Simulation of Soil Water Movement and Root Uptake under Mulched Drip Irrigation of Greenhouse Tomatoes

Abstract

Three irrigation treatments were set up in northeast China to investigate soil water movement and root water uptake of greenhouse tomatoes, and the collected experimental data were simulated by HYDRUS-2D. The computation and partitioning of evapotranspiration data into soil evaporation and crop transpiration was carried out with the double-crop coefficient method. The HYDRUS-2D model successfully simulated the soil water movement, producing RMSE ranging from 0.014 to 0.027, an MRE ranging from 0.062 to 0.126, and R² ranging from 79% to 92%, when comparing model simulations with two-year field measurements. Under different water treatments, 83–90% of the total root quantity was concentrated in 0–20 cm soil layer, and the more the water deficit, the more water the deeper roots will absorb to compensate for the lack of water at the surface. The average area of soil water shortage in W₁ was 2.08 times that in W₂. W₃ treatment hardly suffered from water stress. In the model, parameter n had the highest sensitivity compared with parameters α and K_s, and sensitivity ranking was n > K_s > α. This research revealed the relationships between soil, crop and water under drip irrigation of greenhouse tomatoes, and parameter sensitivity analysis could guide the key parameter adjustment and improve the simulation efficiency of the model.

1. Introduction

Solar greenhouses have been widely used in agricultural production, meeting the growing diversified needs of people [1,2,3,4,5]. Tomatoes are one of the most important crops cultivated in the solar greenhouses [6,7,8,9]. Nowadays, drip-irrigation technology has been widely used in the cultivation of greenhouse crops, which can accurately transport water to the roots of crops and improve water-use efficiency and yield [10,11,12,13]. However, due to a lack of scientific guidance, most farmers irrigate without assessing the water requirements of crops, which leads to the waste of water resources. Studies have shown that, although a large amount of irrigation can promote plant growth and increase yield, it will increase water consumption and reduce fruit quality [14]. In addition, excessive irrigation will increase the air humidity in the greenhouse, leading to the aggravation of pests and diseases, and finally worsening the greenhouse environment [14,15]. Therefore, in order to save water resources, improve crop quality and optimize the greenhouse environment, many scholars have begun to explore the characteristics of the soil water distribution. However, field trials waste time and money and the results are susceptible to uncertainties, such as crops, soils, and meteorology.

Root water uptake is an important process of the terrestrial water cycle, and how this process works depends on the soil water content, root distribution, and root water uptake. Therefore, a comprehensive understanding of when and where plants absorb water from the soil is essential to reveal interrelationships between climate, soil and plant growth, as well as for the design and management of the drip-irrigation systems [16,17,18]. Because the root water uptake is difficult to measure from field experiments, some scholars have estimated root water uptake by the soil water balance method [17]. However, the calculated values were not accurate enough, so many scholars began to explore the laws of root water uptake through modeling. Root zone modeling is divided into two broad categories, microscopic and macroscopic methods, of which macroscopic models have undergone many developments, in which the introduction of sink S, based on Richard’s equation, is a common macroscopic method for simulating root water uptake [19].

With the in-depth study of soil water movement and root water uptake, various monitoring technologies have developed rapidly, and research models have been continuously improved [20,21]. Among them, the HYDRUS model is widely used in the study of soil water movement and root water uptake, with its user-friendly interface and standardized computer program. Nazari et al. [22] conducted a field experiment on the land around an apple tree, which mainly measured the soil water content and root water uptake under the subsurface drip irrigation. Nazari simulated it based on different scenarios in HYDRUS-2D, and the results showed that HYDRUS-2D had a good ability to estimate the water content under subsurface drip irrigation. Geng et al. [23] used the improved HYDRUS-2D model of dynamic root growth model to simulate water movement and root water uptake under different drip-irrigation conditions, and the results showed that the simulation results were in good agreement with the observation results, and the model could provide a basis for accurate irrigation of soilless substrate cultivation under drip irrigation. Karandish and Simunek et al. [24] combined the study of corn under drip irrigation with the HYDRUS-2D model, and the results showed that the HYDRUS-2D model could be reliably used to explore soil–water–plant interactions under water-scarce irrigation and partial root-zone-drying strategies. Li et al. [25] used the HYDRUS-2D model to explore the soil moisture dynamics of the root zone of tomato–maize intercrops under three water treatments, and he said that the results were very useful for designing the optimal irrigation plan for intercropping fields.

