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

: The vadose zone plays a signiﬁcant role during artiﬁcial recharge via the inﬁltration basin. Its thickness, lithology, heterogeneity, among others greatly affect the recharge efﬁciency. The main objective of this research is to establish the role of the vadose zone and the impacts of inﬁltration basin features and vadose zone factors on water distributions. In this work, an ideal conceptual model was considered, and mathematical models were built using HYDRUS (2D/3D) software package version 2.05. A total of 138 numerical experiments were implemented under seven types of experimental conditions. The experimental data were analyzed with the aid of correlation and regression analysis. The results showed that inﬁltration basin features and vadose zone factors had various impacts on water distribution, low permeability formation had various effects on evaporation depending on its depth, and there were consistent, similar, or different variation trends between inﬁltration and recharge. In conclusion, it is recommended that when the vadose zones are to be chosen as an inﬁltration basin site, the trade-off among the inﬁltration, recharge, storage, and evaporation should be seriously considered. This paper may contribute to a better understanding of the vadose zone as a buffer zone for artiﬁcial recharge. 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 con-Water These conclusions may contribute to a better understanding of the vadose zone as a buffer zone for artiﬁcial recharge. In this research, the results were derived from qualitive analyses on the quantitative calculation in ideal numerical models. The generalized variation trends of inﬁltration and of three types of water distributions (i.e., the recharge, the storage, and the evaporation) were depicted under the basic variations of different inﬁltration basin features and vadose zone factors. The consistency, similarity, and difference between inﬁltration and recharge were discussed based on the different variations of inﬁltration and water distributions. These discussions could serve as the guidance during choosing vadose zones as the site of inﬁltration basins. Additionally, the results were just from the point of single approach (i.e., modelling exercises). The intricate details of the structural features of the vadose zone and the moisture dynamic in the vadose zone during artiﬁcial recharge were neglected when the ideal numerical models were conducted. The results were discussed based on qualitive analyses. The lack of validation is a major limitation of this study. Deeper understanding and interpretation of the results are necessary in the further research. The validity of results needs to be veriﬁed by multi-methods and real processes.


Introduction
Groundwater is a vital resource for life forms, which caters for billions of populations [1]. However, the protection of groundwater resources is being threatened by overexploitation and extreme weather conditions such as droughts due to an increase in population (leading to higher water demands) and climate change, respectively [2,3]. On the other hand, managed aquifer recharge can be utilized to increase water resources [4], to alleviate seawater intrusion and land subsidence, both derived from groundwater overexploitation [5][6][7]. This technology also can be used to improve the quality of reclaimed water and desalinated water [8][9][10][11][12][13][14] and could even serve as a water conveyance system [15]. Consequently, it has been a robust water resources management technology in addressing existing challenges nowadays and can furthermore meet larger water demand under more severe drought conditions in the future [3]. The relevant scientific research and engineering practices about this technology can be found across all continents except for Antarctica [16][17][18][19][20]. Infiltration basin, riverbank filtration and recharge well are the dominant managed aquifer recharge technologies at global scale [21][22][23]. This research deals with the impacts of vadose zone factors on artificial recharge via the infiltration basin using modeling exercises. This is because the thickness, lithology, antecedent water content, etc. of the vadose zone affect the artificial infiltration process. Additionally, spreading methods into the role of the vadose zone during artificial recharge, to explore the impacts of infil tration basin features and vadose zone factors on water distributions (i.e., the recharg into the aquifer, the storage in the vadose zone, and the evaporation to the air), and to analyze the consistency, similarity, and difference between infiltration and recharge based on water distributions.

