A bidirectional model for simulating soil water flow and salt transport under mulched drip irrigation with saline water

Agricultural Water Management 146 (2014) 24–33

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A bidirectional model for simulating soil water flow and salt transport under mulched drip irrigation with saline water Li-Juan Chen a,∗ , Qi Feng a , Feng-Rui Li a , Chang-Sheng Li b a b

Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China Plant Protection and Quarantine Station of Gansu Province, Lanzhou 730020, China

a r t i c l e

i n f o

Article history: Received 14 January 2014 Received in revised form 17 July 2014 Accepted 21 July 2014 Keywords: Soil water Soil salinity Drip irrigation Saline water irrigation HYDRUS-2D

a b s t r a c t Here, we present a mathematical model for simulating both soil water flow and salt transport in two directions (perpendicular and parallel to the drip tubing) under mulched drip irrigation with saline water. We evaluated the effectiveness of this model by comparing the simulated values with observed data from the field experiment (one treatment with three replications was imposed with irrigation water electrical conductivity of 4.0 dS m−1 and amounts of 2400 m3 ha−1 under mulched drip irrigation system). The results demonstrated that the model performed reliably in the simulation of water flow and salt transport under field conditions. In addition, the model was also used to simulate the spatial distribution patterns of soil water and salt in the two directions in relation to different treatments of irrigation quantity and quality. The simulation demonstrated that the volume of wetted soil was affected by both the plastic mulching and irrigation amount. The wetted region was expanded to the middle of the plastic mulching when the irrigation amount was high and the uniformity of irrigation increased with increasing irrigation volume. Soil water content in the direction parallel to the drip tubing was higher than that perpendicular to the tubing at the same distance, indicating that the wetting fronts overlapped more rapidly in the direction parallel to the drip tubing. The soil salt concentration was high at the edges of the wetting front, with a fairly large desalinated area immediately underneath and adjacent to the drippers. The model presented here offers an efficient approach to investigating the mechanisms underlying soil water flow and salt transport and for designing mulched drip irrigation systems with saline water. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Scarcity of fresh water constrains irrigated agriculture worldwide (Beltran, 1999; Mantell et al., 1985); consequently, farmers in many irrigated areas are being encouraged to use saline water for agricultural production. However, salt accumulation in soil profiles due to saline water irrigation typically leads to salinization and sodification, producing soils that cannot sustain crop yields. In this context, specialized and efficient methods of irrigation that can attain the twin objectives of higher productivity and optimum use of saline water are indispensable. Mulched drip irrigation, with beds and drip tubing covered with plastic film, is able to maintain high soil matric potential in the root zone as well as promoting weed control and crop production. Furthermore, because this type of irrigation allows application of water at a low rate and high frequency over extended periods of time, the

∗ Corresponding author. Tel.: +86 13919017514. E-mail addresses: [email protected], [email protected] (L.-J. Chen). http://dx.doi.org/10.1016/j.agwat.2014.07.021 0378-3774/© 2014 Elsevier B.V. All rights reserved.

soil salt introduced during the early stages of saline water irrigation can be leached effectively by subsequent applications (Goldberg et al., 1976; Kang, 1998). Thus, mulched drip irrigation is more profitable than other techniques for saline water irrigation (Ayers et al., 1986; Burt and Isbell, 2005; Saggu and Kaushal, 1991). Successful utilization of mulched drip irrigation with saline water depends primarily on effective system design and management. By adjusting the number of drippers, discharge rate, and irrigation frequency, a mulched drip irrigation system can be designed so that the wetted soil volume coincides with the crop rooting pattern as closely as possible (Patel and Rajput, 2008). In addition, accumulation of salts in the root zone should not exceed the tolerance limits of the crop. Therefore, improvements in our understanding of soil water flow and salt transport and their spatial distributions play an important role in the design and performance of such systems. Numerical simulation is an efficient approach for investigating the extent to which water and salt move laterally and vertically away from a dripper and allows more flexible representation of the flow domain, boundary conditions, and soil properties than can be