The HYDRUS model has been used to study soil water movement and root water uptake under drip irrigation by many scholars, but most studies have focused on field crops [26,27,28,29]. The application of the HYDRUS model in greenhouses is rarely reported. Moreover, most scholarly research on root water uptake focuses on the dynamic change of root water uptake during the whole growth period. Some scholars have proposed that due to various factors, such as soil type, irrigation change and uneven root distribution, soil water content in the root zone is usually heterogeneous. Therefore, plants often compensate for water uptake by roots and respond to soil water heterogeneity through adaptive root growth [18]. Thus, accurate estimation of compensating root water uptake is essential to understand root water uptake laws. This article discussed the following objectives: (1) using the HYDRUS-2D model to establish soil water movement model to explore the applicability of HYDRUS-2D model in a greenhouse by comparing observation data and simulation data; (2) establishing soil water movement and root water uptake model to investigate the characteristics of soil water movement and the laws of root water uptake under different water treatments; (3) making the use of numerical simulation method to reveal the soil–water–plant interaction under mulched drip irrigation of greenhouse tomatoes; and (4) find out the more sensitive parameters of the HYDRUS model by sensitivity analysis, which can guide the key parameter adjustment and improve the simulation efficiency of the model.

2. Materials and Methods

2.1. Overview of the Test Area

The experiments were conducted in no. 43 solar greenhouse of Shenyang Agricultural University Test Base, from March to July in 2020 and 2021, with geographical coordinates 41°82′ N, 123°57′ E. The test base is affected by the monsoon, precipitation is concentrated, and the temperature difference is large. January is the coldest month, with an average temperature of −11.0 °C, and July is the hottest month with an average temperature of 24.7 °C. The soil in the greenhouse is brown loam. The soil bulk density is 1.26 g·cm⁻³ and the field capacity (θ_FC) is 0.31 cm³·cm⁻³.

2.2. Experimental Design

In this experiment, tomatoes were used as the test material and the tomato variety was “Fenguang No. 1”. The experiment adopted the planting mode of a double row in a large ridge. Each cell was 7 m long and 1.3 m wide, with tomato planting row spacing of 50 cm and plant spacing of 40 cm. The irrigation conditions of each treatment were consistent. The mulched drip irrigation was adopted, and the drip flow rate was 1.6 L/h. The drip hole spacing was 50 cm, which corresponded to the plant. The test arrangement is shown in Figure 1.

In 2020, tomatoes were planted on 15 March and grown for 130 days. In 2021, tomatoes were planted on 16 March and grown for 125 days. Three water treatments were set up in this experiment and each water treatment was repeated three times. Water treatments were controlled by the upper and lower limits of irrigation, which were W₃: 85%θ_FC–95%θ_FC, W₂: 75%θ_FC–85%θ_FC, and W₁: 65%θ_FC–75%θ_FC. All treatments were fully irrigated at the seedling stage, and deficit irrigation was carried out in the third period of growth, until the experimental treatments were completed at the end of fruit harvesting.

Soil bulk density was measured by the ring knife method. Saturated water conductivity was determined by the constant head method in the interior. Soil particle composition (clay < 0.002 mm, silt < 0.002–0.05 mm and sand > 0.05 mm) was determined by Masterize 2000 laser size detector (Malvern, Greater Manchester, UK). The content of soil organic matter was determined by potassium dichromate volumetric method. Before irrigation, the initial soil water content was measured by the drying method. Soil samples were taken every 20 cm with a soil drill and measured to 60 cm. Three plants with good growth were selected for each treatment. The soil water content was monitored by CR1000X (Campbell Scientific, Inc., Logan, UT, USA) in time. The water probes were inserted into the soil in the center of the ridge, directly below the dropper and in the furrow, and the soil water content was recorded every 30 min at the depths of 10 cm, 20 cm, 40 cm, and 60 cm. The soil water content was corrected by the oven-drying method every 60 days. The arrangement of observation points is shown in Figure 2. A HOBO (Onset, Bourne, MA, USA) was set up in the open area of the test area to automatically record wind speed, air humidity, air temperature, atmospheric pressure, solar radiation, and other data. The data were measured every 15 min and recorded every 15 min. The average value was taken every day. In each growth stage of the plant, six representative plants were selected from each cell, and the roots were taken between the plants and between the rows, with a diameter of 7 cm root drill. The root depth was 60 cm, and each 10 cm had a layer. The roots were washed in the net bag. Black and white image files were scanned by a double-sided scanner (Seiko Epson, Nagano, Japan), and root morphological characteristics were analyzed by WinRHIZO (Regent Instruments, Montreal, QC, Canada). The leaf area index was calculated by AutoCAD in the early stage of growth, and LAI-2200C plant canopy analyzer (LI-COR, Lincoln, NE, USA) was used for measurement in the late stage. When measuring the plant height, six plants were randomly selected from each cell, and their natural plant height was measured with a tape measure. To calculate the root water uptake, after removing the gravity water from the soil profile, it was considered as the starting point for the root water uptake. The difference between the water content of each day, and the days after that, was determined as the root water uptake in that period. The reasons for reducing the soil water content over time were related to three factors: evaporation, root water uptake, and gravity water. After removing the gravity water from the soil, in the top layer of the soil, two factors of evaporation and root water uptake, and at lower depths only root water uptake could affect the outflow of water from the soil. Therefore, to calculate the root water uptake in the top layer, the evaporation was subtracted from the difference of the soil water content (the difference between soil water content was measured by Campbell CR1000X in two consecutive days [22]).

