Estimating Ground Water Recharge using Flow Models of Perched Karstic
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Aquifers – Menachem Weiss and Haim Gvirtzman
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Supplementary Appendix S1.
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This supplement provides additional data and results for the numerical modeling
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efforts conducted on four springs in the Judean and Samarian Mountains in Israel.
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The material includes three figures (Figures 1-3) showing three of the model
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boundaries (the fourth is in the main text) and three figures (Figures 5-7) showing the
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yearly precipitation at the three study areas (besides the fourth shown in the main
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text). The material also includes the water mass-balance calculations for three of the
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springs (the fourth is given in the main text), a description of the sensitivity analyses
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conducted as part of the modeling efforts and four figures (Figures 8-11) showing the
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results of the analyses.
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Water Mass-Balance
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Ein Haniye
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Ein Haniye (Supplementary Figure 1) is located on the southern outskirts of
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Jerusalem. The spring discharges at an elevation of approximately 625 m above sea
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level near the base of a prominent hill (Har Gilo). The recharge area and model
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boundaries are well-defined by the outcrop of the Moza-Amminadav contact nearly
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continuously around the hill; exceptions being along the southeast and northern
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boundaries. Bedding throughout the recharge area dips distinctly towards the spring
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(northwest) except along the southeast boundary where the bedding dips towards the
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southeast. Because of this, we have defined the recharge area boundary near the axis
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Weiss and Gvirtzman
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of this NE-SW trending anticline. Near the northern boundary of the recharge area, a
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vertical offset along a small fault has caused the Bet Me'ir Formation to be juxtaposed
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against the Amminadav Formation. The absence of any other spring in the area
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implies clearly that this fault serves as a natural barrier to ground water flow due to
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infilling of material along the fault plane and thus promoting preferential flow
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towards Ein Haniye. A second spring exists approximately 1.5 km southwest of Ein
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Haniye. Based on mass-balance calculations, the discharge area for this spring
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appears to be from an adjacent hill to the south-southwest of Ein Haniye. Because of
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this, we have defined the western boundary of the model along the valley which
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separates the two hills.
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Rainfall data from the vicinity of Ein Haniye shows an average of approximately
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0.594 m/y (Supplementary Figure 5). Based on the Guttman (2000) relationships this
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translates to an average recharge of 0.202 m/y. With an assumed recharge area of
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2.728 km2 this corresponds to an annual volumetric recharge of 551,094 m3. The
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average discharge of the spring is 98,882 m3/y, suggesting that approximately 18% of
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the overall recharge is discharged via the spring, and 82% penetrates to the lower
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aquifer (Table 1).
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Ein Delbah
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Ein Delbah (Supplementary Figure 2) is located in the southern Hevron Hills near the
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city of Dura. The spring elevation is approximately 770 meters above sea level and
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discharges near the base of a prominent hill that reaches a maximum elevation of
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approximately 890 meters above sea level. The Moza-Amminadav contact
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completely surrounds the topographic high except to the northwest where the recharge
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boundary is defined by the distinct change in dip from south-southeast to north-
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northwest.
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The average rainfall in this area is 0.511 m/y (Supplementary Figure 6) which
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translates to an average recharge of 0.158 m/y according to Guttman (2000). The
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assumed recharge area is 0.699 km2 which corresponds to an annual volumetric
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recharge of 106,467 m3. Since the spring's average discharge is 35,545 m3/year, this
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suggests that approximately 33% of the potential recharge is being discharged via the
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spring, with the remaining 67% penetrating to the lower aquifer. This spring
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discharge percentage is the highest in all of the study areas, which suggests that either
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the aquitard is indeed restricting flow better at this site or that the defined recharge
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area may be too small. Although the Moza-Amminadav contact outcrops
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significantly further to the north, expanding the model area to these boundaries would
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require including the city of Dura as well as a number of other springs within the
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model boundaries. Because of these considerations, we decided to keep the model
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small and assume that the aquitard at this site is particularly effective at restricting
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flow downward.
