Modelling Soil Water Infiltration and Wetting Patterns in Variable Working-Head Moistube Irrigation

Abstract

Moistube irrigation is an efficient method that accurately irrigates and fertilizes agricultural crops. Investigation into the mechanisms of infiltration behaviors under an adjusted working head (WKH) benefits a timely and artificially regulating moisture condition within root zones, as adapted to evapotranspiration. This study explores the laws of Moistube irrigated soil water movement under constant and adjusted working heads. Lysimeter experiments were conducted to measure Moistube irrigation cumulative infiltration, infiltration rate, and to observe wetting front area and water content distribution using digital image processing and time domain reflectometry, respectively. Treatments of constant heads (0, 1, and 2 m), increasing heads (0 to 1, 0 to 2 and 1 to 2 m) and deceasing heads (1 to 0, 2 to 0 and 2 to 1 m) were designed. The results show that (1) under constant heads, the cumulative infiltration increases linearly over time. The infiltration rate and cumulative infiltration are positively correlated with the pressure head. When WKH is increased or decreased, the infiltration rate and cumulative infiltration curves significantly change, followed by a gradual stabilization. The more the head is increased or decreased, the more evident this tendency will be. (2) When WKH is increased, the wetting front migration rate and the wetted soil moisture content marked increase; when WKH is decreased, the wetting front migration rate sharply decelerates, and the water content of the wetted soil slowly grows. They both tend to equilibrium with time. (3) By regarding the same cumulative infiltration of increased WKH and constant WKH treatments as a similar initial condition, we proposed a cumulative infiltration empirical model for Moistube irrigation under variable working head. Additionally, we treat the Moistube as a clayey porous medium and construct a HYDRUS-2D numerical model to predict the infiltration behaviors under variable WKH. The validity of the two models were well proven, with MRE and NRMSE close to 0 and NSE greater than 0.867, indicating good agreements with the experimental results. This model breaks through the limitation of constant boundary of traditional numerical model and applies variable head boundary to the boundary of the Moistube pipe, which can also effectively simulate the response mechanism of Moistube irrigation to variable WKH. The research results further confirmed the feasibility of manually adjusting the WKH to regulate the discharge of the Moistube pipe and soil moisture state. Based on the HYDRUS-2D numerical model simulation results and the root distribution and water demand of typical facility crops, the selection range of placement depth and the adjustable range of WKH of Moistube irrigation were proposed. The research results provide a theoretical reference for manual adjustment or automatic control of Moistube irrigation WKH to adapt to real-time crop water demand in agricultural production.

1. Introduction

With the development of global urbanization and industrialization, the shortage of water resources is becoming increasingly serious [1]. Since water supply is increasingly less than demand, developing new water-saving irrigation technology is essential for improving irrigation efficiency and easing the agricultural water crisis [2]. Moistube irrigation is a precise, continuous and efficient buried line source irrigation technology recently developed. This technology has many advantages, e.g., water and energy conservation, simple technological structure and strong anticlogging ability [3]. The Moistube is made of a high-molecular-weight polymer semipermeable membrane. Driven by the head in the tube and the soil suction outside the tube, a water and fertilizer solution flows from micropores, analogous to perspiration, and infiltrates into the root zone of the crop. It can provide water and nutrients for crops in real time, adaptively and accurately [4]. The irrigation flow can be adjusted to meet the water demand of crops, thus achieving precise irrigation. Appropriate technical parameters should be selected to optimize the design of Moistube irrigation, an important precondition of good irrigation quality [5]. The technical parameters affecting its effectiveness include the soil characteristics, such as its texture, bulk density, and water retention/conductivity [6], and external factors, such as Moistube size, the working head, placement depth, layout, spacing, and anticlogging properties [7,8]. Studies have shown that the wetted soil produced by Moistube irrigation has an inverted pear or round shape in sandy soil and clay loam [9]. Therefore, texture has affected the development pattern of longitudinal wetted soil. The moisture content of the wetted soil produced by Moistube irrigation maintains about 90% of the field capacity, and the irrigation uniformity in the wetted soil is high [10,11]. The Moistube irrigation outflow rate (or wetted soil) is significantly positively correlated with the working head and initial soil moisture content and negatively correlated with the placement depth of the tube, which can cause deep percolation or reduce the effective water utilization rate of crops. However, the placement depth is not just determined based on flow rate. It should also appropriately match the distribution of crop roots and their water absorption demand so as to improve the water storage efficiency at the root layer and reduce ineffective evaporation and deep seepage [12]. Although the Moistube irrigation flow rate depends on both the working head and the initial water content, the initial water content (or matrix suction) can only affect the Moistube irrigation flow rate for 44 h, after which it is driven by the pressure head alone [13]. When designing the working head, dynamic changes in crop water consumption and root water uptake should also be considered [14]. In order to improve the absorption efficiency of irrigation water by the root layer, the placement depth of the Moistube pipe should also be considered to adapt to the water requirement of crops and root morphology [15]. To ensure the dynamic balance between the water supply in Moistube irrigation and the water demand of crops so as to achieve more precise irrigation, the characteristics of the Moistube irrigation water supply head under a constant working head condition must be known, and the water supply characteristics of Moistube irrigation under variable working heads must be further studied. Wang Ce et al. [15] found that the working head played a crucial role in the soil water movement, wetting front transport and water discharge characteristics of Moistube irrigation. For better operation of the Moistube irrigation system, numerous studies have been carried out on the working head [5,6,7,8], pipe spacing, placement depth, and other factors among the basic problems of Moistube irrigation water migration. Nevertheless, we still must further explore the characteristics of water supply in Moistube irrigation under variable water heads and the expansion and shrinkage characteristics of its wetted soil.