2.3. HYDRUS-2D Model

The water movement of tomatoes under drip irrigation in solar greenhouse was simulated based on the HYDRUS-2D model [30]. The Galerkin finite element was used to solve the Richards equation in this model. The formula is as follows:

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

(1)

where θ is soil volumetric moisture content (cm³·cm⁻³), h is the pressure head (cm), K(h) is the water conductivity (cm·d⁻¹), t is the simulation time (d), x and z are horizontal and vertical coordinates (cm), S(h) is the water absorption term of roots, which refers to the water absorption rate of roots in soil per unit time volume (d⁻¹).

In this model, the soil water retention curve, θ(h), by van Genuchten [31], and the unsaturated hydraulic conductivity function, K(h), by Mualem [32], were obtained from Equations (2)–(4) respectively:

$$\theta \left(h\right)={\theta }_r+\frac{{\theta }_s-{\theta }_r}{{\left(1+{\left(\alpha \left|h\right|\right)}^n\right)}^m}\left(m=1-\frac{1}{n}\right)$$

(2)

$$K\left(h\right)=K_s{S}_e^l{\left[1-{\left(1-S_e^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$m$}\right.}\right)}^m\right]}^2$$

(3)

$$S_e=\frac{\theta -{\theta }_r}{{\theta }_s-{\theta }_r},$$

(4)

where θ_r and θ_s denote the residual and saturated water content, respectively (L³·L⁻³), α is the inverse of the air-entry value (L⁻¹), K_s is the saturated hydraulic conductivity (L·T⁻¹), n is the pore-size distribution index, S_e is the effective water content (L³·L⁻³), and l is the pore-connectivity parameter, with an estimated value of 0.5, resulting from averaging conditions in a range of soils [32].

2.3.1. Initial Conditions and Boundary Conditions

In this experiment, the groundwater was buried deep, so the influence of groundwater on the simulated area was not considered. Therefore, the lower boundary of this profile was selected as the “free drainage boundary”. The lateral boundary was set as “zero flux boundary”. The upper boundary was divided into film-covered zone and unfilm-covered zone. The film-covered zone was set as “zero flux boundary”, because it cut off the water transmission path between the atmosphere and the surface, and the unfilm covered zone was set as “atmospheric boundary”. The drip holes were set as “variable flow boundary”, which was determined by the actual irrigation volume. Each boundary condition is shown in Figure 2. Since the whole drip-irrigation belt can be regarded as a symmetrical distribution of wide row centers, the right half of the ridge was selected for simulation in this simulation.

The point-source infiltration was transformed into a linear water flux, which can be calculated by the following formula [33]:

$$q=\frac{Q·L}{L^{\prime }},$$

(5)

where q is the water flux through the upper boundary (cm·d⁻¹), Q is the drip-irrigation flow (cm·d⁻¹), L is the length of the dripper control boundary (cm), and L’ is the drip input flow boundary (cm).

2.3.2. Root Water Uptake

In HYDRUS-2D, root water uptake is modeled as a sink term in the Richards equation, using the stress response function proposed by Feddes [34]:

$$S\left(h\right)=a\left(h\right)\cdot b\left(x,z\right)\cdot T_p\cdot S_t$$

(6)

$$b\left(x,z\right)=\frac{b^{\prime }\left(x,z\right)}{{\displaystyle \underset{{\Omega }_R}{\int }{b}^{\prime }\left(x,z\right)d\Omega }}$$

(7)

$$a\left(h\right)=\{\begin{array}{cc}\frac{h_1-h}{h_1-h_2}& h_2<h\le h_1\\ 1& h_3\le h\le h_2\\ \frac{h-h_4}{h_3-h_4}& h_4\le h\le h_3\end{array},$$

(8)

where b(x, z) is the water absorption distribution parameter of roots, which is determined according to the actual root distribution, T_p is the potential transpiration rate (cm·d⁻¹), a(h) is a dimensionless parameter of soil water pressure, S_t is the soil surface width related to the crop transpiration process (cm), h is the anaerobic point pressure water head of root water absorption (cm), h₂ is the most suitable root water absorption pressure head (cm), h₃ is the pressure water head at the end of root water absorption (cm), and h₄ is the pressure water head at the root water absorption droop point (cm). The specific parameters of root water absorption were directly selected in the HYDRUS-2D software by referring to the reference values proposed by Wesseling et al. [35].

