# Water Distribution from Artificial Recharge via Infiltration Basin under Constant Head Conditions

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Conceptual and Mathematical Models

_{basin}.

_{Basin}, D) infiltrates into the vadose zone with a constant water head, and water of the bare soil between point (r

_{Basin}, D) and point (L, D) evaporates from the vadose zone with a constant potential evaporation. The bottom boundary is the interface between the vadose zone and the saturated zone where the infiltrated water recharges groundwater.

_{r}is the residual water content (-), θ

_{s}is the saturated water content (-), α, n, m, and f are empirical parameters (1/L), (-), (-), and (-), K(h) is the hydraulic conductivity (L/T), K

_{s}is the saturated hydraulic conductivity (L/T), S

_{e}is the effective water content (-).

_{Basin}, D) and from point (r

_{Basin}, D) to point (L, D), respectively. The nodes representing the right and left sides of the flow domain were set to no flux boundaries. The nodes at the bottom boundary were assigned a free drainage boundary condition (i.e., the water table was assumed to be far below this point) because the numerical experiments in this study do not account for the effect of the water table [50]. The initial condition was in water content with a constant distribution in the whole domain.

#### 2.2. Numerical Experiments

_{Basin}). Nine experiments were conducted under the experimental condition of radius of infiltration basin and nine lengths of variable head boundaries represented different radiuses of infiltration basin (r

_{Basin}). Twelve experiments were conducted under the experimental condition of evaporation intensity and twelve potential evaporation rates in atmospheric boundaries represented different evaporation intensities (e). Ten experiments were conducted under the experimental condition of antecedent moisture of the vadose zone and ten moisture saturation in initial conditions represented different antecedent moistures of the vadose zone (s

_{r}). Eleven experiments were conducted under the experimental condition of thickness of the vadose zone and eleven lengths of no flux boundaries represented different thicknesses of the vadose zone (D). Ten experiments were conducted under the experimental condition of saturated hydraulic conductivity of the vadose zone and ten saturated hydraulic conductivities represented different saturated hydraulic conductivities of the vadose zone (K

_{s}).

#### 2.3. Data Analysis

_{e}) of the flow through the bottom boundary of the vadose zone and the radius (r

_{s}) of the saturated part of the flow at the end time of every experiment, and the time (t

_{r}) when the saturated flow reaches the bottom boundary for every experiment were available in output files, too. Furthermore, the ratio of r

_{s}to r

_{e}(r

_{s}/r

_{e}) was calculated for every experiment.

_{e}, r

_{s}, t

_{r}, and r

_{s}/r

_{e}) and h

_{Basin}under the experimental condition of water head in infiltration basin. The correlations between every experimental data and r

_{Basin}, e, s

_{r}, D, K

_{s}, l, and d under different experimental conditions were analyzed with the same method, too. The significance level of these correlations was estimated by the mean of calculating their Pearson correlation coefficients. Furthermore, regression analysis was performed for those variables with significant correlation. During the regression analysis, the determination coefficient and F statistic were the measures of fit quality between experimental and fitted results.

## 3. Results

#### 3.1. Homogeneous Domain Experimental Conditions

_{e}, r

_{s}, and t

_{r}are significantly correlated to h

_{Basin}at 99% confidence levels, and r

_{s}/r

_{e}is not correlated to h

_{Basin}significantly. The correlations of I, R, S, E, R/I, r

_{e}, and r

_{s}to h

_{Basin}are positive, and that of other variables negative. As h

_{Basin}increases, I, R, S, R/I, and r

_{s}grow quadratically, and the growth rate decreases with an increment in h

_{Basin}. Additionally, E grows quadratically, and the growth rate increases with an increment in h

_{Basin}. In addition, S/I, E/I, and t

_{r}decline quadratically, and the decline rate decreases with an increment in h

_{Basin}. Furthermore, r

_{e}grows linearly. These variations are shown in Figure 2.