The numerical simulation provides a practical and convenient method for the study of soil water movement in different situations. HYDRUS-2D was developed for simulating two-dimensional movement of water, solute and heat in variably saturated porous media, It has been widely used in the study of soil water movement [4]. Some researchers have also applied this model to the simulation of water movement in Moistube irrigation. Fan et al. [16] calculated the specific flow data of Moistube pipe. Based on the HYDRUS-2D model, the Moistube pipe was considered as the constant flow boundary to simulate vertical Moistube irrigation. Qiwei et al. [1] built a Moistube irrigation water movement model by treating the tube wall as a porous medium based on the water potential difference driving the flow mechanism of the Moistube pipe. The model built can accurately simulate the Moistube irrigation water process under constant head. Due to the significant changes in the boundary conditions of Moistube irrigation under the control of the variable head, it is unknown whether HYDRUS-2D can accurately simulate soil water dynamics. In this paper, a numerical model of HYDRUS-2D under the control of Moistube irrigation with variable head is established. This model breaks through the limitation of constant boundary of traditional numerical model and applies variable head boundary to the boundary of the Moistube pipe, which can also effectively simulate the response mechanism of Moistube irrigation to variable WKH. However, the water supply characteristics model of Moistube irrigation under variable water head was not explored and established by HYDRUS-2D in previous studies. The specific objectives of this study were the following: (i) based on an indoor Moistube irrigation simulation experiment, this study aims to describe the water supply change characteristics, moisture movement mechanism, and the change in wetted soil movement in Moistube irrigation under variable working heads; (ii) the influence of initial water state on the infiltration characteristics of Moistube irrigation was analyzed by regarding the same cumulative infiltration of increased working head and constant working head treatments as the similar initial condition, so we proposed a cumulative infiltration physical model for Moistube irrigation under variable working head; and (iii) the wall of the Moistube pipe was treated as a porous medium, and the water movement model Moistube irrigation under variable head control was constructed by HYDRUS-2D. The results can provide a theoretical basis for the establishment of Moistube irrigation automatic control and intelligent control system.

2. Materials and Methods

2.1. Laboratory Experiments

2.1.1. Soil Sample for the Experiment

The soil used in this experiment was taken from the experimental field in the water-saving park of Hohai University (31°57′ N, 118°50′ E). The soil sampling depth was 0–20 cm below the surface layer, and the sampling was concentrated to avoid differences in the mechanical composition of the samples. After the soil was loosened by a rotary cultivator, impurities including residual roots and stones were removed with a 6 mm sieve before subjecting it to air drying and then passing it through a 5 mm sieve for use. According to the international system for soil texture classification, the soil sample used in this experiment was clay loam. Soil particle composition was measured by Bettersize2000 laser particle size analyzer (Leheng Technology (Beijing) Co., LTD, Beijing, China). According to Darcy’s law, soil saturated hydraulic conductivity Ks was measured by the Ring-knife method, and the specific values are shown in

Table 1. Soil hydraulic characteristic parameters and soil mechanical composition.

Particle Size Range (Mass Fraction)/%			Water Content of Saturated Soil/%	Saturated Hydraulic Conductivity ${\mathit{K}}_{\mathit{S}}$ (m/s)
$0.020 \mathbf{mm}<$$\mathbf{d} \le$ 2.000 mm	$0.002 \mathbf{mm}<$$\mathbf{d} \le$ 0.020 mm	$\mathbf{d} \le$ 0.002 mm
38.10	36.30	25.60	49.1	2.72 × 10−6

.

2.1.2. Moistube Irrigation Soil Moisture Infiltration Experiment

Laboratory experiments were conducted to investigate the wetting front dynamics and flow characteristics subjected to variable working head. The soil moisture infiltration experiment was carried out in a room with constant temperature and humidity. The testing device, as shown in Figure 1, is composed of a soil box, Moistube irrigation system and data collection system. The soil box is constructed from 0.01 m thick transparent organic glass and is 0.6 m × 0.3 m × 0.7 m (L × W × H). There are symmetrical holes 0.02 m in diameter on the front and back panels of the soil box for Moistube installation and measuring holes 0.01 m in diameter on the back panel; the layout is illustrated in Figure 1b.

The soil samples were evenly filled into the soil box in layers and roughened between layers. The dry bulk density of the filled soil was 1300 kg/m³, the average gravimetric water content of soil was 0.054 kg/kg, and the optimum placement depth of the clay loam was 15 to 20 cm [8]. The Moistube was buried 20 cm deep, and the filling height was as high as 60 cm. The Mariotte bottle was connected to the Moistube through a rubber tube to simulate a simple Moistube irrigation system. Moistube with a fourfold double-layer structure is a third-generation product (Shenzhen Moistube Irrigation Co., Ltd. Guangdong province Shenzhen Nanshan district science development road no. 1); it is 30 cm long and is horizontally layered in the soil box at a 20 cm depth. The pressure head in the tube was controlled by adjusting the height of Mariotte bottle. During the infiltration process, a digital camera (Canon EOS 60D, Canon, 89 Jinbao Street, Dongcheng District, Beijing, China) was used to record the changes in wetting front from the dense area to the sparse area and the liquid level in the Mariotte bottle at corresponding moments so as to calculate the infiltration amount. Three repeated actions were conducted for each treatment. The mean value was considered the test result. Photoshop CS5 software was used to crop the wetting front pictures to capture the sample zone (0.7 m × 0.7 m). Since the wetting area and dry area of the sample have a high contrast, the quick selection tool was directly used to separate the wetting area from the dry area. They were then filled with black and white colors, respectively, and converted into black and white binary images. Ultimately, these binary images were calculated using MATLAB R2018a (Natick, MA, USA: The MathWorks Inc.) software programming to obtain the wetting front data. The specific image processing process is shown in Figure 2.

The Moistube irrigation experiment under a constant working head and variable working heads defines the law of wetted soil movement and the characteristics of soil moisture migration. Three groups of working heads were set in the constant head test: 0, 1 m, and 2 m. Six groups were set in the variable head test: increasing heads, 0→1 m, 0→2 m and 1→2 m; decreasing heads, 2→0 m, 2→1 m and 1→0 m. For details, see Figure 3. The constant heads are denoted as HD(0), HD(1), and HD(2), while the increasing and decreasing heads are represented by TZ(0→1), TZ(0→2), and TZ(1→2) and by TJ(2→0), TJ(2→0), and TJ(2→1), respectively. For the HD heads, the infiltration time of each group was 72 h. The infiltration lasted for 144 h for the TZ and TJ heads. In the first stage, water was continuously irrigated for 72 h under a constant head and then for another 72 h after another constant head was instantaneously increased or decreased. Head increase or decrease was completed instantaneously through the Mariotte bottle. During the infiltration process, time-domain reflectometry (TDR) was used to measure the soil moisture content, once every 2 h for the first 12 h and once every 4 h afterward. The volumetric water contents of the soil profile were continuously monitored by a TDR (Model: TDR/MUX/mpts, produced by the Institute of Agrophysics, Polish Academy of Sciences (IA PAS)) throughout the Moistube irrigation event. Sixteen sensors were installed at −15, −10, −5, 5, 10, 15, 20, 25 cm-distance vertically and −20, −15, −10, −5, 5, 10, 15, 20 cm-distance horizontally from the Moistube, under a Cartesian coordinate system centered at the Moistube (Figure 1). The sensors were calibrated by equations recommended by the manufacturer and by a series of soils with different moisture status. The data of water contents were collected at approximately 0.5 h intervals during the whole Moistube irrigation process.