L.-J. Chen et al. / Agricultural Water Management 146 (2014) 24–33

achieved in field tests (Warrick, 2003). Numerous models for analyzing water flow and solute transport under drip irrigation have been developed over the last 40 years (e.g., Annandale et al., 2003; Arbat et al., 2013; Brandt et al., 1971). Most of these models assume that the wetted regions on both sides of the vertical plane (i.e., the plane perpendicular to the horizontal plane of the drip source) are symmetrical. It has also been a common practice to conceptualize the drip tubing as a line source rather than representing individual drippers along the drip line (Skaggs et al., 2004), ignoring the wetting pattern in the direction parallel to the drip tubing. For mulched drip irrigation, however, the plastic film covers an asymmetric pattern of individual drippers and the plastic mulching may induce pronounced changes in soil water flow and solute transport paths (Amayreh and Al-Abed, 2005). Therefore, it is essential to construct a model that accurately represents the actual patterns of soil water flow and salt transport when using mulched drip irrigation with saline water. Here, we describe a mathematical model using HYDRUS-2D that calculates soil water flow and salt transport both perpendicular and parallel to the drip tubing under mulched drip irrigation with saline water. The performance of the model was evaluated by comparing the simulated values with experimental data. Finally, the spatial distribution patterns of soil water and salt under various irrigation conditions are discussed. 2. Materials and methods

25

group. Two rows of drip tubing were laid in each group, with an 80cm spacing maintained between the two irrigation lines. After each group was mulched with plastic film (140 cm width), four rows of cotton were planted (plants on either side of an irrigation line were 30 cm apart, while plants adjacent to paired irrigation lines were 50 cm apart; see Fig. 1). The plant spacing along the line was 20 cm and an average seeding rate of 58.8 seeds per m2 . The dripper spacing and discharge rate were 30 cm and 2.0 L h−1 , respectively. The dates of irrigation, amounts of fertilizer and pesticides used, and other necessary operations were conducted according to typical local practices and recommendations. Tube access probes (TRIME, Germany) based on time domain reflectometry (TDR; Cichota et al., 2008) were used to measure soil water content. The sensors were installed vertically at three depths (0, −25, and −50 cm) and horizontally at five points (−40, −20, 0, and 20 cm in the direction perpendicular to the drip tubing and at 15 cm in the direction parallel to the drip tubing; see Fig. 2). Measured values were calibrated using the gravimetric method and bulk density. Soil samples used to prepare dilute soil extract solutions were collected using an auger in the same location at which the sensors were installed. Samples were collected before sowing the cotton and before and after each irrigation and significant precipitation event throughout the growing season. The samples were air dried and sieved through a 1-mm mesh. Soluble salt estimates were based on extracts with a 1:5 soil:water ratio, determined using a conductivity meter (EC1:5 ). All data were analyzed using PASW Statistics 18.0 and Surfer 8.0.

2.1. Field experiment 2.2. Model development We conducted a field experiment at the test and demonstration base for agricultural water-saving and ecological construction (103◦ 12 3.4 E, 38◦ 42 40.2 N) in Minqin County, Gansu Province, China from April 25 to October 15, 2013. The experimental soil was classified as sandy loam, with bulk densities of 1.57 and 1.55 g cm−3 in the 0–25-cm and 25–50-cm layers, respectively. Further details of the experimental site can be found in Chen and Feng (2013). A drip irrigation system mulched with plastic film (black polyethylene) was used to deliver saline water with an electrical conductivity (EC) of 4.0 dS m−1 to cotton plants (Gossypium hirsutum L. cv. Xinluzao 7). Irrigation water was obtained by mixing water from two wells in specified proportions. One well was located at the experimental station (fresh water (FW), EC = 1.09 dS m−1 ) and the other was in Huanghui Village (103◦ 36 11.9 E, 39◦ 02 56.4 N) in Minqin County (saline water (SW), EC = 15.92 dS m−1 ). The ion concentrations of the source water are presented in Table 1. The desired salinities were obtained as follows: M=