_{e}, r

_{s}, t

_{r}, and r

_{s}/r

_{e}all are significantly correlated to r

_{Basin}at 99% confidence levels. The correlations of I, R, S, E, R/I, r

_{e}, r

_{s}, and r

_{s}/r

_{e}to r

_{Basin}are positive, and that of other variables negative. As r

_{Basin}increases, I, R, and S grow quadratically, and the growth rate increases with an increment in r

_{Basin}. Additionally, E, R/I, r

_{e}, r

_{s}, and r

_{s}/r

_{e}grow quadratically, and the growth rate decreases with an increment in r

_{Basin}. In addition, S/I, E/I, and t

_{r}decline quadratically, and the decline rate decreases with an increment in r

_{Basin}. These variations are shown in Figure 3.

_{e}, r

_{s}, t

_{r}, and r

_{s}/r

_{e}are not correlated to e significantly. The correlations of I, E, and E/I to e are positive. As e increases, I grows quadratically, and the growth rate decreases with an increment in e. Additionally, E and E/I grow exponentially, and the growth rate increases with an increment in e. These variations are shown in Figure 4.

_{e}, r

_{s}, and t

_{r}are significantly correlated to s

_{r}at 99% confidence levels, and r

_{s}/r

_{e}is not correlated to s

_{r}significantly. The correlations of I, S, S/I, and t

_{r}to s

_{r}are negative, and that of other variables positive. As s

_{r}increases, I, and t

_{r}decline quadratically, and the decline rate decreases with an increment in s

_{r}. Additionally, R and R/I grow exponentially, and the growth rate increases with an increment in s

_{r}. In addition, S and S/I decline quadratically, and the decline rate increases with an increment in s

_{r}. Furthermore, E and E/I grow quadratically, and the growth rate increases with an increment in s

_{r}. To add to this, r

_{e}grows logarithmically, and the growth rate decreases with an increment in s

_{r}. Moreover, r

_{s}grows linearly. These variations are shown in Figure 5.

_{e}, r

_{s}, and t

_{r}are significantly correlated to D at 99% confidence levels, E/I is significantly correlated to D at a 95% confidence level, and I and r

_{s}/r

_{e}are not correlated to D significantly. The correlations of R, R/I, r

_{e}, and r

_{s}to D are negative, and that of other variables positive. As D increases, R and R/I decline quadratically, and the decline rate decreases with an increment in D. Additionally, S grows logarithmically, and the growth rate decreases with an increment in D. In addition, E, S/I, and E/I grow quadratically, and the growth rate decreases with an increment in D. Furthermore, r

_{e}and r

_{s}decline quadratically, and the decline rate increases with an increment in D. To add to this, t grows quadratically, and the growth rate increases with an increment in D. These variations are shown in Figure 6.

_{e}, r

_{s}, t

_{r}, and r

_{s}/r

_{e}all are significantly correlated to K

_{s}at 99% confidence levels. The correlations of I, R, S, E, R/I, r

_{e}, and r

_{s}to K

_{s}are positive, and that of other variables negative. As K

_{s}increases, I, R, and E grow quadratically, and the growth rate increases with an increment in K

_{s}. Additionally, S, R/I, r

_{e}, and r

_{s}grow quadratically, and the growth rate decreases with an increment in K

_{s}. In addition, S/I, E/I, t

_{r}, and r

_{s}/r

_{e}decline quadratically, and the decline rate decreases with an increment in K

_{s}. These variations are shown in Figure 7.

#### 3.2. Heterogeneous Domain Experimental Conditions

_{s}, t

_{r}, and r

_{s}/r

_{e}are significantly correlated to l when l increases from 1 m to 10 m, and are not correlated to l significantly when l increases from 10 m to 60 m. Furthermore, r

_{e}is not correlated to l significantly when l increases from 1 m to 60 m. r

_{s}is significantly correlated to l at a 95% confidence level and other above-mentioned correlated variables are at 99% confidence levels. The correlations of I, R, E, and R/I to l are negative, and that of other variables positive. As l increases from 1 m to 60 m, E declines quadratically, and the decline rate increases with an increment in l. As l increases from 1 m to 15 m, R declines quadratically, and the decline rate decreases with an increment in l. Additionally, S grows quadratically, and the growth rate increases with an increment in l. In addition, R/I declines linearly. Furthermore, S/I grows exponentially, and the growth rate increases with an increment in l. As l increases from 1 m to 10 m, I declines quadratically, and the decline rate increases with an increment in l. Additionally, E/I, t

_{r}, and r

_{s}/r

_{e}grow quadratically, and the growth rate increases with an increment in l. In addition, r

_{s}grows exponentially, and the growth rate increases with an increment in l. These variations are shown in Figure 8.