Conceptual and Mathematical Models
An idealized horizontal and isotropic vadose zone is considered in the study. Th conceptual sketch of the vadose zone and the water distribution from the infiltration basin is shown in Figure 1. The r-axis is horizontal, while the z-axis is vertical. The thickness o the vadose zone is D, and the length of the cross-section is L. The depth, thickness, and length of the low permeability formation is H, d, and l, respectively. The radius of th infiltration basin is rbasin. As shown in Figure 1, the coordinates of the four vertices of the vadose zone cross section are set as (0, 0), (0, D), (L, D), and (L, 0) in the cylindrical coordinates system. Th upper boundary is the earth surface, from which water of an infiltration basin between point (0, D) and point (rBasin, D) infiltrates into the vadose zone with a constant water head and water of the bare soil between point (rBasin, D) and point (L, D) evaporates from th vadose zone with a constant potential evaporation. The bottom boundary is the interfac between the vadose zone and the saturated zone where the infiltrated water recharge groundwater.
The HYDRUS (2D/3D) software package version 2.05 was used to establish numerica models to simulate various experimental conditions of artificial recharge based on th above-mentioned conceptual model. The domain type of numerical models is 2D-Axisym metrical Vertical Flow which is a two-dimensional geometry in cylindrical coordinate (i.e., an axisymmetrical quasi-three-dimensional transport domain). It is radially symmet rical around the vertical z-axis. The vertical z-axis and the horizontal r-axis in Figure  only show one cross-section at one title angle in the cylindrical coordinates. Under 2D Axisymmetrical Vertical Flow, the HYDRUS (2D/3D) can output 3-dimensional outcome automatically. It solves the 2-dimensional axisymmetric form of the Richards equation As shown in Figure 1, the coordinates of the four vertices of the vadose zone crosssection are set as (0, 0), (0, D), (L, D), and (L, 0) in the cylindrical coordinates system. The upper boundary is the earth surface, from which water of an infiltration basin between point (0, D) and point (r 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.
The HYDRUS (2D/3D) software package version 2.05 was used to establish numerical models to simulate various experimental conditions of artificial recharge based on the above-mentioned conceptual model. The domain type of numerical models is 2D-Axisymmetrical Vertical Flow which is a two-dimensional geometry in cylindrical coordinates (i.e., an axisymmetrical quasi-three-dimensional transport domain). It is radially symmetrical around the vertical z-axis. The vertical z-axis and the horizontal r-axis in Figure 1 only show one cross-section at one title angle in the cylindrical coordinates. Under 2D-Axisymmetrical Vertical Flow, the HYDRUS (2D/3D) can output 3-dimensional outcomes automatically. It solves the 2-dimensional axisymmetric form of the Richards equation using the van Genuchten (1980) and Mualem (1976) unsaturated soil hydraulic functions [50]. The Richards equation is given as follows,  (1) where θ is the volumetric soil water content at soil water matric potential (-), t is time (T), r is the radius in cylindrical coordinates (L), K(θ) is the hydraulic conductivity (L/T), h is the hydraulic head in the matrix cell (L), ϕ is the tilt angle in cylindrical coordinates (-), and z is the height in cylindrical coordinates (L).
The van Genuchten (1980) and Mualem (1976) unsaturated soil hydraulic functions are given as follows, where θ(h) is the volumetric soil water content soil water matric potential (-), h is the hydraulic head in the matrix cell (L), θ 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 (-). The simulation domain was discretized using a two-dimensional triangular finite element mesh with the MESHGEN tool available within HYDRUS (2D/3D) [50] and the mesh was refined within the whole domain.
A variable head boundary condition and an atmospheric boundary condition were assigned to the upper boundary from point (0, D) to point (r 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.

