Feasibility Investigation of Improving the Modified Green–Ampt Model for Treatment of Horizontal Infiltration in Soil
Abstract
:1. Introduction
2. Improved Modified Green-Ampt Model
2.1. Theoretical Model Development
2.2. Setup of Calibration and Validation Tests
2.3. Parameter Determination Method
2.4. Numerical Model
3. Results and Discussion
3.1. Parameters Calibration Results
3.2. Infiltration Rate
3.3. Cumulative Infiltration
3.4. Unit Transfer Coefficient
3.5. Moisture Profiles of Different Soils during the Infiltration Process
3.6. Comparison between the IMGA Model and Solutions of Richards’ Equation
4. Conclusions
- The IMGA model enables accurate estimation of the soil moisture profile at any moment. The logarithmic function adopted by the IMGA model can capture changes in moisture content in the transition zone with a reflection of its decrease as the wetting front advances.
- By comparing the estimated cumulative infiltration data obtained using the models with those obtained by measurements, it was found that the IMGA model has the lowest relative error, followed by the MGA and GA models. It was also discovered that the relative errors of the models change with the infiltration time. The relative errors of the IMGA and MGA models monotonically decrease with time; however, for the GA model, the relative error first increases and then decreases. Therefore, the infiltration time should be specified when using this method to evaluate the errors of the models.
- It was demonstrated that the unit transfer coefficient can be inferred from the GA model using the mass conservation law. Soils with different compositions, grain size and structures also have different values, which can be determined by the method suggested in this study. The smaller the grain size, the larger is.
- Due to the unavoidable influence of interfaces and inhomogeneity in soil, the advancement distance of water infiltration calculated using Richards’ equation is shorter than that estimated by the IMGA model and the measured values. Another feature of the numerical solutions of Richards’ equation is that it is unable to reflect transmission zone, wetting zone, and demarcation point between these two zones. The horizontal soil moisture profiles obtained by the IMGA model is closer to the measured data than that of the numerical simulation results.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature and Abbreviations
Nomenclature | |
parameters that described soil moisture profile | |
parameter of IMGA model related to infiltration time | |
coefficient of gradation | |
unit transfer coefficient | |
uniformity coefficient | |
soil water diffusivity (m2/s) | |
ponding water head (m) | |
cumulative infiltration (mm) | |
cross-sectional area of the soil column (m2) | |
parameters that described WF advancing velocity | |
infiltration rate (mm/h) | |
wetting front matric potential (kPa) | |
radius of an idealized soil pore for fine soil (mm) | |
elapsed time (h) | |
surface tension of water (N/m2) | |
temperature characteristic value (°C) | |
V | total supplied water volume (m3/m3) |
water advancement distance at the bottom of the polyvinyl chloride (PVC) column (m) | |
advancement distance of the intersection point between the transmission zone and the wetting zone (m) | |
advancement distance of the intersection point of two linear functions in the wetting zone (m) | |
advancement distance of the WF (m) | |
water advancement distance at the top of the PVC column (m) | |
parameters that described relationship between and | |
Greek letters | |
unit weight of water | |
relative error | |
soil moisture (m3/m3) | |
threshold moisture (m3/m3) | |
soil moisture profile function in the transmission zone (m3/m3) | |
soil moisture profile function collected with TZ in the wetting zone (m3/m3) | |
soil moisture profile function collected with WF in the wetting zone (m3/m3) | |
critical soil moisture in the middle of WZ (m3/m3) | |
critical soil moisture between TZ and WZ (m3/m3) | |
initial soil moisture (m3/m3) | |
residual moisture (m3/m3) | |
saturated soil moisture under a drying path (m3/m3) | |
saturated soil moisture under a wetting path (m3/m3) | |
soil matric suction (kPa) | |
Acronyms | |
AHFO | actively heated fiber optic |
CFHC | carbon fiber heated cable |
DMS | distributed moisture sensing |
GA | Green–Ampt |
MGA | modified Green–Ampt |
IMGA | improved modified Green–Ampt |
SWCC | soil water characteristic curve |
TZ | transmission zone |
WF | wetting front |
WZ | wetting zone |
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Performance Parameters | Values |
---|---|
Distance measurement range (km) | 0 to 50 |
Temperature measurement range (°C) | −40 to 120 |
Soil moisture measurement range (m3/m3) | 0 to 0.65 |
Maximum current (A) | 10 |
Fiber type | Multimode (50/125) |
Moisture accuracy (m3/m3) | 0.02 |
Response time (min) | 20 |
Spatial resolution (m) | 0.31 |
Sampling interval (m) | 0.2 |
Channel number | 2 |
Power consumption (W) | 0 to 2000 |
Soil | Θs (m3/m3) | Θr (m3/m3) | A (1/m) | N | I | Ks (m/s) |
---|---|---|---|---|---|---|
Sand | 0.41 | 0.055 | 7.5 | 1.89 | 0.5 | 6.379 × 10−4 |
Soil Type | θs (m3/m3) | θc (m3/m3) | θb (m3/m3) | xi − xbi (cm) | xbi − xci (cm) | R2 (MGA) | R2 (IMGA) | |
---|---|---|---|---|---|---|---|---|
Soil used in this test | 0.416 | 0.332 | 0.253 | 39.57 | 149.62 | 0.834 | 0.927 | |
Soils used by Mao | BJ | 0.451 | 0.245 | 0.325 | 1.12 | 5.38 | 0.954 | 0.982 |
AS | 0.487 | 0.363 | 0.327 | 2.91 | 4.86 | 0.859 | 0.996 | |
YL | 0.512 | 0.396 | 0.389 | 2.27 | 9.47 | 0.975 | 0.991 |
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Cao, D.-f.; Shi, B.; Zhu, H.-h.; Inyang, H.; Wei, G.-q.; Zhang, Y.; Tang, C.-s. Feasibility Investigation of Improving the Modified Green–Ampt Model for Treatment of Horizontal Infiltration in Soil. Water 2019, 11, 645. https://doi.org/10.3390/w11040645
Cao D-f, Shi B, Zhu H-h, Inyang H, Wei G-q, Zhang Y, Tang C-s. Feasibility Investigation of Improving the Modified Green–Ampt Model for Treatment of Horizontal Infiltration in Soil. Water. 2019; 11(4):645. https://doi.org/10.3390/w11040645
Chicago/Turabian StyleCao, Ding-feng, Bin Shi, Hong-hu Zhu, Hilary Inyang, Guang-qing Wei, Yan Zhang, and Chao-sheng Tang. 2019. "Feasibility Investigation of Improving the Modified Green–Ampt Model for Treatment of Horizontal Infiltration in Soil" Water 11, no. 4: 645. https://doi.org/10.3390/w11040645
APA StyleCao, D.-f., Shi, B., Zhu, H.-h., Inyang, H., Wei, G.-q., Zhang, Y., & Tang, C.-s. (2019). Feasibility Investigation of Improving the Modified Green–Ampt Model for Treatment of Horizontal Infiltration in Soil. Water, 11(4), 645. https://doi.org/10.3390/w11040645