_{s}/r

_{e}are significantly correlated to l when l increases from 3 m to 15 m, and are not correlated to l significantly when l increases from 15 m to 60 m. In addition, I, r

_{e}, r

_{s}, and t

_{r}are significantly correlated to l when l increases from 3 m to 10 m, and are not correlated to l significantly when l increases from 10 m to 60 m. I, R, S, R/I, S/I, and r

_{s}/r

_{e}are significantly correlated to l at a 99% confidence level and other above-mentioned correlated variables are at 95% confidence levels. The correlations of I, R, and R/I to l are negative, and that of other variables positive. As l increases from 3 m to 60 m, E grows quadratically, and the growth rate increases with an increment in l. As l increases from 3 m to 15 m, R declines quadratically, and the decline rate decreases with an increment in l. Additionally, S, S/I, and r

_{s}/r

_{e}grow quadratically, and the growth rate increases with an increment in l. In addition, R/I declines quadratically, and the decline rate increases with an increment in l; E/I grows quadratically, and the growth rate decreases with an increment in l. As l increases from 3 m to 10 m, I declines quadratically, and the decline rate decreases with an increment in l. Additionally, r

_{e}, r

_{s}, and t

_{r}grow quadratically, and the growth rate increases with an increment in l. These variations are shown in Figure 9.

_{s}/r

_{e}are significantly correlated to l when l increases from 1 m to 15 m, and are not correlated to l significantly when l increases from 15 m to 60 m. In addition, I, r

_{e}, r

_{s}, and t

_{r}are significantly correlated to l when l increases from 1 m to 10 m, and are not correlated to l significantly when l increases from 10 m to 60 m. Furthermore, E is not correlated to l significantly when l increases from 1 m to 60 m. E/I is significantly correlated to l at a 95% confidence level and other above-mentioned correlated variables are at 99% confidence levels. The correlations of I, R, and R/I to l are negative, and that of other variables positive. As l increases from 1 m to 20 m, E/I grows quadratically, and the growth rate decreases with an increment in l. As l increases from 1 m to 15 m, R and R/I decline quadratically, and the decline rate increases with an increment in l. Additionally, S, and S/I grow quadratically, and the growth rate increases with an increment in l. In addition, r

_{s}/r

_{e}grows quadratically, and the growth rate decreases with an increment in l. As l increases from 1 m to 10 m, I declines quadratically, and the decline rate increases with an increment in l. Additionally, r

_{e}, r

_{s}, and t

_{r}grow quadratically, and the growth rate increases with an increment in l. These variations are shown in Figure 10.

_{e}, r

_{s}, t

_{r}, and r

_{s}/r

_{e}are significantly correlated to l when l increases from 1 m to 10 m, and are not correlated to l significantly when l increases from 10 m to 30 m. Furthermore, I is not correlated to l significantly when l increases from 1 m to 30 m. r

_{s}/r

_{e}is significantly correlated to l at a 95% confidence level and other above-mentioned correlated variables are at 99% confidence levels. The correlations of R and R/I to l are negative, and that of other variables positive. As l increases from 1 m to 30 m, E and E/I grow quadratically, and the growth rate increases with an increment in l. As l increases from 1 m to 15 m, R and R/I decline quadratically, and the decline rate increases with an increment in l. Additionally, S, and S/I grow quadratically, and the growth rate increases with an increment in l. As l increases from 1 m to 10 m, r

_{e}, r

_{s}, t

_{r,}and r

_{s}/r

_{e}grow quadratically, and the growth rate increases with an increment in l. These variations are shown in Figure 11.

