Dependency of dimensionless shape factors on control parameters for xwD = 0 in the type-I catchment zone: (a) Curves of w/d versus α with different λ values; (b) Curves of w/d versus α with different β values; (c) Curves of w/d versus ywD with different α values; (d) Curves of w/d versus ywD with different λ values; (e) Curves of r/d versus α with different λ values; (f) Curves of r/d versus ywD with different λ values.

Dependency of dimensionless shape factors on control parameters for xwD = 0 in the type-I catchment zone: (a) Curves of w/d versus α with different λ values; (b) Curves of w/d versus α with different β values; (c) Curves of w/d versus ywD with different α values; (d) Curves of w/d versus ywD with different λ values; (e) Curves of r/d versus α with different λ values; (f) Curves of r/d versus ywD with different λ values.

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Unconfined aquifers beneath piedmont pluvial fans are widely distributed in front of mountains and proper for water supply with pumping wells. However, the catchment zone and capture zones of a pumping well in such an unconfined aquifer is not well known. We develop a preliminary simplified model where groundwater flows between a segmental inflow b...

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Context 1
... factors of the catchment zone are controlled by several parameters, such as α, β, γ, and λ, and also dependent on the well location. In Figure 10, the relationship between shape factors and key parameters are illustrated from results of the sensitivity analysis for the Type-I zone. As shown in Figure 10a,b, w/d increases between 0.5 and 2.5, nonlinearly with the decreasing α value between 0.2 and 1.0. ...
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... Figure 10, the relationship between shape factors and key parameters are illustrated from results of the sensitivity analysis for the Type-I zone. As shown in Figure 10a,b, w/d increases between 0.5 and 2.5, nonlinearly with the decreasing α value between 0.2 and 1.0. Since the α value refers to the relative width of an inflow segment, this relationship indicates that a shorter inflow segment will lead to a larger transectional expansion of the catchment zone when groundwater flow toward the well. ...
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... the α value refers to the relative width of an inflow segment, this relationship indicates that a shorter inflow segment will lead to a larger transectional expansion of the catchment zone when groundwater flow toward the well. An increase in the λ value (relative pumping rate) will also increase w/d, as shown in Figure 10a. The w/d value seems to be not sensitive to the change in the β value (relative distance between the inflow and discharge boundaries), as indicated in Figure 10b, even the β value has a slight negative influence. ...
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... increase in the λ value (relative pumping rate) will also increase w/d, as shown in Figure 10a. The w/d value seems to be not sensitive to the change in the β value (relative distance between the inflow and discharge boundaries), as indicated in Figure 10b, even the β value has a slight negative influence. The impacts of α and λ on w/d are also exhibited with the curves in Figure 10c,d, respectively, for the relationship between w/d and the well-location represented by ywD. ...
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... w/d value seems to be not sensitive to the change in the β value (relative distance between the inflow and discharge boundaries), as indicated in Figure 10b, even the β value has a slight negative influence. The impacts of α and λ on w/d are also exhibited with the curves in Figure 10c,d, respectively, for the relationship between w/d and the well-location represented by ywD. It can be seen that w/d is positively correlated with the ywD value, almost in a linear manner. ...
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... can be seen that w/d is positively correlated with the ywD value, almost in a linear manner. The r/d value is generally less than 1.0 and also increases with the decreasing α value as shown in Figure 10e, indicating that the distance from the well to the stagnation point is generally less than the width of source head. Similar to the relationship between w/d and ywD, r/d increases with the increasing ywD value, as shown in Figure 10f, however, the relationship becomes nonlinear when the λ value is large. ...
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... r/d value is generally less than 1.0 and also increases with the decreasing α value as shown in Figure 10e, indicating that the distance from the well to the stagnation point is generally less than the width of source head. Similar to the relationship between w/d and ywD, r/d increases with the increasing ywD value, as shown in Figure 10f, however, the relationship becomes nonlinear when the λ value is large. A line across the well center and parallel to the X-axis within the catchement zone characterizes the size of the catchment zone near the well, which has a length of w [L]. ...
Context 8
... factors of the catchment zone are controlled by several parameters, such as α, β, γ, and λ, and also dependent on the well location. In Figure 10, the relationship between shape factors and key parameters are illustrated from results of the sensitivity analysis for the Type-I zone. As shown in Figure 10a,b, w/d increases between 0.5 and 2.5, nonlinearly with the decreasing α value between 0.2 and 1.0. ...
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... Figure 10, the relationship between shape factors and key parameters are illustrated from results of the sensitivity analysis for the Type-I zone. As shown in Figure 10a,b, w/d increases between 0.5 and 2.5, nonlinearly with the decreasing α value between 0.2 and 1.0. Since the α value refers to the relative width of an inflow segment, this relationship indicates that a shorter inflow segment will lead to a larger transectional expansion of the catchment zone when groundwater flow toward the well. ...
Context 10
... the α value refers to the relative width of an inflow segment, this relationship indicates that a shorter inflow segment will lead to a larger transectional expansion of the catchment zone when groundwater flow toward the well. An increase in the λ value (relative pumping rate) will also increase w/d, as shown in Figure 10a. The w/d value seems to be not sensitive to the change in the β value (relative distance between the inflow and discharge boundaries), as indicated in Figure 10b, even the β value has a slight negative influence. ...
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... increase in the λ value (relative pumping rate) will also increase w/d, as shown in Figure 10a. The w/d value seems to be not sensitive to the change in the β value (relative distance between the inflow and discharge boundaries), as indicated in Figure 10b, even the β value has a slight negative influence. The impacts of α and λ on w/d are also exhibited with the curves in Figure 10c,d, respectively, for the relationship between w/d and the well-location represented by y wD . ...
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... w/d value seems to be not sensitive to the change in the β value (relative distance between the inflow and discharge boundaries), as indicated in Figure 10b, even the β value has a slight negative influence. The impacts of α and λ on w/d are also exhibited with the curves in Figure 10c,d, respectively, for the relationship between w/d and the well-location represented by y wD . It can be seen that w/d is positively correlated with the y wD value, almost in a linear manner. ...
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... can be seen that w/d is positively correlated with the y wD value, almost in a linear manner. The r/d value is generally less than 1.0 and also increases with the decreasing α value as shown in Figure 10e, indicating that the distance from the well to the stagnation point is generally less than the width of source head. Similar to the relationship between w/d and y wD , r/d increases with the increasing y wD value, as shown in Figure 10f, however, the relationship becomes nonlinear when the λ value is large. ...
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... r/d value is generally less than 1.0 and also increases with the decreasing α value as shown in Figure 10e, indicating that the distance from the well to the stagnation point is generally less than the width of source head. Similar to the relationship between w/d and y wD , r/d increases with the increasing y wD value, as shown in Figure 10f, however, the relationship becomes nonlinear when the λ value is large. The impacts of control parameters and the well location on shape factors of the type-III catchment zone are shown in Figure 11. ...
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... The dimensionless width of the catchment zone in the vicinity of the well (related to the source head width) decreases with the relative length of inflow segments but increases with the relative pumping rate, as indicated in Figures 10 and 11; (3) The dimensionless size of capture zones (related to the source head width) increases with the relative travel time almost in a linear manner when the source is contributed by a single inflow segment, as shown in Figure 13. A significant nonlinear relationship exists when the source is contributed by double inflow segments, as shown in Figure 14. ...