Numerical Experiments
Numerical experiments were conducted by using the above-mentioned mathematical models under 7 types of experimental conditions including the water head in infiltration basin, the radius of infiltration basin, the evaporation intensity, the antecedent moisture of the vadose zone, the thickness of the vadose zone, the hydraulic conductivity, the low permeability formation. The first six types of experimental conditions were homogeneous domain experimental conditions, under which there was only one type of soil material for the whole vadose zone (i.e., there was no low permeability formation) and the numerical experiments were calculated for 30 days. The last type of experimental condition (i.e., the low permeability formation) was a heterogeneous domain experimental condition, under which there were two types of soil materials for the vadose zone (i.e., there was a low permeability formation) and the numerical experiments were calculated for 60 days. The experimental condition type, variable of experiments, number of experiments, and variable range of homogeneous domain experimental conditions are shown in Table 1.
Sixty-two experiments were conducted under the homogeneous domain experimental conditions. Among these sixty-two experiments, ten experiments were conducted under the experimental condition of water head in infiltration basin and ten water heads in variable head boundaries represented different water heads in infiltration basin (h 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 con- ducted 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 ). Seventy-six experiments were conducted under the experimental condition of low permeability formation (i.e., heterogeneous domain experimental conditions) with different hydraulic parameters for soil material due to the differences of the sites and sizes of the low permeability formations. The hydraulic parameters of the low permeability formation and the ones of the other parts of the vadose zone were taken from the silty loam and sandy loam of the HYDRUS (2D/3D) Soil Catalog, respectively [50].
Among the seventy-six experiments, forty-four experiments were conducted with the same thickness of the low permeability formation (i.e., d = 0.6 m), and different depths and lengths of it, and were further divided into five experimental conditions. The experimental condition type, variable of experiments, number of experiments, and variable range about these five experimental conditions are shown in Table 2. Among these forty-four experiments, ten experiments were conducted when the depth was 5 m. Additionally, eight experiments were conducted when the depth was 10 m. In addition, nine experiments were conducted when the depth was 20 m. Furthermore, seven experiments were conducted when the depth was 30 m. To add to this, ten experiments were conducted when the depth was 55 m.  Among the above-mentioned seventy-six experiments, the other thirty-two experiments were conducted with the same length of the low permeability formation (i.e., l = 100 m), and different depths and thicknesses of it, and were further divided into five experimental conditions as well. The experimental condition type, variable of experiments, number of experiments, and variable range about these five experimental conditions are shown in Table 2 as well. Among these thirty-two experiments, nine experiments were conducted when the depth was 5 m. Additionally, five experiments were conducted when the depth was 10 m. In addition, eight experiments were conducted when the depth was 20 m. Furthermore, five experiments were conducted when the depth was 30 m. To add to this, five experiments were conducted when the depth was 55 m.

Data Analysis
The cumulative infiltration (I) from infiltration basin, the volume of recharge (R) into the aquifer, the volume of storage (S) in the vadose zone, and the cumulative evaporation (E) to the air during the whole experimental period (i.e., 30 days for the homogeneous domain experimental conditions or 60 days for the heterogeneous domain experimental conditions) in every experiment were available in output files of the HYDRUS (2D/3D) software. Furthermore, the ratios of R to I(R/I), S to I(S/I), and E to I(E/I) were calculated for every experiment to illustrate the proportions of the recharge into the aquifer, the storage in the vadose zone, and the evaporation to the air.
Additionally, the radius (r 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.
The statistical software SPSS (Statistical Product and Service Solutions) was employed to analyze the correlation between every experimental data (i.e., I, R, S, E, R/I, S/I, E/I, r 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.

Results
This chapter details the results from the numerical experiments and the data analysis. They are categorized into homogenous domain experimental conditions and heterogenous domain experimental conditions.