Mf × Qf + Ms × Qs Qf + Qs

(1)

where M is the salinity of the irrigation water after mixing (dS m−1 ), Mf is the salinity of the FW (dS m−1 ), Ms is the salinity of the SW (dS m−1 ), Qf is the amount of FW (m3 ha−1 ), and Qs is the amount of SW (m3 ha−1 ). The ion concentrations of the mixed water are also presented in Table 1. Three tanks were used for the irrigation system. The first and second tanks were filled with FW and SW, respectively, and the third was used for mixing the water. The irrigation water was supplied by a pump controlled by valves, with the exact amounts of water supplied monitored by water meters (Fig. 1). The total irrigation amount was 2400 m3 ha−1 (8 applications of 30 m3 ha−1 each). The irrigation interval was determined based on soil moisture and crop growth requirements. After the experimental field was divided into plots (3 replicate plots, each 15 m long and 3.4 m wide; Fig. 1), two groups of the mulched drip irrigation system were arranged on each plot and a 30-cm space without plastic film was maintained between each

2.2.1. Mathematical model We simulated soil water flow and salt transport using HYDRUS2D (Simunek et al., 1999). Assuming homogeneous and isotropic soil, the governing equation for water flow can be written as follows:









∂ 1 ∂ ∂h ∂ ∂h ∂K(h) rK(h) + K(h) + = −S r ∂r ∂t ∂r ∂z ∂z ∂z

(2)

where  is the volumetric water content of the soil (cm3 cm−3 ), t is time (d), r is the radial coordinate (cm), K(h) is the hydraulic conductivity (cm d−1 ), h is the pressure head (cm), z is the vertical coordinate with positive upwards (cm), and S is a distributed sink function representing water uptake by the roots (1 d−1 ). In HYDRUS-2D, solute transport was described as follows:

∂(c) 1 ∂ = r ∂r ∂t



rDr

∂c ∂r



+

∂ ∂z



Dz

∂c ∂z



−

∂ 1 ∂ (rqr c) − (qz c) r ∂r ∂z (3)

where c is the concentration of the solute in the soil solution (dS m−1 ), D is the dispersion coefficient (cm2 d−1 ), and q is the volumetric flux density (cm d−1 ). 2.2.2. Initial and boundary conditions The origin of the coordinates (r = 0 and z = 0) was placed at the center of the dripper, as illustrated by the schematic diagram presented in Fig. 3. Perpendicular to the drip tubing, the measured soil water pressure heads h0 (r,z) and soil salinities co (h,z) before the experiment were used as initial conditions within the flow domain. Then: h(r, z, t) = h0 (r, z), c(r, z, t) = c0 (r, z), t = 0, −R ≤ r ≤ R , 0 ≤ z ≤ Z (4) where R and Z are the maximum radial and vertical extents of the simulated domain (cm).

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Table 1 Chemical composition of source water and mixed water used in the experiment. Water

HCO3 − (mg L−1 )

Cl− (mg L−1 )

SO4 2− (mg L−1 )

Ca2+ (mg L−1 )

Mg2+ (mg L−1 )

Na+ (mg L−1 )

K+ (mg L−1 )

TDS (mg L−1 )

EC (dS m−1 )

FW SW MW

267 689 526

93 2906 887

307 6334 1460

97 438 274

40 1043 202

109 2655 564

7.0 33.6 5.1

921 14,099 3918

1.09 15.92 4.02

FW, fresh water from the well located at the experimental station; SW, saline water from the well located at Huanghui Village; MW, mixed water with an electrical conductivity of 4.0 dS m−1 ; TDS, total dissolved solids; EC, electrical conductivity.

Fig. 1. Layout of the mulched drip irrigation system with saline water.

Fig. 2. Locations of the observation sites in (a) horizontal plane view and in vertical plane views (b) perpendicular and (c) parallel to the drip tubing.

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Fig. 3. The schematic diagram of the model (a) perpendicular and (b) parallel to the drip tubing.