2.3.3. Transpiration and Evaporation of Greenhouse Tomatoes

In the soil–plant–environment system of the greenhouse, due to the controllable environment, its water and heat transport mode is very different from that in the natural environment. In particular, the total radiation and wind speed in the greenhouse have greatly changed compared with that in the natural environment. Therefore, when calculating the evapotranspiration of crops in the greenhouse, the formula applicable to the natural environment cannot be directly applied. Thus, the double-crop coefficient method was used to calculate potential transpiration and potential evaporation [36].

Due to the characteristics of low wind speed in the greenhouse, Gong [36] set the aerodynamic resistance term as 295 s·m⁻¹, and integrated it into the Penman–Monteith equation to accurately estimate the reference evapotranspiration (ET₀) of greenhouse crops:

$$E{T}_0=\frac{0.408\Delta (R_n-G)+\gamma [628D/(T_a+273)]}{\Delta +1.24\gamma },$$

(9)

where ET₀ is the reference crop evapotranspiration (mm·d⁻¹), R_n is net radiation (MJ·m⁻²·d⁻¹), G is soil heat flux (MJ·m⁻²·d⁻¹), γ is the constant of the wet and dry table (kPa·°C ⁻¹), ∆ is the slope of temperature change with saturated water vapor pressure (kPa·°C ⁻¹), D is the saturated vapor pressure difference (kPa), and T_a is the air temperature (°C).

For dual crops, the crop coefficient (K_c) was divided into two parts: the basic crop coefficient (K_cb) and the soil evaporation coefficient (K_e), which were used to estimate crop transpiration and soil evaporation, respectively. The formula recommended by FAO [37] was used for calculation:

$$E_s=K_e\cdot E{T}_0$$

(10)

$$T_r=K_s\cdot K_{cb}\cdot E{T}_0,$$

(11)

where K_cb is the coefficient of the base crop, K_e is soil evaporation coefficient, and ET₀ is the reference evapotranspiration.

2.4. Susceptivity Analysis

In this paper, single-factor sensitivity analysis was used. Firstly, each parameter was changed by an appropriate multiple, one by one. Then, the sensitivity coefficient was calculated according to the simulation results, and the influence degree of the change of a single parameter on the objective function (water content of different soil layers) was analyzed. A_i > 0 indicates that the independent variable corresponds to a positive influence, and vice versa, an inverse influence. The greater |A_i| suggests the higher sensitivity:

$$A_i=\frac{\Delta y/y}{\Delta x_i/x_i},$$

(12)

where y is the value of the objective function, x_i is the ith parameter, ∆y is the change value in the objective function, ∆x_i is the change value in the ith parameter.

2.5. Calibration and Validation of HYDRUS-2D Model

The simulated and measured values of soil water content were evaluated by the mean relative error (MRE), determination coefficient (R²), and root mean square error (RMSE).

$$\mathrm{MRE}=\frac{1}{n^{\prime }}{\displaystyle \sum _{i=1}^{n^{\prime }}\frac{\left|S_i-M_i\right|}{S_i}}\times 100\%$$

(13)

$${\mathrm{R}}^2=\frac{{\displaystyle \sum _{i=1}^{n^{\prime }}\left(M_i-M_{ave}\right)\left(S_i-S_{ave}\right)}}{\sqrt{{\displaystyle \sum _{i=1}^{n^{\prime }}\left(M_i-M_{ave}\right)}}\sqrt{{\displaystyle \sum _{i=1}^{n^{\prime }}\left(S_i-S_{ave}\right)}}},$$

(14)

$$\mathrm{RMSE}=\sqrt{\frac{1}{n^{\prime }}{\displaystyle \sum _{i=1}^{n^{\prime }}{\left(S_i-M_i\right)}^2}}$$

(15)

where S_i is the simulation value, M_i is the measured value, i is the observation point, n’ is the total number of observation points, S_ave and M_ave are the average simulated value and the average measured value, respectively.

