# 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

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## Abstract

**:**

## 1. Introduction

## 2. Studied Region

## 3. Materials and Methods

_{0}) in meters, and hydraulic conductivity is presented with the symbol (K).

## 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 |

$\sigma $ | standard deviation |

R | correlation coefficient |

L | depth of drainage (cm) |

t | soil type in the study blocks of the region |

$\alpha $ | reaction modulus |

${h}_{0}$ | 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 (${\mathrm{m}}^{2}$) |

K | $\mathrm{hydraulic}\mathrm{conductivity}\left(\frac{\mathrm{m}}{\mathrm{day}}\right)$ |

${\beta}_{1}$ | the calculated distance of drainage in the area (m) |

${\beta}_{2}$ | the distance of the measured drains (m) |

## References

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**Figure 1.**Aerial map of the study area in the Sanjan Plain. Right image of northern lands with residential use. Left image with agricultural use in the southern part.

**Figure 2.**Water accumulation in the northern part of the study area with residential use during 2 days of rainfall in 2021, which has led to the complete burial of urban facilities, buildings and roads.

**Figure 3.**The water retention in the southern parts of the studied region with agricultural use due to 3-day rainfall in rainy seasons in 2021.

**Figure 4.**Ombrothermic diagram based on the meteorological data (1996–2016) at the synoptic station of Arak.

**Table 1.**Practical relationships for calculating hydraulic conductivity (k) in unsteady conditions and inverse auger hole laboratory model [33].

Practical Relation | Numerical Study Model |
---|---|

Dumm Glover | $K=\frac{\frac{{L}^{2}{q}_{t}}{{h}_{t}}}{2\mathsf{\pi}D}$ |

Hemmad | $K=\frac{\left(\frac{{q}_{t}}{{h}_{t}}\right)L\mathrm{ln}\left(\frac{{L}^{2}}{2{\mathsf{\pi}}^{2}\mathrm{rd}}\right)}{2\mathsf{\pi}}$ |

Van Schilfgaarde | $K=\frac{2{L}^{2}\left(\frac{{q}_{t}}{{h}_{t}}\right)}{9\left(2{d}_{e}+{h}_{0}\right)}$ |

Bouwer & Van Schilfgarrde | $K=\frac{{L}^{2}\left(\frac{{q}_{t}}{{h}_{t}}\right)}{4\left(2{d}_{e}+{h}_{0}\right)}$ |

Auger hole method | $K$$=1.15r\mathrm{tan}\mathsf{\alpha}$ |

**Table 2.**Numerical values of soil hydraulic conductivity (k) in 22 agrology boreholes (d) using the inverse auger hole laboratory model.

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 |

**Table 3.**Numerical results obtained for the area of each research block (b) in terms of square meters (s), number of study boreholes (d), and soil type in each research borehole (t).

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 |

**Table 4.**Distances between computational drains based on numerical elationships in time-dependent conditions at a depth of 110 cm; 18 cm above the ground and under a rainfall of 1–5 days.

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 |

**Table 5.**Mean numerical percentage (σ) and (MAE) under the numerical model of unsteady conditions and daily rainfall in the depth of drain (h) of 110 cm; 180 cm.

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 |

**Table 6.**Numerical values of (RMSE) under daily rainfall for 1 to 5 days in the depth of drainage at the rate of 110 cm; 180 cm above the ground.

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 |

**Table 7.**Numerical values of reaction modulus (α) in numerical models of unsteady conditions and depth install drain h under 1- to 5-day rainfall.

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 |

$\mathbf{Range}\left(\mathit{\alpha}\right)$ | μ | L | KD |
---|---|---|---|

$0.3<\alpha <0.2$ | high | high | low |

$2<\alpha <5$ | low | low | high |

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**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Moshayedi, 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