# Evaluating the Water Holding Capacity of Multilayer Soil Profiles Using Hydrus-1D and Multi-Criteria Decision Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Area

#### 2.2. Soil Column Experiments

#### 2.3. Hydrus-1D Simulation

#### 2.3.1. Governing Equation

^{3}L

^{−3}); $h$ is the soil water pressure head (L); z is the vertical spatial coordinate (L) and taken positive upward; K is the unsaturated hydraulic conductivity (L T

^{−1}). Richards’ equation was solved numerically by Hydrus-1D [22].

#### 2.3.2. Soil Hydraulic Parameters

^{3}L

^{−3}); ${\theta}_{r}$ and ${\theta}_{s}$ respectively represent the residual moisture content and saturated water content (L

^{3}L

^{−3}); $\alpha $ (L

^{−1}), $n$, and $m$ are van Genuchten’s equation parameters, and $m=1-1/n$; K

_{s}is the saturated hydraulic conductivity (L T

^{−1}); ${S}_{e}$ is the effective saturation.

#### 2.3.3. Particle Swarm Optimization

#### 2.3.4. Initial and Boundary Conditions

#### 2.3.5. Model Performance Evaluation

^{th}estimated value, ${M}_{i}$ is the i

^{th}measured value, $\overline{M}$ is the mean of the observed values, and $N$ is the number of observations.

#### 2.4. Multi-Criteria Decision Analysis Methods

#### 2.4.1. AHP

#### 2.4.2. TOPSIS

#### 2.4.3. GRA

^{th}data sequence.

#### 2.4.4. Criteria Weights

## 3. Results and Discussion

#### 3.1. Calibration and Validation of Hydrus-1D

^{3}cm

^{−3}) for RMSE, from 0.9662 to 0.9900 (dimensionless) for NSE, and from 0.0066 to 0.0192 (cm

^{3}cm

^{−3}) for MAE. The low MAE, RMSE, and high NSE values indicated that Hydrus-1D performed well. This was consistent with previous studies [17,19], which reported an excellent performance of Hydrus-1D in simulating the water movement, and similar accuracy was also obtained. Consequently, we concluded that the error of the simulation was low enough so that the performance of the model was deemed acceptable for further research. Further, the PSO algorithm accurately converged at the optimal value (Table 4) without falling into a local optimization space; PSO reportedly had the ability to invert multiple parameters at the same time [22,23].

#### 3.2. Water Infiltration Rate and Cumulative Infiltration of Different Soil Profiles

^{−1}. The measured infiltration rate at the initial stage was significantly higher than its simulated value (Figure 6), which was attributed to the low bulk density layer at the surface and the instability of the ponded water depth at the beginning of the infiltration process [10]. Before the water flow entered the second layer, the infiltration rate trend appeared stable. Although it had not reached a completely stable state, the subsequent changes were difficult to capture in the experimental data records because the differences were simply too small. For example, before the water flow entered the second layer (t = 96 min), the infiltration rate of SL-SiL was 0.07 cm min

^{−1}, and after 300 min, the infiltration rate was 0.05 cm min

^{−1}, which only decreased by 0.02 cm min

^{−1}.

^{−1}. The simulation results showed that SL-S reached a stable infiltration rate (0.07 cm/min) at 110.4 min, being the fastest profile to do so, whereas it took at least three times longer (496.8 min) for SL-SiL to reach a stable infiltration rate (0.05 cm/min). The infiltration rate of SL-S-SiL was also maintained at 0.07 cm/min after 110.4 min, but after the wetting front moved across the whole soil column, subsequent simulation results showed its infiltration rate reduced at 501.6 min, where it reached a steady infiltration rate (0.05 min/cm). The reason was that the low K

_{s}of the silt loam layer hindered the infiltration of sandy and sandy loam layers, resulting in a decreased infiltration rate. This phenomenon is called the hydraulic barrier when a coarse-textured soil overlies a fine-textured one [14,20]. The infiltration rate of SL-SiL-S reached a steady state when t = 230.4 min, but the infiltration rate did not decrease further like SL-S-SiL, because the infiltration rates through the sandy loam and silt loam layer were both very slow, and the water content of both layers could reach a saturation state before water flow entered the third layer, thereby enabling SL-SiL-S to achieve a steady infiltration rate quickly. In addition, the first and second layer had similar hydraulic properties, resulting in a weak flow barrier (Figure 7). When the water flow of SL-SiL-S entered the third layer, the water hydraulic barrier did not occur due to the higher K

_{s}of the sandy layer than the silt loam layer, resulting in the water flux being allowed to enter the third layer less than its loss. The low water supply of the silt loam layer and the fast infiltration rate of the sandy layer prevented the latter from reaching saturation (Figure 8).

