# Simulation of the Water Dynamics and Root Water Uptake of Winter Wheat in Irrigation at Different Soil Depths

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}/cm

^{3}. The maximum average relative error was 7.95%. The maximum root mean square error was 0.28 cm

^{3}/cm

^{3}. Therefore, the model has a high simulation accuracy and can be used to simulate the distribution and dynamic changes of SWC of winter wheat in irrigation at different soil depths. The experimental data showed that irrigation soil depth has a significant effect on the root distribution of winter wheat (p < 0.05), and deep irrigation can reduce the root length density (RLD) in the upper soil layers and increase the RLD in the deeper soil layers. The dynamic simulation of RWU and SWC showed that deep irrigation can increase the SWC and RWU in deep soil and decrease the SWC and RWU in upper soil. Consequently, deep irrigation can increase the transpiration of winter wheat, reduce evaporation and evapotranspiration, and increase the yield of winter wheat.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Site

#### 2.2. Experimental Design

#### 2.3. Irrigation Design

_{Di}is the depth of irrigation (cm); α

_{i}is the irrigation depth coefficient, i = 1, 2, 3 (the irrigation depth coefficients of T1, T2, and T3 were 0, 0.4, and 0.7 respectively). H

_{mi}is the root distribution depth of winter wheat (cm).

_{i}and θ

_{0i}denote the initial soil moisture content (cm

^{3}/cm

^{3}) and irrigation upper limit (cm

^{3}/cm

^{3}, 85% of field water capacity), respectively, and H is the thickness of the planned wetting layer of the irrigation hole (cm).

#### 2.4. Measurement Methods

## 3. The Model for the Soil Water Dynamics of Winter Wheat in Irrigation at Different Soil Depths

#### 3.1. Governing Equation

^{3}/cm

^{3}); h is the soil water pressure head (cm); t is the time (hour); z is the vertical space coordinate (cm); K (hour) is the unsaturated hydraulic conductivity (cm/h); and Q is the intensity of water supply at different depths (1/hour), which is meaningful only at the irrigation depth of the irrigation period but 0 at other time and depths; and S is the RWU rate (l/hour).

_{s}is the saturated water content (cm

^{3}/cm

^{3}); θ

_{r}is the residual water content (cm

^{3}/cm

^{3}); l is the tortuosity parameter, generally taken as 0.5; K

_{s}is the saturated hydraulic conductivity (cm/hour); and n and α are the empirically fitted parameters.

^{3}), and z

_{m}is the maximum depth of root distribution (cm).

_{50}represents the pressure head at which the water extraction rate is reduced by 50% under negligible osmotic stress, and p is an experimental constant with the value of approximately 3.

_{c}is the potential crop evapotranspiration, which was estimated as follows:

_{0}is the reference crop evapotranspiration calculated using the Penman–Monteith formula [30], and K

_{c}is the crop coefficient, which is determined according to a previous study [30].

#### 3.2. Initial Condition

#### 3.3. Boundary Conditions

_{s}is the surface evaporation intensity (cm/hour).

_{300}is the pressure head that corresponds to the measured water content at the bottom (cm).

_{s}is calculated using the following:

_{c}and h

_{cc}are the critical values of water potential at the soil surface (cm), and E

_{p}is the potential evaporation on the soil surface (cm/hour) calculated by the following:

#### 3.4. Model Parameter Calibration

_{r}, θ

_{s}, α, n, and K

_{s}in the soil water movement parameter VG model; h

_{c}and h

_{cc}in the soil evaporation model and h

_{50}in the water stress function. The rationality of the model parameters directly affects the simulation accuracy of the model. In this study, the inverse method was used to solve the model parameters. The inverse method was used to determine the model parameters by solving the minimum value of the objective function that represents the difference between the experimental value and the model predicted value:

_{j}is the measured SWC, θ(h

_{j}, X) is the calculated SWC of the model, M is the number of measured soil moisture samples, and X is the parameter vector (θ

_{r}, θ

_{s}, α, n, K

_{s}, h

_{c}, h

_{cc}, h

_{50}) to be solved.

