitter in subsurface trickle irrigation in clay loam soil using HYDRUS-2D software and compared the results with lab and field data of subsurface trickle irrigation with emitters installed at different depths. The results showed very good correspondence between simulations and observations. Yao et al. (2010) used the SWMS-2D 3
software (previous version of HYDRUS-2D) to simulate soil wetted depth and width for subsurface drip irrigation. They found satisfactory agreement between the simulations and observations. Highly affected by emitter spacing, the wetting pattern of a soil profile should be determined before designing a drip irrigation system. The wetting front dimensions mostly depend on soil hydraulic properties, emitter discharge and irrigation duration. Reviewing models of predicting soil water dynamics for drip irrigation, Subbaiah (2011) declared more research is needed to take into account the precision of models in simulating the wetting front and soil–water content. Thus, the objectives of this study were i) to determine the shapes of soil wetting front under different emitter flow rates and installation depths for surface and subsurface drip irrigation systems for silty loam soil, and ii) to evaluate the HYDRUS-2D model with the data measured in the laboratory experiment in terms of wetting area and horizontal and vertical velocity of wetting front. Because of the inability of surface trickle irrigation systems to supply water to deep roots, yield reduction occurs, particularly for perennial plants. To supply water to both surface and deep roots, and prevent moisture evaporation from the soil surface by deep percolation, twodepths subsurface trickle irrigation was used in this study. The HYDRUS-2D model was also evaluated in simulation of this irrigation system.
2. Materials and methods 2.1. Laboratory experiment 4
The experiments were carried out in the water research central laboratory located in University of Tehran, Karaj, Iran. A physical model that included a box with a transparent Plexiglass wall with the dimensions of 0.9, 0.9 and 1.8 m (Figure 1) was used. A water reservoir, equipped with a pressure regulator, was employed to provide a fixed flow rate during irrigation events. In order to transfer water to the box containing silty loam soil (22% clay, 58% silt and 20% sand), a lateral pipe of 16 mm diameter was used. Emitter tubes used in these experiments had an internal diameter of 1 mm and a length of 60 cm. The drippers provide a minimum flow rate required for drip irrigation (4.0 L/h) at a pressure less than 1.5 m (Figure 1). The soil surface was horizontal. The optimum installation depth of emitters in subsurface irrigation systems was reported to be between 20 and 50 cm for various soil textures (Ramezani, 2011). By reducing the dripper installation depth to less than 20cm, the moisture may evaporate from the soil surface, reducing its availability to the plant. By increasing the depth of dripper installation to more than 50cm, the moisture may escape the reach of the plant due to deep percolation. The wetting front for discharges of 4.46 and 6.2 liters per hour were studied in three different conditions: (i) the emitter was installed on the soil surface (DI); (ii). the emitter was installed at a depth of 20 cm (SDI-1P), and (iii) a pair of emitters was installed at different depths (SDI-2P1 at 0cm and 27cm depth, SDI-2P2 at 26cm and 50cm depth and SDI-2P3 at 30cm and 50cm depth). Two emitters were installed at different depths to supply the required moisture for shallow and deep roots. Table 1 presents the properties of different irrigation treatments Under the conditions that one emitter was used for irrigation (i.e. DI and SDI-1P), two different combinations of flow discharge and irrigation time (with constant water volume) were considered in this study. 5
For each irrigation event, the wetting fronts at different time intervals (Table 1) were marked on the transparent box wall and the dimensions of wetting fronts measured. The wetted area during and following the irrigation period was calculated by Autocad software. The horizontal/vertical velocity of soil wetting was also calculated as the horizontal/vertical distance of the soil wetting front divided by time. 2.2. HYDRUS-2D model The HYDRUS-2D model (ŠimGnek et al., 1999) was applied to simulate soil water distribution around the emitter. The governing water flow equation is given by the following modified form of the Richards' equation:
t
=
where
K ( K ij
xi
h + K iz ) xj
[1]
is the volumetric water content (dimensionless), h is the pressure head [L], xi and xj are
the spatial coordinates [L], t is time [T], KijA are components of a dimensionless anisotropy tensor KA and K is the unsaturated hydraulic conductivity function [L T-1]. The HYDRUS-2D model implements the soil-hydraulic functions proposed by van Genuchten (1980) and Mualem (1976) to describe the soil water retention curve,
(h), and the unsaturated
hydraulic conductivity function, K(h), respectively:
(h) =
r
+ s
[1 + h ] s
r n m
h 1
[4]
Se =
[5]
r s
where
r
r
and
s denote
the residual and saturated water content, respectively (dimensionless); K
is the inverse of the air-entry value [L-1]; Ks is the saturated hydraulic conductivity [L T-1], n is the pore-size distribution index (dimensionless), Se is the effective water content (dimensionless); and l is the pore-connectivity parameter (dimensionless). The model inputs for simulating water flow included soil hydraulic parameters, soil layers, irrigation rate and time and geometry, initial and boundary conditions. The soil hydraulic parameters used for model simulations were 1
r=0.07
cm3 cm-3,
s=0.43
cm3 cm-3, K= 0.005 cm-
, Ks=0.01 cm min-1, n= 1.62 and l = 0.5. These parameters were estimated using the Neural
Network approach provided by HYDRUS-2D. Geometry and boundary conditions for defining the physical problem of this study are shown in Figure 2. A variable flux was specified as the boundary condition for the dripper (constant flow during irrigation and zero flux after irrigation). An atmospheric boundary condition was used for the soil surface. A free– drainage condition for water flow was used at the lower boundary of the domain. No–flux boundary conditions were applied to the sides of the flow domain. The boundary conditions for the surface point source were the same as the conditions for subsurface point source(s). The location of emitter(s) was defined depending on irrigation treatments (surface and sub-surface irrigation). Initial soil moisture was considered equal to the residual moisture ( r) as for initial condition. When using a
7
large discharge in HYDRUS-2D, the model needs lower time steps and small spatial discretization to be converged correctly to avoid numerical oscillations and achieve an acceptable mass balance error (Simunek et al. 1999; Valiantzas et al. 2011). For instance, near the saturated zone around the point source (with sharp gradients), the spatial discretization decreased to about 1 cm and it was about 3-4 cm elsewhere. The model was run for each irrigation treatment and with different emitter discharges. The predicted soil wetting front at different times was compared with those observed in the laboratory conditions. The wetting area (A) and horizontal and vertical velocity (Vh and Vv, respectively) were also compared with the measured values during irrigation and soil moisture redistribution. 2. 3. Model evaluation Relative Error (RE) was used for evaluation of the model to estimate the soil wetting area:
RE =
( Pi Oi ) *100 Oi
[6]
where Pi is the predicted value and Oi is the observed (measured) value. The lower limit for RE is zero and a positive or negative value of RE shows the overestimation or underestimation of the model simulation, respectively. To evaluate the model accurately, the wetting front movement was evaluated in horizontal and vertical directions, and root mean squared error (RMSE), coefficient of determination (R2) and residual mass coefficient (CRM) were calculated for surface and subsurface drip irrigation:
8
N
RMSE =
i =1
2
(O i
i =1 N i =1
i =1
O )( Pi
O )2 ×
(O i
N i =1
N
CRM =
[7]
N
N
R2 =
Pi ) 2
( Oi
P) ( Pi
[8] P )2
N
Oi
i =1
Pi
[9]
N i =1
Oi
where N is number of data, O and P are the mean of observed and predicted values, respectively. The value of R2 ranges from 0.0 to 1.0, indicating a better agreement for values close to 1.0. RMSE index limitations are zero to infinity, where near to zero value indicates greater accuracy in model simulation. CRM is an indicator of the model trend to over-prediction or under-prediction compared to observed data. Negative values show model over-prediction and positive values stand for under-prediction The Paired-Samples T Test procedure was also used to statistically compare validation variables (Minitab Inc 1995). The test computes the differences between the values of the two variables for each case and tests whether the average differs from zero. If the p-value exceeds 0.05, no significant differences can be shown between measured and predicted data. 3. Results and discussions To evaluate the HYDRUS-2D model, measured and predicted values of the horizontal and vertical velocity and wetting area were compared for various irrigation treatments: 9