_{e}is significantly correlated to l when l increases from 1 m to 15 m, and is not correlated to l significantly when l increases from 15 m to 60 m. Furthermore, r

_{s}and r

_{s}/r

_{e}are significantly correlated to l when l increases from 1 m to 10 m, and are not correlated to l significantly when l increases from 10 m to 60 m. To add to this, t

_{r}is significantly correlated to l when l increases from 1 m to 7 m, and is not correlated to l significantly when l increases from 7 m to 60 m. Moreover, I is not correlated to l significantly when l increases from 1 m to 60 m. r

_{e}and r

_{s}are significantly correlated to l at 95% confidence levels and other above-mentioned correlated variables are at 99% confidence levels. The correlations of R and R/I to l are negative, and that of other variables positive. As l increases from 1 m to 60 m, E and E/I grow logarithmically, and the growth rate decreases with an increment in l. As l increases from 1 m to 20 m, R and R/I decline quadratically, and the decline rate increases with an increment in l. Additionally, S, and S/I grow quadratically, and the growth rate increases with an increment in l. As l increases from 1 m to 15 m, r

_{e}grows quadratically, and the decline rate increases with an increment in l. As l increases from 1 m to 10 m, r

_{s}grows quadratically, and the growth rate increases with an increment in l. In addition, r

_{s}/r

_{e}grows exponentially, and the growth rate increases with an increment in l. As l increases from 1 m to 7 m, t

_{r}grows quadratically, and the growth rate increases with an increment in l. These variations are shown in Figure 12.

_{e}, r

_{s}, and t

_{r}are significantly correlated to d at 99% confidence levels, and E and r

_{s}/r

_{e}are significantly correlated to d at 95% confidence levels. The correlations of I, R, S, R/I, r

_{e}, r

_{s}, and r

_{s}/r

_{e}to d are negative, and that of other variables positive. As d increases, I declines exponentially, and the decline rate decreases with an increment in d. Additionally, R and R/I decline quadratically, and the decline rate decreases with an increment in d. In addition, S, r

_{e}, r

_{s}, and r

_{s}/r

_{e}decline quadratically, and the decline rate increases with an increment in d. Furthermore, E and E/I grow quadratically, and the growth rate increases with an increment in d. To add to this, S/I and t

_{r}grow quadratically, and the growth rate decreases with an increment in d. These variations are shown in Figure 13.

_{e}, r

_{s}, t

_{r}, and r

_{s}/r

_{e}are significantly correlated to d at 99% confidence levels, and E is not correlated to d significantly. The correlations of I, R, R/I, r

_{e}, r

_{s}, and r

_{s}/r

_{e}to d are negative, and that of other variables positive. As d increases, I declines logarithmically, and the decline rate decreases with an increment in d. Additionally, R, R/I, and r

_{s}decline exponentially, and the decline rate decreases with an increment in d. In addition, S, S/I, E/I, and t

_{r}grow quadratically, and the growth rate decreases with an increment in d. Furthermore, r

_{e}declines quadratically, and the decline rate increases with an increment in d. To add to this, r

_{s}/r

_{e}declines quadratically, and the decline rate decreases with an increment in d. These variations are shown in Figure 14.

_{s}, t

_{r}and r

_{s}/r

_{e}are significantly correlated to d at 99% confidence levels, r

_{e}is significantly correlated to d at a 95% confidence level, and E is not correlated to d significantly. The correlations of I, R, R/I, r

_{e}, r

_{s}, and r

_{s}/r

_{e}to d are negative, and that of other variables positive. As d increases, I, r

_{e}, r

_{s}, and r

_{s}/r

_{e}decline quadratically, and the decline rate increases with an increment in d. Additionally, R and R/I decline exponentially, and the decline rate decreases with an increment in d. In addition, S, S/I, and t

_{r}grow quadratically, and the growth rate decreases with an increment in d. Furthermore, E/I grows quadratically, and the growth rate increases with an increment in d. These variations are shown in Figure 15.

_{s}, t

_{r}, and r

_{s}/r

_{e}are significantly correlated to d at 99% confidence levels, and I, E, E/I, and r

_{e}are not correlated to d significantly. The correlations of R, R/I, r

_{s}, and r

_{s}/r

_{e}to d are negative, and that of other variables positive. As d increases, R and R/I decline quadratically, and the decline rate decreases with an increment in d. Additionally, S, S/I, and t

_{r}grow quadratically, and the growth rate decreases with an increment in d. In addition, r

_{s}, and r

_{s}/r

_{e}decline quadratically, and the decline rate increases with an increment in d. These variations are shown in Figure 16.