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Ein Harrasha
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Ein Harrasha (Supplementary Figure 3) is situated in the center of the Ramallah
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Anticline, one of the few places in central Israel where lower Cretaceous rocks are
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exposed. The spring discharges perched ground water from the contact between the
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relatively impermeable marly Qatana Formation (aquitard) below and the extensively
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fractured, limestone and dolomite Kefira Formation (perched aquifer) above. The
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spring elevation is approximately 670 meters above sea level. The recharge area of
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the spring is east-northeast of the spring and reaches a maximum elevation of
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approximately 750 m above sea level. The underlying aquitard is well-exposed
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around nearly the entire recharge area and dips towards the spring. The only location
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where the aquitard is not exposed is along a 400 m length at the northeastern
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boundary of the model and along a 400 m length at the western boundary of the
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model. Towards the northeast, the stratigraphy becomes horizontal and even dips
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slightly to the northeast forming a topographic saddle. It is evident from these
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observations that both a surface and subsurface water divide exist in this area. To the
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west, a small synclinal structure separates the model area from an adjacent
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topographic high and spring. Based on the similar geomorphologic features this are
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has with the northeast area, we believe that the latter spring discharges water from that
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high area alone thereby allowing us to define the western boundary of our model with
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high confidence.
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Our definition of the recharge area is supported by the following mass-balance
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calculations. Rainfall stations in the area show an average rainfall of approximately
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0.589 m/y (Supplementary Figure 7) which corresponds to an average recharge of
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approximately 0.199 m/y (based on Guttman, 2000). The assumed recharge area of
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the system is 1.431 km2 which corresponds to an annual volumetric recharge of
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284,797 m3. The spring has a mean discharge of 79,866 m3/year, implying that
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approximately 28% of the overall recharge to the subsurface is discharged through the
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spring and the remaining 72% penetrates the aquitard and infiltrates to the lower-most
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water-bearing horizons within the Ein Qinya Formation.
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Supplementary Figure 1. Topographic and Geological map showing the model
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boundaries of Ein Haniye. Ground elevations are in meters above sea level.
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Supplementary Figure 2. Topographic and Geological map showing the model
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boundaries of Ein Delbah. Ground elevations are in meters above sea level.
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Supplementary Figure 3. Topographic and Geological map showing the model
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boundaries of Ein Harrasha. Ground elevations are in meters above sea level.
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Supplementary Figure 4. Legend for Geologic Maps.
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Ein Haniye
Yearly Rain Data (meters)
1.4
1.2
1
0.8
0.6
0.4
0.2
93
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92
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91
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90
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89
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88
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87
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86
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85
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84
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83
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82
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81
80
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79
0
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Supplementary Figure 5. Yearly Precipitation at Ein Haniye
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Ein Delbah
Yearly Rain Data (meters)
1.2
1.0
0.8
0.6
0.4
0.2
94
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92
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90
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88
19
86
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84
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82
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80
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78
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76
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74
0.0
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Supplementary Figure 6. Yearly Precipitation at Ein Delbah
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Ein Harrasha
Yearly Rain Data (meters)
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
96
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94
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92
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88
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86
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84
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82
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80
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78
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76
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74
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72
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70
0.0
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Supplementary Figure 7. Yearly Precipitation at Ein Harrasha
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Sensitivity Analyses
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Sensitivity analyses were conducted to determine the impact of each parameter on the
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model's output. The sensitivity analysis was directed at the following five parameters:
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1) extent of drain coverage, 2) drain conductance, 3) horizontal hydraulic conductivity
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of the perched aquifer, 4) vertical hydraulic conductivity of the aquiclude and 5)
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recharge.
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Figures 8-11 show three-year portions of reference models from the simulations of
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one of the model areas (Ein Al Matwi). The simulations are shown along with the
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actual spring discharge data. The reference models are subjected to varying values of
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one of the five major parameters individually while the other four parameters are held
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constant.
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All other model parameters (besides the five major ones) were held
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constant. The error value shown in the figure legends represent the error calculated
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using equation 2, taken over the entire modeling period (26 years).
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The results show how the discharge varies according to slight changes in the model's
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hydraulic characteristics. Of particular note is the fact that no model convergence is
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obtained at aquitard vertical hydraulic conductivity values greater than 1.25e-4 m/d or
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at hydraulic conductivity values in the perched aquifer greater than 0.050 m/d. These
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values define the upper bounds of these parameters for the models since the upper
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perched aquifer remains completely dry under these conditions. The lower bounds of
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these parameters are less clear, however the extensive (majority) flooding of the
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MODFLOW grid cells which occurred at the lowest values shown in the figures
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appear to be unreasonable. When the percentage of area defined as drains reached
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30% or higher, the GMS (version 5.1) platform could not handle the memory
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requirements.
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The model simulation sensitivity to aquitard vertical hydraulic conductivity and
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percentage of drain coverage is relatively straightforward; less vertical hydraulic
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conductivity leads to higher spring discharges and a lower percentage of drains results
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in lower spring discharges. These trends are consistent throughout the entire time
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period.