In the Moistube irrigation test under a constant or variable head, TDR with a multiplexer (TDR/MUX) was used to monitor soil moisture and the change in water potential, record Mariotte bottle readings, and calculate the infiltration amount and infiltration rate. For a variable head, the head was adjusted when the wetted soil became stable. During the test, an image of the wetted soil was taken with photographic techniques, and this image was later processed and its morphological parameters extracted using an automatic recognition and calculation system.

2.2. Prediction Model for the Cumulative Infiltration Amount of Moistube Irrigation under a Variable Working Head

Model Selection and Establishment

The cumulative infiltration amount of Moistube irrigation is positively correlated with the pressure head, and the infiltration time is consistent with the Kostiakov infiltration model [17]. In addition, it can also be simulated by the first term of the Horton infiltration model [18] and Philip infiltration model. These models are purely empirical models or semi-physical and semi-empirical models, which belong to the same category. When using the above models to simulate the relationship between cumulative infiltration and time under constant working head, it is found that the fitting effect of several models is very good. In this paper, we chose the Philip infiltration model as the basic model to fit the infiltration parameters of Moistube irrigation under different constant working heads. The same cumulative infiltration of TZ and HD treatment is regarded as the same initial soil moisture content condition; a cumulative infiltration prediction model for Moistube irrigation under variable working head is proposed.

$$I=S{t}^{\frac{1}{2}}+At$$

(1)

where $I$ is the cumulative infiltration amount, $S$ is the Soil sorptivity, $t$ is the infiltration time, and $A$ is the stable infiltration rates.

Using Equation (1), we obtain the relational expression between cumulative infiltration amount and time of the HD(1) and HD(2) treatments. At $t_1$ and $t_2$, the infiltration amounts of HD(1) and HD(2) are the same. Accordingly, we can obtain the time relational expression when the infiltration amounts of the different treatments are the same. The general formula diagram of the prediction model is shown in Figure 4. The specific calculation process is as follows:

$$I_1=I_2=S_1{t_1}^{\frac{1}{2}}+A_1{t}_1=S_2{t_2}^{\frac{1}{2}}+A_2{t}_2$$

(2)

$$t_2={\left({\left(\frac{S_1{t_1}^{\frac{1}{2}}+A_1{t}_1}{A_2}+{\left(\frac{S_2}{2A_2}\right)}^2\right)}^{\frac{1}{2}}-\frac{S_2}{2A_2}\right)}^2$$

(3)

$$\left\{\begin{array}{c}I=S_1{t}^{\frac{1}{2}}+A_{1}t \left(0\le t\le t_1\right) \\ I=S_2{\left(t-∆t\right)}^{\frac{1}{2}}+A_2 \left(t-∆t\right) \left(t\ge t_1\right) \\ ∆t=t_1-t_2 \end{array}\right.$$

(4)

where $I_1 \mathrm{a}\mathrm{n}\mathrm{d} I_2$ denote the cumulative infiltration amounts of the different treatments; $S_1$ and $S_2$ denote the Soil sorptivity of the different treatments; $A_1$ and $A_2$ denote the stable infiltration rates of the different treatments; $t_1$ is the moment the head changes; and $∆t$ is the translation amount.

Using Equations (1)–(3), we obtain the relational expression (4) between the cumulative infiltration amount and the time under the control of variable head in Moistube irrigation.

2.3. HYDRUS-2D Simulations

2.3.1. Numerical Modeling Theory

Water movement under Moistube irrigation is simulated using the HYDRUS-2D software package (version 2.05, program for numerical simulations of water, heat, and solute transport in variably saturated porous media) [19]. It solves the Richards equation by the Galerkin finite-element method. Moistube irrigation belongs to line source irrigation. At the same time, since the length of the pipe used in this paper is only 30 cm, the water loss along the pipe is small. It can be assumed that the water discharge rate of Moistube irrigation is evenly distributed along the pipe direction. In addition, assuming that the soil is homogeneous and isotropic, the soil water movement can be simplified as a two-dimensional movement problem in the vertical plane. The governing Richards equation is written as follows:

$$\frac{\partial \theta }{\partial t}=\frac{\partial }{\partial x}\left[K\left(\theta \right)\frac{\partial h}{\partial x}\right]+\frac{\partial }{\partial z}\left[K\left(\theta \right)\frac{\partial h}{\partial z}\right]+\frac{\partial K\left(\theta \right)}{\partial z}$$

(5)

where θ is volumetric water content (L³ L⁻³); h is soil water pressure head (L); t is time (T); x and z are, respectively, horizontal and vertical space coordinate (L); and K is hydraulic conductivity (L T⁻¹).

The soil hydraulic properties are described by the van Genuchten–Mualem model as follows:

$$\theta =\left\{\begin{array}{cc}{\theta }_r+\frac{{\theta }_s-{\theta }_r}{(1+{\mid \alpha h\mid }^n{)}^m}& h<0\\ {\theta }_s& h⩾0\end{array}\right.$$

(6)

$$K \left(\theta \right)=K_s{S}_e^l{\left[1-{\left(1-S_e^{\frac{1}{m}}\right)}^m\right]}^2$$

(7)

where ${\theta }_r$ and ${\theta }_s$ are, respectively, the residual and saturated water content (L³ L⁻³); α is an empirical parameter that is approximately equal to the inverse of the air-entry value (L⁻¹); n, m and l are shape parameters (unitless), $m=1-\frac{1}{n}$; $K_s$ is the saturated hydraulic conductivity (L T⁻¹); and $s_e$ is the effective saturation, $s_e=\frac{\theta -{\theta }_r}{{\theta }_s-{\theta }_r}$.

