# Modelling Soil Water, Salt and Heat Dynamics under Partially Mulched Conditions with Drip Irrigation, Using HYDRUS-2D

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Design

**Figure 1.**Layout of the mulched drip-irrigation system in the indoor soil tank: (

**a**) Sketch map of design; (

**b**) photograph of equipment.

#### 2.2. Monitoring Methods

**Figure 2.**Locations of the observation sites: (

**a**) Temperature monitoring and water-salt observation sites in horizontal plane view; (

**b**) temperature monitoring points in vertical plane view; (

**c**) water-salt observation sites in vertical plane view.

#### 2.3. Model Introduction

#### 2.3.1. Equation of Water Transport

#### 2.3.2. Solute Transport Equation

#### 2.3.3. Heat Transport Equation

#### 2.3.4. Initial and Boundary Conditions

#### 2.3.5. Parameters and Model Calibration/Validation

**Table 2.**Values of soil parameters for water, salt, and heat transport under partially mulched conditions with drip irrigation.

Parameters | Value | Source | |||
---|---|---|---|---|---|

Soil characteristic parameter | Soil particle composition | Sand | $\%$ | 26.252 | Measured via experiment |

Silt | $\%$ | 70.858 | |||

Clay | $\%$ | 2.89 | |||

${\mathsf{\rho}}_{\mathrm{b}}$ | ${\mathrm{g}\mathrm{cm}}^{-3}$ | 1.55 | |||

Soil hydraulic parameters | ${\mathsf{\theta}}_{\mathrm{r}}$ | ${\mathrm{cm}}^{3}{\mathrm{cm}}^{-3}$ | 0.0353 | Rosetta pedotransfer functions [44] | |

${\mathsf{\theta}}_{\mathrm{s}}$ | ${\mathrm{cm}}^{3}{\mathrm{cm}}^{-3}$ | 0.42 | |||

$\mathsf{\alpha}$ | ${\mathrm{cm}}^{-1}$ | 0.0072 | |||

$\mathrm{n}$ | $-$ | 1.6613 | |||

${\mathrm{K}}_{\mathrm{s}}$ | ${\mathrm{cm}\mathrm{h}}^{-1}$ | 1.875 | |||

l | $-$ | 0.5 | |||

Solute transport parameters | ${\mathrm{D}}_{\mathrm{L}}$ | $\mathrm{Cm}$ | 26 | Calibrated | |

${\mathrm{D}}_{\mathrm{T}}$ | $\mathrm{Cm}$ | $1$ | |||

$\mathrm{f}$ | $-$ | $0.9$ | |||

${\mathrm{D}}_{\mathrm{W}}$ | ${\mathrm{cm}}^{2}{\mathrm{h}}^{-1}$ | $0.09$ | |||

${\mathrm{K}}_{\mathrm{d}}$ | ${\mathrm{cm}}^{3}{\mathrm{g}}^{-1}$ | 0.6 | |||

$\mathsf{\beta}$ | $-$ | 1 | |||

${\mathsf{\mu}}_{\mathrm{w}}$ | ${\mathrm{h}}^{-1}$ | $2\times {10}^{-4}$ | |||

${\mathsf{\mu}}_{\mathrm{S}}$ | ${\mathrm{h}}^{-1}$ | $4.16\times {10}^{-4}$ | |||

${\mathsf{\mu}}_{\mathrm{w}}^{\prime}$ | ${\mathrm{h}}^{-1}$ | $2\times {10}^{-4}$ | |||

${\mathsf{\mu}}_{\mathrm{S}}^{\prime}$ | ${\mathrm{h}}^{-1}$ | $2.92\times {10}^{-4}$ | |||

${\mathsf{\gamma}}_{\mathrm{w}}$ | ${\mathrm{mg}\mathrm{cm}}^{-3}{\mathrm{h}}^{-1}$ | $9\times {10}^{-3}$ | |||

${\mathsf{\gamma}}_{\mathrm{S}}$ | ${\mathrm{h}}^{-1}$ | $7.33\times {10}^{-3}$ | |||