3. Results

3.1. Parameter Determination and Validation of Soil Water Movement Model

The test data of 2020 was used to determine the model parameters, and the test data of 2021 was used to validate the model. The measured values and simulated values of different soil layers at different times under each treatment are shown in Figure 3. Figure 3 shows that the simulated values and measured values of each treatment are evenly distributed on both sides of the 1:1 line. Therefore, the greenhouse soil water movement model, constructed by the HYDRUS-2D model, has a high simulation accuracy. The MRE of each treatment in two years ranged from 0.062 to 0.126 cm³·cm⁻³, the R² ranged from 79% to 92%, and the RMSE ranged from 0.014 to 0.027 cm³·cm⁻³. Detailed error analysis values are shown in

Table 1. Statistical indicators to evaluate the accuracy of the HYDRUS-2D model in the estimation of soil water content (cm³·cm⁻³) under different water treatments.

Year	Moisture Treatment	R2	MRE (cm3·cm−3)	RMSE (cm3·cm−3)
2020	W1	0.86	0.1260	0.0230
	W2	0.79	0.1040	0.0270
	W3	0.89	0.0620	0.0140
2021	W1	0.87	0.0840	0.0170
	W2	0.89	0.0790	0.0160
	W3	0.92	0.0820	0.0160

Notes: MRE represents the mean relative error, R² represents the determination coefficient and RMSE represents the root mean square error.

. Soil hydraulic parameters were predicted based on the Rosetta model built into the HYDRUS-2D model. Soil particle composition (clay, silt, sand, volume percentage) and initial bulk density were used to predict soil hydraulic parameters. The 0–60 cm soil layer was divided into three layers, and the average value of each layer was considered. The soil hydraulic parameters, after calibration, are shown in

Table 2. Soil hydraulic parameters of different soil layers.

Index	Soil Layer (cm)
	0–20	20–40	40–60
Residual soil moisture (cm3·cm−3)	0.09	0.08	0.07
Saturated soil moisture (cm3·cm−3)	0.42	0.40	0.38
Shape parameter (cm−1)	0.0070	0.0070	0.0050
Parameter n	1.68	1.48	1.48
Saturated hydraulic conductivity (cm·d−1)	10.45	1.43	1.20
l	0.50	0.50	0.50

.

3.2. Simulation of Soil Water Movement

Figure 4 shows that under different water treatments, with the increase of irrigation level, the surface soil moisture content kept rising. Most soil water content data under different water treatments were within the range of 1.5 IQR (interquartile distance). The width of the box reflects the fluctuation degree of the data to some extent. In Figure 4, it can be observed that irrigation made the water soil content of the 0–40 cm fluctuate greatly, and the width of the box of 20 cm soil layer was the largest, indicating that irrigation had a significant impact on the soil water content of the 0–20 cm layer. The water content of shallow soil was lower than that of deep soil under each water treatment, which was related to water absorption of tomato roots and evaporation of the surface soil. The water content of the deep soil was large and relatively stable, which was related to the low distribution of tomato roots and the redistribution of the soil water.

Figure 5 shows the soil water movement at 1 h, 5 h, 12 h, and 24 h after one irrigation, under three water treatments at flowering and fruiting stages. Figure 5 shows that the soil water migrated to 30 cm at 1h after irrigation began, indicating that water migrated fast in the vertical direction of the soil. At 5 h after irrigation began, the water movement of W₁ treatment began to slow down. W₂ and W₃ treatments still had a downward trend, but W₃ treatment had an obvious downward trend. At 12 h after irrigation began, the soil water under W₁ and W₂ treatments stopped moving downward, and the vertical depth reached about 35 cm and 40 cm, respectively. Due to the higher water content of W₃ treatment, water continued to move at 12 h after irrigation began, which had an impact on the soil water content below 40 cm, indicating that adequate irrigation would make water leak into the deep layer, resulting in the waste of water resources. At 24 h after irrigation began, water movement under each treatment remained stable. It could be seen that the soil water content of each soil layer under W₃ treatment was significantly higher than that under W₁ and W₂ treatment. At the depth of 0–20 cm, the average soil water content under W₃ treatment was 16.2% and 8.5% higher than that under W₁ and W₂ treatment, 14.8% and 7.6% higher in the depth of 20–40 cm, and 10.9% and 6.1% higher in the depth of 40–60 cm during the whole growth period of tomatoes in 2020.

