The Sensitivity Analysis of the Drainage Unsteady Equations against the Depth of Drain Placement and Rainfall Time at the Shallow Water-Bearing Layers: A Case Study of Markazi Province, Iran
Abstract
:1. Introduction
2. Studied Region
3. Materials and Methods
4. Conclusions
- The numerical model of Bouwer & Van Schilfgarrd was announced as the best-selected model in this project.
- The distance between the drains in the superior model was chosen to be 51.26 m, which is 15 m more than the previously measured values in the region.
- The depth of placement of the drains was determined to be 130 cm, which is 70 cm less than the previously implemented values.
- By increasing the distance between the drains and reducing the digging depth, a 40% reduction in project implementation costs has been reported.
- By increasing the distance between the drains and reducing the digging depth, an increase in efficiency by 60% has been reported due to the presence of a wide stone bed.
- Due to the proximity of the impervious layer to the ground surface, the best response in the performance of computational drains is 5-day rainfall, which is a very favorable performance compared to the previous measurement values that showed 1-day rainfall.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
MAE | mean absolute error |
RMSE | root mean squared error |
standard deviation | |
R | correlation coefficient |
L | depth of drainage (cm) |
t | soil type in the study blocks of the region |
reaction modulus | |
standard depth of the drain (cm) | |
r | radius of study boreholes (m) |
h | water depth in study boreholes (cm) |
d | agrology borehole (cm) |
b | study blocks in the region (number) |
s | area of study blocks () |
K | |
the calculated distance of drainage in the area (m) | |
the distance of the measured drains (m) |
References
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Practical Relation | Numerical Study Model |
---|---|
Dumm Glover | |
Hemmad | |
Van Schilfgaarde | |
Bouwer & Van Schilfgarrde | |
Auger hole method |
d | K | d | K |
---|---|---|---|
1 | 0.795 | 12 | 0.596 |
2 | 0.596 | 13 | 0.795 |
3 | 0.596 | 14 | 0.795 |
4 | 0.596 | 15 | 0.596 |
5 | 0.795 | 16 | 0.795 |
6 | 0.596 | 17 | 0.795 |
7 | 0.596 | 18 | 0.795 |
8 | 0.795 | 19 | 0.795 |
9 | 0.596 | 20 | 0.795 |
10 | 0.596 | 21 | 0.795 |
11 | 0.596 | 22 | 0.795 |
t | d | s | b | t | d | s | b |
---|---|---|---|---|---|---|---|
GC | 34–50 | 6051.11 | 23 | GW | 15 | 11,614.68 | 1 |
GC | 35 | 25,992.26 | 24 | SC | 16 | 8924.52 | 2 |
GM-GC-GC | 10–11–12 | 27,365.27 | 25 | SC | 22 | 8122.71 | 3 |
GC | 7 | 12,157.96 | 26 | SC | 21 | 6494.13 | 4 |
