Simulation of Soil Wetting Pattern of Vertical Moistube-Irrigation - MDPI

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Simulation of Soil Wetting Pattern of Vertical Moistube-Irrigation Yan-Wei Fan 1,2 , Ning Huang 1, *, Jie Zhang 1 and Tong Zhao 2 1

2

*

Key Laboratory of Mechanics on Disaster and Environment in Western China, the Ministry of Education of China, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China; [email protected] (Y.-W.F.); [email protected] (J.Z.) College of Energy and Power Engineering, Lanzhou University of Technology, Lanzhou 730050, China; [email protected] Correspondence: [email protected]; Tel.: +86-931-8914-569

Received: 11 April 2018; Accepted: 3 May 2018; Published: 4 May 2018

Abstract: Knowledge of the soil wetting pattern characteristics of vertical moistube-irrigation is essential for the design of cost-effective and efficient irrigation systems. We conducted laboratory experiments to determine the specific discharge calculation formula and compare the accuracy of HYDRUS-2D simulation. The cumulative infiltrations, wetting pattern distances, and water content distributions predicted with HYDRUS-2D were found to align well with experimental data. The results provide support for using HYDRUS-2D as a tool for investigating and designing moistube-irrigation management practices. Numerical simulations were carried out with HYDRUS-2D to investigate the influence of soil texture, initial water content, pressure head, moistube length, and buried depth on wetting pattern characteristics. There are small differences in the shape of the soil wetting pattern, as well as significant differences in size. The wetting pattern and water content contour are approximately “ellipsoid” around the moistube. Soil texture has a significant effect on the wetting pattern characteristics, the vertical and horizontal wetting front distance, and the wetted soil volume decrease along with the increase of soil clay content. The initial water content, pressure head, and moistube length have great influence on the wetting front distance and the wetted soil volume. Both are positively correlated with the initial water content, pressure head, and length. Moistube buried depth affects the wetting pattern position. The soil wetting pattern decreases synchronously as the buried depth drops. Keywords: vertical moistube-irrigation; soil wetting pattern; influencing factors; HYDRUS-2D

1. Introduction The forest fruit industry is a good choice for achieving economic growth and ecological conservation in arid regions of northwest China [1]. However, the area has limited rainfall, and fruit tree production largely depends on irrigation [2,3]. Traditional flood irrigation has a large amount of water and low water use efficiency, which is not conducive to the sustainable development of the ecological economy [4]. Considering the strong surface evaporation and the deep-rootedness characteristics of fruit trees in arid areas, effective irrigation methods are urgently needed to transport the water directly to the root zone soil of the fruit trees, in order to reduce soil evaporation and improve irrigation water use efficiency. Vertical line source moistube-irrigation (VLSMI) is a water-saving irrigation technique suitable for deep-rooted plants. It introduces membrane technology into the irrigation field, uses macromolecular polymer semipermeable membranes to make moistube, and irrigates water through moistube for subsurface irrigation [5,6]. The surface of the moistube contains nano-pores, which are uniformly

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and densely distributed. During irrigation, the soil water movement is approximately line source infiltration. Compared to subsurface drip irrigation, the main advantages of VLSMI include a line source infiltration increasing the wetted depth, a freely settable spacing, and a low-pressure head and less power consumption. Given that the fruit trees are wider in spacing and deeper in the system of root, this type of tree is more appropriate for applying the VLSMI technique [7]. The rational design of VLSMI systems requires knowledge of the soil wetting pattern characteristics around the line source to minimize the soil surface moisture and deep percolation [8]. The dynamic changes and water distribution of wetting patterns depend on many factors, including soil physical properties (texture, bulk density, and initial water content) and emitter parameters (discharge rate, line source length, and buried depth) [9–13]. Several studies have shown that soil texture is an important factor for determining irrigation design parameters because it has a great influence on infiltration. Therefore, the design of the subsurface irrigation system should involve consideration of soil texture [10,13–15]. Generally, under the same soil conditions, when the soil bulk density increases, the soil becomes dense and porosity decreases. This results in a decrease of soil infiltration capacity [16–19]. The initial water content determines the soil water potential at the initial stages of infiltration. The higher the initial soil water content, the larger the size of the wetting pattern in all directions [10,12,20]. To ascertain the impact of the emitter discharge rate on the wetting pattern sizes, the researchers conducted many laboratory and field experiments. For an equal volume of applied water, an increase in the emitter discharge rate leads to an increase in horizontal diffusion distance and a decrease in vertical wetted depth [21–24]. Ismail et al. [25] set up “a hydraulic barrier” (with a secondary drip line buried below the primary line), and found that when the secondary drip line wets the soil below the primary drip line, it will force water from the primary drip line to redistribute horizontally and upwards, instead of moving downward. El-Nesr et al. [12] showed that the dual-drip irrigation system can improve water distribution in sandy soils. Additionally, the sequential and concurrent dual-drip irrigation system can efficiently limit downward leaching of the solutes. In addition, the soil-wetting pattern depends on the emitter’s position relative to the soil surface. It is a key factor for achieving an effective match between wetted soil volume and crop roots [12,26]. Numerical simulation is an efficient method for studying optimal irrigation management practices. In order to efficiently describe the soil water movement from a point source or line source, the researchers designed some models [27–31]. The numerical model HYDRUS developed by Šimunek et al. [32] has been widely used to simulate soil water movement for various irrigation methods. Many investigators have used this model to evaluate either field or laboratory experiments, as well as other mathematical models [12,13,33–36]. The HYDRUS model enables its users to trace the movement of water, solutes, and the wetting patterns in both simple and complex geometries, for homogeneous or heterogeneous soils, and for different combinations of initial and boundary conditions. The objectives of this study are to assess the feasibility of HYDRUS-2D for simulation of the soil water movement of vertical line source moistube-irrigation through a laboratory experiment, and to investigate numerically the influence of soil texture, initial water content, pressure head, moistube length, and buried depth on the soil wetting pattern. 2. Materials and Methods 2.1. Specific Discharge Calculation Moistube is a porous semipermeable membrane, which is the same as a porous medium (e.g., soil). Its seepage process conforms to Darcy’s law [37,38]. Q = k · π · Dn · L ·

∆H d

(1)

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where Q is moistube discharge (mL/min), k is moistube permeability coefficient (cm/min), Dn is moistube inner diameter (cm), L is moistube length (cm), ∆H is pressure difference between the inside and outside of moistube (cm), and d is moistube thickness (cm). The moistube is not only the delivery pipe but also the seepage pipe and the pipe wall is permeable everywhere. Assuming the surface pore is evenly distributed on the moistube, the specific discharge of the moistube can be obtained. qs = Q/L (2) where qs is moistube specific discharge (mL/(cm·min)). Substituting Equation (2) into Equation (1), the following equation is generated. q s = k · π · Dn ·

∆H d

(3)