#### 3.3. Wetting Front of Different Soil Profiles

^{−1}). The simulation results showed that after passing through the first layer, the advancing speed of the wetting front in each profile began to differ. Because of the sandy texture of the second layer in the SL-S, the advance speed of the wetting front in this profile remained relatively fast, and its penetration time was thus the shortest of all four profiles: it took just 303.4 min for the water to reach the bottom of SL-S (Table 6). SL-SiL had the longest penetration time, at 546.1 min. The penetration times of SL-S-SiL and SL-SiL-S were between those of SL-S and SL-SiL. Compared with SL-S-SiL (444.8 min), the wetting front penetration time of SL-SiL-S was slightly shorter (430.4 min). In SL-SiL, after passing through the first layer, the wetting front advance speed in the silt loam layer was always higher than that of SL-SiL-S in the silt loam layer, but the simulation results showed no such difference. The simulation performance of Hydrus-1D with respect to the wetting front was not as robust as that for cumulative infiltration and infiltration rate, which underestimated the wetting front of all soil profiles. This may have arisen from preferential flow. The numerical model presumed a uniformly advancing wetting front in a soil profile, but in the natural soil profile, it was non-uniform. This could therefore explain why the recorded (i.e., observed) wetting front data values were larger than the estimated (i.e., predicted) ones from Hydrus-1D.

#### 3.4. Water Distribution with Different Soil Profiles

#### 3.5. Evaluation of Soil Profiles

_{30}S

_{70}ranked the worst in Entropy-TOPSIS and AHP-TOPSIS. This result arose from different weight assignments, but the GRA methods (i.e., entropy-GRA and AHP-GRA) maintained the same result under the two weight calculation methods used. In this study, the results appeared less affected by the weight values. According to the five methods, SL-S-SiL was considered to have a better water holding effect, followed by SL-SiL-S, SL-SiL, and lastly, SL-SiL (Figure 13). Except for entropy-TOPSIS, the remaining four MCDA methods had the same ordering, and the overall performance of SL-S-SiL was the best profile. Therefore, the profile of SL-S-Sil was suggested for land reclamation in ShengLi open pit mine.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Schematic diagram of the four designed soil profiles. SL, sandy loam; SiL, silt loam; S, sand.

**Figure 8.**Measured and simulated water content at different depths in the infiltration process, (

**a**) SL-SiL; (

**b**) SL-S; (

**c**) SL-S-SiL and (

**d**) SL-SiL-S.

**Figure 10.**Simulated water content in the drainage process at (

**a**) SL-SiL; (

**b**) SL-S; (

**c**) SL-S-SiL and (

**d**) SL-SiL-S.

**Figure 11.**The actual water holding capacity of each layer at different times, (

**a**) SL-SiL; (

**b**) SL-S; (

**c**) SL-S-SiL and (

**d**) SL-SiL-S.

Sample | Clay (%) | Silt (%) | Sand (%) | Texture | Bulk Density (g cm^{−3}) | Porosity (%) | The Proportion of Total Profile (%) |
---|---|---|---|---|---|---|---|

Layer A | 4.55 | 37.73 | 57.72 | Sandy Loam | 1.23 | 0.51 | 4.6% |

Layer B | 4.43 | 34.04 | 61.54 | Sandy Loam | 1.59 | 0.39 | 21.8% |

Layer C | 3.32 | 21.8 | 74.87 | Loamy Sand | 1.72 | 0.33 | 2.2% |

Layer D | 0.15 | 2.69 | 97.16 | Sand | 1.54 | 0.37 | 35.6% |

Layer E | 7.44 | 71.72 | 20.83 | Silt Loam | 1.22 | 0.51 | 35.9% |

Intensity of Importance | Definition |
---|---|

1 | Equal importance |

3 | Moderate importance |

5 | Strong importance |

7 | Very strong importance |

9 | Extreme importance |

2, 4, 6, 8 | Intermediate values between the two adjacent judgments |

Dataset | Soil Profile | RMSE | NSE | MAE |
---|---|---|---|---|

Validation data | SL-S-SiL | 0.0170 ± 0.0036 | 0.9840 ± 0.0090 | 0.0118 ± 0.0041 |

Calibration data | SL-SiL | 0.0265 ± 0.0045 | 0.9662 ± 0.0261 | 0.0192 ± 0.0052 |

SL-S | 0.0107 ± 0.0031 | 0.9900 ± 0.0087 | 0.0066 ± 0.0019 | |

SL-SiL-S | 0.0207 ± 0.0044 | 0.9679 ± 0.0111 | 0.0135 ± 0.0025 |

**Table 4.**Optimized parameters used in PSO and the search space. Residual moisture content (${\theta}_{r}$), saturation moisture content (${\theta}_{s}$), $a$ and $n$ the shape parameters of the soil water characteristic curves, and saturated hydraulic conductivity ($Ks$).