GC | 41 | 11,951.67 | 27 | SC | 18 | 2893.8 | 5 |
GC | 42 | 9836.43 | 28 | SC | 19 | 4271.94 | 6 |
GC-GM | 2–9 | 16,771.18 | 29 | SC | 20 | 13,104.62 | 7 |
GM | 6 | 11,091.26 | 30 | GC | 21 | 12,575.75 | 8 |
GM | 4 | 17,787.80 | 31 | GC | 22 | 11,635.48 | 9 |
GM | 3 | 23,200.77 | 32 | GC | 23 | 3374.63 | 10 |
CL | 40 | 8913.84 | 33 | GC | 28 | 4565.15 | 11 |
CL | 8 | 10,353.99 | 34 | GC | 29 | 2498.23 | 12 |
CL | 1 | 12,823.66 | 35 | GC | 24 | 1276.9 | 13 |
SC | 5 | 5859.6 | 36 | GC | 30 | 8547.28 | 14 |
SC | 38–49 | 27,184.81 | 37 | SC | 31 | 8183.47 | 15 |
SC | 37–48 | 54,228.83 | 38 | SC | 25 | 10,561.25 | 16 |
GM | 39 | 15,777.17 | 39 | SC | 32 | 5369.74 | 17 |
GM | 44 | 20,923.78 | 40 | SC | 26 | 11,672.63 | 18 |
GM | 36 | 5441.3 | 41 | SC | 27 | 5754.96 | 19 |
GM | 46–47 | 79,925.02 | 42 | SM | 14 | 10,390.87 | 20 |
GM | 43 | 16,866.26 | 43 | SM | 33 | 9944.25 | 21 |
GM | 45 | 14,284.55 | 44 | SM | 17 | 10,492.21 | 22 |
Depth of Drainage h (cm) | 1-Day Rainfall | 2-Day Rainfall | 3-Day Rainfall | 4-Day Rainfall | 5-Day Rainfall |
---|---|---|---|---|---|
Drain spacing in numerical model Dumm (m) | |||||
h = 110 cm | 12.02 | 12.53 | 14.01 | 17.01 | 36.67 |
h = 120 cm | 13.76 | 14.47 | 16.51 | 20.41 | 26.6 |
h = 130 cm | 15.06 | 15.91 | 18.34 | 22.68 | 28.81 |
h = 140 cm | 16.13 | 17.09 | 19.79 | 24.37 | 30.22 |
h = 150 cm | 17.05 | 18.11 | 21 | 25.68 | 31.2 |
h = 160 cm | 17.87 | 19 | 22.03 | 26.73 | 31.92 |
h = 170 cm | 18.61 | 19.8 | 22.93 | 27.6 | 32.48 |
h = 180 cm | 19.28 | 20.51 | 23.72 | 28.33 | 32.92 |
Drain spacing in numerical model Glover (m) | |||||
h = 110 cm | 9.59 | 14.28 | 19.89 | 28.19 | 68.73 |
h = 120 cm | 10.77 | 16.17 | 23 | 33.2 | 67.4 |
h = 130 cm | 10.77 | 16.17 | 23 | 33.2 | 67.4 |
h = 140 cm | 11.54 | 17.43 | 25.02 | 36.17 | 66.03 |
h = 150 cm | 12.51 | 18.99 | 27.43 | 38.04 | 64.63 |
h = 160 cm | 12.8 | 19.45 | 27.43 | 39.19 | 61.7 |
h = 170 cm | 13 | 19.76 | 28.52 | 40.11 | 60.16 |
h = 180 cm | 13.11 | 19.93 | 28.72 | 40.08 | 58.56 |
Drain spacing in numerical model Hemmad (m) | |||||
h = 110 cm | 3.52 | 4.83 | 5.79 | 7.1 | 11.23 |
h = 120 cm | 4.28 | 5.82 | 7.72 | 9.88 | 11.92 |
h = 130 cm | 4.75 | 6.41 | 8.35 | 10.4 | 12.19 |
h = 140 cm | 5.08 | 6.82 | 8.75 | 10.69 | 12.34 |
h = 150 cm | 5.34 | 7.12 | 9.03 | 10.89 | 12.43 |
h = 160 cm | 5.53 | 7.36 | 9.25 | 11.04 | 12.49 |
h = 170 cm | 5.7 | 7.54 | 9.42 | 11.14 | 12.53 |
h = 180 cm | 5.83 | 7.7 | 9.55 | 11.22 | 12.57 |
Drain spacing in numerical model Bouwer (m) | |||||
h = 110 cm | 5.64 | 8.42 | 11.87 | 17.46 | 29.2 |
h = 120 cm | 6.62 | 10 | 14.55 | 26.33 | 47.46 |
h = 130 cm | 7.4 | 11.27 | 16.74 | 26.52 | 47.85 |