Given that inner diameter and thickness of moistube are constant, Equation (3) can be simplified using the equation below. ( qs = K · ∆H (4) K = k · π · Dn /d where K is the comprehensive permeability coefficient ((mL/(cm2 ·min)). When the moistube is vertically placed in the soil, the pressure difference between the inside and outside of the moistube is mainly affected by the pressure head, the soil lateral pressure, and the soil water suction. Niu et al. [39] found that water pressure was the key factor in controlling the moistube discharge, which is followed by soil bulk density. The initial water content had the least effect on discharge. Based on Equation (4), the expression of specific discharge in the soil was established using the following equation. qs = K ( H + M + aγN + b) (5) where H is inlet pressure head (cm), M is distance between compute nodes and water inlet (cm), γ is soil bulk density (g/cm3 ), N is buried depth of compute nodes (cm), and a and b are fitting parameters. 2.2. Laboratory Experiments The experimental equipment, presented in Figure 1, was comprised of five parts including the soil box, the mariotte battle, the moistube, the height adjustable stand, and the hydraulic hose. The soil box was made of transparent acrylic material with the thickness of 10 mm, and measured 60 cm long, 60 cm wide, and 100 cm deep. A considerable amount of air holes with a diameter of 2 mm were opened at the bottom of the soil box for ventilation. The soil holes with a diameter of 2 cm and a spacing of 5 cm were designed on the side of the soil box near the moistube to measure soil water content (SWC) after irrigation. The moistube had a 16 mm inside diameter, a thickness of 1 mm, and seepage holes of 10 to 900 nm. A Mariotte bottle was used to maintain a constant pressure head. The experiment was carried out in air and soil conditions. In the air, we aimed to determine the comprehensive permeability coefficient, which was performed for the six different pressure heads (0 cm, 55 cm, 75 cm, 177 cm, 204 cm, and 241 cm) and a fixed moistube length of 100 cm. A study of water infiltration under moistube-irrigation was conducted on aeolian sand and silt loam, which were taken from Jingtai and Qilihe District, China. Basic physical properties of these tested soils are listed in Table 1. The soil sample was loaded into a soil box at 5-cm per layer to acquire a homogeneous soil profile. The moistube was placed close to the wall of the soil box to observe the soil wetting pattern. The moistube in aeolian sand and silt loam was 40 cm and 30 cm in length, respectively. Its water inlet was located 20 cm below the soil surface. Two pressure heads (1.2 m and 1.8 m) were adopted. The experimental data under the pressure head of 1.2 m was used to fit the formula parameters of specific discharge and the experimental data under 1.8 m pressure head was used for simulating verification. Cumulative infiltration was recorded and the wetting pattern was drawn during the

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used for simulating verification. Cumulative infiltration was recorded and the wetting pattern was infiltration. Finally, after infiltration 70 h, the waterfor supply stopped and soil drawn during the infiltration. Finally,for after infiltration 70 h, was the water supply wassamples stopped were and collected from taking soil holes and the SWC was determined by recording the weight loss of the soil samples were collected from taking soil holes and the SWC was determined by recording the ◦ samples after drying after at 105oven C for 24 h.at 105 °C for 24 h. weight loss of oven the samples drying Height adjustable stand

Mariotte bottle

Hydraulic hose

H

Taking soil hole

Moistube Soil box Air hole

Figure Figure1.1.Schematic Schematicdiagram diagramof ofexperimental experimentalequipment equipment(H (Hrepresents representsinlet inletpressure pressure head). head). Table Table 1. 1. Basic Basicphysical physicalproperties properties of of tested tested soils. soils. Particle Size/mm Soil SoilType Type Aeolian Aeolian sand sand Silt loam Silt loam

Particle Size/mm

0.02~2.00 0~0.002 0.02~2.00 0.002~0.02 0.002~0.02 0~0.002

Field

Bulk Density Saturated Soil Water Field Capacity Bulk Density Saturated Soil Water Capacity 3) 3 3/cm 3 /cm 3 ) 3) (g/cm (g/cm ) Content (cm Content (cm (cm33 /cm33) (cm /cm )

Wilting Wilting Coefficient (%) Coefficient (%)

97.69 97.69

2.31

0.00

1.60

0.43

0.051 0.051

24.35

65.55

10.10

1.30

0.50

0.286

6.7

0.286

6.7

24.35

2.31

65.55

0.00

10.10

1.60

0.43

1.30

0.50

1.8 1.8

2.3. Numerical Model 2.3. Numerical Model Assuming the soil is homogeneous and isotropic, the water infiltration of the vertical line Assuming the soil is homogeneous and isotropic, the water infiltration of the vertical line source source moistube-irrigation can be conceptualized as an axisymmetric three-dimensional process. moistube-irrigation can be conceptualized as an axisymmetric three-dimensional process. We We simulated water infiltration using HYDRUS-2D [40]. The governing equation for water flow is the simulated water infiltration using HYDRUS-2D [40]. The governing equation for water flow is the 2D 2D Richards equation. Richards equation. ∂θ 1 ∂ ∂h ∂ ∂h ∂K (h) = rK (h) + K (h) − (6) ∂t r ∂r ∂r ∂z ∂z  1   h    h  K (∂z h)  rK ( h )    K ( h )   (6) t content r r  (cm3 r·cm ztime z where θ is the volumetric water (min), r is the radial (horizontal)  −3z),t is the  coordinate (cm), K(h) is the unsaturated hydraulic conductivity (cm·min−1 ), h is the soil water pressure where θ is the volumetric water content (cm3∙cm−3), t is the time (min), r is the radial (horizontal) head (cm), and z is the vertical coordinate that is positive downward (cm). coordinate (cm), K(h) is the unsaturated hydraulic conductivity (cm∙min−1), h is the soil water The water retention curve and hydraulic conductivity curve are important soil characteristics [41]. pressure head (cm), and z is the vertical coordinate that is positive downward (cm). A centrifugal machine (SCR-20) was used to determine a water retention curve under rotational speeds The water retention curve and hydraulic conductivity curve are important soil characteristics of 900 rpm, 1700 rpm, 2200 rpm, 2800 rpm, 3100 rpm, 5300 rpm, 6900 rpm, and 8100 rpm, respectively. [41]. A centrifugal machine (SCR-20) was used to determine a water retention curve under rotational Each speed was maintained for 60 min. Then SWC was measured for each rotational speed in which speeds of 900 rpm, 1700 rpm, 2200 rpm, 2800 rpm, 3100 rpm, 5300 rpm, 6900 rpm, and 8100 rpm, the soil water suction was calculated using Equation (14). respectively. Each speed was maintained for 60 min. Then SWC was measured for each rotational speed in which the soil water suction was calculated using S= 1.118 × R × (rpm )2 Equation × 10−5 (14). (7) 5

S  1.118  R  ( rpm)  10 (7) where R is the radial distance to the midpoint of the soil sample (cm) and rpm is rotational speed. whereAfter R is the radial distance to water the midpoint of curve, the soilsaturated sample (cm) and rpm iswas rotational speed. determining the soil retention conductivity measured on the sameAfter soil samples usingthe a constant head permeameter [34]. determining soil water retention curve, saturated conductivity was measured on the 2

same soil samples using a constant head permeameter [34].

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The van Genuchten-Mualem model [42,43] was used to describe the constitutive soil hydraulic properties.

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 (h)   r 



s  r

5 of 19



(8) n m  h used to describe the constitutive soil The van Genuchten-Mualem model [42,43]1 was hydraulic properties. 2  θs − θ1r m m  (9) K θ( h(h) )= K sθSr e0.5 +1  1  Sen m  (8) 1 + |αh| h−3), r is residual m i2water contents (cm3∙cm−3), Ks is where s is saturated water contents (cm3∙cm K (h) = Ks S−1e0.5 1 − 1 − Se1/m (9) saturated hydraulic conductivity (cm∙min ), Se is the effective degree of saturation equal to





3 ·cm−3 ), θ is 3 ·cm−3 ), K is (  r )θ/s (is s saturated  r ) (–), water where contents is ancontents empirical(cm parameter (cm inverselywater related to the air(cm entry value, and r −1) residual s − 1 saturated hydraulic conductivity (cm · min ), S is the effective degree of saturation equal e m and n are empirical constants affecting the shape of the retention curve (–). The value of m to is (θ − θr )/(by θs − θr )(–), α is an empirical parameter (cm−1 ) inversely related to the air entry value, restricted m=1-1/n. and m and n empirical affecting the shape the (9) retention curve (–). The value is (hare ) and K (h) constants relationships in Equations (8)ofand were simultaneously fitted of tomthe The restricted by m=1-1/n. experimentally obtained  (h) and K (h) data using the RETC software [44]. The van GenuchtenThe θ (h) and K (h) relationships in Equations (8) and (9) were simultaneously fitted to the Mualem analytical model parameters [Equations (8) and (9)] for the soil water retention and experimentally obtained θ (h) and K (h) data using the RETC software [44]. The van Genuchten-Mualem conductivity curves are listed in Table 2. analytical model parameters [Equations (8) and (9)] for the soil water retention and conductivity curves are listed in Table 2.