During irrigation, a constant flux boundary condition was imposed when there was a surface pond surrounding the dripper at the soil surface. The solute flux was determined from the irrigation water salinity and amount of irrigation, as follows: −K(h)

∂h + K(h) = q0 , ∂z

− D

∂c + qc = εcR , ∂z

−K(h)

0 < t < ta ,

rl ≤ r ≤ rr , z = 0

(5)

where rl and rr are the left and right boundaries, respectively, of the surface pond (cm), q0 is the dripper flux (m3 s−1 ), q is the volumetric flux density (cm d−1 ), c is the concentration of the solute in the soil solution (dS m−1 ),ε is the volumetric flux density of irrigation (cm d−1 ), cR is the salinity of the irrigation water (dS m−1 ), and ta is the irrigation duration (s). After irrigation, a zero flux boundary condition was imposed for the surface pond area: −K(h)

∂h + K(h) = 0, ∂z

rl ≤ r ≤ rr ,

− D

∂c + qc = 0, ∂z

t > ta ,

z=0

(6)

A zero flux boundary condition was also imposed beyond the surface pond area due to the plastic mulching: −K(h)

∂h + K(h) = 0, ∂z

rr < r ≤ R ,

− D

∂c + qc = 0, ∂z

t > 0,

− R ≤ r ≤ rl ,

z=0

(7)

Finally, because the groundwater table of the experimental field lay below the domain of interest (approximately 18.0 m below the soil surface), a free drainage bottom boundary condition was used for both water flow and solute transport. Parallel to the drip tubing, the initial condition was as follows: h(r, z, t) = h0 (r, z),

c(r, z, t) = c0 (r, z),

t = 0,

0 ≤ r ≤ R,

0≤z≤Z

(8)

where R and Z are the maximum radial and vertical extents of the simulated domain (cm). During irrigation, the top boundary condition surrounding the surface pond was: −K(h)

∂h + K(h) = q0 , ∂z

0 ≤ r ≤ rs ,

z=0

− D

∂c + qc = εcR , ∂z

where rs is the maximum radius of the surface pond (cm). After irrigation, a zero flux boundary condition was imposed for the surface pond area as follows:

0 < t < ta , (9)

∂h + K(h) = 0, ∂z

0 ≤ r ≤ rs ,

− D

∂c + qc = 0, ∂z

t > ta ,

z=0

(10)

A zero flux boundary condition was also imposed beyond the surface pond area: −K(h)

∂h + K(h) = 0, ∂z

rs ≤ r ≤ R,

− D

∂c + qc = 0, ∂z

z=0

t > 0, (11)

Finally, a free drainage bottom boundary condition was used for both water flow and solute transport. For all simulations (i.e., in all directions), it was assumed that no flow of water or salt took place along the two perpendicular sides of the flow domain. Accordingly, we enforced a no-flow boundary condition for these regions. 2.3. Parameters and simulation inputs The soil profiles (0 to −50 cm) were assumed to be composed of uniform and isotropic sandy loam soil. Undisturbed soil samples were collected at the beginning of the experiment from different soil layers within the soil profiles to measure soil hydraulic properties. Soil water characteristic curves and hydraulic conductivities were determined in the laboratory using a soil moisture suction meter (SXY-2, China) and an unsaturated hydraulic conductivity meter (FS-1, China), respectively. The mean values obtained for the measured parameters are as follows: saturated water content  s = 0.382 cm3 cm−3 , residual water content  r = 0.062 cm3 cm−3 , retention curve shape parameters a = 0.0121 and n = 1.408, saturated hydraulic conductivity Ks = 45.85 cm d−1 , and pore connectivity parameter l = 0.5. According to Ramos et al. (2011), potential root water uptake can decrease in response to water and salinity stress. We described the reduction due to water stress using the model developed by Feddes et al. (1978), the parameters for which were taken from the HYDRUS-2D internal database. Similarly, we described the reduction due to salinity stress using the threshold and slope function

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Table 2 Irrigation schedule for the simulations. Treatment