3.3. Simulation of Root Water Uptake

Figure 6 shows the root density of tomatoes in the 0–60 cm soil layer under three water treatments, in 2020 and 2021. It can be seen from Figure 6 that the distribution of root density in two years was consistent. Muller showed that at each stage of growth, the distribution of root density was similar regardless of treatment [38]. This study showed that the root density of tomatoes was mainly concentrated in the 0–20 cm soil layer under different water treatments, and 83–90% of the total root quantity of tomato was concentrated in the 0–20 cm soil layers under different water treatments. However, the root density under different water treatments varied greatly in different soil layers. In 2020, the root density at the depth of 0–20 cm under W₁ treatment was 51.19% higher than that under W₃ treatment, indicating that the higher the water deficit, the more concentrated the tomato roots would be in the surface soil. The root density under W₁ treatment decreased approximately linearly after reaching the maximum value in the 0–10 cm soil layer, and the root density in the deep soil was less than that of adequate irrigation. It is worth noting that in the 50–60 cm soil layer, the root density under W₁ treatment (0.53 cm³·cm⁻³) was slightly higher than that under W₂ (0.46 cm³·cm⁻³) and W₃ treatments (0.42 cm³·cm⁻³), which might be due to the water deficit in the surface soil caused by root water uptake and soil evaporation. At this point, the tomato roots extended deeper into the soil, absorbing water from the deeper soil to sustain their life activities. The experimental results also showed that the longest root under W₁ treatment was about 58 cm, and was slightly higher than that under W₂ and W₁ treatments.

The blooming and setting stage (the third period) and the fruiting stage (the fourth period) of tomatoes were the periods when the roots were more active in water uptake. Figure 7 shows the root water uptake of tomatoes in the blooming and setting stage and fruiting stage in 2020. Under the same water treatment, the water absorption of roots in the blooming and setting stage was higher than that in the fruiting stage. This was because as the plants began to age in the later stage, the leaf appeared curled up, and the decrease of leaf area led to the decrease of plant transpiration, thus reducing the root water uptake. Under different water treatments in the blooming and setting stage and fruiting stage, the water absorption of tomato roots was mainly concentrated in the 0–20 cm layer. This was because the 0–20 cm soil layer was the area with the highest root density, so 0–20 cm was the main water uptake layer of tomatoes. W₁ water treatment was irrigated on 16 May (the 63rd day of transplantation). One day before irrigation (the 62nd day of transplantation), the water absorption of tomato roots was mainly concentrated in the 10–30 cm soil layer, while the roots of the 0–10 cm soil layer did not absorb water at all. This was due to the decrease of soil water content caused by water uptake of surface roots and soil evaporation. Water deficit inhibited the water absorption of surface roots. At this time, tomatoes would absorb soil water through deep roots to maintain their life activities. Studies have shown that when the water content of the surface soil with high root density decreases, crops would increase the water absorption rate of the deep roots to compensate [18]. In the next irrigation, the water absorption rate of 0–10 cm roots reached 0.03 cm³·cm⁻³, indicating that water deficit promotes the water absorption of surface roots in the next irrigation to some extent.

3.4. Two-Dimensional Distribution of Soil Water Content

Since the variation trend of soil water content in two years was the same, the two-dimensional distribution characteristics of soil water content before the day of three irrigations were analyzed in 2020. Figure 8 shows the two-dimensional distribution of soil water content on the day before three irrigations, under different water treatments. As can be seen in Figure 8, soil water deficit and root distribution were highly consistent. Water deficit under different water treatments was mainly concentrated in the surface soil layer (0–20 cm), which was consistent with the main distribution layer of roots. Therefore, water deficit in surface soil was mainly affected by water absorption by roots. The deep soil almost always maintained a higher soil water content, because there were fewer tomato roots in the 40–60 cm soil layer, and water redistribution would recharge the water in the deep soil. The degree of soil water deficit and the main water-deficient area were different under different treatments. W₁ treatment had the highest water deficit degree, with the main water-deficient area concentrated in 0–40 cm, while W₂ treatment had a lower water deficit degree, with the main water-deficient layer area concentrated in 0–20 cm. There was almost no water deficit in W₃ treatment.

Although the amount of water up to the withering point is theoretically considered to be effective water, the amount of water absorbed by crops decreases significantly before the withering point appears. When soil water content is very low, soil water is tightly bound to the surface of the soil, and soil water is difficult to be absorbed by crops. When the soil water content drops to a critical level, the water in the soil no longer flows rapidly to the roots to meet the transpiration needs of the crops, and the plants begin to face water stress [37]. According to the soil texture data given by the UNSODA database, the soil water content was about 0.21–0.24 cm³·cm⁻³ when water stress began to appear in the soil [25]. It can be seen that when the soil water content was lower than this value, the tomato roots were in a state of stress. Under W₁ treatment, the soil-water-deficit areas on the day before three irrigations were 1848.67 cm², 2209.37 cm², and 2148.76 cm². Under W₂ treatment, the soil-water-deficit areas on the day before three irrigations were 903.65 cm², 881.75 cm², and 1200.73 cm². W₃-treated soil was almost always moist. Therefore, soil water distribution is greatly affected by water absorption by crop roots. Hence, it is of great significance to explore the laws of root water uptake and the characteristics of soil water movement for water-saving irrigation.