For the DI treatment with 4.46 L/h discharge, the predicted values of the wetting area were less and larger than the observed values during irrigation and redistribution, respectively (Figure 3 and Table 2). The model over- and underpredicted the values of horizontal velocity during irrigation and redistribution, respectively (Table 3). Predicted values of vertical velocity were smaller and equal to observed values during irrigation and redistribution, respectively. Although there was over-prediction of horizontal velocity during irrigation, the model under-predicted deep infiltration values (Figure 3). Thus, the total wetting area was predicted smaller than the observed value of the wetting area. For this method with 6.26 L/h discharge, the model predicted greater values of wetting area during both irrigation and redistribution (Figure 4 and Table 2). As a consequence, HYDRUS-2D over-predicted the vertical and horizontal velocity of the wetting front during irrigation and redistribution (Table 3). For the SDI-1P treatment, the HYDRUS-2D model predicted smaller and greater values of the wetted area for 4.46 and 6.2 L/h discharges, respectively (Table 2). The model underpredicted the wetted area during irrigation and redistribution in the case of 4.46 L/h (Figure 5 and Table 2). The simulated horizontal and vertical velocities of the wetting front were less and greater than measured ones during irrigation and redistribution, respectively (Table 3). In the discharge of 6.26 L/h, the predicted values of the wetting area were smaller than the observed values during irrigation (Figure 6). However, the model predicted it very well during redistribution. Both model and experimental results indicated that wetting area was greater during irrigation than during redistribution. Wetting velocity was much higher in the irrigation period than in the redistribution period for both the DI and SDI-1P treatments. The horizontal velocity of the wetting front was greater than the vertical velocity during irrigation owing to higher capillary
10
(matric) gradients, while similar values of velocity were observed in different directions during redistribution. This result showed that there were the same gradients of capillary and gravity after the irrigation period. Both simulations and observations indicated that higher total wetting areas were obtained in SDI-1P compared to DI. The wetted area during irrigation and redistribution was higher for a discharge of 4.46 L/h than for 6.26 L/h in both the DI and SDI-1P treatments. Since the irrigation time for a 4.46 L/h flow rate was more than it for 6.26 L/h, the advance of moisture during irrigation would be greater. Using a higher flow rate, a large volume of water was applied in a shorter time and, thus, the moisture had no adequate time to be spread in the soil. For this reason, the wetting area was smaller during irrigation for the larger discharge but the water velocity was greater for 6.26 L/h discharge during irrigation due to supplying a fixed volume of water in a shorter time than in the 4.46 L/h discharge. The depth of the wetting front in the SDI-1P treatment was 13.5 and 10.7 cm for 4.46 and 6.26 L/h, respectively. Furthermore, when using a low flow rate, due to the increased irrigation time, the moisture has more time to advance within the soil, including upwards towards the soil surface. As a consequence, increased evaporation arises for lower flow rates for subsurface drip irrigation. The reason for greater upward movement of moisture towards the soil surface in reality than in the simulation results was due to the more compact soil above the emitter than below it, while the model assumed them to be equal. The difference between assumptions of the model led to more errors in simulation results. Because of the near-to-real assumption of the model for soil compactness under the emitter, the water movement was simulated more accurately under than above the emitter.