_{e}, r

_{s}, t

_{r}and r

_{s}/r

_{e}are significantly correlated to d at 99% confidence levels, and I, E, and E/I are not correlated to d significantly. The correlations of R, R/I, r

_{s}, and r

_{s}/r

_{e}to d are negative, and that of other variables positive. As d increases, R and R/I decline quadratically, and the decline rate decreases with an increment in d. Additionally, S and t

_{r}grow exponentially, and the growth rate increases with an increment in d. In addition, S/I grows quadratically, and the growth rate decreases with an increment in d. Furthermore, r

_{e}grows logarithmically, and the growth rate decreases with an increment in d. To add to this, r

_{s}, and r

_{s}/r

_{e}decline quadratically, and the decline rate increases with an increment in d. These variations are shown in Figure 17.

## 4. Discussion

#### 4.1. Analysis on the Impacts of Infiltration Basin Features and Vadose Zone Factors on Water Distribution

#### 4.1.1. Storage in the Vadose Zone

_{s}/r

_{e}increased. In addition, with an increment in the water head in infiltration basin, although S increased, S/I declined. Furthermore, with an increment in saturated hydraulic conductivity, although S increased and r

_{s}/r

_{e}declined, S/I declined. The increment in the thickness of the vadose zone generated negative effects on the reduction in the storage. With an increment in the thickness of the vadose zone, both S/I and S increased. The increment in the evaporation intensity did not generate any effect on the reduction in the storage. With an increment in the evaporation intensity, S/I, S, and r

_{s}/r

_{e}did not vary significantly.

_{e}showed different variation trends with an increment in thickness of low permeability formation in different depths. When the depth of low permeability formation was 5 m, with an increment in thickness, S declined. Additionally, when the depths were 10 m, 20 m, and 30 m, with an increment in thickness, S grew quadratically, and the growth rate decreased. Furthermore, when the depth was 55 m, with an increment in thickness, S grew exponentially. When the depths were 5 m and 10 m, r

_{e}was correlated with the thickness significantly at a 99% confidence level, and with an increment in thickness, r

_{e}declined. Additionally, when the depth was 20 m, r

_{e}was correlated with the thickness significantly at a 95% confidence level, and with an increment in thickness, r

_{e}declined. Furthermore, r

_{e}did not show any significant correlation in thickness with a depth of 30 m. To add to this, when the depth was 55 m, r

_{e}was correlated with the thickness significantly at a 99% confidence level, and with an increment in thickness, r

_{e}grew. The trends of S and r

_{e}with an increment in thickness reversed gradually with an increment in depth as the low permeability formation in the shallow zone hindered the infiltration into the vadose zone while the low permeability formation in the deep zone hindered the recharge into the saturated zone from the vadose zone.

#### 4.1.2. Evaporation to the Air

#### 4.1.3. Recharge into the Aquifer

_{r}declined. The increment in the thickness of the vadose zone generated negative effects on the augment of the recharge. With an increment in the thickness of the vadose zone, both R/I and R declined, and t

_{r}increased. The increment in the evaporation intensity did not generate any effect on the augment of the recharge. With an increment in the evaporation intensity, R/I, R, and t did not vary significantly.

_{r}increased. When the depth was 5 m, 20m, or 30 m, R/I and R declined with the increment from 1 m to 15 m in length, and t

_{r}increased with the increment from 1 m to 10 m in length. Additionally, when the depth was 10 m, R/I and R declined with the increment from 3 m to 15 m in length, and t

_{r}increased with the increment from 3 m to 10 m in length. In addition, when the depth was 55 m, R/I and R declined with the increment from 1 m to 20 m in length, and t

_{r}increased with the increment from 1 m to 7 m in length. With an increment in thickness of low permeability formation in different depths, both R/I and R declined, and t

_{r}increased, too. When the depth was 5 m, R/I and R declined and t

_{r}increased with the increment from 0.6 m to 1.4 m in thickness. Additionally, when the depth was 10 m, R/I and R declined and t

_{r}increased with the increment from 0.8 m to 1.4 m in thickness. In addition, when the depth was 20 m, R/I and R declined and t

_{r}increased with the increment from 0.6 m to 1.5 m in thickness. Furthermore, when the depth was 30 m, R/I and R declined and t

_{r}increased with the increment from 0.7 m to 1.4 m in thickness. To add to this, when the depth was 55 m, R/I and R declined and t

_{r}increased with the increment from 0.6 m to 1.3 m in thickness.