Table 2. The van Genuchten-Mualem Parameters of experimental soils.

SoilSoil Type Type Aeolian

Aeoliansand sand Silt loam Silt loam

Table 2. The van Genuchten-Mualem Parameters of experimental soils. Parameter n Parameter α in Saturated Residual Soil Saturated Soil in the Soil the Soil Water Hydraulic Residual Soil Saturated Soil Parameter α in the Soil Parameter n in the Soil Water Content Water Content Water Saturated Hydraulic Water Content Water Content Water RetentionRetention Water Retention Conductivity Conductivity (cm/min) 33/cm3) 3/cm3) 3 3 3 (cm (cm Retention (cm /cm ) (cm /cm ) Function (1/cm) Function (-) Function (1/cm) (cm/min) Function (-) 0.02 0.43 0.162 2.24 0.4210 0.02 0.43 0.162 2.24 0.4210 0.02 0.50 0.014 1.51 0.0143 0.02 0.50 0.014 1.51 0.0143

The infiltration space can be described as a three-dimensional three-dimensional axisymmetric domain, which is shown in Figure 2. The transport domain was 30 cm wide (radius) and 100 cm deep (depth).

Atmospheric BC

r

No Flux C

B'

B

100cm

A

Constant flow bourdary

A'

No Flux

Initial condition in h (r,z)

Free Drainage BC 30cm

z Figure Figure 2. 2. Schematic Schematic diagram diagram of of the the transport transport domain domain used used in in simulations. simulations.

The initial and boundary conditions (BC) are also presented in Figure 2. In the simulation, the The initial and boundary conditions (BC) are also presented in Figure 2. In the simulation, initial condition was the initial pressure head, the upper boundary was the atmospheric condition, the initial condition was the initial pressure head, the upper boundary was the atmospheric condition, and the lower boundary was the free drainage condition. Boundaries at both vertical sides were ‘‘No and the lower boundary was the free drainage condition. Boundaries at both vertical sides were Flux’’ condition. The moistube with a radius of 8 mm was represented as a line source and located “No Flux” condition. The moistube with a radius of 8 mm was represented as a line source and on the left vertical boundary of the transport domain. The moistube bottom was assigned a ‘‘Constant located on the left vertical boundary of the transport domain. The moistube bottom was assigned a “Constant flow” condition, which corresponds with the calculated moistube specific discharge shown in Equation (5).

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2.4. Statistical Analysis The HYDRUS-2D simulations performance was assessed by using the mean absolute error (MAE), the root mean square error (RMSE), the percent bias (PBIAS), and Nash-Sutcliffe efficiency (NSE) [45]. These parameters are defined by the equations below. n ∑ Yiobs − Yisim

MAE =

i =1

s RMSE = n

∑

PBI AS =

i =1

(10)

n 2 1 n Yiobs − Yisim n i∑ =1

(11)

Yiobs − Yisim ∗ 100 n

∑

i =1

(12) Yiobs

2 n ∑ Yiobs − Yisim

NSE = 1 −

i =1 n

∑ Yiobs − Y mean

(13)

2

i =1

where Yiobs is the ith observed data, Yisim is the ith simulated data, Y mean is the mean of the observed data for the constituent being evaluated, and n is the total number of observations. The MAE can potentially identify the presence of bias. The RMSE provides an overall measure of the degree to which the data differ from the model predictions. MAE and RMSE values of 0 indicate a perfect fit. However, the PBIAS is the deviation of data being evaluated and expressed as a percentage. If PBIAS is within ± 10, the PBIAS values are considered to be within a very accurate range. NSE ranges between −∞ and 1.0. If NSE = 1, it will be the optimal value. 3. Results and Discussion 3.1. Comprehensive Permeability Coefficient When the moistube was placed vertically in the air, the moistube pressure gradually increases from the top (point A) to the bottom (point B) and its center (point C) is the median point, which represents the average pressure head. Therefore, it is advisable to calculate the pressure head at the C point. According to the experimental data, the moistube flow characteristic curve under a different pressure head was obtained, as shown in Figure 3. Water 2018, 10, x FOR PEER REVIEW

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Cumulative seepage / L

0.3

0.2

H=241cm H=204cm H=177cm H=75cm H=55cm H=0cm

0.1

0 20

40

60

Duration / h

Figure Cumulativeseepage seepage of the air.air. Figure 3. 3. Cumulative ofmoistube moistubeinin the

As expected, the cumulative seepage of the moistube is in a good linear relationship with the time, and increases with the pressure head. Based on the linear regression calculation of cumulative seepage and time, the influence of the average pressure head on specific discharge was given in Figure 4. Using Equation (4) to fit, we obtained K = 0.00015 mL/(cm2∙min). The coefficient of determination R2 = 0.966 indicates that the center position of moistube can be used as the calculation point of the average specific discharge.

0 20

40

60

Duration / h

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Figure 3. Cumulative seepage of moistube in the air.

As expected, the cumulative seepage of the moistube is in a good linear relationship with the time, As expected, the cumulative seepage of the moistube is in a good linear relationship with the and increases with the pressure head. Based on the linear regression calculation of cumulative seepage time, and increases with the pressure head. Based on the linear regression calculation of cumulative and time, the influence of the average pressure head on specific discharge was given in Figure 4. seepage and time, the influence of the average pressure head on specific discharge was given in Using Equation (4) to fit, we obtained K = 0.00015 mL/(cm2 ·min). The coefficient of determination Figure 4. Using Equation (4) to fit, we obtained K = 0.00015 mL/(cm2∙min). The coefficient of R2 = 0.966 indicates that the center position of moistube can be used as the calculation point of the determination R2 = 0.966 indicates that the center position of moistube can be used as the calculation average specific discharge. point of the average specific discharge.

Specific Discharge / (mL·cm-1·min-1)

0.05 qs=0.00015ΔH R2=0.966

0.025

0 100 200 Pressure head / cm

300

Figure 4. 4. The The relationship relationship between between specific specificdischarge dischargeand andpressure pressurehead. head. Figure

3.2. Specific Specific Discharge DischargeDetermination Determination 3.2. Figure 5 5 shows of the moistube in aeolian sand sand and silt loam. Figure showsthe theseepage seepagecharacteristics characteristics of the moistube in aeolian and silt Linear loam. q ) with two soils and regression analysis was used to determine the average specific discharge ( s (q Linear regression analysis was used to determine the average specific discharge ) with two soils anda s q HM , M and  , from Figure 5 resulted in apressure pressurehead headofof1.2 1.2m. m.The Therelationship relationshipbetween between qss and H, and γ, from Figure 5 resulted in the following equation. the following equation. qs = K ( H + M − 1.3γN + 58.2) (14) qs  K  H  M  1.3 N  58.2  (14) ofPEER fitting parameters a and b were −1.3 and 58.2, respectively. Water The 2018,values 10, x FOR REVIEW 8 of 20 The values of fitting parameters a and b were −1.3 and 58.2, respectively.