11
The values of R2 indicated good correlations between the predicted and measured values of horizontal and vertical movements of the wetting front for both surface and subsurface drip irrigation (Table 4). Minimum and maximum values of RMSE were 1.36 and 5.35cm, respectively. The model somewhat overpredicted the wetting front movement for subsurface drip irrigation. For the SDI-2P1 treatment, the observed values of wetting area were greater than the predicted values during irrigation and redistribution (Figure 7 and Table 5). But for SDI-2P2, HYDRUS2D under- and overpredicted the area for irrigation and redistribution times, respectively (Figure 8 and Table 5). The total wetting area was larger in the laboratory condition than in the simulation results. For SDI-2P3, the predicted values of wetting area were smaller than the observed values during irrigation, whereas HYDRUS-2D predicted greater values of them during redistribution (Figure 9 and Table 5). In this case, the model accuracy was relatively good. The upward flux of moisture after irrigation was larger in the HYDRUS-2D results than in the measured results, while greater downward flux was observed in the laboratory condition. Significant differences could not be established between measured and predicted values of the wetting area of the DI and SDI-1P treatments according to the Paired-Samples T Test procedure (p-value > 0.05). But there were significant differences between measured and predicted values of the wetting area for subsurface drip irrigation with two emitters (SDI-2P1 to SDI-2P3). The wetting area for all three subsurface irrigation with two emitters was almost greater during irrigation than during redistribution. The model underpredicted the total wetting area for these irrigation treatments. As described earlier, the HYDRUS-2D model used soil hydraulic 12
parameters estimated via the Neural Network approach and soil properties such as soil particle sizes, bulk density and field capacity moisture. Predicted smaller total wetting area, these estimated parameters represented heavier soil than the soil used in the laboratory conditions. The shapes of the wetting front were almost ellipsoid and spherical for surface and subsurface drip irrigation, respectively. As expected, the values of the wetting area were larger for subsurface drip irrigation with two emitters than for other treatments. There was underprediction and overprediction of wetting area during irrigation and redistribution for almost for all irrigation treatments, respectively. It should be mentioned that the model was evaluated without any calibration process (inverse solution) and it should be expected that a calibrated model would simulate soil water flow more accurately (Ebrahimian et al., 2012). However, RE values for predicting total soil wetting area varied between 4.6 and 34.6 %. HYDRUS-2D had a high ability to simulate water flow in the soil in the case of using one emitter for irrigation. But when two emitters were used simultaneously for irrigation, the model provided lower accuracy. 4. Conclusions In this study, the soil wetting front under different strategies of surface and subsurface drip irrigation were analyzed through laboratory experiments and bidimensional simulation model, HYDRUS-2D. The HYDRUS-2D model had better performance in estimating of the dimensions of the wetting front when using one emitter than when using two emitters for irrigation. The predicted values of wetting area and velocity in surface drip irrigation were closer to the measured values for higher discharge. While the model had higher accuracy with less discharge for subsurface irrigation. Both simulations and observations indicated that the wetting area was greater during irrigation than during redistribution. As a consequence, wetting velocity was much 13
higher during irrigation. The predicted wetting area by HYDRUS-2D was less than observations during irrigation, whereas the model over-predicted it in most cases for after-irrigation times. Statistical tests indicated that there were no significant differences between measured and predicted values of wetting area for surface and subsurface drip irrigation with one emitter. However, significant differences could be established between measured and predicted values for subsurface drip irrigation with two emitters. The HYDRUS-2D model proved successful in simulating soil water flow for various kinds of surface and subsurface irrigation systems. The model could also distinguish the difference between the irrigation treatments studied in this paper. The performance of the model could be significantly improved by calibrating soil hydraulic parameters using inverse solutions. Using the robust simulation model HYDRUS-2D, various management aspects such as lateral distances, discharge and emitter installation depth could be analyzed in order to find the best design of surface and subsurface drip irrigation.