#### 4.2. Analysis on Consistency, Similarity, and Difference between Infiltration and Recharge Based on Water Distribution

#### 4.2.1. Consistency

#### 4.2.2. Similarity

#### 4.2.3. Differences

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Acronym | Definition/Notation |

d | Thickness of the low permeability formation (L) |

D | Vadose zone thickness (L) |

e | Potential evaporation rate (L/T) |

E | Cumulative evaporation to the air (L^{3}) |

E/I | Ratio of the cumulative evaporation to the cumulative infiltration (-) |

h | Hydraulic head in the matrix cell (L) |

H | Depth of the low permeability formation (L) |

h_{Basin} | Water head in infiltration basin (L) |

I | Cumulative infiltration from infiltration basin (L^{3}) |

K | Hydraulic conductivity (L/T) |

K_{s} | Saturated hydraulic conductivity (L/T) |

l | Length of the low permeability formation (L) |

L | Vadose zone length (L) |

r | Radius in cylindrical coordinates (L) |

R | Volume of recharge into the aquifer (L^{3}) |

r_{Basin} | Infiltration basin radius (L) |

r_{e} | Radius of the flow through the bottom boundary of the vadose zone at the end time of infiltration (L) |

r_{s} | Radius of the saturated part of the flow through the bottom boundary of the vadose zone at the end time of infiltration (L) |

r_{s}/r_{e} | Ratio of the radius of the saturated part of the flow through the bottom boundary of the vadose zone to the radius of the whole flow at the end time of infiltration (-) |

R/I | Ratio of the volume of recharge to the cumulative infiltration (-) |

S | Volume of storage in the vadose zone (L^{3}) |

S_{e} | Effective water content (-) |

s_{r} | Antecedent moistures of the vadose zone (-) |

S/I | Ratio of the volume of storage to the cumulative infiltration (-) |

t | Time (T) |

t_{r} | Time when the saturated flow reaches the bottom boundary (T) |

z | Height in cylindrical coordinates (L) |

α, n, m, and f | Empirical parameters (L^{−1}), (-), (-), and (-) |

θ | Volumetric soil water content at soil water matric potential (-) |

θ_{r} | Residual water content (-) |

θ_{s} | Saturated water content (-) |

φ | Tilt angle in cylindrical coordinates (-) |

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**Figure 1.**The conceptual sketch of a vadose zone and the water distribution from infiltration basin.

**Figure 2.**The variations with an increment in h

_{Basin}. ((

**a**) variation of I; (

**b**) variation of R; (

**c**) variation of S; (

**d**) variation of E; (

**e**) variation of R/I; (

**f**) variation of S/I; (

**g**) variation of E/I; (

**h**) variation of r

_{e}; (

**i**) variation of r

_{s}; (

**j**) variation of t

_{r}.).

**Figure 3.**The variations with an increment in r

_{Basin}. ((

**a**) variation of I; (

**b**) variation of R; (

**c**) variation of S; (

**d**) variation of E; (

**e**) variation of R/I; (

**f**) variation of S/I; (

**g**) variation of E/I; (

**h**) variation of r

_{e}; (

**i**) variation of r

_{s}; (

**j**) variation of t

_{r}; (

**k**) variation of r

_{s}/r

_{e}.).

**Figure 4.**The variations with an increment in e. ((

**a**) variation of I; (

**b**) variation of E; (

**c**) variation of E/I.).

**Figure 5.**The variations with an increment in s

_{r.}((

**a**) variation of I; (

**b**) variation of R; (

**c**) variation of S; (

**d**) variation of E; (

**e**) variation of R/I; (

**f**) variation of S/I; (

**g**) variation of E/I; (

**h**) variation of r

_{e}; (

**i**) variation of r

_{s}; (

**j**) variation of t

_{r}.).

