Influencing Factors and Simplified Model of Film Hole Irrigation
Abstract
:1. Introduction
2. Materials and Methods
2.1. Laboratory Experiments
2.2. Numerical Model Establishment and Calibration
2.3. Simplified Kostiakov Model for Film Hole Infiltration
2.4. Error Analysis
3. Results and Discussion
3.1. Application of SWMS-2D to Film Hole Irrigation and Comparison with the Experimental Results
3.2. Different Factors Affecting Cumulative Infiltration of Film Hole Irrigation
3.2.1. Effect of Initial SWC on Cumulative Infiltration
3.2.2. Effect of Irrigation Depth on Cumulative Infiltration
3.2.3. Effect of Layered-Soil Depth on Cumulative Infiltration
3.2.4. Effect of Film Hole Diameter and Opening Ratio on Cumulative Infiltration
3.3. Establishment and Universality of a Simplified Model
3.3.1. Establishment of a Simplified Model
3.3.2. Evaluation of the Simplified Model Universality
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Treatment | Soil Type * | Bulk Density (g/cm3) | Distance between Film Holes (cm) | Hole Diameter (cm) | Initial Water Content ** (%) | Irrigation Depth (cm) | Irrigation Amount (m3/hm2) | Irrigation Volume *** (mL) |
---|---|---|---|---|---|---|---|---|
1 | Silt loam | 1.30 | 20 | 4 | 40 | 4 | 225 | 900 |
2 | 1.40 | 20 | 4 | 60 | 6 | 450 | 1800 | |
3 | 1.30 | 30 | 6 | 60 | 6 | 225 | 2025 | |
4 | 1.40 | 30 | 6 | 40 | 4 | 450 | 4050 | |
5 | Sandy loam | 1.35 | 30 | 4 | 60 | 4 | 450 | 4050 |
6 | 1.45 | 30 | 4 | 40 | 6 | 225 | 2025 | |
7 | 1.35 | 20 | 6 | 40 | 6 | 450 | 1800 | |
8 | 1.45 | 20 | 6 | 60 | 4 | 225 | 900 |
Soil Type | Bulk Density (g/cm3) | θr (cm3/cm3) | θs (cm3/cm3) | α (1/cm) | n | l | Ks (cm/min) |
---|---|---|---|---|---|---|---|
Silt loam | 1.30 | 0.113 | 0.492 | 0.014 | 1.72 | 0.5 | 0.0208 |
1.40 | 0.123 | 0.456 | 0.017 | 1.55 | 0.5 | 0.0154 | |
Sandy loam | 1.35 | 0.057 | 0.38 | 0.025 | 1.76 | 0.5 | 0.0409 |
1.45 | 0.049 | 0.362 | 0.024 | 1.69 | 0.5 | 0.0257 | |
Sand | - | 0.045 | 0.430 | 0.145 | 2.68 | 0.5 | 0.4950 |
Sandy loam | - | 0.065 | 0.410 | 0.075 | 1.89 | 0.5 | 0.0737 |
Loam | - | 0.078 | 0.430 | 0.036 | 1.56 | 0.5 | 0.0173 |
Loamy sand | - | 0.057 | 0.040 | 0.124 | 2.28 | 0.5 | 0.2432 |
Silt | - | 0.034 | 0.460 | 0.016 | 1.37 | 0.5 | 0.0042 |
Silt loam | - | 0.067 | 0.450 | 0.020 | 1.41 | 0.5 | 0.0075 |
Sandy clay loam | - | 0.100 | 0.390 | 0.059 | 1.48 | 0.5 | 0.0218 |
Clay loam | - | 0.095 | 0.410 | 0.019 | 1.31 | 0.5 | 0.0043 |
Silty clay loam | - | 0.089 | 0.430 | 0.001 | 1.23 | 0.5 | 0.0012 |
Treatment | MAE (cm3/cm3) | RMSE (cm3/cm3) | PBIAS (%) | NS |