Water salinity (dS m−1 )

Total irrigation amount (m3 ha−1 )

CMD1 CMD2 CMD3 CMD4 CMD5 CMD6 CMD7 CMD8 CMD9

0.9 4.0 7.0 0.9 4.0 7.0 0.9 4.0 7.0

2100 2100 2100 2400 2400 2400 2700 2700 2700

The index of agreement (IA) is a descriptive measure of the relative size of the differences and is useful to compare the performance of different models: n 

IA = 1 −

(Yio − Yie )2

i=1

       2 Y + Y io ie

(14)

 and Y  are the differences with respect to the average where Yio ie observation, of the observed and simulated values, respectively.

CMD, mulched drip irrigation for cotton.

3. Results and discussion

of Maas (1990); we obtained the parameters for this function from Ramos et al. (2011). Solute transport parameters were obtained from solute displacement experiments conducted on undisturbed cylindrical samples (see Ramos et al., 2011). In our simulations, R = 15 cm, Z = 50 cm, and R = 40 cm. Meteorological data were obtained from the meteorological observation station at the base. Initial soil water content and salinity were based on measurements obtained in the field. Soil depths, initial soil water content, and initial soil salinity content for the three soil layers were as follows: 0 cm, 0.26 cm3 cm−3 , and 0.22 dS m−1 ; −25 cm, 0.28 cm3 cm−3 , and 0.30 dS m−1 ; and −50 cm, 0.15 cm3 cm−3 , and 0.22 dS m−1 , respectively. The dripper flux (q0 ) during irrigation was 254.78 cm d−1 , calculated based on the emitter discharge of 2.0 L h−1 (Selim et al., 2012). We assumed a longitudinal dispersivity of 5.0 cm, with the transverse dispersivity being one-tenth of the longitudinal dispersivity, neglecting molecular diffusion. Our simulations were conducted for a complete growth period, considering three irrigation water salinity levels (0.9, 4.0, and 7.0 dS m−1 ) and three total irrigation amounts (210, 240, and 270 m3 ha−1 ) (Table 2). The irrigation durations and intervals in the simulation were consistent with those of the field experiment.

2.4. Statistical analysis To evaluate the model performance for simulation, three different statistical indexes were used. The first two indexes, the mean absolute error (MAE) and the root mean square error (RMSE) reflect the differences between observations and simulations. They were calculated as follows:

 1   Yio − Yie  n n

MAE =

(12)

i=1

 n 1 RMSE =

(Yio − Yie )2 n

(13)

i=1

where Yio and Yie are the observed and simulated values and n is the number of pair values.

3.1. Simulated versus observed results The simulated values for soil water and salt contents after four irrigation applications (i.e. July 1 for the second irrigation, July 17 for the fourth irrigation, August 4 for the sixth irrigation, and August 23 for the eighth irrigation) were compared graphically with the observed results in Fig. 4. While there were some differences between the simulations and the observations, the overall simulations were very good. For four irrigation applications, both the observations and simulations showed simultaneous increases in soil water content after irrigation at −20 cm in depth. In addition, soil salt content exhibited the same responses after irrigation. The statistical evaluation results for model performance in the mean absolute error (MAE), root mean square error (RMSE) and index of agreement (IA) are summarized in Table 3. The region of the MAE (RMSE, IA) values for soil water and salt contents were 0.0031–0.0080 (0.0051–0.0093, 0.9985–0.9995) and 0.0001–0.0005 (0.0002–0.0006, 0.9972–0.9999), respectively. Based on these values, we conclude that our model reproduces water flow and salt transport under field conditions reliably. 3.2. Spatial distribution patterns of soil water content 3.2.1. Perpendicular to the drip tubing Fig. 5 illustrates the simulated soil water contents for CMD3, CMD6, and CMD9 on July 1 (immediately after the second irrigation). The soil water contents for all three treatments were consistently low at the surface and subsequently decreasing with depth. For CMD3, the soil water content distribution was similar to that of point source irrigation without plastic mulching. The wetted region under the dripper was nearly symmetrical around r = 0. The soil was barely moistened in the middle of the plastic film (r = −40 cm and z = 0 to −50 cm; Fig. 5); i.e., where the water from two adjacent drippers did not converge, resulting in extremely dry soil in the middle of the plastic film. Thus, the uniformity of irrigation was quite low when the irrigation amount was small. For CMD6 and CMD9, however, the wetted region under the dripper was asymmetrical, but inclined toward the middle of the plastic film. For CMD9, the mean soil water content at r = −20 cm (z = 0 to −50 cm; Fig. 5) was 0.136 cm3 cm−3 , greater than that on the other side of the dripper (r = 20 cm and z = 0 to −50 cm; mean soil water content, 0.126 cm3 cm−3 ). Several previous studies have reported