3.5. Sensitivity of Parameters

Parameter sensitivity analysis is the basis of soil water dynamic simulation. In this paper, the single-factor sensitivity analysis method was used to calculate the sensitivity coefficient (A_i) according to the simulation results. The ratings of parameter sensitivity are shown in

Table 3. Rating of parameter sensitivity.

Level	The Range of Ai Value	Sensitivity Characterization
Ⅰ	≥1	Highly sensitive
II	[0.2, 1)	Sensitive
III	[0.05, 0.2)	Moderate sensitivity
IV	[0, 0.05)	Insensitive

Note: A_i represents sensitivity coefficient.

.

It is well known that α is the intake value, and K_s and α have a good correlation. θ_s and θ_r can be determined accurately according to the measured maximum and minimum water content. However, the parameters α, n and K_s are determined with great uncertainty. Therefore, this paper focused on the analysis of the sensitivity of parameters α, n and K_s. The independent variables of the sensitivity analysis were parameters α, n and K_s in the three-layer soil, a total of nine parameters. The target function of sensitivity analysis was the water content of 20 cm, 40 cm, and 60 cm soil layers. In

Table 4. Sensitivity analysis of parameters α, n and K_s to water content of 20 cm, 40 cm, and 60 cm soil layer.

Independent Variable	Sensitivity Coefficient
	$\mathit{\theta }$20cm	$\mathit{\theta }$40cm	$\mathit{\theta }$60cm
α1	−0.098	0.041	0.058
n1	−0.918 *	0.128	0.233 *
KS1	−0.033	−0.043	0.022
α2	0.114	−0.255 *	−0.058
n2	0.098	−1.404 *	0.291 *
KS2	−0.033	−0.043	0.012
α3	0.066	0.128	−0.116
n3	0.033	0.128	−1.279 *
KS3	−0.033	−0.085	−0.116

Notes: * indicate that the absolute value of sensitivity coefficient is greater than 0.2. θ_20cm represents the average sensitivity coefficient of water content in the 20 cm soil layer to different independent variable, and the others are the same. A_i > 0 indicates that the independent variable corresponds to a positive influence, and vice versa, an inverse influence.

, the hydraulic parameters α, n and K_s of the three soil layers, were increased by −5%, −10%, −15%, −20%, 5%, 10%, 15%, and 20%, respectively, to obtain the average sensitivity coefficients of the water content of 20 cm, 40 cm, and 60 cm soil layers. Table 4 shows that parameter n had the highest sensitivity compared with parameters α and K_s, and the sensitivity coefficients of parameter n in three soil layers were more than 0.2, reaching the degree of sensitivity. In addition, parameter n of each soil layer had the highest sensitivity to water content of the corresponding soil layer. The sensitivity coefficient of parameter n₁ was up to 0.098, and the sensitivity coefficients of n₂ and n₃ were both over 1, which was highly sensitive. However, the sensitivity of the parameters α and K_s to the soil water content of the three layers only reached moderate sensitivity.

4. Discussion

Mulching drip irrigation is an efficient water-saving irrigation technology that has been widely used in China’s agricultural production [39]. For drip irrigation, too much irrigation can lead to subsurface seepage and water loss. Too much or too little moisture in the soil is bad for the growth of crops [12,23], so it is particularly important to explore the laws of soil water movement. According to this study, under different water treatments, irrigation mainly affected the water content of the 0–40 cm soil layer, which significantly affected the 0–20 cm soil layer and had no effect on the 40–60 cm soil layer. The insignificant change in the water content of the 40–60 cm soil layer was related to the small distribution of the roots and water redistribution. This conclusion is similar to the conclusions of the soil moisture study by Li [40]. Shan [41] came to a similar conclusion when he explored the redistribution of soil water in the field environment of slope under drip-irrigation conditions. The results showed that the wetting circle extended to 18–20 cm in 24 h, and when water penetrated deeper into the soil, the adjacent wetting volume merged, and the wetting front disappeared before reaching 50 cm. This also proved that soil water mainly moved in 0–40 cm soil layer under drip irrigation.