On the other hand, sensitivity to changes in the horizontal hydraulic
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conductivity of the perched aquifer zone and changes in the drain conductance is a
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result of a more complicated relationship influenced by both storage capabilities and
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the transient recharge. Regarding the horizontal hydraulic conductivity, at relatively
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low values, water is unable to flow through the matrix towards the drains or directly
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towards the simulated spring. This produces relatively low spring discharges. As the
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hydraulic conductivity increases, more water is able to flow through the matrix and
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spring discharges increase due to both direct matrix flow and the karstic channels.
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However, further increases in the hydraulic conductivity, along with significant
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recharge to the aquifer during the winter months, allows for a significant amount of
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water to be "released" from the matrix thus lowering the overall water table which in
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turn decreases the flow in the drains (the latter being dependent on this head
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difference as discussed earlier). The overall effect in this case is for less spring
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discharge and more penetration of water to the lower aquifer. In the summer months
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when ground water levels are low and flow occurs primarily through the matrix, the
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increase in hydraulic conductivity does not significantly impact flow through the
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drains by lowering the water table. In this case the increase in conductivity only has
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the effect of increasing the overall discharge to the simulated spring via matrix flow.
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Regarding the drain conductance, at low Cd values the spring discharge is relatively
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low as most of the water flows through the matrix either towards the spring or down
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to the lower aquifer. An intermediate increase in the drain conductance causes the
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spring discharge to increase as conduit flow becomes more significant. As drain
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conductance gets much higher, and with relatively high recharge, the drains
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effectively remove the water from the system as expected and spring discharges
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appear high. In fact, the drains are so effective at removing the water that by the time
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summer comes around (little or no recharge) the water table has been lowered to such
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an extent that the only flow still occurring in the system is via the matrix from storage.
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In this scenario, even though Cd may be relatively high, the overall spring discharge
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decreases even to rates lower than the simulations where the Cd is less.
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Ein Matwi
Kv = 9.0e-5 (51.8% error)
Kv = 1.1e-4 (6.7% error)
Kv = 1.2e-4 (13.9% error)
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Discharge (liters/second)
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10
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6
4
2
0
10/1/1980
10/1/1981
10/1/1982
10/2/1983
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Supplementary Figure 8.
Sensitivity to Vertical Hydraulic Conductivity in
Aquitard. No convergence of numerical model at Kv > 1.25e-4 m/d.
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Ein Matwi
24.7% Drain Coverage (6.7% error)
15% Drain Coverage (13.2% error)
27% Drain Coverage (8.2% error)
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Discharge (liters/second)
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10
8
6
4
2
0
10/1/1980
10/1/1981
10/1/1982
10/2/1983
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Supplementary Figure 9. Sensitivity to Extent of Drain Coverage. Not enough
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memory available to numerical model at drain coverage extent greater than
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30.0%.
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Ein Matwi
Kh = 0.001 (27.0% error)
Kh = 0.010 (6.7% error)
Kh = 0.050 (1.9% error)
Discharge (liters/second)
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12
10
8
6
4
2
0
10/1/1980
10/1/1981
10/1/1982
10/2/1983
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Supplementary Figure 10. Sensitivity to Horizontal Hydraulic Conductivity in
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Perched Aquifer. No convergence of numerical model at Kh > 0.051 m/d.
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Ein Matwi
Cd = 0.020 (6.7% error)
Cd = 0.002 (19.3% error)
Cd = 0.200 (10.8% error)
Discharge (liters/second)
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20
15
10
5
0
10/1/1980
10/1/1981
10/1/1982
10/2/1983
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Supplementary Figure 11. Sensitivity to Drain Conductance.
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A "covariant" sensitivity analysis was done to determine the relative impact of
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varying both the recharge (the primary calibration parameter in this study) and the
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horizontal hydraulic conductivity. In these simulations, all other parameters were
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held constant. The results showed that varying Kh within the reasonable bounds of the
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model, while keeping the recharge rate constant, creates an average yearly error
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between the spring discharge data and the model simulation ranging from 0.21 to
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0.38. On the other hand, varying the recharge while keeping Kh constant creates a
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more significant error ranging from 0.38 to 1.37. For comparison, the Guttman
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equations create an average yearly error of 1.15. The significance of this analysis is
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that it shows that the numerical model is more sensitive to changes in recharge than to
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changes in the hydraulic conductivity. This shows that while correctly defining the
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hydraulic conductivity is very important, correctly defining the recharge parameter is
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even more significant to the model simulation results. It also shows that estimating
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recharge using inverse modeling techniques (be they formal automated techniques or
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manual calibration procedures) can be estimated with more accuracy than the
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hydraulic conductivity.
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