Cumulative Infiltration / L

6

Aeolian sand, H=1.2 m Silt loam, H=1.2 m Aeolian sand, H=1.8 m Silt loam, H=1.8 m

4

2

0 0

24

48

72

Duration / h

of moistube moistube in in the the soil. soil. Figure 5. Cumulative infiltration of

3.3. Simulation Simulation Verification Verification 3.3. Figure 66 shows shows the the measured measured and and simulated simulated cumulative cumulative infiltration infiltration for for two two soils soils with with aa 1.8 1.8 m m Figure pressure head. The specific discharge at different nodes is calculated by using Equation (14). The pressure head. The specific discharge at different nodes is calculated by using Equation (14). measured cumulative infiltration is represented by dots while simulation results obtained through HYDRUS-2 D are shown as lines. Value of MAE, RMSE, PBIAS, and NSE are 0.04 L, 0.03 L, 0.05, and 0.998, respectively. It indicates that the prediction model (see Equation (14)) is suitable for describing cumulative infiltrations of vertical moistube-irrigation.

0 0

24

48

72

Duration / h

Figure 5. Cumulative infiltration of moistube in the soil.

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Figure 6 shows the measured and simulated cumulative infiltration for two soils with a 1.8 m pressure head. The specific discharge at different nodes is calculated by using Equation (14). The The measured cumulative infiltration is represented by dots while simulation results obtained through measured cumulative infiltration is represented by dots while simulation results obtained through HYDRUS-2D are shown as lines. Value of MAE, RMSE, PBIAS, and NSE are 0.04 L, 0.03 L, 0.05, HYDRUS-2 D are shown as lines. Value of MAE, RMSE, PBIAS, and NSE are 0.04 L, 0.03 L, 0.05, and and 0.998, respectively.It indicates It indicates that the prediction model (see(14)) Equation (14)) suitable for 0.998, respectively. that the prediction model (see Equation is suitable for is describing describing cumulative infiltrations of vertical moistube-irrigation. cumulative infiltrations of vertical moistube-irrigation.

Cumulative Infiltration / L

6

Measured silt loam Simulated silt loam Measured aeolian sand Simulated aeolian sand

4

2

0 24

48

72

Duration / h

Figure 6. Measured and predictedcumulative cumulative infiltration two soils. Figure 6. Measured and predicted infiltrationforfor two soils.

Three eigenvalues of wetting front distance, i.e., vertical upward at point A, vertical downward

Three eigenvalues of wetting frontatdistance, i.e., vertical upward at point A, vertical at point B, and horizontal direction point C, were respectively selected. The wetting frontdownward distance at point is B,quantitatively and horizontal direction at point C,with were selected. wetting front7.distance analyzed and compared therespectively measured value, which The is shown in Figure MAE, is quantitatively analyzed andreach compared the −4.79, measured value, which is shown in Figure 7. MAE, RMSE, PBIAS, and NSE 0.79 cm,with 1.11 cm, and 0.972, respectively. Therefore, HYDRUS-2 can accurately simulate the cm, dynamic changes of the pattern during vertical moistubeRMSE,DPBIAS, and NSE reach 0.79 1.11 cm, −4.79, andwetting 0.972, respectively. Therefore, HYDRUS-2D irrigation.simulate the dynamic changes of the wetting pattern during vertical moistube-irrigation. can accurately Water 2018, 10, x FOR PEER REVIEW

20

Upward(measured) Horizontal(measured) Downward(measured) Upward(simulited) Downward(simulited) Horizontal(simulited)

Wetting pattern distance/cm

Wetting pattern distance/cm

30

9 of 20

15

Upward(measured) Horizontal(measured) Downward(measured) Upward(simulited) Downward(simulited) Horizontal(simulited)

10

Aeolian sand

Silt loam

0

0 35 Duration / h

70

35 Duration / h

70

Figure 7. Comparison between simulatedand and measured measured values the wetting front distance. Figure 7. Comparison between simulated valuesofof the wetting front distance.

Figure 8 shows the measured and simulated water content distributions after irrigation (70 h). It

Figure 8 shows the measured and simulated water content distributions afterisirrigation (70 h). is clear from the contour plots in Figure 8 that the predicted water content distribution in excellent 3 3 It is clear fromwith the contour plotsdata. in Figure 8 thatPBIAS, the predicted agreement experimental MAE, RMSE, and NSE water values content are 0.01 distribution cm /cm , 0.03 is in 3, −4.75, and 0.955, respectively. Therefore, HYDRUS-2 D can be used to simulate water cm3/cm excellent agreement with experimental data. MAE, RMSE, PBIAS, and NSE values are 0.01 cm3 /cm3 , 3 /cmdistribution 3 , −4.75, and content of soil under vertical moistube-irrigation. 0.03 cm 0.955, respectively. Therefore, HYDRUS-2D can be used to simulate water Radial distance (cm) Radial distance (cm) content distribution of soil10under vertical moistube-irrigation. 0 0 20 30 10 20 30 10

0. 0 6 0.096 0.079

4 0.1

20

0.163 0.115 0.098

0.316

30

0.170 0.231

0.112

0.329

0.239

0.180 0.1

depth (cm)

0.32

0.10

depth (cm)

0.287

0.28

0.06

0.16

0.166 0.132 0.103 0.092

A

0.061 6 0.1

0.238 0.194 0.2 4

0.144 0.090 0.067

0.161 0.127 0.084 0.064

40 C

0.088 0.1

0. 2

30

0.133

10

0.122 0.086 0 0.1

20 A

Duration / h

Duration / h

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Radial distance (cm)

Radial distance (cm) 0

10

10

20

0

30

10

20

30

0. 0 6 0.096 0.079

A

0.287

Soil depth (cm)

C

0.32

0.175 0.142 0.120 0.108

50 B

B

0.251

0.16

0.142 0.133 0.122 0.079 0.062

60

0.132 0.125 0.084 0.079 4 0 .1 0.130 0.118 0.09 0.067

70

0 .1 0

80

0.180

0.332

0.245

0.179

0.330

0.242

0.319

0.227

0.287

0.208

0.199

0.115 0.109

0.187

0.16

0.114 0.101

0.162 0.155 0.136 0.095 0.075

70

0.239

0.2

40

0.14

0.180 0.145

60

0.329

0.134

0.2 8

Soil depth (cm)

30

0.1

0.164 0.133 0.108 0.100

0.112

0.32

0.10

0.168 0.131 0.106 0.093

0.231

0.28

0.06

0.16

0.166 0.132 0.103 0.092

50

0.170

0.316

0.161 0.127 0.084 0.064

40 C

6 0.1

0. 2

20

0.061

0.24

4 0.1

0 0.1

0.238 0.194 0.2 4

0.144 0.090 0.067 0.163 0.115 0.098

30

0.088 0.1

0.133

10

0.122 0.086

20 A

4 0 .2 0.231

0.181

. 16 0.2 0 0.151 0.133 1 . 0

6 0 .0

80

90

(a) Aeolian sand

(b) Silt loam

Figure 8. Comparison between simulated and measured values of water content distributions.

Figure 8. Comparison between simulated and measured values of water content distributions.

Overall, we judge the accuracy of the HYDRUS-2D simulations to be very satisfactory and clearly accurate enough to justify of using a tool for investigating influence and of soil Overall, we judge the accuracy theHYDRUS-2D HYDRUS-2Dassimulations to be very the satisfactory clearly accurate enough to justify using HYDRUS-2D as a tool for investigating the influence of soil texture, initial water content, pressure head, line source length, and buried depth on the wetting pattern.