h = 140 cm | 8.09 | 12.4 | 18.68 | 30.1 | 55.06 |
h = 150 cm | 8.72 | 13.43 | 20.45 | 33.36 | 61.59 |
h = 160 cm | 9.31 | 14.39 | 22.11 | 36.39 | 67.62 |
h = 170 cm | 9.87 | 15.31 | 23.68 | 39.25 | 73.28 |
h = 180 cm | 10.41 | 16.18 | 25.18 | 41.96 | 78.64 |
Drain spacing in numerical model Bouwer & Van Schilfgarrde (m) | |||||
h = 110 cm | 6.04 | 9.01 | 12.68 | 18.61 | 31.08 |
h = 120 cm | 7.12 | 10.74 | 15.6 | 24.01 | 42.23 |
h = 130 cm | 7.99 | 12.16 | 18 | 28.45 | 51.26 |
h = 140 cm | 8.77 | 13.41 | 20.14 | 32.38 | 59.17 |
h = 150 cm | 9.48 | 14.57 | 22.12 | 36 | 66.37 |
h = 160 cm | 10.14 | 15.65 | 23.98 | 39.37 | 73.07 |
h = 170 cm | 10.78 | 16.69 | 25.74 | 42.57 | 79.4 |
h = 180 cm | 11.4 | 17.69 | 27.44 | 45.64 | 85.44 |
Day Rainfall | h = 110 cm | h = 120 cm | h = 130 cm | h = 140 cm | h = 150 cm | h = 160 cm | h = 170 cm | h = 180 cm | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
σ | MAE | σ | MAE | σ | MAE | σ | MAE | σ | MAE | σ | MAE | σ | MAE | σ | MAE | |
Numerical values of σ and MAE in the Dumm numerical model | ||||||||||||||||
1-day Rainfall | 0.76 | 38.03 | 0.73 | 36.36 | 0.7 | 34.99 | 0.68 | 33.92 | 0.66 | 32.99 | 0.64 | 32.17 | 0.63 | 31.43 | 0.62 | 30.76 |
2-day Rainfall | 0.75 | 37.57 | 0.71 | 35.71 | 0.68 | 34.18 | 0.66 | 33 | 0.64 | 31.98 | 0.62 | 31.09 | 0.61 | 30.3 | 0.59 | 29.58 |
3-day Rainfall | 0.72 | 36.12 | 0.67 | 33.74 | 0.64 | 31.8 | 0.61 | 30.35 | 0.58 | 29.14 | 0.56 | 28.11 | 0.54 | 27.21 | 0.53 | 26.42 |
4-day Rainfall | 0.66 | 33.18 | 0.6 | 29.99 | 0.55 | 27.5 | 0.52 | 25.82 | 0.49 | 24.51 | 0.47 | 23.45 | 0.45 | 22.59 | 0.44 | 21.86 |
5-day Rainfall | 0.27 | 27.19 | 0.47 | 24.1 | 0.43 | 21.42 | 0.4 | 20.01 | 0.38 | 19.03 | 0.37 | 18.3 | 0.36 | 17.75 | 0.35 | 17.3 |
Numerical values of σ and MAE in the Glover numerical model | ||||||||||||||||
1-day Rainfall | 0.81 | 40.45 | 0.79 | 39.38 | 0.79 | 39.28 | 0.77 | 38.5 | 0.75 | 37.54 | 0.75 | 37.24 | 0.74 | 37.05 | 0.74 | 36.94 |
2-day Rainfall | 0.72 | 35.81 | 0.68 | 34.17 | 0.68 | 33.92 | 0.65 | 32.66 | 0.62 | 31.1 | 0.61 | 30.64 | 0.61 | 30.33 | 0.6 | 30.16 |
3-day Rainfall | 0.61 | 30.24 | 0.54 | 27.77 | 0.54 | 27.14 | 0.5 | 25.11 | 0.45 | 22.7 | 0.45 | 22.7 | 0.43 | 21.62 | 0.43 | 21.42 |
4-day Rainfall | 0.44 | 21.99 | 0.34 | 19.01 | 0.34 | 16.99 | 0.28 | 14.16 | 0.24 | 13.4 | 0.22 | 13.27 | 0.2 | 13.93 | 0.2 | 14.45 |
5-day Rainfall | −0.37 | 19.62 | −0.34 | 24.41 | −0.34 | 19.04 | −0.32 | 18.49 | −0.29 | 17.95 | −0.23 | 17.41 | −0.20 | 17.56 | −0.17 | 17.86 |
Numerical values of σ and MAE in the Hemmad numerical model | ||||||||||||||||
1-day Rainfall | 0.93 | 46.52 | 0.92 | 45.77 | 0.91 | 45.29 | 0.9 | 44.96 | 0.89 | 44.71 | 0.89 | 44.51 | 0.89 | 44.35 | 0.88 | 44.21 |