14
References Ben-Gal A, Lazarovitch N and Shani U (2004) Subsurface drip irrigation in gravel-Plled cavities. Journal of Vadose Zone, 3: 1407–1413. Clothier B, Scotter D and Havper E (1985) Three-dimensionation and trickle irrigation. Transaction of ASAE, 28(2): 497–501. Cote CM, Bristow KL, Charlesworth PB, Cook FJ and Thorburn PJ (2003) Analysis of soil wetting and solute transport in subsurface trickle irrigation. Journal of Irrigation Science, 22: 143–156. Ebrahimian H, Liaghat A, Parsinejad M, Abbasi F and Navabian M (2012) Comparison of one- and two dimensional models to simulate alternate and conventional furrow fertigation. Journal of Irrigation and Drainage Engineering, ASCE, 138(10): 929-938. . Li J, Zhang J and Ren L (2003) Water and nitrogen distribution as affected by fertigation of ammonium nitrate from a point source. Journal of Irrigation Science, 22: 19–30. Kandelous MM and Simunek J (2010) Numerical simulations of water movement in a subsurface drip irrigation system under field and laboratory conditions using HYDRUS-2D. Journal of Agricultural Water Management, 97: 1070–1076. Metin SS, Yazar A and Eker S (2006) Effect of drip irrigation regimes on yield and quality of field grown bell pepper. Journal of Agricultural Water Management, 81: 115–131.
Minitab Inc (1995) The student edition of MINITAB for Windows. Addison-Wesley Publishing Co. State College, PA. Mualem Y (1976) A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resource Research, 12(3): 513–522. 15
Oron G, Demalach Y, Gillerman L, David I, and Raco VP (1999) Improved saline water under subsurface drip irrigation. Journal of Agricultural Water Management, 39(1): 19–33. Peter JT, Ian KD, Ian MB, Craig PB, Mike AS and Brian AK (2003) The fate of nitrogen applied to sugarcane by trickle irrigation. Journal of Irrigation Science, 22: 201–209. Provenzano G (2007) Using HYDRUS-2D simulation model to evaluate wetted soil volume in subsurface drip irrigation systems. Journal of Irrigation and Drainage Engineering, ASCE 133(4): 342–349. Ramezani M (2011) Assessment of wetting pattern in subsurface drip irrigation for different soil texture. MSc Thesis, Department of Irrigation and Reclamation Engineering, University of Tehran, Karaj, Iran (in Persian). Ruhi B, Karaguzel O, Aydinsakir K and Buyukas D (2006) The effects of drip irrigation on flowering and flower quality of glasshouse gladiolus plant. Journal of Agricultural Water Management, 81: 132– 144. ŠimGnek J, Sejna M and van Genuchten MTh (1999) The HYDRUS-2D software package for simulating the two dimensional movement of water, heat, and multiple solutes in variably saturated media. Version 2.0, IGWMCTPS-70, Int. Ground Water Modeling Center, Colorado School of Mines, Golden, Co. Skaggs TH, Trout TJ, Simunek J and Shouse PJ (2004) Comparison of HYDRUS-2D simulations of drip irrigation with experimental observations. Journal of Irrigation and Drainage Engineering, ASCE 130(4): 304–310. Suarez E, Choi CY, Waller PM and Kopec DM (2000) Comparison of subsurface drip irrigation and sprinkler irrigation for grass turf in Arizona. Transaction of ASAE, 43(3): 631–640.
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Subbaiah R (2011) A review of models for predicting soil water dynamics during trickle irrigation. Journal of Irrigation Science, DOI 10.1007/s00271-011-0309-x. Thompson TL, Huan-cheng PANG and Yu-yi LI (2009) The Potential Contribution of Subsurface Drip Irrigation to Water-Saving Agriculture in the Western USA. Agricultural Sciences in China, 8(7): 850–854. Valiantzas JD, Pollalis ED, Soulis KX, Londra PA (2011) Rapid Graphical Detection of Weakness Problems in Numerical Simulation Infiltration Models Using a Linearized Form Equation. Journal of Irrigation and Drainage Engineering, ASCE 137(8), 524–529. van Genuchten MT (1980) A closed form equation for predicting the hydraulic conductivity of unsaturated soils. American Journal of Soil Science Society, 44: 892–898. Yao W, Xiao YM, Juan L and Parkes M (2010) Simulation of point source wetting pattern of subsurface drip irrigation. Journal of Irrigation Science, 29(4): 331–339.