3.4. Different Factors Affecting Wetting Patterns of Moistube-Irrigation To investigate the influence of soil texture, initial water content, pressure head, moistube length, and buried depth on wetting pattern characteristics, we have chosen eleven scenarios for simulation, which are listed in Table 3. Table 3. Simulation scenarios for vertical moistube-irrigation. Case

Soil Texture

Initial Water Content *

Pressure Head **

Moistube Length

Buried Depth***

a b c d e f g h i j k

Silt loam Loam Sandy loam Loam Loam Loam Loam Loam Loam Loam Loam

50% 50% 50% 40% 60% 50% 50% 50% 50% 50% 50%

1.5 1.5 1.5 1.5 1.5 1.0 2.0 1.5 1.5 1.5 1.5

20 20 20 20 20 20 20 10 30 20 20

40 40 40 40 40 40 40 40 40 30 50

* Initial water content is the percentage of field capacity; ** Pressure head takes the water inlet; *** Buried depth represents distance between the bottom of moistube and soil surface.

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Simulations were carried out for soils representing three textural classes: silt loam, loam, and sandy loam. Soil hydraulic parameters for the three textural classes were taken from the soil catalog provided by the HYDRUS software [46] and are given in Table 4. The field capacity of three soils (silt loam, loam, and sandy loam) are 0.238 cm3 /cm3 , 0.290 cm3 /cm3 , and 0.321 cm3 /cm3 , respectively. [47]. Table 4. Physical properties of soils considered in HYDRUS simulations. Soil Texture

Residual Soil Water Content (cm3 ·cm−3 )

Saturated Soil Water Content (cm3 ·cm−3 )

Parameter α in the Soil Water Retention Function (cm−1 )

Parameter n in the Soil Water Retention Function (-)

Saturated Hydraulic Conductivity (cm·min−1 )

Silt loam Loam Sandy loam

0.067 0.078 0.065

0.450 0.430 0.410

0.020 0.036 0.075

1.41 1.56 1.89

0.0075 0.0173 0.0737

3.4.1. Influence of Soil Texture Figure 9 shows the dynamic changes of the wetting pattern in different soil textures. Before the wetting front reaches the surface, the shape of the wetting pattern with different observation times is approximately “ellipsoidal” around the moistube. The size of the wetting pattern in each direction increases with the irrigation time. In the initial period of irrigation, the wetting front moves faster in all directions with the horizontal moving fastest. As time goes on, the wetting front migration rate is slowed down. This is because the gradient of matric potential between the moistube and the wetting front is relatively large at the initial stage of infiltration, while the difference in soil water content (matric potential) at each node of the moistube is small. The horizontal gradient of the matric potential is greater than the gradient of the vertical matric potential. Water 2018, 10, x FOR PEER REVIEW

Radial distance (cm) 10 20 30

0


0

10

10

20

20

20

30 8d 6d

40 2d

4d

Soil depth (cm)

10

Soil depth (cm)

Soil depth (cm)

0

11 of 20

30 40 2d 4d

6d

8d

30 40

50

50

50

60

60

60

70

70

Case a


2d

4d 6d

8d

70

Case b

Case c

Figure 9. Dynamic changes of wetting pattern for different soil textures.

Figure 9. Dynamic changes of wetting pattern for different soil textures.

There are significant differences in the wetting front distance under different soil textures. For a given the maximum horizontal vertical downward wetting distances are soil small for fine-For a There time, are significant differences in and the wetting front distance under different textures. soil,maximum and largerhorizontal for coarse-texture soil. With the increase of soil clay content, the for maximum giventexture time, the and vertical downward wetting distances are small fine-texture vertical upward wetting distances tend to increase at first and then decrease, and the difference soil, and larger for coarse-texture soil. With the increase of soil clay content, the maximum vertical between the maximum vertical upward and maximum vertical downward wetting distances upward wetting distances tend to increase at first and then decrease, and the difference between the decreases. The finer the soil texture, the smaller the intergranular pores, the weaker the permeability, maximum vertical upward and maximum vertical downward wetting distances decreases. The finer and the stronger the capillary action. This results in the slower wetting front migration were more the soil texture, intergranular pores, thethe weaker thethe permeability, stronger uniform in the the smaller vertical the direction. On the contrary, coarser soil texture, and the the greater the the intergranular pore, the larger the penetration, and the stronger the gravitational force. Therefore, the vertical downward wetted depth is greater than vertical upward wetted height. The influence of three soil texture classes on water content distribution after irrigation cut-off (8 days) is shown in Figure 10. The contour lines of soil water content are all approximately “ellipsoids” around the moistube and the soil water content gradually decreases from the moistube to the surrounding area. Since the moistube specific discharge is less than the soil infiltration rate, the soil

Water 2018, 10, 601

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capillary action. This results in the slower wetting front migration were more uniform in the vertical direction. On the contrary, the coarser the soil texture, the greater the intergranular pore, the larger the penetration, and the stronger the gravitational force. Therefore, the vertical downward wetted depth is greater than vertical upward wetted height. The influence of three soil texture classes on water content distribution after irrigation cut-off (8 days) is shown in Figure 10. The contour lines of soil water content are all approximately “ellipsoids” around the moistube and the soil water content gradually decreases from the moistube to the surrounding area. Since the moistube specific discharge is less than the soil infiltration rate, the soil water content near the moistube is not saturated. Water 2018, 10, x FOR PEER REVIEW

2 0 .2

50

2 0. 7 0.1

4

70

70

Case a

0.14

Soil depth (cm)

40

0 .1 70

4

30

60

60

60

16 0.

20

0.1

0. 17

0.17

5

0.22

8

2 0.

9

50

0. 2

40

0.1

0.10.21 8

0 0.24 .27

0.3 3

0.16

30


0.2

20

0

10

0.19

50

0 0.3 .27 0 4 0.2

0.1 9 22 0. .25 0 8 0.2

30 40


10

0 0.2 .24 7

0.18 0.21

Soil depth(cm)

0.210.18

0.30 0.33

20

0

16 0.

10


Soil depth (cm)

0

12 of 20

Case b

Case c

Figure 10. Volumetric water content distribution for different soil textures after irrigation cut-off.

Figure 10. Volumetric water content distribution for different soil textures after irrigation cut-off.

The soil texture has a significant effect on the water content distribution. Compared with the coarse-texture soil,has the awater content effect near the in the fine-texture soil is slightly higher,with the the The soil texture significant onmoistube the water content distribution. Compared contour linesoil, of water contentcontent is denser,near and the the volume of the pattern is smaller. The reason coarse-texture the water moistube in wetting the fine-texture soil is slightly higher, for this is that the wetting front migration rate of heavy clay soil is slow, which leads to small wetted the contour line of water content is denser, and the volume of the wetting pattern is smaller. The reason soil volume. In addition, relative to the coarse grained soil, the surface of fine grained soil has strong for this is that the wetting front migration rate of heavy clay soil is slow, which leads to small wetted adsorption and good water retention, which results in a higher soil water content in the same profile. soil volume. In addition, relative to the coarse grained soil, the surface of fine grained soil has strong adsorption and good water retention, which results in a higher soil water content in the same profile. 3.4.2. Influence of Soil Initial Water Content Figure 11 the dynamic changes of the wetting pattern in different soil initial water content. 3.4.2. Influence of shows Soil Initial Water Content As can be seen in Figure 11, the wetting front distance is positively correlated with the initial water

Figure shows the dynamic changes the wetting patternThis in different water content. content,11 and increases with the rise in theof initial water content. appears tosoil be initial in contradiction As can bethe seen Figure 11, the front distance is positively correlated with the with factinthat the higher thewetting initial soil water content is, the larger the matric potential, theinitial smallerwater the soil suction, andthe therise slower the wetting front migration thebe higher the soil content, andwater increases with in the initial water content. rate. ThisHowever, appears to in contradiction initial water content, the greater the soil water conductivity, which is conducive to the movement of with the fact that the higher the initial soil water content is, the larger the matric potential, the smaller water in the soil. In addition, due to the high initial water content of the soil, the amount of water the soil water suction, and the slower the wetting front migration rate. However, the higher the soil needs to be filled the soilthe pores reduced, which accelerates fronttomigration. initialthat water content, the in greater soiliswater conductivity, whichthe is wetting conducive the movement of water in the soil. In addition, due to the high initial water content of the soil, the amount of water that needs to be filled in the soil pores is reduced, which accelerates the wetting front migration.