Table 3 Results of the statistical analysis between measured and simulated soil water and salt contents. Statistics

MAE RMSE IA

Perpendicular to the drip tubing

Parallel to the drip tubing

Soil water content (cm3 cm−3 )

Soil salt content (dS m−1 )

Soil water content (cm3 cm−3 )

Soil salt content (dS m−1 )

0.0052 0.0073 0.9989

0.0002 0.0003 0.9988

0.0050 0.0077 0.9985

0.0002 0.0004 0.9980

MAE, mean absolute error; RMSE, root mean square error; IA, index of agreement.

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Fig. 4. Simulated (a) and observed (b) soil water contents (cm3 cm−3 ) and simulated (c) and observed (d) soil salt contents (dS m−1 ) in the direction perpendicular to the drip tubing as well as simulated (e) and observed (f) soil water contents (cm3 cm−3 ) and simulated (g) and observed (h) soil salt contents (dS m−1 ) in the direction parallel to the drip tubing after four irrigation applications. The date for the irrigation applications was July 1, July 17, August 4 and August 23. The observing data was obtained three days after the irrigation applications.

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Fig. 5. Simulated soil water distributions for treatments CMD3, CMD6, and CMD9 perpendicular to the drip tubing.

Fig. 6. Simulated soil water distributions for treatments CMD3, CMD6, and CMD9 parallel to the drip tubing.

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Fig. 7. Simulated soil salinity distributions for treatments CMD7, CMD8, and CMD9 perpendicular to the drip tubing.

that water transfer under drip irrigation is symmetrical on either side of the drip tubing (e.g., Patel and Rajput, 2008). Therefore, our results demonstrated that the volume of wetted soil under mulched drip irrigation is affected by the plastic mulching. More soil water was retained in the middle of the plastic film, which improved soil water conditions under the plastic film. Moreover, a comparison of the results for CMD3, CMD6, and CMD9 demonstrates that the wetted region of soil increased horizontally and vertically when the irrigation amount increased. Taking the soil water content of 0.125 cm3 cm−3 for instance, this value was only detected from −7 to 6 cm (along the r-axis in Fig. 5) for CMD3, while from −34 to 20 cm for CMD6 and −40 to 20 cm for CMD9. Under the dripper of CMD3 (where r = 0 cm, z from 0 to −50 cm in Fig. 5), the soil water content was 0.130 cm3 cm−3 on the surface, 0.099 cm3 cm−3 at −25 cm and 0.067 cm3 cm−3 at −50 cm. Conversely, for CMD6, the above three values were 0.149, 0.120 and 0.083 cm3 cm−3 while for CMD9 were 0.166, 0.134 and 0.096 cm3 cm−3 , respectively. The soil water content contours for CMD9 were much straighter than those for CMD3. The volume of wetted soil for CMD9 was also larger than that for CMD3. Thus, both the wetted area of soil and the uniformity of irrigation under the plastic film were increased with increasing irrigation.