2.3.2. Input Hydraulic Parameters

The hydraulic parameters of the tested soil were determined by fitting the data of soil water retention with the van Genuchten–Mualem model using the software of RETC [20]. In order to study the discharge of the Moistube pipe, the air discharge test of the Moistube pipe under a different pressure head was carried out. It was found that the unit time discharge of the Moistube pipe has a linear relationship with the pressure head. Taking the wall of the Moistube tube as a porous medium, Darcy’s law is used to describe its flow characteristics. Then, by combining the relationship between flow rate and pressure head with Darcy’s law formula, the saturated hydraulic conductivity ks of the Moistube pipe is obtained. When simulating ceramic irrigation, Cai et al. [21] pointed out that the residual moisture content and saturated moisture content of the irrigator were non-sensitive factors to the simulation results, so the residual moisture content and saturated moisture content of the Moistube pipe were temporarily set at 0.010 and 0.300 m³/m³, respectively, in this paper. Considering that the wall thickness of the Moistube tube is small and the tube is easily saturated after water filling, a small value of α should be taken as 6.00 × 10⁻⁶ cm⁻¹.

According to the equation of VG model, the smaller the n value, the better the water holding capacity of the medium. The pores in the Moistube tube are nanoscale pores. The smaller the pore size, the less likely it is to lose water, so the smaller value of n should be 1.10. The values of the hydraulic parameters of the soil and the Moistube are listed in

Table 2. Hydraulic parameters of the soil and the Moistube.

	θr (m3 m−3)	θs (m3 m−3)	α (1/m)	n	l	Ks (m/s)
Soil	0.61	0.491	2.4	1.51	0.5	2 × 10−6
Moistube	0.010	0.300	6.00 × 10−4	1.10	0.5	2.03 × 10−9

.

2.3.3. Computational Domain, Initial and Boundary Conditions

The Geometry module of HYDRUS-2D/3D software was used to build the simulation area. Figure 5 is a schematic diagram of the simulation area. According to the soil moisture infiltration experiment and considering the symmetry of infiltration, the simulated area was set as a rectangular area with a height of 60 cm and a width of 30 cm. A half-ring with an inner diameter of 1.5 cm and an outer diameter of 1.7 cm is used to represent the Moistube pipe. The initial suction of soil is set according to the suction value corresponding to the volume water content. For model validation, the soil water content was 0.07 m³/m³. In the process of irrigation, surface boundary is the atmospheric boundary without considering the influence of evaporation. The bottom boundary was set as “Free Drainage”. It must be mentioned that in all simulations the wetting fronts did not reach the bottom boundary at the end of irrigation, thus in fact the bottom boundary condition had little effect on the water movement. The internal boundary of the Moistube was assigned “variable head”, and the other areas of the left boundary and the right boundary are the “no flux” boundary.

2.4. Statistical Analysis

The agreement of the HYDRUS-2D and cumulative infiltration prediction model simulation results with the measured data was quantified using the mean relative error (MRE), the normalized root mean square error (NRMSE), and normalized squared error (NSE). The expressions of these parameters are as follows:

$$\mathrm{MRE}=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\frac{\left({\mathrm{S}}_{\mathrm{i}}-{\mathrm{M}}_{\mathrm{i}}\right)}{{\mathrm{M}}_{\mathrm{i}}}$$

(8)

$$\mathrm{NRMSE}=\frac{1}{\stackrel{-}{\mathrm{M}}}\sqrt{\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{M}}_{\mathrm{i}}-{\mathrm{S}}_{\mathrm{i}}\right)}^2}$$

(9)

$$\mathrm{NSE}=1-\frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{M}}_{\mathrm{i}}-{\mathrm{S}}_{\mathrm{i}}\right)}^2}{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{M}}_{\mathrm{i}}-\stackrel{-}{\mathrm{M}}\right)}^2}$$

(10)

where $n$ is the number of data points, and $i=\mathrm{1,2},\cdots ,n;{ M}_i$ is the $i$th measured value; $S_i$ is the $i$th simulation value; and $\stackrel{-}{M}$ represents the mean value of the measured values.

The closer the values of MRE and $\mathrm{N}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ are to 0 and the closer the value of NSE is to 1, the closer the measured values are to the simulated values and the higher the model simulation accuracy.

3. Results

3.1. Mechanism of Moistube Irrigation Soil Water Movement under Constant and Variable Working Heads

The cumulative infiltration and infiltration rate of Moistube irrigation were obtained by observing the liquid level of the Mariotte bottle. For the constant head test, Figure 6 indicates that the cumulative infiltration amount of Moistube irrigation follows a significantly linear growth trend over time, and the infiltration rate and cumulative infiltration amount are positively correlated with the pressure head [17], which is consistent with previous research results. The cumulative infiltration amounts of HD(0), HD(1), and HD(2) are 1.8307 L, 7.3503 L, and 13.5593 L, respectively; the stable infiltration rates are 0.0230 L/h, 0.0947 L/h, and 0.1548 L/h, respectively.

Figure 7 the figure shows the trend of the Moistube irrigation infiltration and the infiltration rate over time when the water head increases. The figure indicates that when the working head is increased, the infiltration rate and cumulative infiltration curves both sharply rise and then tend to stabilize over time. The more the head is increased, the more evident the tendency, because once the working head increases, the water potential difference inside and outside the Moistube grows, and the infiltration rate also increases, so that both the infiltration rate and cumulative infiltration curves sharply rise. For TZ(0→1), TZ(0→2), and TZ(1→2), within 72 h after the head is increased, the cumulative infiltration amounts reach 6.2556 L, 12.3355 L, and 11.9579 L, respectively, and the infiltration rates stay at 0.0827 L/h, 0.1518 L/h, and 0.1431 L/h, respectively. The water contents near the Moistube are 30.8%, 31.8%, and 39.3%, respectively, when the head is increased.

As shown in Figure 6 and Figure 7, within the same period of time, compared to HD(1), HD(2), and HD(2), the infiltration amounts and infiltration rates of TZ(0→1), TZ(0→2), and TZ(1→2) decrease by 15%, 9%, and 12% and by 13%, 2%, and 8%, respectively, within 72 h after the head is increased.