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13 of 20

Water 2018, 10,Radial x FORdistance PEER REVIEW (cm)

0

0 0

Radial distance (cm) 10 20 30 Radial distance (cm) 10 20 30

Radial distance (cm)13 of 20 10 20 30 Radial distance (cm) 10 20 30

0 0

10

10

10 20

10 20

10 20

20 30 30 40

2d 4d 6d

40 50

2d 4d 6d

8d 8d

Soil depth Soil depth (cm) (cm)

10



0

10 20 30 Radial distance (cm) 10 20 30

20 30 30 40 2d 4d

40 50

6d

2d 4d

6d

8d 8d

20 30 30 40 40 50

50 60

50 60

50 60

60 70

60 70

60 70

2d

4d

2d

4d

6d 6d

8d 8d

Case b Case e 70 70 Figure 11.dDynamic changes of the wetting pattern different soil initial water contents. Case b for Case econtents. Figure 11. Dynamic changes of the wettingCase pattern for different soil initial water 70

Case d

Figure 11. of Dynamic changes of the wetting pattern different soil initial water contents. The influence three soil initial water contents onfor water content distributions after irrigation The influence ofshown three soil initial cut-off (8 days) is in Figure 12.water contents on water content distributions after irrigation The influence of three soil initial water contents on water content distributions after irrigation cut-off (8 days) is shown in Figure 12. cut-off (8 days) is distance shown(cm) in Figure 12. Radial distance (cm) Radial Radial distance (cm)

16 0.

9 0 .1

50 60

9 0.1

60 70

9 0.1

9 0 .1

0.25 0.25

0.2 2

25 0.

0.2 2

8 0.2

8 0.2

Soil (cm) depth (cm) Soil depth

0.10. 0 9 22 .22

9 0.1


0 0 0.2 .280.2 .28 5 5


0. 0.10.16 0.100..16 0. 0 22 22 319 .19 3

2 0 .2

16 0.

25 0.

9 9 0.1 0.1

60 70

2 0.02.25

40 50

2 0 .2 2 0 .2

60 70

50 60

25

30 40

0.2 2 0.2 50 .22 0.2 5

8 0.2

50 60

40 50

0.

20 30


8 0.2

40 50

2 0. 2 9 1 0. 2 0. 2 9 0.1

30 40

10 20

0.16 0.16

30 40

20 30

0.1 9

0 10

9 0.19 0.1 16 0.

20 30

10 20

0

16 0.

0.13 0.13 6 6 0.1 0.1 1 9 0 .1 9 5 5 0 .2 0 .2

10 20 0.2 2

22 22 0. .250. .25 0 8 80 0.2 0.2

0.

0.02.1 0.13 26

8

0 10

10 20 30 Radial distance (cm) 10 20 30 0.1 9

0. 2

0

8

0 10

10 20 30 Radial distance (cm) 10 20 30 0.160.13

0. 2

0

70 Case d Case b Case e 70 70 Figure 12. Case Volumetric water content distribution Case for different soil initial water contentsCase aftereirrigation d b

cut-off. Figure 12. Volumetric water content distribution for different soil initial water contents after irrigation

Figure 12. Volumetric water content distribution for different soil initial water contents after cut-off. As the initial water content increases, the volume of the wetting pattern increases and the irrigation cut-off. gradient of water content decreases. The volume of the wetting pattern with 50% and 60% field As the initial water content increases, the volume of the wetting pattern increases and the capacity was 1.6 times and 2.1 times that of 40%, respectively. The reason is that the wetted soil gradient of water decreases. The with 50% and As the initial watercontent content increases, thevolume volumeofofthe thewetting wettingpattern pattern increases and60% thefield gradient volume is mainly affected by the wetting front migration rate. This means the higher the soil water capacity was 1.6 times and 2.1 times that of 40%, respectively. The reason is that the wetted soil of water content decreases. The volume of the wetting withthe 50% and 60% field capacity content, the faster the wetting front migration rate andpattern the greater wetting range, for the same was volume is mainly affected by the wetting front migration rate. This means the higher the soil water 1.6 times and 2.1 times that of 40%, respectively. The reason is that the wetted soil volume is mainly irrigation time. content, the faster the wetting front migration rate and the greater the wetting range, for the same affected by the wetting front migration rate. This means the higher the soil water content, the faster irrigation time.

the wetting front migration rate and the greater the wetting range, for the same irrigation time.

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14 of 20

Water 2018, 10, x FOR REVIEW 3.4.3. Influence of PEER Pressure Head

14 of 20

3.4.3. Influence of Pressure Head

Figure 13 shows the dynamic changes of the wetting pattern in a different pressure head. It can be shows the dynamic changes of the wetting patterncorrelated in a different pressure head. Ithead can and seen from Figure1313 the wetting distance is positively with the pressure 3.4.3.Figure Influence ofthat Pressure Head front be seen from Figure 13 that the wetting front distance is positively correlated with the pressure head increases Figure with pressure head. As the changes pressureofhead increases, the moistube specific dischargeIt becomes 13 with shows the dynamic the wetting pattern in the a different pressure can increases pressure head. As the pressure head increases, moistube specifichead. largerand and the amount of water entering the soil per unit time increases, which leads to a discharge faster wetting be seen from Figure 13 that the wetting front distance is positively correlated with the pressure head becomes larger and the amount of water entering the soil per unit time increases, which leads to a front and migration rate. increases with pressure head. As the pressure head increases, the moistube specific discharge faster wetting front migration rate. becomes larger and the amount of water entering the soil per unit time increases, which leads to a faster wetting front migration Radial distance (cm) rate. Radial distance (cm) Radial distance (cm) 0

0 0


0 0

10

10

10 20

10 20

10 20

20 30 30 40 40 50

2d 2d

4d 4d

6d 6d

8d 8d

20 30 30 40 2d 4d

40 50

2d 4d

6d 6d

8d


10



0


8d

20 30 30 40 40 50

50 60

50 60

50 60

60 70

60 70

60 70

70


2d

8d 4d 6d

2d

8d 4d 6d

Case f

Case b Case g 70 70 Figure Dynamic changes of wetting different pressure heads. g Case f13. 13. Case pattern bpatternfor Figure Dynamic changes of wetting for different pressureCase heads.

Figure 13. Dynamic changes wetting pattern for distributions different pressure heads. The influence of three pressure headsofon water content after irrigation cut-off (8 days) is shown in Figure 14. The influence of three pressure heads on water content distributions after irrigation cut-off (8 days) The influence of three pressure heads on water content distributions after irrigation cut-off (8 is shown in Figure 14. days) is shown indistance Figure(cm) 14. Radial distance (cm) Radial distance (cm) Radial

60 70

50 60 60 70

5 0.2

6 0.1

0.1 6

5 0.2

0.1 6

0 0 0.2 .310.2 .31 8 8

40 50

0. 0. 0 0.1 220.1 22 0.25 .25 9 9

16 0.