The mean soil water contents (r = −40 to 20 cm and z = 0 to −25 cm; Fig. 5) for CMD6 and CMD9 were 0.129 and 0.149 cm3 cm−3 , respectively, 22.86% and 41.90% higher than for CMD3 (0.105 cm3 cm−3 ). However, the mean soil water contents (r = −40 to 20 cm and z = −25 to −50 cm; Fig. 5) for CMD6 and CMD9 were 0.101 and 0.116 cm3 cm−3 , respectively, 26.04% and 45.83% higher than for CMD3 (0.080 cm3 cm−3 ). These results suggest that the effects of the amount of irrigation on soil water content are more pronounced in the deep soil layers (i.e., from −25 to −50 cm) than in the shallower layers. We attribute this to the fact that mulched drip irrigation is a type of pulse irrigation. Typically, infiltration to deep soil layers occurs under the influence of gravity once the surface soil water content has reached a certain threshold. However, the water remains in the shallow soil when the amount of irrigation water is small, resulting in insufficient water being transported to the deep soil. 3.2.2. Parallel to the drip tubing Fig. 6 illustrates the simulated soil water contents for CMD3, CMD6, and CMD9 on July 1 parallel to the drip tubing. The soil water content (where r = 15 cm and z = 0 cm) was 0.120 and 0.166 cm3 cm−3 for CMD3 and CMD9, respectively, indicating that

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L.-J. Chen et al. / Agricultural Water Management 146 (2014) 24–33

Fig. 8. Simulated soil salinity distributions for treatments CMD7, CMD8, and CMD9 parallel to the drip tubing.

increasing the irrigation amount increases the soil water content in the overlap region. Accordingly, increasing the irrigation amount can facilitate overlap of the wetted region beneath the drippers to achieve more uniform wetting. Meanwhile, the wetted depth also increased when the irrigation amount increased. The average soil water content at z = −50 cm (r = 0 to 15 cm) was 0.096 cm3 cm−3 for CMD9, 44.07% higher than that for CMD3 (0.067 cm3 cm−3 ). We also compared these results with the soil water content distribution perpendicular to the drip tubing (Fig. 5). The soil water content at r = 15 cm and z = −15 cm in Fig. 6 (Fig. 5) was 0.111 (0.106), 0.134 (0.122), and 0.153 cm3 cm−3 (0.137 cm3 cm−3 ) for CMD3, CMD6, and CMD9, respectively. Thus, it is clear that soil water content parallel to the drip tubing was greater than that perpendicular to the drip tubing at the same position. This phenomenon illustrates that the wetting front overlapped earlier parallel to the drip tubing such that more water was driven to deeper levels in the soil under the effects of gravity in this direction. This phenomenon was very difficult to detect in our field measurements. Therefore, numerical simulation is an invaluable method for investigating the mechanisms underlying soil water and salt movement under mulched drip irrigation. Based on the above analysis, we divided soil water movement into two stages. The first stage occurred prior to overlapping of the wetting fronts of adjacent drippers. The infiltration characteristics during this stage were similar to those of point source irrigation, where the soil matric potential (which is equal in the horizontal and vertical directions) is the dominant factor controlling soil water movement. The second stage occurred after overlap. The ability of the soil to absorb water was reduced in the overlap region. Under these conditions, gravitational potential energy began to play a key role, resulting in more widespread dispersion of water. When the soil became saturated, soil water suction approached 0 and the water was only dispersed vertically. 3.3. Spatial distribution patterns of soil salinity 3.3.1. Perpendicular to the drip tubing The simulated salinity distributions for the soil profiles of CMD7, CMD8, and CMD9 on July 1 are illustrated in Fig. 7. Compared to soil water movement for CMD9 (Fig. 5), soil salts tended to move toward