Figure 7 shows how the cumulative infiltration amount and infiltration rate of Moistube irrigation changes over time under constant and variable heads when the head is decreased. The figure indicates that when the working head is decreased, the infiltration rate and cumulative infiltration curves both sharply decline and then tend to stabilize over time. The more the head is decreased, the more evident this tendency, because once the head pressure decreases, the water potential difference inside and outside the Moistube diminishes, and the outflow rate also decreases, which then causes the soil moisture content to decrease so that the infiltration rate becomes instantaneously small. Before TJ treatment, the constant working head is high, so there is a high soil moisture content and a small water potential gradient near the Moistube. The force of soil moisture suction to pull the water in the Moistube irrigation zone decreases accordingly. In the later period of soil water movement, the function of pressure potential relying on the pressure head [17], the cumulative water infiltration curve, and the infiltration rate curve all tend to stabilize. For TJ(1→0), TJ(2→0), and TJ(2→1), within 72 h after the head is decreased, the cumulative infiltration amounts reach 1.5730 L, 1.3377 L, and 4.5700 L, respectively, and infiltration rates maintain at 0.0201 L/h, 0.0184 L/h, and 0.0598 L/h, respectively. When the head is decreased, the water contents near the Moistube are 40.7%, 43.5%, and 41.1%, respectively. Figure 6 and Figure 8 indicate that within the same period of time, compared to HD(0), HD(0), and HD(1), the infiltration amounts and stable infiltration rates of TJ(1→0), TJ(2→0), and TJ(2→1) decrease by 14%, 27%, and 38% and by 13%, 20%, and 37%, respectively, within 72 h after the head is decreased.

Upon analysis of the change law of the cumulative infiltration amount, infiltration rate, and water content near the Moistube when the head is increased or decreased, the test figures reveal that the water content can affect water infiltration in Moistube irrigation. The higher the initial water content near the Moistube is, the smaller the cumulative infiltration amount and infiltration rate under an equal time period and working head. The results indicate that the high moisture around the Moistube greatly lowers the water supply efficiency of the Moistube.

3.2. Prediction Model for the Cumulative Infiltration Amount of Moistube Irrigation under a Variable Working Head

To determine the relationship between the cumulative infiltration curves of Moistube irrigation under constant and variable heads, we identify the time points where the wetting front and infiltration amount are the same for different treatments and judge whether the cumulative infiltration curves of the two treatments overlap each other. If the cumulative infiltration curves of the HD and TZ treatments overlap each other well under the same initial conditions, the cumulative infiltration curve of the HD treatment can be used to predict that of TZ treatment and establish a prediction model. For the specific translation comparison method, see Figure 9.

In Figure 9, at points A and C, the TZ and HD treatments have the same wetting front area at $t_A$ and $t_C$. In particular, $t_A$ is the moment when the head is increased in the TZ treatment. Translating the cumulative infiltration curve ① (section AB) in the TZ treatment causes points A and C to overlap each other, leading to curve ② (CD). Then, a linear fit line of the cumulative infiltration curves ③ and ② in HD treatment is drawn.

Table 3. Cumulative infiltration amounts and water contents near Moistube of different treatments under the same wetting front area.

Treatment	Time	Infiltration Amount (mL)	Average Water Content near Moistube	Wetting Front Area (cm2)
TZ(0→1)	$t_{A1}$	1860.45	30.80%	292.3
HD(1)	$t_{C1}$	2241.2	34.60%	304.8
TZ(0→2)	$t_{A2}$	1682.6	31.80%	223.8
HD(2)	$t_{C2}$	1800.1	34.90%	233.4
TZ(1→2)	$t_{A3}$	7353.5	39.30%	1029.1
HD(2)	$t_{C3}$	8639.5	42.80%	1060.8

provides the cumulative infiltration amounts and water contents near the Moistube of different treatments when the wetting front area is the same. As shown in the table, when the two treatments have the same wetting front area, the water contents and cumulative infiltration amounts near the Moistube are somewhat different. TZ(0→1-1), TZ(0→2-2), and TZ(1→2-2) match the linear fit line of the curve obtained by translating the TZ(0→1), TZ(0→2), and TZ(1→2) treatments. In Figure 8, the linear fit lines TZ(0→1-1), HD(1), TZ(0→2-2), HD(2), TZ(1→2-2), and HD(2) have slopes of 91.19, 98.73, 176.9, 183.25, 176.32, and 199.09, respectively. Curves ③ and ② do not overlap significantly, and the slopes of the linear fit lines are quite different from each other; thus, the same wetting front cannot be used as an initial condition of the prediction model.

In Figure 10, at points A and C, the TZ and HD treatments have the same infiltration amount at $t_A$ and $t_C$ on the cumulative infiltration curve. In particular, $t_A$ is the moment when the head is increased in the TZ treatment. Assuming that the TZ and HD treatments have the same initial conditions at $t_A$ and $t_C$, the cumulative infiltration curve ① (section AB) in the TZ treatment is translated so that points A and C overlap each other, yielding curve ② (CD). Then, a linear fit line of the cumulative infiltration curves ③ and ② in the HD treatment is drawn.

Table 4. Wetting front area and water content near Moistube of different treatments under the same infiltration amount.

Treatment	Time	Infiltration Amount (mL)	Average Water Content near Moistube	Wetting Front Area (cm2)
TZ(0→1)	$t_{A1}$	1860.3	30.80%	288.5
HD(1)	$t_{C1}$	1860.5	32.40%	294.9
TZ(0→2)	$t_{A2}$	1950	31.80%	223.8
HD(2)	$t_{C2}$	1947.2	32.80%	263.5
TZ(1→2)	$t_{A3}$	7500.3	39.90%	1029.1
HD(2)	$t_{C3}$	7500.3	41.70%	1060.8

presents the wetting front area and water contents near the Moistube of the different treatments under the same infiltration amount. According to the table, when the two treatments have the same cumulative infiltration amount, the water contents near the Moistube and the size of the wetting front are very close. In Figure 8, the linear fit lines TZ(0→1-1), HD(1), TZ(0→2-2), HD(2), TZ(1→2-2), and HD(2) have slopes of 91.19, 97.65, 176.21, 180.64, 175.86, and 182.66, respectively. Curve ③ almost overlaps curve ②, and the maximum relative error of the slopes of the two linear fit lines is 6.6%; thus, the initial conditions can be considered the same when the infiltration amounts are the same. For the TZ and HD treatments, under the same initial conditions, the cumulative infiltration curve under a constant working head can be used to predict the cumulative infiltration curve under a variable working head.