0.10. 0 922 .22

9

16 0.

0.1

8



0. 2 8 0. 2

2 0.2.25 0 2 0 .2

0.16 0.196 0.1 0.19

50 60

0.

30 40

2 0.2

40 50

25

2 0.2

30 40

20 30

8 0.2

20 30

0.1 9

10 20 30 Radial distance (cm) 10 20 30 0 0.1 9 0 . 2 10 2 0.2 0 5 .1 9 10 0.22 20 0 .2 5 0

8 0.2

10 20

0.16 0.16

60 70

2 0.2

10

0.19 0.19 16 0.

50 60

2 0.2

0

10 20 30 Radial distance (cm) 10 20 30 0.1 9

22 22 0. .250. .25 0 8 80 0.2 0.2

40 50

0.16 0.16 0.19 0.19

30 40

5 0.2

20 30

5 0.2

10 20

0

16 0.

10

0 0 0.1 .109.1 .19 0.22 0.22 6 6

0

10 20 30 Radial distance (cm) 20 30 010 .16 0.19 0.2 0.16 0.192 0.2 2

0.2 0.280.2 0.28 5 5

0

6 0.1 Case g

Case f Case b 70 70 70 Figure 14.Case Volumetric water content distribution forbdifferent pressure heads after irrigation f Case Case g cut-off. Figure 14. Volumetric water content distribution for different pressure heads after irrigation cut-off.

Figure 14. Volumetric water content distribution for different pressure heads after irrigation cut-off.

Water 2018, 10, 601 x FOR PEER REVIEW

14 of 20 19 15

From Figure 14, we can see that the pressure head has a larger effect on water content From Figure 14,pressure we can see thatincreases, the pressure hassoil a larger effect onthe water content distribution. distribution. As the head the head wetted volume and water content near the As the pressure head increases, the wetted soil volume and the water content near the moistube moistube increases. The soil water content near the moistube at the three heads (1.0 m, 1.5 m, and 2.0 increases. The soil water content near the moistube at the three heads (1.0 m, 1.5 m, and 2.0 m) 3 3 3 3 3 3 m) were 0.34 cm /cm , 0.36 cm /cm , and 0.38 cm /cm , respectively. The volume of the wetting pattern 3 /cm3 , 0.36 cm3 /cm3 , and 0.38 cm3 /cm3 , respectively. The volume of the wetting were 0.34 cm of 1.5 m and 2.0 m increased by 50% and 90%, respectively, when compared with 1.0 m. Because the pattern ofhead 1.5 m and 2.0 m 50% and 90%, respectively, when compared with 1.0soil m. pressure increases, theincreased moistubebyspecific discharge increases, which is limited by the Because the pressure head increases, the moistube specificresults discharge increases, is limited the permeability. Soil water does not spread rapidly, which in the increasewhich of water contentbynear soil permeability. Soil water does not spread rapidly, which results in the increase of water content the moistube. At the same time, as the wetting front migration rate accelerates, the wetted soil volume near the moistube. At the same time, as the wetting front migration rate accelerates, the wetted soil increases. volume increases. 3.4.4. Influence of Moistube Length 3.4.4. Influence of Moistube Length Figure 15 shows the dynamic changes of the wetting pattern in different moistube lengths. From Figure 15 shows the dynamic changes of the wetting pattern in different moistube lengths. Figure 15, we can see that the wetting front migration distance has a positive correlation with From Figure 15, we can see that the wetting front migration distance has a positive correlation with moistube length and grows with the increase of the length. The longer the moistube, the larger the moistube length and grows with the increase of the length. The longer the moistube, the larger the seepage area, the more water enters the soil within a unit of time, and the faster the wetting front seepage area, the more water enters the soil within a unit of time, and the faster the wetting front moves. At the same buried depth (40 cm), the water of the long moistube (30 cm) reaches the soil moves. At the same buried depth (40 cm), the water of the long moistube (30 cm) reaches the soil surface first. After the wetting front reaches the surface, the soil surface wetted radius rapidly surface first. After the wetting front reaches the surface, the soil surface wetted radius rapidly increases increases and the shape of the wetting pattern in the upper part of the moistube is similar to a and the shape of the wetting pattern in the upper part of the moistube is similar to a “trapezoid” shape. “trapezoid” shape. Radial distance (cm) 10 20 30

0


0

10

10

20

20

20

30 8d

40 50

2d

4d

60 70

Soil depth (cm)

10

Soil depth (cm)

Soil depth (cm)

0

30 40

6d

2d 4d

30 40

50

50

60

60

6d 8d 2d 4d

70

70

Case h

6d

8d


Case b

Case i

Figure 15. Dynamic changes of the wetting pattern for different moistube lengths. Figure 15. Dynamic changes of the wetting pattern for different moistube lengths.

The influence of three moistube lengths on water content distributions after irrigation cut-off (8 influence of three onFigure water 16, content distributions cut-off days)The is shown in Figure 16. moistube As can be lengths seen from the moistube lengthafter hadirrigation a greater impact (8 days) is shown in Figure 16. As can be seen from Figure 16, the moistube length had a greater impact on water content distribution. The longer the moistube, the more the irrigation amount, the faster the on waterfront content distribution. Thegreater longer the the irrigation amount, the faster the wetting migration, and the the moistube, volume ofthe themore wetting pattern. The irrigation amount wetting front migration, and of the wetting pattern. The amount with with a moistube length of 20the cm greater and 30 the cm volume is 2.4 times and 3.6 times that of 10irrigation cm and the volume of a moistube length of 20 cm and 30 cm is 2.4 times and 3.6 times that of 10 cm and the volume of the wetting pattern is 1.8 times and 2.3 times respectively. This shows that increasing the lengththe of wetting pattern is 1.8 times and 2.3 times respectively. This shows that increasing the length of the the moistube can increase the average water content of the wetted body. moistube can increase the average water content of the wetted body.

Water 2018, 10, 601

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16 of 20

50

2 0 .2

60

70

40 40 50

16 0. 16 0.

50 60

60 70

Case h

30 30

5 0.2 5 2 00..22 9 02.1 0.2 9 0.1

60 70

Case b

70

30

0.16 0.16

40

25 0. 225 0.02.

20 20

20

0.25 0.25 0.22 0.22 0 .1 9 0 .1 9

Soil Soil depthdepth (cm)(cm)

0.1 0. 0 6 16 .19 0.19

0. 0.02. 8 0.28 25 25


40

10

0. 10 25 0. 25

6 0.1 0.16 0.19 0.19

30

50

60 70 70

30

0 10

0.16 0.16

60

0.19

20

0.19 0.19

50

2 0 .2 2 2 00.1. 9

0.16 0.16

50

2 0 .2 0 .2 2

40

20

0.1 9

0

30

0.28 0.28

10

0.01 .619 0.1 20 0 .25 9 30 0 .25 30

20

40

10

0.1 9

22 2 0. .02.52 25 0 08. 8 0.2 0.2

10

0.1 6

20

16 6 0. 0.1

10

0

10

0.2 00.3. 1 0.31 8 28

0

30

0.1 0. 0. 0 9 19 22 .22

0

20

Radial distance (cm) 20(cm) 30 Radial10distance

2 2 0.2 0.2

10

16 of 20


0. 2 0. 8 28

0




6 0.1 6 0.1

Case i

h Case Case i Figure 16.Case Volumetric water content distribution forb different moistube lengths after irrigation cutoff. Figure 16. Volumetric water content distribution for different moistube lengths after irrigation cutoff.

Figure 16. Volumetric water content distribution for different moistube lengths after irrigation cut-off.