2-day Rainfall | 0.91 | 45.26 | 0.89 | 44.28 | 0.87 | 43.68 | 0.87 | 43.27 | 0.86 | 42.97 | 0.86 | 42.74 | 0.85 | 42.55 | 0.85 | 42.39 |
3-day Rainfall | 0.89 | 44.34 | 0.85 | 42.43 | 0.84 | 41.79 | 0.83 | 41.39 | 0.82 | 41.1 | 0.82 | 40.89 | 0.81 | 40.72 | 0.81 | 40.59 |
4-day Rainfall | 0.86 | 43.08 | 0.81 | 40.32 | 0.8 | 39.79 | 0.79 | 39.49 | 0.79 | 39.29 | 0.78 | 39.15 | 0.78 | 39.04 | 0.78 | 38.96 |
5-day Rainfall | 0.78 | 39 | 0.77 | 38.34 | 0.76 | 38.04 | 0.76 | 37.89 | 0.76 | 37.8 | 0.76 | 37.74 | 0.75 | 37.69 | 0.75 | 37.66 |
Numerical values of σ and MAE in the Bouwer numerical model | ||||||||||||||||
1-day Rainfall | 0.89 | 44.41 | 0.87 | 43.43 | 0.85 | 42.64 | 0.84 | 41.95 | 0.83 | 41.32 | 0.82 | 40.73 | 0.8 | 40.17 | 0.79 | 39.64 |
2-day Rainfall | 0.83 | 41.67 | 0.8 | 40.09 | 0.78 | 38.82 | 0.75 | 37.69 | 0.73 | 36.66 | 0.71 | 35.7 | 0.7 | 34.78 | 0.68 | 33.91 |
3-day Rainfall | 0.83 | 38.26 | 0.71 | 35.59 | 0.67 | 33.39 | 0.63 | 31.46 | 0.59 | 29.68 | 0.56 | 28.03 | 0.53 | 26.46 | 0.5 | 24.96 |
4-day Rainfall | 0.65 | 32.72 | 0.48 | 23.88 | 0.47 | 23.66 | 0.4 | 20.08 | 0.34 | 16.82 | 0.28 | 13.79 | 0.22 | 10.94 | 0.16 | 8.22 |
5-day Rainfall | 0.42 | 21.03 | 0.06 | 3.52 | 0.05 | 2.38 | −0.10 | 4.84 | −0.23 | 11.36 | −0.35 | 17.39 | −0.46 | 23.05 | −0.57 | 28.42 |
Numerical values of σ and MAE in the Bouwer & Van Schilfgarrde numerical model | ||||||||||||||||
1-day Rainfall | 0.88 | 44 | 0.86 | 42.92 | 0.84 | 42.05 | 0.83 | 41.28 | 0.81 | 40.57 | 0.8 | 39.9 | 0.79 | 39.26 | 0.77 | 36.65 |
2-day Rainfall | 0.82 | 41.08 | 0.79 | 39.35 | 0.76 | 37.93 | 0.73 | 36.68 | 0.71 | 35.52 | 0.69 | 34.44 | 0.67 | 33.4 | 0.65 | 32.4 |
3-day Rainfall | 0.75 | 37.46 | 0.69 | 34.54 | 0.64 | 32.14 | 0.6 | 29.99 | 0.56 | 28.02 | 0.52 | 26.16 | 0.49 | 24.39 | 0.45 | 22.7 |
4-day Rainfall | 0.63 | 31.57 | 0.52 | 26.19 | 0.44 | 21.73 | 0.36 | 17.8 | 0.28 | 14.19 | 0.22 | 10.81 | 0.15 | 7.61 | 0.09 | 4.54 |
5-day Rainfall | 0.38 | 19.15 | 0.16 | 8.13 | −0.02 | 1.78 | −0.18 | 8.95 | −0.32 | 16.15 | −0.46 | 22.85 | −0.58 | 29.18 | −0.70 | 35.22 |
Numerical Model | h = 110 cm | h = 120 cm | h = 130 cm | h = 140 cm | h = 150 cm | h = 160 cm | h = 170 cm | h = 180 cm |
---|---|---|---|---|---|---|---|---|
1-Day rainfall | ||||||||
Hemmad | 46.524 | 45.765 | 45.297 | 44.966 | 44.715 | 44.517 | 44.355 | 44.219 |
Bouwer & Van | 44.004 | 42.924 | 42.052 | 41.28 | 40.569 | 39.9 | 39.263 | 38.65 |
Bouwer | 44.411 | 43.43 | 42.645 | 41.955 | 41.324 | 40.735 | 40.175 | 39.64 |
Dumm | 38.078 | 36.355 | 35.074 | 34.018 | 33.109 | 32.305 | 31.583 | 29.93 |