---|---|---|---|---|
1 | 0.013 | 0.016 | 2.947 | 0.979 |
2 | 0.022 | 0.028 | 2.711 | 0.998 |
3 | 0.026 | 0.034 | 3.648 | 0.997 |
4 | 0.011 | 0.013 | 1.962 | 0.995 |
5 | 0.020 | 0.023 | 3.508 | 0.968 |
6 | 0.011 | 0.013 | 1.438 | 0.998 |
7 | 0.013 | 0.016 | 0.461 | 0.998 |
8 | 0.026 | 0.028 | 2.762 | 0.999 |
Opening Ratio (%) | Film Hole Diameter (cm) | Silt Loam | Silt Loam | Sandy Loam | Sandy Loam | Loam | Sand | Sandy Loam | |||||||
(γd = 1.30 g/cm3) | (γd = 1.40 g/cm3) | (γd = 1.35 g/cm3) | (γd = 1.45 g/cm3) | ||||||||||||
k | α | k | α | k | α | k | α | k | α | k | α | k | α | ||
2.18 | 3 | 0.2553 | 0.877 | 0.1636 | 0.858 | 0.2919 | 0.901 | 0.199 | 0.89 | 0.1247 | 0.866 | 1.5957 | 0.96 | 0.3166 | 0.923 |
4 | 0.2104 | 0.871 | 0.135 | 0.853 | 0.2325 | 0.902 | 0.161 | 0.888 | 0.105 | 0.861 | 1.281 | 0.955 | 0.2658 | 0.912 | |
5 | 0.1811 | 0.866 | 0.1155 | 0.852 | 0.1987 | 0.901 | 0.138 | 0.886 | 0.0928 | 0.854 | 1.0895 | 0.95 | 0.2327 | 0.904 | |
Mean | 0.2156 | 0.871 | 0.138 | 0.855 | 0.241 | 0.901 | 0.166 | 0.888 | 0.1075 | 0.86 | 1.3221 | 0.955 | 0.2717 | 0.913 | |
3.14 | 2 | 0.5242 | 0.858 | 0.3354 | 0.839 | 0.6107 | 0.875 | 0.414 | 0.865 | 0.2503 | 0.849 | 3.2732 | 0.954 | 0.6146 | 0.923 |
3 | 0.3825 | 0.861 | 0.2466 | 0.841 | 0.4345 | 0.885 | 0.298 | 0.873 | 0.186 | 0.852 | 2.3225 | 0.953 | 0.4627 | 0.915 | |
4 | 0.3164 | 0.856 | 0.2052 | 0.836 | 0.3469 | 0.888 | 0.243 | 0.873 | 0.1582 | 0.846 | 1.8665 | 0.948 | 0.3912 | 0.903 | |
Mean | 0.4077 | 0.858 | 0.2624 | 0.839 | 0.464 | 0.883 | 0.318 | 0.87 | 0.1982 | 0.849 | 2.4874 | 0.951 | 0.4895 | 0.913 | |
4.91 | 3 | 0.6265 | 0.835 | 0.4062 | 0.815 | 0.7098 | 0.857 | 0.448 | 0.846 | 0.303 | 0.83 | 3.6961 | 0.937 | 0.7405 | 0.899 |
4 | 0.5152 | 0.834 | 0.335 | 0.815 | 0.5732 | 0.863 | 0.397 | 0.851 | 0.2558 | 0.828 | 2.9535 | 0.937 | 0.6232 | 0.891 | |
5 | 0.4495 | 0.83 | 0.294 | 0.813 | 0.4959 | 0.862 | 0.346 | 0.849 | 0.2321 | 0.82 | 2.5265 | 0.932 | 0.5543 | 0.881 | |
Mean | 0.5304 | 0.833 | 0.3451 | 0.814 | 0.593 | 0.861 | 0.397 | 0.849 | 0.2636 | 0.826 | 3.0587 | 0.935 | 0.6393 | 0.89 | |
7.07 | 6 | 0.6129 | 0.806 | 0.4041 | 0.788 | 0.6652 | 0.84 | 0.467 | 0.827 | 0.3208 | 0.796 | 3.2753 | 0.916 | 0.7475 | 0.859 |
13.6 | 5 | 1.408 | 0.855 | 0.9345 | 0.737 | 1.5422 | 0.776 | 1.087 | 0.768 | 0.7197 | 0.759 | 7.3773 | 0.863 | 1.6553 | 0.828 |
Opening Ratio (%) | Film Hole Diameter (cm) | Loamy Sand | Silt | Silt Loam | Sandy Clay Loam | Clay Loam | Silt Clay Loam | ||||||||
k | α | k | α | k | α | k | α | k | α | k | α | ||||