3.4.5. 3.4.5. Influence of Moistube Buried Depth Influence of Moistube Buried Depth

3.4.5.Figure Influence of Moistube Buried Depth of 17 shows dynamic changes ofthe the wetting inin different moistube buried depths. Figure 17 shows thethe dynamic changes wettingpattern pattern different moistube buried depths. Figure 17, we see that themoistube moistube buried affects the shape andand position of the Figure shows the dynamic changes of theburied wettingdepth pattern in different moistube buried depths. FromFrom Figure 17,17we cancan see that the depth affects the shape position of the wetting pattern. When the depth is shallow, soil water easily reaches the soil surface and the wetting From Figure 17, we can see that the moistube buried depth affects the shape and position of the wetting pattern. When the depth is shallow, soil water easily reaches the soil surface and the wetting radius ofpattern. the soilWhen surface which boosts surface water the depth wetting theincreases depthrapidly, israpidly, shallow, soil water easily reaches theevaporation. soil surface When and the wetting radius of the soil surface increases which boosts surface water evaporation. When the depth is is greater, thesoil soilsurface water increases tends to stay away fromboosts the root zone,water which causes deep seepage and a radius of the rapidly, which surface evaporation. When the depth greater, the soil water tends to stay away from the root zone, which causes deep seepage and a topsoil topsoil water deficit. Therefore, depththe should be adapted the soil root is greater, the soil water tends to the stayburied away from root zone, which to causes deepconditions, seepage and a waterdistribution, deficit. Therefore, the buried depth should be adapted to the soil conditions, root distribution, farming requirements. topsoil waterand deficit. Therefore, the buried depth should be adapted to the soil conditions, root and farming requirements. distribution, and farming requirements. 0

0 0

Radial distance (cm) 20(cm) 30 0 Radial10distance 10 10 20 30 0 10

Radial distance (cm) 20(cm) 30 Radial10distance 10

20

30

10

20

10

10

20

20

20

20 30 30 40

2d

4d

2d

4d

40

6d 6d

8d 8d

20 30 30 40 40

2d 4d

50

50

2d 4d

50

50

60

60

60 70

60 70

70

Case j

6d 6d

8d 8d


10



0

Radial distance (cm) 20(cm) 30 Radial10distance 10 20 30

30 30 40 40 50 50

2d

60

2d

8d 4d 6d 8d 4d 6d

60 70 70 80

Case b

Case k 70 80 Case j Case b Case k Figure 17. Dynamic changes of the wetting pattern for different moistube buried depths. Figure 17. Dynamic changes of the wetting pattern for different moistube buried depths.

Figure 17. Dynamic changes of the wetting pattern for different moistube buried depths.

The influence of three moistube buried depths on water content distributions after irrigation cut-off (8 days) is shown in Figure 18.


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Water 2018, 601 16 of 19 The 10, influence of three moistube buried depths on water content distributions after irrigation cut-

off (8 days) is shown in Figure 18.

2

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0 60

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Case k

Figure 18. Volumetric water content distribution for different moistube buried depths after irrigation Figure 18. Volumetric water content distribution for different moistube buried depths after cut-off. irrigation cut-off.

It can be seen from Figure 18 that the difference in the volume of the wetting pattern is small, It can be seen from Figure 18 that the difference in the volume of the wetting pattern is small, but the difference of location is great. When the wetting front with a buried depth of 30 cm reaches but the difference of location is great. When the wetting front with a buried depth of 30 cm reaches the the surface, the water content of the soil surface increases. As the depth moves down, the contour of surface, the water content of the soil surface increases. As the depth moves down, the contour of the the soil water content moves downwards synchronously, and the wetting front with a buried depth soil content movesthe downwards of 50water cm does not reach surface. synchronously, and the wetting front with a buried depth of 50 cm does not reach the surface. 4. Conclusions 4. Conclusions Based on Darcy’s law, the linear relationship between the specific discharge and the pressure Based on Darcy’s law, the linear relationship between the specific discharge and the pressure head, the bulk density, and the water content was determined during the laboratory experiments. head, the bulk density, and the water content was determined during the laboratory experiments. We evaluated the accuracy of HYDRUS-2D simulations of water infiltration and distribution under We evaluated the accuracy of HYDRUS-2D simulations of water infiltration and distribution under moistube-irrigation of aeolian sand and silt loam soil. The cumulative infiltrations, wetting pattern moistube-irrigation of aeolian sand and silt loam soil. The cumulative infiltrations, wetting pattern distances, and water content distributions predicted with HYDRUS-2D were found to be in very good distances, and water content distributions predicted with HYDRUS-2D were found to be in very agreement with experimental data. The results provide support for using HYDRUS-2D as a tool for good agreement with experimental data. The results provide support for using HYDRUS-2D as a investigating and designing moistube-irrigation management practices. We simulated the influence tool for investigating and designing moistube-irrigation management practices. We simulated the of soil texture, initial water content, pressure head, moistube length, and buried depth on the influence of soil texture, initial water content, pressure head, moistube length, and buried depth on characteristics of the soil wetting pattern. There were small differences in the shape of the soil wetting the characteristics of the soil wetting pattern. There were small differences in the shape of the soil pattern but significant differences in size. The wetting pattern and water content contour are wetting pattern but significant differences in size. The wetting pattern and water content contour approximately “ellipsoidal” in shape around the moistube. Soil texture has a significant effect on the are approximately “ellipsoidal” in shape around the moistube. Soil texture has a significant effect on wetting pattern characteristics. Both the vertical and horizontal wetting front distance and the wetted the wetting pattern characteristics. Both the vertical and horizontal wetting front distance and the soil volume decreases with an increase in soil clay content. The initial water content, pressure head, wetted soil volume decreases with an increase in soil clay content. The initial water content, pressure and moistube length have great influence on the wetting front distance and wetted soil volume. Both head, and moistube length have great influence on the wetting front distance and wetted soil volume. the wetted soil volume and the wetting front distance have a positive correlation with the initial water Both the wetted soil volume and the wetting front distance have a positive correlation with the initial content, pressure head, and moistube length. Moistube buried depth will affect the distribution of water content, pressure head, and moistube length. Moistube buried depth will affect the distribution the soil wetting pattern. When the buried depth is shallow, the wetting front can easily reach the of the soil wetting pattern. When the buried depth is shallow, the wetting front can easily reach the surface and the water content of the soil surface increases. When the buried depth is deeper, the soilsurface and the water content of the soil surface increases. When the buried depth is deeper, the wetting pattern moves down synchronously. soil-wetting pattern moves down synchronously. Water-savings have significant benefits for expanding irrigated areas, reducing food prices, Water-savings have significant benefits for expanding irrigated areas, reducing food prices, developing regional economic and restoring downstream ecosystems. However, efficient water use developing regional economic and restoring downstream ecosystems. However, efficient water use in

Water 2018, 10, 601

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agriculture reduces the recharge of groundwater on which natural vegetation depends, and affects regional ecological stability. Therefore, it is necessary to study how to create a multifunctional agricultural ecosystem by considering the allocation and regulation of water to increase synergies of environment, economy and ecosystem, so as to achieve a win-win situation between efficient agricultural water use and eco-environmental health. Author Contributions: Y.F. designed the experiments and wrote the paper; T.Z. performed the experiments; and N.H. and J.Z. revised the paper. Acknowledgments: This research was supported by National Key Research and Development Program of China (No. 2016YFC0500901) and the National Natural Science Foundation of China (No. 51409137). Special and sincere thanks to the Key Laboratory of Mechanics on Disaster and Environment in Western China, the Ministry of Education of China for the support for the experiments. Conflicts of Interest: The authors declare no conflict of interest.

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