Soil Texture | Parameters | Initial Values | Lower Boundary | Upper Boundary | Optimized Values |
---|---|---|---|---|---|

Sandy loam | ${\theta}_{r}$ (cm^{3} cm^{−3}) | 0.000 | 0.00 | 0.050 | 0.003 |

${\theta}_{s}$ (cm^{3} cm^{−3}) | 0.440 | 0.374 | 0.506 | 0.450 | |

$a$ (cm^{−1}) | 0.020 | 0.017 | 0.023 | 0.019 | |

$n$ | 1.530 | 1.301 | 1.761 | 1.514 | |

$Ks$ (cm min^{−1}) | 0.500 | 0.051 | 0.069 | 0.06 | |

Sand | ${\theta}_{r}$ (cm^{3} cm^{−3}) | 0.000 | 0.00 | 0.050 | 0.007 |

${\theta}_{s}$(cm^{3} cm^{−3}) | 0.310 | 0.264 | 0.357 | 0.312 | |

$a$ (cm^{−1}) | 0.055 | 0.047 | 0.063 | 0.059 | |

$n$ | 2.500 | 2.125 | 2.875 | 2.599 | |

$Ks$ (cm min^{−1}) | 0.500 | 0.213 | 0.288 | 0.238 | |

Silt loam | ${\theta}_{r}$ (cm^{3} cm^{−3}) | 0.00 | 0.000 | 0.050 | 0.016 |

${\theta}_{s}$ (cm^{3} cm^{−3}) | 0.470 | 0.400 | 0.541 | 0.479 | |

$a$ (cm^{−1}) | 0.020 | 0.017 | 0.023 | 0.021 | |

$n$ | 1.400 | 1.190 | 1.610 | 1.462 | |

$Ks$ (cm min^{−1}) | 0.500 | 0.034 | 0.046 | 0.045 |

Profiles | Type | Initial Infiltration (cm min ^{−1}) | Steady Infiltration Rate (cm min^{−1}) | Accumulation Infiltration (cm) |
---|---|---|---|---|

SL-SiL | Measured | 0.8 | 0.04 | 38.5 |

Simulated | 0.3 | 0.05 | 44.0 | |

SL-S | Measured | 0.5 | 0.08 | 27.0 |

Simulated | 0.3 | 0.07 | 28.4 | |

SL-S-SiL | Measured | 0.9 | 0.06 | 34.7 |

Simulated | 0.3 | 0.05 | 39.2 | |

SL-SiL-S | Measured | 0.9 | 0.06 | 32.9 |

Simulated | 0.3 | 0.06 | 36.6 |

Profile | Data Type | Infiltration Time of Each Layer (min) | |||
---|---|---|---|---|---|

First Layer | Second Layer | Third Layer | Total Time | ||

SL-SiL | Measured | 77.1 | 469.0 | — | 546.1 |

Simulated | 96.0 | 546.0 | — | 642.0 | |

SL-S | Measured | 79.2 | 224.2 | — | 303.4 |

Simulated | 96.0 | 235.5 | — | 331.5 | |

SL-S-SiL | Measured | 79.8 | 105.8 | 259.2 | 444.8 |

Simulated | 96.0 | 99.0 | 288.0 | 483.0 | |

SL-SiL-S | Measured | 83.1 | 193.1 | 154.2 | 430.4 |

Simulated | 96.0 | 204.0 | 165.0 | 465.0 |

Indices | Description | Unit |
---|---|---|

Index 1 | Steady infiltration rate | cm min^{−1} |

Index 2 | Accumulation infiltration amount | cm |

Index 3 | Breakthrough time of wetting front | min |

Index 4 | Total profile moisture | mm |

Index 5 | Total profile moisture at 7d | mm |

Index 6 | Water moisture of first layer at 7d | mm |

Profile | Index 1 | Index 2 | Index 3 | Index 4 | Index 5 | Index 6 |
---|---|---|---|---|---|---|

SL-S | 0.07 | 28.4 | 331.5 | 353 | 137 | 95.0 |

SL-SiL | 0.05 | 44.0 | 642.0 | 481 | 285 | 74.0 |

SL-S-SiL | 0.05 | 39.2 | 483.0 | 426 | 222 | 95.0 |

SL-SiL-S | 0.06 | 36.6 | 465.0 | 408 | 224 | 86.0 |

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## Share and Cite

**MDPI and ACS Style**

Wang, X.; Zhao, Y.; Liu, H.; Xiao, W.; Chen, S.
Evaluating the Water Holding Capacity of Multilayer Soil Profiles Using Hydrus-1D and Multi-Criteria Decision Analysis. *Water* **2020**, *12*, 773.
https://doi.org/10.3390/w12030773

**AMA Style**

Wang X, Zhao Y, Liu H, Xiao W, Chen S.
Evaluating the Water Holding Capacity of Multilayer Soil Profiles Using Hydrus-1D and Multi-Criteria Decision Analysis. *Water*. 2020; 12(3):773.
https://doi.org/10.3390/w12030773

**Chicago/Turabian Style**

Wang, Xin, Yanling Zhao, Huifang Liu, Wu Xiao, and Shuzhao Chen.
2020. "Evaluating the Water Holding Capacity of Multilayer Soil Profiles Using Hydrus-1D and Multi-Criteria Decision Analysis" *Water* 12, no. 3: 773.
https://doi.org/10.3390/w12030773