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Notations The following symbols are used in this paper: AI= wetted area during irrigation (cm2) AR= wetted area during moisture redistribution (cm2) AT= total wetted area (cm2) CRM= residual mass coefficient (dimensionless) h= pressure head (cm) K= unsaturated hydraulic conductivity function KijA= components of a dimensionless anisotropy tensor KA Ks= saturated hydraulic conductivity (cm h-1) l = pore-connectivity parameter (dimensionless) n= pore-size distribution index (dimensionless) N= number of data Oi:= observed (measured) value
O = mean of observed values
18
Pi= predicted value
P = mean of predicted values
R2= coefficient of determination (dimensionless) RMSE= root mean squared error (cm) RE= Relative Error (dimensionless) Se= effective water content (dimensionless) Vh= horizontal velocity (cm h-1) Vv= vertical velocity (cm h-1) t= time (h) xi and xj= spatial coordinates (cm)
K = inverse of the air-entry value (cm-1) = volumetric water content (dimensionless) r=
residual water content (dimensionless)
s=
saturated water content (dimensionless)
19
List of Tables Table 1. Descriptions of different irrigation treatments and measurement conditions Table 2. Observed (Ob) and predicted (Pre) wetting area during irrigation and moisture redistribution for surface and subsurface (with one emitter) drip irrigation Table 3. Observed (Ob) and predicted (Pre) horizontal and vertical velocities of wetting front during irrigation and moisture redistribution for surface and subsurface (with one emitter) drip irrigation Table 4. Values of R2, RMSE and CRM in prediction of horizontal (H) and vertical (V) wetting front for surface and subsurface drip irrigation Table 5. Observed (Ob) and predicted (Pre) wetting area during irrigation and moisture redistribution for subsurface drip irrigation with two emitters
20
Table 1. Descriptions of different irrigation treatments and measurement conditions Irrigation method
Surface
Irrigation time
Measurement
(L/h)
(min)
times (min)
4.46
22.5
6.26
16.0
4.46
22.5
6.26
16.0
Abbreviation
DI
Subsurface one point
Discharge
142.5 5, 10, 16, 136 5, 10, 15, 22.5, 142.5
SDI-1P
(20 cm) Subsurface two points
5, 10, 15, 22.5,
5, 10, 16, 136
5, 15, 23, 36, 50, SDI-2P1
4.46
67.5
67.5, 199, 1318, 2133
(0 cm , 27cm) Subsurface two points
SDI-2P2
4.46
67.5
5, 10, 15, 25, 45, 67.5, 812
(26 cm , 50 cm) Subsurface two points
5, 10, 25, 40, 53, SDI-2P3
6.26
53.0
173, 426, 1570, 2778
(30 cm , 50 cm)
21
Table 2. Observed (Ob) and predicted (Pre) wetted area during irrigation and moisture redistribution for surface and subsurface (with one emitter) drip irrigation DI Wetting
Area
Time
(cm2)
SDI-1P Discharge (L/h)
4.46
6.26
4.46
6.26
Ob
Pre
Ob
Pre
Ob
Pre
Ob
Pre
Irrigation
AI
302.6
237.2
230.6
245.4
430.4
239.8
354.3
245. 8
Redistribution
AR
115.2
145.1
106.7
183.6
147.5
191.0
109.2
229.8
Total
AT
417.8
382.4
337.3
429.0
577.9
430.7
454.5
475.6
RE (%)
-8.5
27.2
22
-25.6
4.6
Table 3. Observed (Ob) and predicted (Pre) horizontal and vertical velocities of wetted front during irrigation and moisture redistribution for surface and subsurface (with one emitter) drip irrigation DI
Wetting
Velocity