Homogeneous Domain Experimental Conditions
Under the experimental condition of water head in infiltration basin, I, R, S, E, R/I, S/I, E/I, r 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.
S/I, E/I, re, rs, and tr are significantly correlated to hBasin at 99% confidence levels, and rs/re is not correlated to hBasin significantly. The correlations of I, R, S, E, R/I, re, and rs to hBasin are positive, and that of other variables negative. As hBasin increases, I, R, S, R/I, and rs grow quadratically, and the growth rate decreases with an increment in hBasin. Additionally, E grows quadratically, and the growth rate increases with an increment in hBasin. In addition, S/I, E/I, and tr decline quadratically, and the decline rate decreases with an increment in hBasin. Furthermore, re grows linearly. These variations are shown in Figure 2. Under the experimental condition of radius of infiltration basin, I, R, S, E, R/I, S/I, E/I, re, rs, tr, and rs/re all are significantly correlated to rBasin at 99% confidence levels. The correlations of I, R, S, E, R/I, re, rs, and rs/re to rBasin are positive, and that of other variables negative. As rBasin increases, I, R, and S grow quadratically, and the growth rate increases Under the experimental condition of radius of infiltration basin, I, R, S, E, R/I, S/I, E/I, r 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. with an increment in rBasin. Additionally, E, R/I, re, rs, and rs/re grow quadratically, and the growth rate decreases with an increment in rBasin. In addition, S/I, E/I, and tr decline quadratically, and the decline rate decreases with an increment in rBasin. These variations are shown in Figure 3. Under the experimental condition of evaporation intensity, I, E, and E/I are significantly correlated to e at 99% confidence levels, and R, S, R/I, S/I, re, rs, tr, and rs/re 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. Under the experimental condition of evaporation intensity, I, E, and E/I are significantly correlated to e at 99% confidence levels, and R, S, R/I, S/I, r 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.  Under the experimental condition of antecedent moisture of the vadose zone, I, R, S, E, R/I, S/I, E/I, re, rs, and tr are significantly correlated to sr at 99% confidence levels, and rs/re is not correlated to sr significantly. The correlations of I, S, S/I, and tr to sr are negative, and that of other variables positive. As sr increases, I, and tr decline quadratically, and the Under the experimental condition of antecedent moisture of the vadose zone, I, R, S, E, R/I, S/I, E/I, r 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. Under the experimental condition of antecedent moisture of the vadose zone, I, R, S, E, R/I, S/I, E/I, re, rs, and tr are significantly correlated to sr at 99% confidence levels, and rs/re is not correlated to sr significantly. The correlations of I, S, S/I, and tr to sr are negative, and that of other variables positive. As sr increases, I, and tr decline quadratically, and the decline rate decreases with an increment in sr. Additionally, R and R/I grow exponentially, and the growth rate increases with an increment in sr. In addition, S and S/I decline quadratically, and the decline rate increases with an increment in sr. Furthermore, E and E/I grow quadratically, and the growth rate increases with an increment in sr. To add to this, re grows logarithmically, and the growth rate decreases with an increment in sr. Moreover, rs grows linearly. These variations are shown in Figure 5.  Under the experimental condition of thickness of the vadose zone, R, S, E, R/I, S/I, r 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.
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, re and rs 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. Under the experimental condition of saturated hydraulic conductivity of the vadose zone, I, R, S, E, R/I, S/I, E/I, re, rs, tr, and rs/re all are significantly correlated to Ks at 99% confidence levels. The correlations of I, R, S, E, R/I, re, and rs to Ks are positive, and that of other variables negative. As Ks increases, I, R, and E grow quadratically, and the growth rate increases with an increment in Ks. Additionally, S, R/I, re, and rs grow quadratically, and the growth rate decreases with an increment in Ks. In addition, S/I, E/I, tr, and rs/re decline quadratically, and the decline rate decreases with an increment in Ks. These variations are shown in Figure 7. Under the experimental condition of saturated hydraulic conductivity of the vadose zone, I, R, S, E, R/I, S/I, E/I, r 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.

Heterogeneous Domain Experimental Conditions
Under the experimental condition that the depth of low permeability formation is 5 m, and the thickness is 0.6 m, E is significantly correlated to l when l increases from 1 m to 60 m. Additionally, R, S, R/I, and S/I 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, E/I, 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 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.