The reasons for the difference in results under different initial conditions are discussed further. The VG model of $s_e$ represents the means effective saturation and can reflect the soil hydraulic conductivity. When the wetting front area of the two treatments is the same, it can be seen from Table 3 that there is a difference between the cumulative infiltration and the average soil moisture content at this moment, which leads to the difference of the soil effective saturation $s_e$ mentioned in the above formula, which further affects the soil water conductivity. Therefore, the growth trend of infiltration rate and cumulative infiltration is different. According to the actual soil moisture content and effective saturation, the average soil moisture content is similar under the same infiltration volume, and the calculated $s_e$ value is also similar. Therefore, the same infiltration amount is selected as the initial condition.

The same cumulative infiltration of TZ and HD treatment is regarded as the same initial soil moisture content condition, a cumulative infiltration prediction model for Moistube irrigation under a variable working head is proposed. Using Equations (1)–(3), we obtain the relational expression (4) between the cumulative infiltration amount and the time under the control of variable head in Moistube irrigation.

Table 5. Infiltration parameters under different constant working heads in Moistube irrigation.

Fitting Parameters	Treatment
	HD(0)	HD(1)	HD(2)
S	0.301	0.412	0.601
A	0.751	3.301	6.040
R2	0.999	0.999	0.999

shows the infiltration parameters under different constant working heads in Moistube irrigation. If different constant infiltration parameters are substituted into Equation (4), the relationship between cumulative infiltration and time during the regulation between different constant heads can be obtained. The fitting results of model simulation values and measured values are shown in Figure 11 below.

Following the analysis of the statistical characteristics of the value predicted by the model and the measured value, both MRE and NRMSE values approach 0.016, with NSE values all being greater than 0.997. Therefore, the value predicted by the model coincides well with the test measured value. The specific fitting results are shown in Figure 10. Above all, the model built in this study has a high accuracy: it can accurately predict how the cumulative infiltration amount of Moistube irrigation changes over time under variable heads.

3.3. Validation of the HYDRUS Model

The cumulative infiltration and infiltration rate were selected as the eigenvalues to verify the effectiveness of the model. Comparisons between the measured and simulated cumulative infiltration amount and infiltration rate are shown in Figure 12 and Figure 13. It can be seen from the figure that the change trend of the simulated value and the measured value is consistent. According to the statistical analysis of the simulated and measured values, the MRE and NRMSE values of cumulative infiltration and infiltration rate are close to 0, and the NSE values are greater than 0.867, indicating that the simulated values of the model are in good agreement with the measured values of the test. In conclusion, the HYDRUS-2D model simulation can well predict the change process of the cumulative infiltration and infiltration rate of Moistube Irrigation under the control of the variable head. The results can confirm the feasibility of artificially regulating Moistube pipe outflow, infiltration characteristics and water content distribution by adjusting the working head of Moistube irrigation in real time. In terms of practical application, the appropriate technical parameter range and irrigation mode of Moistube irrigation for different facility crops can be drawn up based on the scenario simulation results of moistened body under variable head irrigation and the water requirement rule of typical facility crops roots.

3.4. Wetting Front Migration in Moistube Irrigation under Constant and Variable Heads

The wetting front migration process in Moistube irrigation under constant and variable heads is shown in Figure 14, Figure 15 and Figure 16. In the figure, Y+, Y− and X represent the migration distances of the wetting front upward, downward, and horizontally to the right, respectively. The figures indicate that when the working head is increased, the wetting front migration rate significantly increase in all directions and stabilizes over time. When the working head is decreased, the wetting front migration rate decreases significantly in all directions and also stabilizes over time. The more the head is increased or decreased, the more evident this tendency, because with the increase in the head pressure, the water potential difference rises, accelerating the outflow rate of the Moistube. Likewise, once the head pressure is decreased, the water potential difference inside and outside the Moistube diminishes, and the outflow rate also decreases, leading to reduced soil moisture content and reduced wetting front migration rate. The migration rate finally tends to stabilize because at the initial stage of infiltration, the radius of the wetting front is small, the soil moisture content around it is high, and there are large water potential gradients and high water suction on both sides, so the wetting front advances quickly. As time elapses, the radius of the wetting front grows, while the soil moisture content around it becomes increasingly smaller, and the water potential gradient and water suction on both decrease accordingly; thus, the wetting front slows down [22] and eventually becomes stable.

We used the surfer11 software (Version 11.0.642, Golden, CO, USA, Golden Software) [1] to plot the contours of water distribution in the section of the wetted soil of the Moistube irrigation under variable working heads, as shown in Figure 17 and Figure 18. The Moistube is located at (0, 0).

As shown in Figure 17 and Figure 18, the contours of water content in the wetted soil are distributed in concentric circles surrounding the Moistube. With increasing distance, the contours gradually become dense, the soil water potential gradient grows, and the soil water content decreases. When the head is increased in the TZ treatment, the wetting front migration rate and the average moisture content of the wetted soil significantly increase; when the head is decreased in the TJ treatment, the wetting front migration slows down, and the average water content of the wetted soil slowly grows.

3.5. The Application of Moistube Irrigation Variable Head Control in Practical Irrigation

The WKH of Moistube irrigation has great influence on crop yield and water use efficiency. Previous studies have pointed out that the growth rate of crops at different growth stages is closely related to soil water content [23]. Before the soil moisture content reaches the optimum level, crop growth rate and yield increase with the increase of soil moisture content, but decrease when the soil moisture content exceeds the optimum level. If the soil water content can be kept in the best state during different growth stages of crops, the crop growth rate can reach the best level, and the dry matter accumulation of crops will increase [23]. Therefore, it is of great significance and value to maintain the optimum state of soil moisture content in agricultural production. The range of soil wet zone formed by the irrigator and the moisture content of the wet zone directly affect the water and nutrient absorption efficiency of crop roots [24].