**Figure 6.**The variations with an increment in D

_{.}((

**a**) variation of R; (

**b**) variation of S; (

**c**) variation of E; (

**d**) variation of R/I; (

**e**) variation of S/I; (

**f**) variation of E/I; (

**g**) variation of r

_{e}; (

**h**) variation of r

_{s}; (

**i**) variation of t

_{r}.).

**Figure 7.**The variations with an increment in K

_{s}. ((

**a**) variation of I; (

**b**) variation of R; (

**c**) variation of S; (

**d**) variation of E; (

**e**) variation of R/I; (

**f**) variation of S/I; (

**g**) variation of E/I; (

**h**) variation of r

_{e}; (

**i**) variation of r

_{s}; (

**j**) variation of t

_{r}; (

**k**) variation of r

_{s}/r

_{e}.).

**Figure 8.**The variations with an increment in l when the depth is 5 m. ((

**a**) variation of I; (

**b**) variation of R; (

**c**) variation of S; (

**d**) variation of E; (

**e**) variation of R/I; (

**f**) variation of S/I; (

**g**) variation of E/I; (

**h**) variation of r

_{s}; (

**i**) variation of t

_{r}; (

**j**) variation of r

_{s}/r

_{e}.).

**Figure 9.**The variations with an increment in l when the depth is 10 m. ((

**a**) variation of I; (

**b**) variation of R; (

**c**) variation of S; (

**d**) variation of E; (

**e**) variation of R/I; (

**f**) variation of S/I; (

**g**) variation of E/I; (

**h**) variation of r

_{e}; (

**i**) variation of r

_{s}; (

**j**) variation of t

_{r}; (

**k**) variation of r

_{s}/r

_{e}.).

**Figure 10.**The variations with an increment in l when the depth is 20 m. ((

**a**) variation of I; (

**b**) variation of R; (

**c**) variation of S; (

**d**) variation of R/I; (

**e**) variation of S/I; (

**f**) variation of E/I; (

**g**) variation of r

_{e}; (

**h**) variation of r

_{s}; (

**i**) variation of t

_{r}; (

**j**) variation of r

_{s}/r

_{e}.).

**Figure 11.**The variations with an increment in l when the depth is 30 m. ((

**a**) variation of R; (

**b**) variation of S; (

**c**) variation of E; (

**d**) variation of R/I; (

**e**) variation of S/I; (

**f**) variation of E/I; (

**g**) variation of r

_{e}; (

**h**) variation of r

_{s}; (

**i**) variation of t

_{r}; (

**j**) variation of r

_{s}/r

_{e}.).

**Figure 12.**The variations with an increment in l when the depth is 55 m. ((

**a**) variation of R; (

**b**) variation of S; (

**c**) variation of E; (

**d**) variation of R/I; (

**e**) variation of S/I; (

**f**) variation of E/I; (

**g**) variation of r

_{e}; (

**h**) variation of r

_{s}; (

**i**) variation of t

_{r}; (

**j**) variation of r

_{s}/r

_{e}.).

**Figure 13.**The variations with an increment in d when the depth is 5 m. ((

**a**) variation of I; (

**b**) variation of R; (

**c**) variation of S; (

**d**) variation of E; (

**e**) variation of R/I; (

**f**) variation of S/I; (

**g**) variation of E/I; (

**h**) variation of r

_{e}; (

**i**) variation of r

_{s}; (

**j**) variation of t

_{r}; (

**k**) variation of r

_{s}/r

_{e}.).

**Figure 14.**The variations with an increment in d when the depth is 10 m. ((

**a**) variation of I; (

**b**) variation of R; (

**c**) variation of S; (

**d**) variation of R/I; (

**e**) variation of S/I; (

**f**) variation of E/I; (

**g**) variation of r

_{e}; (

**h**) variation of r

_{s}; (

**i**) variation of t

_{r}; (

**j**) variation of r

_{s}/r

_{e}.).

