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

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{2}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 W

_{1}was 2.08 times that in W

_{2}. W

_{3}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

## 2. Materials and Methods

#### 2.1. Overview of the Test Area

^{−3}and the field capacity (θ

_{FC}) is 0.31 cm

^{3}·cm

^{−3}.

#### 2.2. Experimental Design

_{3}: 85%θ

_{FC}–95%θ

_{FC}, W

_{2}: 75%θ

_{FC}–85%θ

_{FC}, and W

_{1}: 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.

#### 2.3. HYDRUS-2D Model

^{3}·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}).

_{r}and θ

_{s}denote the residual and saturated water content, respectively (L

^{3}·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 (L

^{3}·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

^{−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

_{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), h

_{2}is the most suitable root water absorption pressure head (cm), h

_{3}is the pressure water head at the end of root water absorption (cm), and h

_{4}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

^{−1}, and integrated it into the Penman–Monteith equation to accurately estimate the reference evapotranspiration (ET

_{0}) of greenhouse crops:

_{0}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).

_{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:

_{cb}is the coefficient of the base crop, K

_{e}is soil evaporation coefficient, and ET

_{0}is the reference evapotranspiration.

#### 2.4. Susceptivity Analysis

_{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:

_{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

^{2}), and root mean square error (RMSE).

_{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

^{3}·cm

^{−3}, the R

^{2}ranged from 79% to 92%, and the RMSE ranged from 0.014 to 0.027 cm

^{3}·cm

^{−3}. Detailed error analysis values are shown in Table 1. 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.

#### 3.2. Simulation of Soil Water Movement

_{1}treatment began to slow down. W

_{2}and W

_{3}treatments still had a downward trend, but W

_{3}treatment had an obvious downward trend. At 12 h after irrigation began, the soil water under W

_{1}and W

_{2}treatments stopped moving downward, and the vertical depth reached about 35 cm and 40 cm, respectively. Due to the higher water content of W

_{3}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 W

_{3}treatment was significantly higher than that under W

_{1}and W

_{2}treatment. At the depth of 0–20 cm, the average soil water content under W

_{3}treatment was 16.2% and 8.5% higher than that under W

_{1}and W

_{2}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

_{1}treatment was 51.19% higher than that under W

_{3}treatment, indicating that the higher the water deficit, the more concentrated the tomato roots would be in the surface soil. The root density under W

_{1}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 W

_{1}treatment (0.53 cm

^{3}·cm

^{−3}) was slightly higher than that under W

_{2}(0.46 cm

^{3}·cm

^{−3}) and W

_{3}treatments (0.42 cm

^{3}·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 W

_{1}treatment was about 58 cm, and was slightly higher than that under W

_{2}and W

_{1}treatments.

_{1}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 cm

^{3}·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

_{1}treatment had the highest water deficit degree, with the main water-deficient area concentrated in 0–40 cm, while W

_{2}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 W

_{3}treatment.

^{3}·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 W

_{1}treatment, the soil-water-deficit areas on the day before three irrigations were 1848.67 cm

^{2}, 2209.37 cm

^{2}, and 2148.76 cm

^{2}. Under W

_{2}treatment, the soil-water-deficit areas on the day before three irrigations were 903.65 cm

^{2}, 881.75 cm

^{2}, and 1200.73 cm

^{2}. W

_{3}-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

_{i}) according to the simulation results. The ratings of parameter sensitivity are shown in Table 3.

_{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, 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 n

_{1}was up to 0.098, and the sensitivity coefficients of n

_{2}and n

_{3}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

_{1}treatment were higher than that under W

_{2}and W

_{3}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].

_{s}, and both of them are highly sensitive. Cheviron [48] also came to the same conclusion.

## 5. Conclusions

^{2}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 W

_{1}and W

_{2}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 cm

^{3}·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 W

_{1}was 2.08 times that in W

_{2}. W

_{3}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.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Coefficient of determination (R

^{2}) between simulated and measured soil water content (cm

^{3}·cm

^{−3}) under different water treatments, in 2020 and 2021.