${\mathsf{\alpha}}^{\prime}$ | ${\mathrm{h}}^{-1}$ | 0.05 | |||

Heat transport parameters | ${\mathrm{b}}_{1}$ | ${\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ | −0.5519 | Wang et al. [45] | |

${\mathrm{b}}_{2}$ | ${\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ | −4.05 | |||

${\mathrm{b}}_{3}$ | ${\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ | 3.75 | |||

${\mathrm{C}}_{\mathrm{w}}$ | ${\mathrm{J}\mathrm{m}}^{-3}{\mathbb{C}}^{-1}$ | $4.16\times {10}^{6}$ | Pan et al. [46] | ||

${\mathrm{C}}_{\mathrm{n}}$ | ${\mathrm{J}\mathrm{m}}^{-3}{\mathbb{C}}^{-1}$ | $2.23\times {10}^{6}$ | |||

${\mathsf{\lambda}}_{\mathrm{L}}$ | $\mathrm{cm}$ | $5$ | Hu et al. [47] | ||

${\mathsf{\lambda}}_{\mathrm{T}}$ | $\mathrm{cm}$ | 1 |

#### 2.4. Statistical Analysis

## 3. Results and Discussion

#### 3.1. Results of Model Calibration and Validation

#### 3.2. Water Transport under Various Irrigation Treatments

**Figure 4.**Simulated contours of soil water content under W1: (

**a**) The middle of first irrigation; (

**b**) the middle of third irrigation; (

**c**) the middle of fifth irrigation; (

**d**) at the end of experiment.

**Figure 5.**The simulated contours of soil water content under W2: (

**a**) The middle of first irrigation; (

**b**) the middle of third irrigation; (

**c**) the middle of fifth irrigation; (

**d**) at the end of experiment.

**Figure 6.**The measured 2D distribution of soil water content at the end of experiment: (

**a**) Measured distribution under W1; (

**b**) measured distribution under W2.

#### 3.3. Salt Transport under Various Irrigation Treatments

**Figure 7.**Simulated contours of soil salinity under W1, for (

**a**) the middle of the first irrigation; (

**b**) the middle of the third irrigation; (

**c**) the middle of the fifth irrigation; (

**d**) at the end of experiment.

**Figure 8.**Simulated contours of soil salinity under W2, for (

**a**) the middle of first irrigation; (

**b**) the middle of third irrigation; (

**c**) the middle of fifth irrigation; (

**d**) at the end of experiment.

**Figure 9.**Measured 2D distribution of soil salinity at the end of experiment: (

**a**) Measured distribution under W1; (

**b**) under W2.

**Figure 10.**Simulated 2D distribution of soil salinity with instantaneous equilibrium adsorption at the end of experiment: (

**a**) Simulated distribution under W1; (

**b**) under W2.

#### 3.4. Heat Transport under Various Irrigation Treatments

**Figure 11.**The 2D distribution diagram of average soil temperatures for the entire period: (

**a**) Measured distribution under W1; (

**b**) simulated distribution under W1; (

**c**) measured distribution under W2; (

**d**) simulated distribution under W2.

**Figure 12.**The daily mean temperature of soil at different depths and mulched conditions during the entire period for W2.

#### 3.5. Discussion on the Coupling of Water, Salt, and Heat Transport

#### 3.6. Simulation Scenarios

**Figure 13.**Soil salinity under different total irrigation amounts, with Ivar, at the end of scenario. (

**a**) Soil salinity in the root zone; (

**b**) soil salinity in the un-mulched soil surface.

**Figure 14.**The 2D distribution of soil salinity at the end of scenario under different total irrigation amounts, and Ivar, for simulations.

## 4. Conclusions

- (1)
- The HYDRUS-2D model compared reasonably well with the measured data, demonstrating that it can reflect differences in water, salt, and heat migration in the vertical and lateral directions. For solute transport, compared with instantaneous equilibrium adsorption, kinetic adsorption could better reflect the characteristics of solute transport in this experiment.
- (2)
- Under partially mulched drip irrigation, a significant difference was found in the migration of water, salt, and heat between the mulched and the un-mulched soil area. The un-mulched soil area was drier than the mulched soil area, and it also had higher soil salinity level and higher temperature rise with radiation.
- (3)
- For different irrigation intensities with the same total irrigation amount, lower intensity drip irrigation showed smaller spatial distribution difference for water, and larger spatial distribution differences in salinity and heat at the end of the process. Such treatment can lead to effective desalination in the mulched area; more serious salt accumulation was restricted to the un-mulched soil.
- (4)
- Scenario simulations showed that the total quantity of drip irrigation had an obvious effect on the desalination boundary in the deep soil layer. Drip irrigations with appropriate incremental intensity could improve salt leaching in the root zone, as more water migrates laterally.