the fringes of the wetted areas. Because mulched drip irrigation reduces evaporation considerably, the effects of water evaporation on salt distribution can be ignored. The consequent decrease in the upward movement of water restricted the upward movement of salt, thus reducing salt accumulation in the surface soil. Accordingly, a clearly desalinated area was created in the shallower layers (Fig. 7). Soil salinity were lowest near r = 0 cm and z = 0 cm below the drippers and increased gradually with depth (Fig. 7). The distribution of soil salt was different from that of soil water. Drip irrigation can form a pond of variable size under the dripper during irrigation, resulting in variable irrigation conditions under the plastic film. Under such conditions, the front of soluble salt movement in the soil does not coincide with that of the water, but lags behind. Additionally, due to the leaching effect of drip irrigation, the center of the desalinated area was nearly located beneath the dripper. 3.3.2. Parallel to the drip tubing Fig. 8 illustrates the simulated salinity distributions for the soil profiles of CMD7–CMD9 on July 1. For a constant amount of irrigation water, salt content was typically higher with increased irrigation water salinity. For the soil layer from 0 to −50 cm, the mean value of EC1:5 at r = 15 cm was 0.254, 0.681, and 1.054 dS m−1 for CMD7, CMD8, and CMD9, respectively. Conversely, both the width and depth of the desalination zone decreased with increasing irrigation water salinity. Although the wetting fronts under the drippers overlapped with each other more rapidly when the amount of irrigation water was increased, the soil salt contents at the overlapping fronts remained high when the irrigation water salinity was increased (e.g., CMD9). This result is closely linked to the mechanisms of soil water and salt movement under mulched drip irrigation. As the water is continuously irrigated, soil salt is transported to the edge of the wetting front. When the irrigation amount is high, water from adjacent drippers overlaps laterally and moves downward, forming a water plane through which the soil salt can be easily leached. Conversely, when the irrigation amount is low, a portion of the salt will be retained at points at which water movement is slow. At the overlap front, the force that drives the water downward is weaker than near the dripper. Finally, when the salinity of the irrigation water

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is high, the salt that could not be leached is typically retained in the upper part of the soil column at the overlap front.

Academy of Sciences (KZZD-EW-04-05)and National Science and Technology Support Program (2011BAD29B04).

4. Conclusions

References

In the present study, we developed a mathematical model describing soil water flow and salt transport perpendicular and parallel to drip tubing under mulched drip irrigation with saline water. We conducted field experiments in Minqin County, China and used the resulting data to evaluate the performance of our model by comparing the simulated values with the experimental data. This comparison demonstrated that the model performed reliably in reproducing water movement and salt transport under field conditions. We then used the model to simulate the spatial distributions of soil water and salt concentrations with various irrigation amounts and water qualities. Higher levels of irrigation produced more overlap of wetted areas and thus, promoted more uniform irrigation. In particular, the wetted area of CMD9 reached the middle of the plastic film, indicating that plastic mulching can substantially affect the direction of soil water flow and improve uniformity of wetting. Moreover, soil water contents parallel to the drip tubing were higher than those perpendicular to the drip tubing at the same position, illustrating that the wetting front overlapped earlier parallel to the drip tubing. Our salt transport simulations displayed a clear desalination region in the shallower layers due to the plastic mulching. Both the horizontal and vertical extents of the desalination zone increased with decreasing irrigation water salinity, and an accumulation zone with higher salt content was formed at the overlapping front of adjacent drippers when the irrigation water salinity was high. Soil moisture status and salinity concentrations could affect the growth, shape, structure, physiological function and water uptake characteristics of crop root system, and would further affect crop evapotranspiration rates, leaf area index and crop yield. Previous studies revealed that the cotton root system under mulched drip irrigation distributed mainly in the shallow soil layer in the film covered field, and increased in hydrotropism (Wei et al., 2002; Fang et al., 2007). The results in our study provide thinking for investigating the vertical and horizontal distribution of root system of cotton under mulched drip irrigation with saline water. The model presented in this study offers an efficient approach to exploring the mechanisms underlying soil water flow and salt transport under mulched drip irrigation with saline water. It has the potential to be applied to a variety of soil types, water qualities, and water application strategies (e.g., blending, cyclic) and thus is broadly applicable to designing mulched drip irrigation systems with saline or fresh water.

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Acknowledgments This research was supported by China Postdoctoral Science Foundation (2013M542407), Foundation for Excellent Youth Scholars of CAREERI CAS (Y451051001), the Key Project of the Chinese