#### 3.5. Model Evaluation

^{s}is the simulated water content (cm

^{3}/cm

^{3}), θ

^{R}is the measured moisture content (cm

^{3}/cm

^{3}), $\overline{\theta}$ is the average water content (cm

^{3}/cm

^{3}), and l is the number of measuring points.

## 4. Results and Discussion

#### 4.1. Spatial and Temporal Distributions of Winter Wheat at Different Irrigation Depths

^{3}); z is the vertical space coordinate (cm); t is the number of days after winter wheat sowing(day); and a, b, c, d, and f are the fitting parameters.

#### 4.2. Evaluation of the Soil Water Movement Model in Irrigation at Different Soil Depths

#### 4.3. Simulation Analysis of Soil Water Dynamics at Different Irrigation Depths

#### 4.4. Simulation Analysis of RWU of Winter Wheat During Irrigation at Different Soil Depths

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The schematic diagram of the test layout. (

**a**) Field layout; (

**b**) Test equipment. TRIME refers to the time domain reflectometry with intelligent microElements.

**Figure 2.**The distributions of the RLD of winter wheat. (

**a**) Jointing stage; (

**b**) Heading stage; (

**c**) Filling stage; (

**d**) Maturity stage.

**Figure 3.**The linear relationship between the experimental and simulated values of SWC. (

**a**) T1 treatment; (

**b**) T2 treatment; (

**c**) T3 treatment.

**Figure 4.**The comparison of the calculated and measured soil water dynamics of winter wheat during irrigation at different soil depths. (

**a**) T1 treatment; (

**b**) T2 treatment; (

**c**) T3 treatment.

**Figure 5.**The dynamics of the RWU rate of winter wheat at different irrigation depths. (

**a**) T1 treatment; (

**b**) T2 treatment; (

**c**) T3 treatment.

**Figure 6.**The comparison of the total RWU of winter wheat in different soil layers (

**a**) and the water consumption composition of winter wheat (

**b**) at different soil depths irrigation. Tr is the transpiration of winter wheat, E is the evaporation of winter wheat, and ET is the evapotranspiration of winter wheat.

Depths | Soil Texture Composition (%) | Soil Texture | Bulk Density | Field Capacity | ||
---|---|---|---|---|---|---|

(cm) | 0.02–2 mm | 0.002–0.02 mm | <0.002 mm | (g/cm^{3}) | (cm^{3}/cm^{3}) | |

0–20 | 34.4 | 49.0 | 16.6 | Silty clay loam | 1.49 | 0.295 |

20–50 | 33.6 | 50.0 | 16.4 | Silty clay loam | 1.61 | 0.277 |

50–90 | 33.3 | 45.8 | 20.9 | Silty clay loam | 1.62 | 0.291 |

90–160 | 29.8 | 49.3 | 20.9 | Silty clay loam | 1.63 | 0.304 |

160–210 | 22.3 | 53.0 | 24.7 | Silty clay loam | 1.54 | 0.340 |

210–300 | 25.4 | 51.7 | 22.9 | Silty clay loam | 1.51 | 0.317 |

**Table 2.**The irrigation time, irrigation hole setting, irrigation scheme depth, and irrigation quota of winter wheat.

Treatment | Irrigation Time | Irrigation Hole Depth (cm) | Amount of Irrigation Per Hole (mm) | Maximum Root Depth (cm) | Irrigation Scheme Depth (cm) |
---|---|---|---|---|---|