Time
(cm/h)
SDI-1P Discharge (L/h)
4.46
6.26
4.46
6.26
Ob
Pre
Ob
Pre
Ob
Pre
Ob
Pre
Vh
84.0
94.2
122.1
133.8
62.4
48.0
80.4
67.8
Vv
32.1
28.2
34.3
38.4
60.6
47.4
76.2
67.2
Vh
1.9
0.6
1.7
3.6
1.8
2.4
1.2
1.2
Vv
1.3
1.2
1.4
1.8
1.8
2.4
1.2
3.0
Irrigation
Redistribution
23
Table 4. Values of R2, RMSE and CRM in prediction of horizontal (H) and vertical (V) wetting front for surface and subsurface drip irrigation Irrigation method
Discharge (L/h) 4.46
Surface drip 6.26
Movement direction
R2
RMSE (cm)
CRM
H
0.93
3.19
-0.02
V
0.96
1.36
0.08
H
0.86
5.35
-0.16
V
0.94
1.66
-0.16
H
0.96
3.65
0.18
V
0.95
3.68
0.18
H
0.92
3.05
0.14
V
0.95
1.91
0.07
4.46 Subsurface drip 6.26
24
Table 5. Observed (Ob) and predicted (Pre) wetted area during irrigation and moisture redistribution for subsurface drip irrigation with two emitters
Wetting Time
SDI-2P1
Area (cm2)
SDI-2P2
SDI-2P3
Ob
Pre
Ob
Pre
Ob
Pre
Irrigation
AI
1785.5
1004.9
1774.4
970.7
1431.2
1085.9
Redistribution
AR
1276.7
997.9
755.7
1045.6
1291.0
1476.3
Total
AT
3062.2
2002.8
2530.1
2016.3
2722.2
2562.1
RE (%)
-34.6
-20.3
25
-5.9
List of Figures Figure 1. Experimental setup for subsurface drip irrigation and measuring area and rate of expansion of wetting front Figure 2. The geometry and boundary conditions used in HYDRUS-2D for subsurface drip irrigation Figure 3. Observed (solid line) and predicted (dashed line) soil wetting front for DI with discharge of 4.46 L/h. Figure 4. Observed (solid line) and predicted (dashed line) soil wetting front for DI with discharge of 6.26 L/h Figure 5. Observed (solid line) and predicted (dashed line) soil wetting front for SDI-1P with discharge of 4.46 L/h. Figure 6. Observed (solid line) and predicted (dashed line) soil wetting front for SDI-1P with discharge of 6.26 L/h. Figure 7. Observed (solid line) and predicted (dashed line) soil wetting front for SDI-2P1 Figure 8. Observed (solid line) and predicted (dashed line) soil wetting front for SDI-2P2 Figure 9. Observed (solid line) and predicted (dashed line) soil wetting front for SDI-2P3
26
Figure 1. Experimental setup for subsurface drip irrigation and measuring water wetting front
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Figure 2. The geometry and boundary conditions of subsurface drip irrigation and spatial discretization set up of the numerical model.
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Figure 3. Observed (solid line) and predicted (dashed line) soil wetting front for DI with discharge of 4.46 L/h.
29
Figure 4. Observed (solid line) and predicted (dashed line) soil wetting front for DI with discharge of 6.26 L/h
30
Figure 5. Observed (solid line) and predicted (dashed line) soil wetting front for SDI-1P with discharge of 4.46 L/h.
31
Figure 6. Observed (solid line) and predicted (dashed line) soil wetting front for SDI-1P with discharge of 6.26 L/h.
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Figure 7. Observed (solid line) and predicted (dashed line) soil wetting front for SDI-2P1
33
Figure 8. Observed (solid line) and predicted (dashed line) soil wetting front for SDI-2P2
34
Figure 9. Observed (solid line) and predicted (dashed line) soil wetting front for SDI-2P3
35