Heterogeneous Domain Experimental Conditions
Under the experimental condition that the depth of low permeability formation is 5 m, and the thickness is 0.6 m, E is significantly correlated to l when l increases from 1 m to 60 m. Additionally, R, S, R/I, and S/I 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, E/I, rs, tr, and rs/re 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, re is not correlated to l significantly when l increases from 1 m to 60 m. rs 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, tr, Under the experimental condition that the depth of low permeability formation is 10 m, and the thickness is 0.6 m, E is significantly correlated to l when l increases from 3 m to 60 m. Additionally, R, S, R/I, S/I, E/I, and r 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.
Water 2021, 13, x FOR PEER REVIEW 12 of 27 and rs/re grow quadratically, and the growth rate increases with an increment in l. In addition, rs grows exponentially, and the growth rate increases with an increment in l. These variations are shown in Figure 8. Under the experimental condition that the depth of low permeability formation is 10 m, and the thickness is 0.6 m, E is significantly correlated to l when l increases from 3 m to 60 m. Additionally, R, S, R/I, S/I, E/I, and rs/re 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, re, rs, and tr 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 rs/re 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 rs/re grow quadratically, and the growth rate increases with an increment in l. In addition, R/I declines quadratically, and the decline Under the experimental condition that the depth of low permeability formation is 20 m, and the thickness is 0.6 m, E/I is significantly correlated to l when l increases from 1 m to 20 m and is not correlated to l significantly when l increases from 20 m to 60 m. Additionally, R, S, R/I, S/I, and r 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.
Water 2021, 13, x FOR PEER REVIEW 13 of 27 and the decline rate decreases with an increment in l. Additionally, re, rs, and tr grow quadratically, and the growth rate increases with an increment in l. These variations are shown in Figure 9. Under the experimental condition that the depth of low permeability formation is 20 m, and the thickness is 0.6 m, E/I is significantly correlated to l when l increases from 1 m to 20 m and is not correlated to l significantly when l increases from 20 m to 60 m. Additionally, R, S, R/I, S/I, and rs/re 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, re, rs, and tr 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 As l increases from 1 m to 10 m, I declines quadratically, and the decline rate increases with an increment in l. Additionally, re, rs, and tr grow quadratically, and the growth rate increases with an increment in l. These variations are shown in Figure 10. Under the experimental condition that the depth of low permeability formation is 30 m, and the thickness is 0.6 m, E and E/I are significantly correlated to l when l increases from 1 m to 30 m. Additionally, R, S, R/I, and S/I 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 30 m. In addition, re, rs, tr, and rs/re 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. rs/re 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, re, rs, tr, and rs/re grow quadratically, Under the experimental condition that the depth of low permeability formation is 30 m, and the thickness is 0.6 m, E and E/I are significantly correlated to l when l increases from 1 m to 30 m. Additionally, R, S, R/I, and S/I 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 30 m. In addition, r 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. and the growth rate increases with an increment in l. These variations are shown in Figure  11. Under the experimental condition that the depth of low permeability formation is 55 m, and the thickness is 0.6 m, E and E/I are significantly correlated to l when l increases from 1 m to 60 m. Additionally, R, S, R/I, and S/I are significantly correlated to l when l increases from 1 m to 20 m, and are not correlated to l significantly when l increases from 20 m to 60 m. In addition, re 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, rs and rs/re 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, tr 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. re and rs 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, Under the experimental condition that the depth of low permeability formation is 55 m, and the thickness is 0.6 m, E and E/I are significantly correlated to l when l increases from 1 m to 60 m. Additionally, R, S, R/I, and S/I are significantly correlated to l when l increases from 1 m to 20 m, and are not correlated to l significantly when l increases from 20 m to 60 m. In addition, r 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.
Water 2021, 13, x FOR PEER REVIEW 16 of 27 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, re grows quadratically, and the decline rate increases with an increment in l. As l increases from 1 m to 10 m, rs grows quadratically, and the growth rate increases with an increment in l. In addition, rs/re grows exponentially, and the growth rate increases with an increment in l. As l increases from 1 m to 7 m, tr grows quadratically, and the growth rate increases with an increment in l. These variations are shown in Figure 12. Under the experimental condition that the depth of low permeability formation is 5 m, and the length is 100 m, I, R, S, R/I, S/I, E/I, re, rs, and tr are significantly correlated to d at 99% confidence levels, and E and rs/re are significantly correlated to d at 95% confidence levels. The correlations of I, R, S, R/I, re, rs, and rs/re 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, re, rs, and rs/re 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 tr grow quadratically, and the growth rate decreases with an increment in d. These variations are shown in Figure 13. Under the experimental condition that the depth of low permeability formation is 5 m, and the length is 100 m, I, R, S, R/I, S/I, E/I, r 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. Under the experimental condition that the depth of low permeability formation is 10 m, and the length is 100 m, I, R, S, R/I, S/I, E/I, re, rs, tr, and rs/re are significantly correlated to d at 99% confidence levels, and E is not correlated to d significantly. The correlations of I, R, R/I, re, rs, and rs/re 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 rs decline exponentially, and the decline rate decreases with an increment in d. In addition, S, S/I, E/I, and tr grow quadratically, and the growth rate decreases with an increment in d. Furthermore, re declines quadratically, and the decline rate increases with an increment in d. To add to this, rs/re declines quadratically, and the decline rate decreases with an increment in d. These variations are shown in Figure 14. Under the experimental condition that the depth of low permeability formation is 10 m, and the length is 100 m, I, R, S, R/I, S/I, E/I, r 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. Under the experimental condition that the depth of low permeability formation is 20 m, and the length is 100 m, I, R, S, R/I, S/I, E/I, rs, tr and rs/re are significantly correlated to d at 99% confidence levels, re 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, re, rs, and rs/re to d are negative, and that of other variables positive. As d increases, I, re, rs, and rs/re 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 tr 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. Under the experimental condition that the depth of low permeability formation is 20 m, and the length is 100 m, I, R, S, R/I, S/I, E/I, r 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. Under the experimental condition that the depth of low permeability formation is 30 m, and the length is 100 m, R, S, R/I, S/I, rs, tr, and rs/re are significantly correlated to d at 99% confidence levels, and I, E, E/I, and re are not correlated to d significantly. The correlations of R, R/I, rs, and rs/re 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 tr grow quadratically, and the growth rate decreases with an increment in d. In addition, rs, and rs/re decline quadratically, and the decline rate increases with an increment in d. These variations are shown in Figure 16. Under the experimental condition that the depth of low permeability formation is 30 m, and the length is 100 m, R, S, R/I, S/I, r 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.
Under the experimental condition that the depth of low permeability formation is 55 m, and the length is 100 m, R, S, R/I, S/I, r 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. Under the experimental condition that the depth of low permeability formation is 55 m, and the length is 100 m, R, S, R/I, S/I, re, rs, tr and rs/re 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, rs, and rs/re 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 tr 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, re grows logarithmically, and the growth rate decreases with an increment in d. To add to this, rs, and rs/re decline quadratically, and the decline rate increases with an increment in d. These variations are shown in Figure 17.