Previous researchers have also found that the WKH of Moistube irrigation is the main factor regulating the flow of Moistube irrigation [8]. The results of this study also confirmed the feasibility of adjusting the discharge of Moistube pipe and soil water state by artificially adjusting the working head. Different soil moisture content models can be obtained by adjusting the WKH of the Moistube pipe. In different growth stages of crops, the most suitable soil moisture content for crop growth is not consistent, and the water requirement of crops changes with the influence of crop transpiration under different meteorological conditions. According to the needs of crops, the WKH of Moistube irrigation is adjusted to a higher WKH, so that the soil water content reaches the level suitable for crop growth, and then the WKH of Moistube irrigation is adjusted to a lower working water head, so that the soil water content is kept at the most suitable level during this growth period, and the crops can maintain the ideal maximum growth rate during the whole growth period. Crops grow to another growth period or change into another water demand mode because of changes in meteorological conditions, and then adjust the working water head according to the actual water demand of crops, so as to achieve continuous, accurate and efficient irrigation. The following part discusses the theory of variable head control and the practical application of related models.

Section 3.3 of this paper proves that the HYDRUS-2D numerical model can simulate the water transport process under the control of variable water head. The model can be applied to simulate the change of discharge rate and soil moisture content when the WKH of Moistube irrigation is adjusted manually in real time. Previous studies on the depth of Moistube irrigation found that the depth of the Moistube pipe had no significant effect on water transport under Moistube irrigation, but had a significant effect on the distribution of wetting front in soil [8]. The cumulative infiltration under different placement depth was compared and analyzed with that under the actual test at the placement depth of 20 cm, and the growth trend of the cumulative infiltration curve under different placement depths was similar. Figure 19 shows the comparative analysis of the accumulated infiltration of Moistube tubes under different placement depths treated by TZ(0→1). Based on the numerical model established in this paper under the control of WKH of Moistube irrigation, the water transport process under the control of different variable head of Moistube irrigation was simulated, respectively, when the placement depth of the Moistube pipe was 5 cm, 10 cm, 15 cm and 20 cm, as shown in Figure 20.

Through simulation, the process of soil water transport and wetting front change under the control of varying water head under different placement depths of the Moistube pipe was obtained. In terms of practical application, based on the simulation of wetting front migration, wetting body shrinkage and expansion, and water content evolution under different water head adjustment and reduction, the evolution of wetting front and water content under different treatments is obtained, and the evolution of wetting front and water content under different treatments is classified into several typical models. According to the root distribution of different crops, root development and root water demand in different growth stages of crops, several typical growth period water demand nodes were selected to regulate the WKH of the Moistube pipe to provide a suitable water and fertilizer soil environment for crop roots, and the Moistube irrigation head regulation model was obtained, so as to achieve accurate, precise and adaptive irrigation. While meeting the water demand of different growth stages of crops, it promotes water use efficiency and avoids soil structure breakage, deep percolation and pipeline blockage.

Table 6. Root system types of typical facility crops [25].

Crop	Tomato	Garlic	Chili, Spinach	Cucumber	Chive
Root type	Deep straight root system	Deep whisker root system	Shallow/medium straight root system	Root system of middle whisker	Shallow palpate root system

and

Table 7. Water requirement for root distribution and growth of different crops [25].

Crop	Root Depth (cm)	Root Width (cm)	Lower Limit of Root Zone Water Requirement (cm3 cm3)
Tomato [26]	0–30	0–20	15
garlic [27]	5–25	15–30	15
Pepper [28,29]	0–14	7–19	15
cucumber [30,31]	0–8	6–8	24
spinach [32]	0–5	3–5	21
chive [33,34]	0–5	3–5	21

show the root distribution and water requirement for root growth of crops in different typical facilities.

The growth of each crop at different growth stages has different requirements for soil water content, and creating a suitable soil environment for crop roots can not only promote crop growth, but also achieve precision irrigation. Moistube irrigation continuously provides water to the root zone of the crop and adapt to the water needs of the crop, thereby avoiding sudden changes in soil water that affect crop growth. Studies have shown that continuous maintenance of a suitable water and fertilizer environment is conducive to maize growth and yield, especially in the flowering and pollination stages [35]. Jia Tengyue et al. [36] analyzed the root length density of sunflowers at different growth stages and found that the root growth of sunflowers was the fastest before and after the bud stage, and reached the maximum at the flowering stage, while the root growth had stagnated or even shrunk at the maturity stage. The analysis of sunflower root length density under different irrigation quota showed that proper water deficit could maintain the activity of root at the later stage of growth and reduce the wilt rate. Zhu Yu meng et al. [37] found that the root distribution of crops varied greatly at different growth stages, and adequate water supply during crop growth could promote root growth. In the critical water demand period of crops, it is necessary to adjust the WKH artificially to actively adjust the soil water content.

The distribution of moisture content in the moist body under the control of Moistube irrigation variable head showed that the moisture content in the moist body was maintained at 30~43% (volume moisture content) when the control was between three working heads, and the soil moisture content did not reach saturation state. This provides a suitable growth environment for crop roots, which are not stressed by low oxygen due to poor soil ventilation. In the key water demand period, high WKH can be used to make the initial soil water content quickly reach the best state suitable for crop growth, and then reduce the water head to make the soil water content and moisture front maintain or slow growth, and maintain the dynamic balance between crop water demand and water supply.