Accurately quantifying root water uptake (RWU) and characterizing its temporal variation can help optimize irrigation planning and increase crop productivity for sustainable development [42]. Tomatoes are a kind of shallow-rooted crop. Under different water treatments, the water absorption of the roots mainly concentrated in the 0–20 cm soil layer, because the maximum root density of tomatoes is mainly concentrated in the 0–20 cm soil layer, and the root density of the soil below 20 cm decreased linearly. Muller’s study [38] showed that the root density of tomatoes increased sharply from the ground, with a depth of 5–12 cm and an average depth of 7 cm, and then decreased relatively linearly to the maximum root depth. The experiment found that the lower the irrigation level, the more the roots concentrated in the surface soil, which was similar to the experimental results of Muller [38]. Of the total root density of tomatoes, 83–90% was concentrated in the 0–20 cm soil layers under different water treatments. The maximum root length of tomatoes under W₁ treatment were higher than that under W₂ and W₃ treatments, which was due to the less frequent irrigations. The water absorption of the surface roots and soil evaporation led to less water content in the surface soil, which made the upper roots subject to water stress. Tomatoes only maintained their life activities by growing downward and absorbing water from deep soil. This conclusion is similar to that of Thomas [18], Ge [43] and Shabbir et al. [44]. This characteristic of root growth was also shown in other crops. Li [45] also found that the root of jujube would spread deeper into the soil under the condition of deficit irrigation when he studied the root growth under drip irrigation. Studies showed that low irrigation levels could promote the water absorption rate of surface roots at the next irrigation, which was similar to Deb [46].

Soil water distribution before irrigation under different treatments showed a high consistency between soil water distribution and root distribution [45]. Muller [38] also showed that when plants were subjected to water stress, root growth would adapt to the water changes, reflecting the adaptation of roots to high-soil-moisture areas. Nazari’s research [22] showed that the root density and soil water content were two important factors that determined the water absorption of roots, and they had an interactive effect. On the day before the irrigations, the surface soil under each treatment produced different degrees of water shortage, which was due to the root absorption of tomatoes and the evaporation of the surface soil, Malash [47] also said that on the day before irrigations, the surface soil (0–30 cm) water content would be low, which was related to surface soil evaporation and root water uptake. Therefore, it is of great significance to master the relationship between soil moisture and root water absorption for saving irrigation.

The sensitivity analysis of three parameters of the HYDRUS-2D model showed that n is the most sensitive parameter compared with α and K_s, and both of them are highly sensitive. Cheviron [48] also came to the same conclusion.

5. Conclusions

In this study, based on a two-year field experiment, models of soil water movement and root water uptake of greenhouse tomatoes under drip irrigation were established by the HYDRUS-2D model, in order to explore the characteristics of soil water movement and the laws of root water uptake under different water treatments, and finally reveal the relationships between soil, water and plants under water-saving irrigations in a greenhouse. It provided the theoretical basis for formulating the strategy of precise drip irrigation in a solar greenhouse. This article drew the following conclusions through research: (1) The HYDRUS-2D model can be used to investigate the soil water movement of tomatoes under drip irrigation in solar greenhouse. The MRE of each treatment in two years ranged from 0.062 to 0.126, the R² ranged from 79% to 92%, and the RMSE ranged from 0.014 to 0.027. (2) Under different treatments, irrigation mainly affected the water content of 0–40 cm soil, and significantly affected the water content of 0–20 cm soil, but had almost no effect on the soil layer of 40–60 cm. At 12 h after irrigation began, water stopped moving under W₁ and W₂ treatments, and water moved to about 35 cm and 40 cm in the vertical direction, respectively. At 24 h after irrigation began, water movement tended to be stable. (3) The results showed that 83–90% of total root quantity of tomato was concentrated in the 0–20 cm soil layers under different water treatments, and the higher the water deficit, the more concentrated the roots were on the surface soil. A certain degree of water stress would inhibit the water absorption of surface roots. In this case, the roots would extend downward and maintain life activities by absorbing deep-soil water. Certain water stress could promote the water absorption rate of 0–10 cm root in the next irrigation, and the maximum was up to 0.03 cm³·cm⁻³. (4) There was a high consistency between soil water distribution and root distribution. On the day before irrigations, different degrees of water deficit appeared in the surface soil under different treatments, and the main deficit area was concentrated in the surface soil (0–20 cm). The average area of soil water shortage in W₁ was 2.08 times that in W₂. W₃ treatment hardly suffered from water stress. (5) In the model, parameter n had the highest sensitivity compared with parameters α and K_s, and sensitivity ranking was n > K_s > α.