Storage in the Vadose Zone
For the homogeneous domain experimental conditions, the increment in the antecedent moisture of the vadose zone, the radius of infiltration basin, the water head in infiltration basin, and the saturated hydraulic conductivity generated positive effects on the reduction in the storage in the vadose zone from infiltration. With an increment in the antecedent moisture, both S/I and S declined. Additionally, with an increment in the radius of infiltration basin, although S increased, S/I declined and r 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.
For the heterogeneous domain experimental conditions, low permeability formation generated negative effects on the reduction in the storage in the vadose zone. With an increment in the length and thickness of low permeability formation in different depths, S/I increased. However, S and r 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.

Evaporation to the Air
For the homogeneous domain experimental conditions, the increment in the radius of infiltration basin, the water head in infiltration basin, and the saturated hydraulic conductivity generated positive effects on the reduction in the evaporation to the air from the vadose zone. With an increment in the radius of infiltration basin, the water head in infiltration basin, and the saturated hydraulic conductivity, although E increased, E/I declined. The increment in the thickness of the vadose zone, the evaporation intensity, and the antecedent moisture of the vadose zone generated negative effects on the reduction in the evaporation. With an increment in the thickness of the vadose zone, the evaporation intensity, and the antecedent moisture of the vadose zone, both E/I and E increased.
For the heterogeneous domain experimental conditions, the increment in the length of low permeability formations in different depths generated negative effects on the reduction in the evaporation. E/I values increased with an increment in the length at any depth. However, the effects of the increment in the thickness of low permeability formation in different depths showed different variation trends. The increment in thickness in the shallow zone (i.e., the depths were 5 m, 10 m, and 20 m) generated negative effects on the reduction in the evaporation, while the increment in deep zone (i.e., the depths were 30 m and 55 m) did not generate any effects significantly. With an increment in the thickness in the depths that were 5 m, 10 m, and 20 m, E/I increased, while with an increment in the thickness in the depths that were 30 m and 55 m, E/I did not vary significantly. In addition, with an increment in the depth of low permeability formation, the variation scope of the length of low permeability formation which generated effects on the evaporation increased. When the depth was 50 m, the evaporation only varied significantly with the increment from 1m to 10 m in length. Additionally, when the depth was 10 m, the evaporation varied significantly with the increment from 3 m to 15 m in length. Furthermore, when the depth was 20 m, the evaporation varied significantly with the increment from 1 m to 20 m in length. To add to this, when the depths were 30 m and 55m, the evaporation varied significantly with the increment from 1 m to 60 m in length.

Recharge into the Aquifer
For the homogeneous domain experimental conditions, the increment in the water head in infiltration basin, the radius of infiltration basin, the antecedent moisture of the vadose zone, and the saturated hydraulic conductivity generated positive effects on the augment of the recharge into the aquifer. With an increment in the water head in infiltration basin, the radius of infiltration basin, the antecedent moisture of the vadose zone, and the hydraulic conductivity, both R/I and R increased, and t 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.
For the heterogeneous domain experimental conditions, low permeability formation generated negative effects on the augment of the recharge. With an increment in length of low permeability formation in different depths, both R/I and R declined, and t 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.