2.18 | 3 | 0.7757 | 0.967 | 0.0311 | 0.905 | 0.0445 | 0.923 | 0.0789 | 0.946 | 0.0236 | 0.922 | 0.0989 | 0.805 | ||
4 | 0.6049 | 0.969 | 0.0258 | 0.898 | 0.0426 | 0.896 | 0.0619 | 0.946 | 0.0247 | 0.886 | 0.1071 | 0.752 | |||
5 | 0.4996 | 0.973 | 0.0194 | 0.915 | 0.0314 | 0.917 | 0.0491 | 0.956 | 0.0152 | 0.93 | 0.0441 | 0.861 | |||
Mean | 0.6268 | 0.969 | 0.0255 | 0.906 | 0.0395 | 0.912 | 0.0633 | 0.95 | 0.0212 | 0.913 | 0.0833 | 0.806 | |||
3.14 | 2 | 1.6726 | 0.944 | 0.1024 | 0.827 | 0.1384 | 0.847 | 0.1731 | 0.924 | 0.0683 | 0.861 | 0.3556 | 0.686 | ||
3 | 1.2272 | 0.952 | 0.0605 | 0.864 | 0.0877 | 0.878 | 0.1277 | 0.931 | 0.0474 | 0.879 | 0.2041 | 0.737 | |||
4 | 0.9004 | 0.96 | 0.0358 | 0.903 | 0.0555 | 0.91 | 0.0941 | 0.937 | 0.0329 | 0.896 | 0.1171 | 0.791 | |||
Mean | 1.2668 | 0.952 | 0.0662 | 0.865 | 0.0939 | 0.879 | 0.1316 | 0.931 | 0.0495 | 0.879 | 0.2256 | 0.738 | |||
4.91 | 3 | 1.8915 | 0.932 | 0.1062 | 0.833 | 0.15 | 0.848 | 0.2123 | 0.904 | 0.0801 | 0.851 | 0.3878 | 0.678 | ||
4 | 1.4747 | 0.941 | 0.0709 | 0.864 | 0.1104 | 0.867 | 0.1662 | 0.911 | 0.0634 | 0.86 | 0.2464 | 0.726 | |||
5 | 1.2257 | 0.947 | 0.0581 | 0.872 | 0.0914 | 0.874 | 0.1355 | 0.919 | 0.0518 | 0.868 | 0.1781 | 0.754 | |||
Mean | 1.5306 | 0.94 | 0.0784 | 0.856 | 0.1173 | 0.863 | 0.1713 | 0.912 | 0.0651 | 0.86 | 0.2708 | 0.719 | |||
7.07 | 6 | 1.6189 | 0.929 | 0.0856 | 0.847 | 0.1336 | 0.848 | 0.1858 | 0.902 | 0.0762 | 0.843 | 0.2581 | 0.720 | ||
13.6 | 5 | 4.0632 | 0.846 | 0.3217 | 0.738 | 0.4536 | 0.746 | 0.5099 | 0.838 | 0.2412 | 0.763 | 0.9397 | 0.580 |
Soil | MAE (mm) | RMSE (mm) | PBIAS (%) | NS |
---|---|---|---|---|
Loam from Wugong | 0.190 | 0.190 | −2.131 | 0.995 |
Silt Loam from Weihe Bench | 0.391 | 0.552 | −1.082 | 0.997 |
Loam from Luochuan | 2.299 | 2.722 | −1.756 | 0.989 |
Sandy Loam from Ansai | 0.508 | 0.830 | −1.375 | 0.985 |
Sandy Loam from Yulin | 0.431 | 0.566 | 1.479 | 0.999 |
Silt Loam from Handan | 0.141 | 0.177 | −1.569 | 0.982 |
Sand from Yulin | 0.390 | 0.466 | −1.170 | 0.998 |
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Li, Y.-B.; Fan, Y.-W.; Liu, Y.; Ma, X.-Y. Influencing Factors and Simplified Model of Film Hole Irrigation. Water 2017, 9, 543. https://doi.org/10.3390/w9070543
Li Y-B, Fan Y-W, Liu Y, Ma X-Y. Influencing Factors and Simplified Model of Film Hole Irrigation. Water. 2017; 9(7):543. https://doi.org/10.3390/w9070543
Chicago/Turabian StyleLi, Yi-Bo, Yan-Wei Fan, Ye Liu, and Xiao-Yi Ma. 2017. "Influencing Factors and Simplified Model of Film Hole Irrigation" Water 9, no. 7: 543. https://doi.org/10.3390/w9070543