An Empirical Model for Aeolian Sandy Soil Wetting Front Estimation with Subsurface Drip Irrigation
Abstract
:1. Introduction
Category | Applied Soil | Irrigation Method | Equation | Basis for Establishment |
---|---|---|---|---|
Mathematical Model | Silt | Surface point source [27] | Derivation of Richards’ equation | |
Numerical Model | All soil types [28,29,30,31] | - | Inversion of soil parameters | |
Empirical Model | Sandy clay loam | Surface point source [32] | Test fitting | |
All soil types | Surface point source [33] | |||
Loam, sandy loam | Point source [34] | |||
All soil types | Surface [35] | |||
All soil types | Surface [38] | |||
Loam, silty and sandy loam | Subsurface line source [22] |
2. Materials and Methods
2.1. Infiltration Experiment of Aeolian Sand
2.1.1. Experimental Soil Characteristics
2.1.2. Experimental Setup
2.1.3. Experimental Trials
2.2. Model Establishment Method
2.2.1. Wetting Front Distance Model
2.2.2. Wetting Body Elliptical Model
2.2.3. Model Evaluation
2.2.4. Numerical Model
3. Results
3.1. Wetting Front Distribution
3.2. Proposed Model
3.2.1. Wetting Front Distance Model
3.2.2. Wetting Body Elliptical Model
4. Discussion
4.1. Wetting Front Distribution
4.2. Comparison with a Numerical Model
5. Conclusions
- (1)
- The aeolian sandy soil wetting front shape resembles a “bowl”. At the same irrigation volume, the wetting front shape is more significant when the flow rate is low, while at the same irrigation time, the wetting front shape is more prominent when the flow rate is significant. As the time increases, the wetting front transport distance increment first increases and then decreases, and the transport direction is mainly horizontal and then vertical.
- (2)
- The point source infiltration model (Equation (12)) is more suitable for calculating the wetting front transport distance in the horizontal direction. The line source infiltration model (Equation (13)) is more suitable for calculating the wetting front transport distances in the vertical direction. The model proposed in this study (Equation (14)) can accurately calculate the wetting front transport pattern of aeolian sandy soil with subsurface drip irrigation.
- (3)
- The prediction degree of the model is consistent with that of HYDRUS-2D/3D and shows a better fit than HYDRUS-2D/3D in the horizontal direction. In practical applications, the model parameters are easy to obtain and use.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Soil | Particle Size (mm) | Saturated Water Content (%) | Saturated Hydraulic Conductivity Ks (cm/s) | Soil Bulk Density (g/cm3) | ||
---|---|---|---|---|---|---|
>0.075 (%) | 0.075~0.002 (%) | <0.002 (%) | ||||
Aeolian sandy soil | 90 | 2.1 | 7.9 | 41.54 | 2.37 × 10−3 | 1.565 |
Point source infiltration | A1 | n1 | A2 | n2 | A3 | n3 |
0.5096 | 0.2273 | 2.4990 | 0.4922 | 1.5700 | 0.3128 | |
Line source infiltration | A4 | n4 | A5 | n5 | A6 | n6 |
0.1985 | 0.2273 | 1.3440 | 0.4922 | 0.6784 | 0.3128 |
Model | MAE (cm) | RMSE (cm) | PBIAS (%) | NSE (−) |
---|---|---|---|---|
Downward | 0.50 | 0.61 | 1.007 | 0.99 |
Horizontal | 1.16 | 1.39 | −5.89 | 0.94 |
Model | MAE (cm) | RMSE (cm) | PBIAS (%) | NSE (−) | |
---|---|---|---|---|---|
1.0 L/h | 30° | 0.70 | 0.95 | 1.28 | 0.98 |
60° | 0.83 | 0.95 | −3.01 | 0.98 | |
1.5 L/h | 30° | 0.71 | 0.95 | 1.37 | 0.98 |
60° | 0.88 | 0.96 | −3.47 | 0.99 |
Flowrate | Q = 0.5 L/h | Q = 1.0 L/h | Q = 1.5 L/h | |||
---|---|---|---|---|---|---|
Wetted Body Scale | Maximum Width d | Maximum Depth D | Maximum Width d | Maximum Depth D | Maximum Width d | Maximum Depth D |
Test | 47.5 | 34.6 | 46.6 | 32.9 | 44.2 | 32.2 |
Zur’s model | 17.5 | 34.6 | 21.6 | 32.9 | 24.5 | 32.2 |
Soil | Saturated Water Content θs (cm3/cm3) | Residual Water Content θr (cm3/cm3) | Parameter α | Parameter n | Saturated Hydraulic Conductivity (cm/s) |
---|---|---|---|---|---|
Aeolian sandy soil | 0.415 | 0.025 | 0.292 | 2.428 | 3.02 × 10−3 |
Model | Irrigation Flow (L/h) | Wetting Front Direction | MAE (cm) | RMSE (cm) | NSE (−) |
---|---|---|---|---|---|
Hydrus 3D | 1.0 | Horizontal | 2.53 | 2.69 | 0.84 |
Downward | 1.05 | 1.16 | 0.98 | ||
1.5 | Horizontal | 3.06 | 3.10 | 0.68 | |
Downward | 0.54 | 0.62 | 0.99 | ||
Proposed model | 1.0 | Horizontal | 1.00 | 1.20 | 0.95 |
Downward | 0.75 | 0.83 | 0.98 | ||
1.5 | Horizontal | 1.16 | 1.39 | 0.94 | |
Downward | 0.50 | 0.61 | 0.99 |
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Qiao, W.; Luo, Z.; Lin, D.; Zhang, Z.; Wang, S. An Empirical Model for Aeolian Sandy Soil Wetting Front Estimation with Subsurface Drip Irrigation. Water 2023, 15, 1336. https://doi.org/10.3390/w15071336
Qiao W, Luo Z, Lin D, Zhang Z, Wang S. An Empirical Model for Aeolian Sandy Soil Wetting Front Estimation with Subsurface Drip Irrigation. Water. 2023; 15(7):1336. https://doi.org/10.3390/w15071336
Chicago/Turabian StyleQiao, Wei, Zhihua Luo, Daming Lin, Zhongjian Zhang, and Songjiang Wang. 2023. "An Empirical Model for Aeolian Sandy Soil Wetting Front Estimation with Subsurface Drip Irrigation" Water 15, no. 7: 1336. https://doi.org/10.3390/w15071336
APA StyleQiao, W., Luo, Z., Lin, D., Zhang, Z., & Wang, S. (2023). An Empirical Model for Aeolian Sandy Soil Wetting Front Estimation with Subsurface Drip Irrigation. Water, 15(7), 1336. https://doi.org/10.3390/w15071336