Consistency
For three homogeneous domain experimental conditions (i.e., water head in infiltration basin, radius of infiltration basin, and saturated hydraulic conductivity of the vadose zone) and four heterogeneous domain experimental conditions (i.e., the depth of low permeability formation is 10 m and the thickness is 0.6 m, the depth is 20 m and the thickness is 0.6 m, the depth is 5 m and the length is 100 m, and the depth is 10 m and the length is 100 m), the volume of recharge into the aquifer had the same variation trends as the cumulative infiltration from the infiltration basin. When the volume of recharge and the cumulative infiltration decreased, both S/I values and E/I values increased. Additionally, when the volume of recharge and the cumulative infiltration increase, both S/I values and E/I values decreased.

Similarity
For the other two heterogeneous domain experimental conditions (i.e., the depth is 5 m and the thickness is 0.6 m, and the depth is 20 m and the length is 100 m), the volume of recharge into the aquifer had similar variation trends with the cumulative infiltration from the infiltration basin. When the cumulative infiltration declined and the decline rate increased with its decline, the volume of recharge declined as well, but the decline rate decreased with its decline, due to both S/I values and E/I values grew but the growth rate of S/I values decreased with its growth. This decline of the growth rate of S/I values played a role as a buffer when the decline of the cumulative infiltration from the infiltration basin led to the decline of the volume of recharge into the aquifer.

Differences
For the rest of the three homogeneous domain experimental conditions (i.e., antecedent moisture of the vadose zone, evaporation intensity, and thickness of the vadose zone) and the rest of the four heterogeneous domain experimental conditions (i.e., the depth is 30 m and the thickness is 0.6 m, the depth is 55 m and the thickness is 0.6 m, the depth is 30 m and the length is 100 m, and the depth is 55 m and the length is 100 m), the volume of recharge into aquifer had different variation trends with the cumulative infiltration from the infiltration basin. With reference to the experimental condition of antecedent moisture of the vadose zone, when the cumulative infiltration decreases, the volume of recharge increases, because S/I values decreased, and the reduction in the storage transferred to the augment of the recharge. With reference to the experimental condition of evaporation intensity, when the cumulative infiltration increased, the volume of recharge did not vary significantly, because S/I values did not vary significantly, and the augment of the infiltration only led to the augment of the evaporation. With reference to the experimental condition of thickness of the vadose zone and the rest of the four heterogeneous domain experimental conditions, when the cumulative infiltration did not vary significantly, the volume of recharge decreased, due to the volume of storage increased.

Conclusions
Numerical experiments were implemented to explore the water distribution from artificial recharge via the infiltration basin under constant head conditions. The impacts of infiltration basin features and vadose zone factors on water distribution were calculated and analyzed with the aid of correlation and regression analysis.
Results demonstrated that infiltration basin features and vadose zone factors had various impacts on water distribution. The increment in the water head and radius of infiltration basin and the saturated hydraulic conductivity generated positive effects on the recharge into the aquifer and negative effects on the storage in the vadose zone and the evaporation to the air. The increment in the antecedent moisture generated positive effects on the recharge and negative effects on the storage in the vadose zone.
Low permeability formation generated positive effects on the storage in the vadose zone and negative effects on the recharge. The increment in the length of low permeability formation generated positive effects on the evaporation while the increment in its thickness generated various effects on the evaporation depending on its depth.
There were consistent, similar, or different variation trends between the cumulative infiltration from the infiltration basin and the volume of recharge into the aquifer. During artificial recharge applications, the differences between the cumulative infiltration and the volume of recharge should be noticed. When the vadose zones with different features are to be chosen as an infiltration basin site, the trade-off among the infiltration, recharge, storage, and evaporation should be considered.
These conclusions may contribute to a better understanding of the vadose zone as a buffer zone for artificial recharge. In this research, the results were derived from qualitive analyses on the quantitative calculation in ideal numerical models. The generalized variation trends of infiltration and of three types of water distributions (i.e., the recharge, the storage, and the evaporation) were depicted under the basic variations of different infiltration basin features and vadose zone factors. The consistency, similarity, and difference between infiltration and recharge were discussed based on the different variations of infiltration and water distributions. These discussions could serve as the guidance during choosing vadose zones as the site of infiltration basins. Additionally, the results were just from the point of single approach (i.e., modelling exercises). The intricate details of the structural features of the vadose zone and the moisture dynamic in the vadose zone during artificial recharge were neglected when the ideal numerical models were conducted. The results were discussed based on qualitive analyses. The lack of validation is a major limitation of this study. Deeper understanding and interpretation of the results are necessary in the further research. The validity of results needs to be verified by multi-methods and real processes.