**Figure 4.**Soil water content (cm

^{3}·cm

^{−3}) of 20 cm, 40 cm, and 60 cm soil layer under different treatments, in 2020 and 2021.

**Figure 5.**Soil water movement (cm) at 1 h, 5 h, 12 h, and 24 h after irrigation began under different water treatments, in blooming and setting stage.

**Figure 6.**Root density (cm

^{3}·cm

^{−3}) of tomatoes in the 0–60 cm soil layer under different water treatments, in 2020 and 2021.

**Figure 7.**Water absorption of tomato roots (cm

^{3}·cm

^{−3}) in the 0–60 cm soil layer under different water treatments in blooming and setting stage and fruiting stage, in 2020.

**Figure 8.**Distribution of soil water content (cm

^{3}·cm

^{−3}) on the day before three irrigations under different water treatments, in 2020.

**Table 1.**Statistical indicators to evaluate the accuracy of the HYDRUS-2D model in the estimation of soil water content (cm

^{3}·cm

^{−3}) under different water treatments.

Year | Moisture Treatment | R^{2} | MRE (cm^{3}·cm^{−3}) | RMSE (cm^{3}·cm^{−3}) |
---|---|---|---|---|

2020 | W_{1} | 0.86 | 0.1260 | 0.0230 |

W_{2} | 0.79 | 0.1040 | 0.0270 | |

W_{3} | 0.89 | 0.0620 | 0.0140 | |

2021 | W_{1} | 0.87 | 0.0840 | 0.0170 |

W_{2} | 0.89 | 0.0790 | 0.0160 | |

W_{3} | 0.92 | 0.0820 | 0.0160 |

^{2}represents the determination coefficient and RMSE represents the root mean square error.

Index | Soil Layer (cm) | ||
---|---|---|---|

0–20 | 20–40 | 40–60 | |

Residual soil moisture (cm ^{3}·cm^{−3}) | 0.09 | 0.08 | 0.07 |

Saturated soil moisture (cm ^{3}·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 |

Level | The Range of A_{i} Value | Sensitivity Characterization |
---|---|---|

Ⅰ | ≥1 | Highly sensitive |

II | [0.2, 1) | Sensitive |

III | [0.05, 0.2) | Moderate sensitivity |

IV | [0, 0.05) | Insensitive |

_{i}represents sensitivity coefficient.

**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} | |

α_{1} | −0.098 | 0.041 | 0.058 |

n_{1} | −0.918 * | 0.128 | 0.233 * |

K_{S1} | −0.033 | −0.043 | 0.022 |

α_{2} | 0.114 | −0.255 * | −0.058 |

n_{2} | 0.098 | −1.404 * | 0.291 * |

K_{S2} | −0.033 | −0.043 | 0.012 |

α_{3} | 0.066 | 0.128 | −0.116 |

n_{3} | 0.033 | 0.128 | −1.279 * |

K_{S3} | −0.033 | −0.085 | −0.116 |

_{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.

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## Share and Cite

**MDPI and ACS Style**

Sun, L.; Li, B.; Yao, M.; Mao, L.; Zhao, M.; Niu, H.; Xu, Z.; Wang, T.; Wang, J.
Simulation of Soil Water Movement and Root Uptake under Mulched Drip Irrigation of Greenhouse Tomatoes. *Water* **2023**, *15*, 1282.
https://doi.org/10.3390/w15071282

**AMA Style**

Sun L, Li B, Yao M, Mao L, Zhao M, Niu H, Xu Z, Wang T, Wang J.
Simulation of Soil Water Movement and Root Uptake under Mulched Drip Irrigation of Greenhouse Tomatoes. *Water*. 2023; 15(7):1282.
https://doi.org/10.3390/w15071282

**Chicago/Turabian Style**

Sun, Lei, Bo Li, Mingze Yao, Lizhen Mao, Mingyu Zhao, Hongfei Niu, Zhanyang Xu, Tieliang Wang, and Jingkuan Wang.
2023. "Simulation of Soil Water Movement and Root Uptake under Mulched Drip Irrigation of Greenhouse Tomatoes" *Water* 15, no. 7: 1282.
https://doi.org/10.3390/w15071282