T1 | 20 December | 0 | 67.5 | 100 | 0 |

8 March | 0 | 67.5 | 200 | 0 | |

4 April | 0 | 67.5 | 300 | 0 | |

27 April | 0 | 67.5 | 300 | 0 | |

10 May | 0 | 67.5 | 300 | 0 | |

T2 | 20 December | 0 | 67.5 | 100 | 0 |

8 March | 0, 30 | 66.5,1 | 200 | 40 | |

4 April | 0, 30, 60, 90 | 43.1, 9.3, 8.4, 6.7 | 300 | 120 | |

27 April | 0, 30, 60, 90 | 20, 15, 16, 16.5 | 300 | 120 | |

10 May | 0, 30, 60, 90 | 14.1, 18, 16.2, 19.2 | 300 | 120 | |

T3 | 20 December | 0 | 67.5 | 100 | 0 |

8 March | 0, 30, 60, 90, 120 | 60.8, 2.1, 1.8, 1.8, 1 | 200 | 140 | |

4 April | 0, 30, 60, 90, 120, 150, 180 | 34, 12.5, 7.1, 7.9, 0, 1.6, 4.4 | 300 | 210 | |

27 April | 0, 30, 60, 90, 120, 150, 180 | 10, 15, 14, 13, 7, 7.7, 0.8 | 300 | 210 | |

10 May | 0, 30, 60, 90, 120, 150, 180 | 3.7, 11.6, 13.8, 13.9, 11.3, 10.9, 2.4 | 300 | 210 |

Soil Layer (cm) | θ_{r} (cm^{3}/cm^{3}) | θ_{s} (cm^{3}/cm^{3}) | α | n | k_{s} (cm/hour) | h_{50} (cm) | h_{cc} (cm) | h_{c} (cm) |
---|---|---|---|---|---|---|---|---|

0–20 | 0.032 | 0.418 | 0.060 | 1.526 | 1.780 | −378.35 | −5272.42 | −47.76 |

20–50 | 0.045 | 0.406 | 0.045 | 1.435 | 1.792 | |||

50–90 | 0.060 | 0.402 | 0.078 | 1.387 | 0.793 | |||

90–130 | 0.040 | 0.415 | 0.063 | 1.446 | 0.601 | |||

130–210 | 0.025 | 0.442 | 0.044 | 1.598 | 0.407 | |||

210–300 | 0.033 | 0.450 | 0.050 | 1.645 | 0.133 |

Treatment | a | b | c | d | f | R |
---|---|---|---|---|---|---|

T1 | 8.28 | 0.0348 | 5.00 | 0.0084 | 199 | 0.96 |

T2 | 6.50 | 0.0266 | 7.00 | 0.0098 | 192 | 0.93 |

T3 | 5.50 | 0.0130 | 7.00 | 0.0260 | 205 | 0.86 |

Treatment | MAE (cm^{3}/cm^{3}) | MRE (%) | RMSE (cm^{3}/cm^{3}) |
---|---|---|---|

T1 | 0.016 | 6.17 | 0.021 |

T2 | 0.022 | 7.95 | 0.028 |

T3 | 0.017 | 6.38 | 0.025 |

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**MDPI and ACS Style**

Guo, X.; Sun, X.; Ma, J.; Lei, T.; Zheng, L.; Wang, P.
Simulation of the Water Dynamics and Root Water Uptake of Winter Wheat in Irrigation at Different Soil Depths. *Water* **2018**, *10*, 1033.
https://doi.org/10.3390/w10081033

**AMA Style**

Guo X, Sun X, Ma J, Lei T, Zheng L, Wang P.
Simulation of the Water Dynamics and Root Water Uptake of Winter Wheat in Irrigation at Different Soil Depths. *Water*. 2018; 10(8):1033.
https://doi.org/10.3390/w10081033

**Chicago/Turabian Style**

Guo, Xianghong, Xihuan Sun, Juanjuan Ma, Tao Lei, Lijian Zheng, and Pu Wang.
2018. "Simulation of the Water Dynamics and Root Water Uptake of Winter Wheat in Irrigation at Different Soil Depths" *Water* 10, no. 8: 1033.
https://doi.org/10.3390/w10081033