## Supplementary Materials

**a**) The simulated result in the middle of first irrigation; (

**b**) simulated result in the middle of fifth irrigation; (

**c**) simulated result in the middle of fifth irrigation; (

**d**) simulated result at the end of experiment; Figure S2: Measured temperature contour under W1: (

**a**) The measured result in the middle of the first irrigation; (

**b**) the middle of third irrigation; (

**c**) the middle of the fifth irrigation; (

**d**) at the end of experiment title; Figure S3: Simulated contour of temperature under W2: (

**a**) The simulated result in the middle of the first irrigation; (

**b**) simulated result in the middle of the third irrigation; (

**c**) simulated result in the middle of the fifth irrigation; (

**d**) simulated result at the end of experiment; Figure S4: Measured contour of temperature under W2: (

**a**) The measured result in the middle of the first irrigation; (

**b**) the middle of the third irrigation; (

**c**) the middle of the fifth irrigation; (

**d**) measured result at the end of experiment.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Time (d) | 1 | 4 | 7 | 10 | 13 | 16 | 19 | 22 | 25 | 28 | $\mathrm{The}\mathrm{total}\mathrm{amount}\left(\mathrm{L}\right)$ | |

Number of irrigation $i$-th | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||

Irrigation amount $\left(\mathrm{L}\right)$ | W1 ^{1} | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 2 | 1 | 1 | 31 |

W2 ^{1} | 5 | 5 | 5 | 5 | 5 | 2 | 1 | 1 | 1 | 1 | 31 |

^{1}The drip-irrigation flow rate of W1 and W2 was 0.4 L/h throughout the experiment.

$\mathbf{Water}\mathbf{Contents}\left({\mathbf{cm}}^{3}{\mathbf{cm}}^{-3}\right)$ | $\mathbf{Salinity}\left({\mathbf{g}\mathbf{kg}}^{-1}\right)$ | $\mathbf{Temperature}(\xb0\mathbf{C})$ | ||||
---|---|---|---|---|---|---|

W1 | W2 | W1 | W2 | W1 | W2 | |

MAE | 0.0051 | 0.0074 | 1.16 | 1.13 | 1.32 | 1.76 |

RMSE | 0.0064 | 0.0092 | 1.48 | 1.52 | 1.60 | 2.16 |

NRMSE (%) | 1.63 | 2.32 | 16.35 | 16.64 | 5.04 | 6.63 |

${R}^{2}$ | 0.67 | 0.70 | 0.66 | 0.54 | 0.79 | 0.71 |

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**MDPI and ACS Style**

Tian, H.; Bo, L.; Mao, X.; Liu, X.; Wang, Y.; Hu, Q.
Modelling Soil Water, Salt and Heat Dynamics under Partially Mulched Conditions with Drip Irrigation, Using HYDRUS-2D. *Water* **2022**, *14*, 2791.
https://doi.org/10.3390/w14182791

**AMA Style**

Tian H, Bo L, Mao X, Liu X, Wang Y, Hu Q.
Modelling Soil Water, Salt and Heat Dynamics under Partially Mulched Conditions with Drip Irrigation, Using HYDRUS-2D. *Water*. 2022; 14(18):2791.
https://doi.org/10.3390/w14182791

**Chicago/Turabian Style**

Tian, Huiwen, Liyuan Bo, Xiaomin Mao, Xinyu Liu, Yan Wang, and Qingyang Hu.
2022. "Modelling Soil Water, Salt and Heat Dynamics under Partially Mulched Conditions with Drip Irrigation, Using HYDRUS-2D" *Water* 14, no. 18: 2791.
https://doi.org/10.3390/w14182791