Glover | 40.524 | 39.376 | 39.376 | 38.625 | 37.711 | 37.447 | 37.281 | 37.202 |
2-Day rainfall | ||||||||
Hemmad | 45.263 | 44.277 | 43.688 | 43.281 | 42.979 | 42.744 | 42.555 | 42.399 |
Bouwer & Van | 41.08 | 39.347 | 37.936 | 36.683 | 35.528 | 34.441 | 33.404 | 32.407 |
Bouwer | 41.674 | 40.093 | 38.817 | 37.693 | 36.663 | 35.7 | 34.787 | 33.913 |
Dumm | 37.623 | 35.707 | 34.285 | 33.121 | 32.125 | 31.253 | 30.476 | 29.17 |
Glover | 35.985 | 34.17 | 34.17 | 32.991 | 31.588 | 31.202 | 30.976 | 30.89 |
3-Day rainfall | ||||||||
Hemmad | 44.347 | 42.428 | 41.803 | 41.399 | 41.114 | 40.901 | 40.736 | 40.604 |
Bouwer & Van | 37.462 | 34.543 | 32.141 | 30.001 | 28.029 | 26.175 | 24.411 | 22.71 |
Bouwer | 38.266 | 35.585 | 33.396 | 31.462 | 29.691 | 28.037 | 26.471 | 24.977 |
Dumm | 36.202 | 33.741 | 31.956 | 30.538 | 29.362 | 28.363 | 27.497 | 26.739 |
Glover | 30.641 | 27.772 | 27.772 | 25.984 | 24.059 | 24.059 | 23.45 | 23.487 |
4-Day rainfall | ||||||||
Hemmad | 43.089 | 40.315 | 39.806 | 39.5 | 39.309 | 39.169 | 39.064 | 38.983 |
Bouwer & Van | 31.578 | 26.187 | 21.754 | 17.83 | 14.24 | 10.893 | 7.748 | 4.81 |
Bouwer | 32.723 | 23.875 | 23.676 | 20.105 | 16.858 | 13.84 | 11.018 | 8.345 |
Dumm | 33.311 | 29.994 | 27.789 | 26.172 | 24.923 | 23.925 | 23.107 | 22.424 |
Glover | 23.072 | 19.008 | 19.008 | 17.021 | 16.108 | 15.82 | 16.277 | 16.827 |
5-Day rainfall | ||||||||
Hemmad | 39.021 | 38.335 | 38.065 | 37.919 | 37.829 | 37.767 | 37.722 | 37.688 |
Bouwer & Van | 19.181 | 8.126 | 2.02 | 9.167 | 16.302 | 22.982 | 29.304 | 35.342 |
Bouwer | 21.057 | 3.516 | 2.887 | 5.189 | 11.552 | 17.541 | 23.183 | 28.543 |
Dumm | 15.081 | 24.098 | 22.031 | 20.728 | 19.831 | 19.174 | 18.673 | 18.278 |
Glover | 25.169 | 24.414 | 24.414 | 23.706 | 23.057 | 21.993 | 21.614 | 21.368 |
Depth of Drainage h (cm) | Numerical Model Hemmad | Numerical Model Bouwer & Van | Numerical Model Bouwer | Numerical Model Dumm | Numerical Model Glover |
---|---|---|---|---|---|
1-Day rainfall | |||||
h = 110 cm | 26.676 | 9.355 | 10.761 | 2.263 | 3.725 |
h = 120 cm | 17.964 | 6.731 | 7.802 | 1.725 | 2.977 |
h = 130 cm | 14.566 | 5.344 | 6.235 | 1.439 | 2.977 |
h = 140 cm | 12.712 | 4.447 | 5.22 | 1.254 | 2.613 |
h = 150 cm | 11.531 | 3.808 | 4.495 | 1.121 | 2.28 |
h = 160 cm | 10.71 | 3.325 | 3.946 | 1.021 | 2.215 |
h = 170 cm | 10.103 | 2.946 | 3.514 | 0.941 | 2.194 |
h = 180 cm | 9.636 | 2.64 | 3.165 | 0.877 | 2.216 |
2-Day rainfall | |||||
h = 110 cm | 28.709 | 8.449 | 9.691 | 4.2 | 3.372 |
h = 120 cm | 19.659 | 5.933 | 6.856 | 3.143 | 3.143 |
h = 130 cm | 16.158 | 4.635 | 5.389 | 2.596 | 2.646 |
h = 140 cm | 14.258 | 3.809 | 4.456 | 2.246 | 2.298 |