As shown from the root shape of typical facility crops [25] and the root distribution and growth water requirement of different crops in Table 7, the main roots of crops with shallow bearded roots have a shallow distribution layer in the soil and a wide horizontal distribution of roots. Therefore, a shallow Moistube pipe placement depth should be selected according to the root distribution; for example, the placement depth should be between 0 and 5 cm. According to different growth period, crop water demand and meteorological conditions, the WKH control range is suggested to be between 0 and 1 m. For crops with intermediate roots, the main roots of crops are widely distributed in the soil, and the vertical extension range of the roots in the soil is slightly larger than the horizontal extension range. Therefore, a deeper placement depth can be chosen, and it is recommended that the placement depth should be between 0 and 10 m. According to different actual conditions such as different growth periods, crop water demand and weather, the WKH control range is recommended to be between 1 and 1.5 m. For crops with deep straight roots or deep bearded roots, the main roots of crops have wider distribution in the soil, and the vertical distribution of roots is also deeper, and the vertical extension range of roots in the soil is significantly larger than the horizontal extension range. Therefore, a deeper placement depth can be selected. According to the characteristics of root distribution of crops with different deep roots, it is recommended to choose a placement depth range of 15~20 cm. According to different actual conditions such as different growth periods, crop water demand and weather, the WKH control range is recommended to be between 1 and 2 m. Although the vertical distribution of crops with deep straight roots is very deep, the main root distribution is still in the relatively shallow soil layer, so choosing the placement depth and regulating the water head to select the appropriate range to prevent deep percolation is required. It should be emphasized that the above proposed placement depth and WKH control range need to be further verified by actual tests. In addition, according to the needs of crop root water absorption and crop transpiration, how to ensure the dynamic balance between water supply and crop water demand for Moistube irrigation needs to be further studied and verified by tests.

4. Discussion

The working head pressure plays a decisive role in controlling Moistube water outflow. It determines the irrigation intensity of Moistube irrigation to a large extent. When the head pressure is very low, the irrigation intensity is too small to meet the crop water demand. However, a very high head pressure leads to a large scope of wetting, which may cause ground surface evaporation and deep seepage. Many researchers have found that for underground trickle irrigation, the soil near the dripper often forms a continuously saturated wetting area during irrigation [38,39,40]. It is normal for crop roots to grow toward the vicinity of a dripper with a high water content [41]. Therefore, during underground trickle irrigation, crop roots are always threatened by low oxygen content due to poor soil aeration, resulting in declining quality and production [38,42]. For the TZ(1→2) Moistube irrigation treatment, the wetting front reached the upper, left, and right boundaries of the experimental equipment after continuous irrigation for 240 h. However, the soil was still not saturated at this time. The water content of the soil around the Moistube reached approximately 45%. Therefore, Moistube irrigation, featuring low-pressure operation, slow outflow, and migration of water by means of soil matrix suction, more reasonably distributes irrigation water and has little impact on soil aeration. Analyzing how the local initial water content affects the Moistube irrigation infiltration law suggests that the higher the local initial water content is, the smaller the cumulative infiltration amount and infiltration rate under equal time periods and working heads. The results indicate that the high moisture around the Moistube greatly lowers the Moistube water supply efficiency. Subsequent research further explores the effect of high moisture around the Moistube on the Moistube irrigation water supply efficiency. Then, according to the distribution features of crop roots in typical facilities and the law of water demand, the head is adjusted so that the irrigation flow matches the crop water demand so as to accomplish precise and accurate irrigation.

Previous Moistube irrigation studies found that the migration distance of the wetting front in all directions follows the order lower wetting front > horizontal wetting front > upper wetting front [17], which is due to the effect of gravitational potential. However, the migration distance of the wetting front in this experiment is horizontal wetting front > lower wetting front > upper wetting front. The potential reason for this difference is as follows. The filling of the test container ensured bulk density uniformity, and the method of layered compaction filling was used. Soil pores and conduction pores are the main channels for soil water flow [43]. During vertical and layered compacted filling, stratification occurs between the soil layers, and longitudinal compression leads to dense vertical pores and large horizontal infiltration. The vertical soil aggregate structure is compact, the internal pores are small, the small pores hinder the vertical infiltration of water, the horizontal infiltration is larger, and the horizontal infiltration is accelerated, which all result in a larger lateral migration distance of the wetting front than the vertical migration distance.

At this stage, the water consumption of crops in different stages and meteorological factors cannot be considered as variable factors when formulating the working head for Moistube irrigation. Moistube irrigation is based on the water potential difference between the water in the pipe and the soil outside the pipe. The outflow conditions can be automatically adapted to the change in soil moisture content at any time. Water can be supplied continuously during the entire plant growth period, and the outflow size can be adjusted by changing the head pressure. Therefore, further study is needed on whether Moistube irrigation has self-adaptation properties and whether atmospheric influence can change the outflow situation to achieve accurate irrigation development.

5. Conclusions

With a focus on Moistube irrigation characteristics, soil moisture migration characteristics and law of wetting front expansion and shrinkage, this study explores the laws of Moistube irrigated soil water movement under constant and variable working head (WKH) based on the moisture content, wetting front area, cumulative Moistube irrigation infiltration amount and infiltration rate as measured by a lysimeter. The results suggest the following: (1) under a constant WKH, the cumulative infiltration amount increases linearly over time, and the infiltration rate and cumulative infiltration amount are positively correlated with the WKH. When the WKH is increased or decreased, the infiltration rate and cumulative infiltration curves both significantly changes. As time elapses, the cumulative infiltration amount and the infiltration rate tend to stabilize. The more the WKH is increased or decreased, the more evident this tendency. (2) When the WKH is increased, the wetting front migration rate and the wetted soil average moisture content significantly increase; when the WKH is decreased, the wetting front migration rate decreases significantly, the average water content of the wetted soil slowly grows, and they both tend to stabilize over time. (3) By regarding the same cumulative infiltration of increased WKH and constant WKH treatments as the similar initial condition, Based on the Philip infiltration model, we proposed a cumulative infiltration empirical model for Moistube irrigation under variable WKH. Additionally, we treat the Moistube as a clayey porous medium and construct a HYDRUS-2D numerical model to predict the infiltration behaviors under variable WKH. The validity of the two models were well proven, with MRE and NRMSE close to 0 and NSE greater than 0.867, indicating good agreements with the experimental results. This model breaks through the limitation of the constant boundary of the traditional numerical model and applies the variable head boundary to the boundary of the Moistube pipe, which can also effectively simulate the response mechanism of Moistube irrigation to variable WKH. The research results further confirmed the feasibility of manually adjusting the WKH to regulate the discharge of the Moistube pipe and soil moisture state. Based on the HYDRUS-2D numerical model simulation results and the root distribution and water demand of typical facility crops, the selection range of placement depth and the adjustable range of WKH of Moistube irrigation were proposed. The research results provide a theoretical reference for manual adjustment or automatic control of Moistube irrigation WKH to adapt to real-time crop water demand in agricultural production.