**Figure 15.**The variations with an increment in d when the depth is 20 m. ((

**a**) variation of I; (

**b**) variation of R; (

**c**) variation of S; (

**d**) variation of R/I; (

**e**) variation of S/I; (

**f**) variation of E/I; (

**g**) variation of r

_{e}; (

**h**) variation of r

_{s}; (

**i**) variation of t

_{r}; (

**j**) variation of r

_{s}/r

_{e}.).

**Figure 16.**The variations with an increment in d when the depth is 30 m. ((

**a**) variation of R; (

**b**) variation of S; (

**c**) variation of R/I; (

**d**) variation of S/I; (

**e**) variation of r

_{s}; (

**f**) variation of t

_{r}; (

**g**) variation of r

_{s}/r

_{e}.).

**Figure 17.**The variations with an increment in d when the depth is 55 m. ((

**a**) variation of R; (

**b**) variation of S; (

**c**) variation of R/I; (

**d**) variation of S/I; (

**e**) variation of r

_{e}; (

**f**) variation of r

_{s}; (

**g**) variation of t

_{r}; (

**h**) variation of r

_{s}/r

_{e}.).

**Table 1.**The experimental condition type, variable of experiments, number of experiments, and variable range of homogeneous domain experimental conditions.

Experimental Condition Type | Variable of Experiments | Number of Experiments | Variable Range |
---|---|---|---|

Water head in infiltration basin | Water head | 10 | 0.1 to 1 m |

Radius of infiltration basin | Infiltration basin radius | 9 | 7 to 21 m |

Evaporation intensity | Potential evaporation rate | 12 | 4 to 22 mm/d |

Antecedent moisture of the vadose zone | Moisture saturation | 10 | 17.1 to 40% |

Thickness of the vadose zone | Vadose zone thickness | 11 | 48 to 75 m |

Hydraulic conductivity of the vadose zone | Saturated hydraulic conductivity | 10 | 1 to 2.8 m/d |

**Table 2.**The experimental condition type, variable of experiments, number of experiments, and variable range under the experimental condition of low permeability formation.

Experimental Condition Type | Variable of Experiments | Number of Experiments | Variable Range (m) |
---|---|---|---|

The depth is 5 m, and the thickness is 0.6 m | Length of low permeability formation | 10 | 1 to 60 |

The depth is 10 m, and the thickness is 0.6 m | 8 | 3 to 60 | |

The depth is 20 m, and the thickness is 0.6 m | 9 | 1 to 60 | |

The depth is 30 m, and the thickness is 0.6 m | 7 | 1 to 30 | |

The depth is 55 m, and the thickness is 0.6 m | 10 | 1 to 60 | |

The depth is 5 m, and the length is 100 m | Thickness of low permeability formation | 9 | 0.6 to 1.4 |

The depth is 10 m, and the length is 100 m | 5 | 0.8 to 1.4 | |

The depth is 20 m, and the length is 100 m | 8 | 0.6 to 1.5 | |

The depth is 30 m, and the length is 100 m | 5 | 0.7 to 1.4 | |

The depth is 55 m, and the length is 100 m | 5 | 0.6 to 1.3 |

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**MDPI and ACS Style**

Qi, T.; Shu, L.; Li, H.; Wang, X.; Men, Y.; Opoku, P.A.
Water Distribution from Artificial Recharge via Infiltration Basin under Constant Head Conditions. *Water* **2021**, *13*, 1052.
https://doi.org/10.3390/w13081052

**AMA Style**

Qi T, Shu L, Li H, Wang X, Men Y, Opoku PA.
Water Distribution from Artificial Recharge via Infiltration Basin under Constant Head Conditions. *Water*. 2021; 13(8):1052.
https://doi.org/10.3390/w13081052

**Chicago/Turabian Style**

Qi, Tiansong, Longcang Shu, Hu Li, Xiaobo Wang, Yanqing Men, and Portia Annabelle Opoku.
2021. "Water Distribution from Artificial Recharge via Infiltration Basin under Constant Head Conditions" *Water* 13, no. 8: 1052.
https://doi.org/10.3390/w13081052