h = 150 cm | 13.055 | 3.23 | 3.8 | 2 | 1.984 |
h = 160 cm | 12.222 | 2.798 | 3.309 | 1.816 | 1.922 |
h = 170 cm | 11.609 | 2.463 | 2.928 | 1.673 | 1.902 |
h = 180 cm | 11.139 | 2.195 | 2.622 | 1.557 | 1.92 |
3-Day rainfall | |||||
h = 110 cm | 23.378 | 6.404 | 7.31 | 5.067 | 2.609 |
h = 120 cm | 16.836 | 4.221 | 4.85 | 3.638 | 1.964 |
h = 130 cm | 14.362 | 3.166 | 3.661 | 2.946 | 1.964 |
h = 140 cm | 13.042 | 2.529 | 2.94 | 2.526 | 1.673 |
h = 150 cm | 12.217 | 2.098 | 2.453 | 2.242 | 1.426 |
h = 160 cm | 11.652 | 1.786 | 2.1 | 2.036 | 1.426 |
h = 170 cm | 11.239 | 1.55 | 1.832 | 1.879 | 1.37 |
h = 180 cm | 10.925 | 1.366 | 1.622 | 1.755 | 1.388 |
4-Day rainfall | |||||
h = 110 cm | 17.389 | 3.95 | 4.49 | 4.603 | 1.731 |
h = 120 cm | 17.389 | 3.95 | 4.49 | 4.603 | 1.731 |
h = 130 cm | 13.709 | 2.367 | 1.973 | 3.186 | 1.256 |
h = 140 cm | 12.37 | 1.684 | 1.938 | 2.573 | 1.256 |
h = 150 cm | 11.245 | 1.052 | 1.225 | 2.005 | 0.975 |
h = 160 cm | 10.954 | 0.88 | 1.03 | 1.849 | 0.931 |
h = 170 cm | 10.745 | 0.753 | 0.886 | 1.734 | 0.923 |
h = 180 cm | 10.586 | 0.656 | 0.776 | 1.645 | 0.914 |
5-Day rainfall | |||||
h = 110 cm | 13.325 | 1.761 | 1.997 | 1.228 | 0.362 |
h = 120 cm | 11.8 | 0.951 | 0.757 | 2.343 | 0.379 |
h = 130 cm | 11.27 | 0.65 | 0.74 | 1.995 | 0.379 |
h = 140 cm | 11 | 0.485 | 0.559 | 1.812 | 0.399 |
h = 150 cm | 10.836 | 0.385 | 0.447 | 1.699 | 0.421 |
h = 160 cm | 10.727 | 0.318 | 0.371 | 1.622 | 0.477 |
h = 170 cm | 10.648 | 0.27 | 0.317 | 1.567 | 0.512 |
h = 180 cm | 10.589 | 0.233 | 0.275 | 1.524 | 0.555 |
μ | L | KD | |
---|---|---|---|
high | high | low | |
low | low | high |
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Moshayedi, B.; Najarchi, M.; Najafizadeh, M.M.; Khaghani, S. The Sensitivity Analysis of the Drainage Unsteady Equations against the Depth of Drain Placement and Rainfall Time at the Shallow Water-Bearing Layers: A Case Study of Markazi Province, Iran. Water 2022, 14, 2693. https://doi.org/10.3390/w14172693
Moshayedi B, Najarchi M, Najafizadeh MM, Khaghani S. The Sensitivity Analysis of the Drainage Unsteady Equations against the Depth of Drain Placement and Rainfall Time at the Shallow Water-Bearing Layers: A Case Study of Markazi Province, Iran. Water. 2022; 14(17):2693. https://doi.org/10.3390/w14172693
Chicago/Turabian StyleMoshayedi, Behzad, Mohsen Najarchi, Mohammad Mahdi Najafizadeh, and Shahab Khaghani. 2022. "The Sensitivity Analysis of the Drainage Unsteady Equations against the Depth of Drain Placement and Rainfall Time at the Shallow Water-Bearing Layers: A Case Study of Markazi Province, Iran" Water 14, no. 17: 2693. https://doi.org/10.3390/w14172693