# Comparative Study of Methods for Delineating the Wellhead Protection Area in an Unconfined Coastal Aquifer

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Delineation Methods Selection

_{L}, the maximum width of the up-gradient zone Y

_{L}and the distance to up-gradient boundary r

_{x}(with regard to the specified TOT) to delineate the envelope-shaped protection zone. WhAEM2000 is a semi-analytical model developed by U.S. EPA for facilitating capture zone and protection area mapping. WhAEM2000 includes the CFR and uniform flow methods, but also has its own semi-analytical solution to model steady pumping wells and can solve the influence of hydrological boundaries. HYBRID method combines some of the analytical equations from the CFR and uniform flow equation method. By following the five steps illustrated by Paradis and Martel [30], this method is relatively straight forward. MODFLOW-MODPATH is a widely used groundwater numerical model. All of the WHPA delineation analysis was based on the data compiled from past annual average values which covered both the dry and wet seasons.

#### 2.2. Reference WHPA

_{i}to quantify the difference between the reference WHPA and the WHPAs produced by other methods. C

_{i}index represents how the WHPA from the tested method fits the WHPA from the reference method. The principle of C

_{i}can be illustrated by Figure 1 and C

_{i}is calculated by Equation (1):

#### 2.3. Stochastic Modeling for Uncertainty Analysis

#### 2.4. Study Area

^{2}/day, and hydraulic conductivity is 50–300 m/day. The porosity of the supplying aquifer is estimated as 30% [40]. The Nahariya pumping well has a nearly constant pumping rate of 6600 m

^{3}/day [41]. In the multi-well pumping field (the Rehovot Site), the local aquifer recharge rate is around 208 mm/year with a hydraulic conductivity of 10.5 m/day [35]. Eight pumping wells in the wellfield are distributed as shown in Figure 2c. The average pumping rate of Well 1 is 3000 m

^{3}/day, with 1500 m

^{3}/day of Well 2 and 2500 m

^{3}/day of Well 6; the remaining wells have the same pumping rate, i.e., 1000 m

^{3}/day.

## 3. Results

#### 3.1. WHPA Delineation of the Nahariya Site (Single Well)

^{3}/day and the saturated thickness of well is 15.5 m, the radii of Level-B (TOT = 100 days) and Level-C (TOT = 400 days) protection zone was 211 m and 421 m, respectively. The surface area of Level-B zone was 0.14 km

^{2}and the area of the Level-C zone was 0.56 km

^{2}. Applying the uniform flow equation method, an average hydraulic gradient of 0.0025 and hydraulic conductivity of 250 m/day [41] were used. The calculated distances from well to the down-gradient boundary (X

_{L}) and the maximum width (Y

_{L}) were 108 m and 341 m. X

_{L}and Y

_{L}values were the same for both Level-B and Level-C protection zone. The size of WHPA depends on distance to the up-gradient boundary (r

_{x}), which is the travel distance of contaminants with the up-gradient groundwater flow to enter pumping well. r

_{x}of Level-B zone was 365 m and was 1098 m for Level-C zone. Thus, two envelope-shaped WHPAs with different dimensions that extend to the up-gradient direction were produced by uniform flow method. The WHPAs delineated by HYBRID method were represented by two ellipses with different horizontal dimensions (d/2) and vertical dimensions (w/2). Surface area of Level-B and Level-C protection zones were 0.14 km

^{2}and 0.55 km

^{2}.

^{2}and a Level-C WHPA with the surface area of 0.37 km

^{2}were delineated.

^{2}and the Level-C protection zone was 0.29 km

^{2}. Reference WHPAs aligned with the groundwater flow direction.

#### 3.2. WHPA Delineation of the Rehovot Site (Multi-Well Field)

_{L}, Y

_{L}and r

_{x}. Therefore, the WHPAs of all pumping wells delineated by the uniform equation method expanded significantly in the direction that was perpendicular to the groundwater flow direction, which already deviated from the realistic protection areas for protecting groundwater resources. Owning to this, the uniform flow equation was not used for delineating WHPAs in the Rehovot wellfield and the surface area of WHPAs were not calculated. Since WhAEM2000 is incapable of simulating the aquicludes within aquifer, a homogeneous aquifer similar to the Nahariya site was built and eight pumping wells were distributed with different saturation thickness and pumping rates.

#### 3.3. Uncertainty Analysis Results of Numerical Modeling (MODFLOW-MODPATH) Method

## 4. Discussion and Recommendation

#### 4.1. Comparison of WHPA Delineation Results

#### 4.1.1. Comparison of Level-B Protection Zones

^{3}/day), and it was located in an unconfined aquifer where a significant asymmetrical drawdown could be created, and the difference between X

_{L}and Y

_{L}values were appropriately small. However, the uniform flow method does not guarantee the water balance between extraction and storage as the CFR method does [30]. Therefore, the ${\mathrm{C}}_{\mathrm{i}}$ value (25.0%) of the uniform flow method was still small at the Nahariya site.

#### 4.1.2. Comparison of Level-C Protection Zones

#### 4.2. Recommendation for Selecting Delineation Method

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Siebert, S.; Burke, J.; Faures, J.M.; Frenken, K.; Hoogeveen, J.; Döll, P.; Portmann, F.T. Groundwater use for irrigation—A global inventory. Hydrol. Earth Syst. Sci.
**2010**, 14, 1863–1880. [Google Scholar] [CrossRef] - Shah, T.; Burke, J.; Villholth, K.G.; Angelica, M.; Custodio, E.; Daibes, F.; Hoogesteger, J.; Giordano, M.; Girman, J.; Van Der Gun, J.; et al. Groundwater: A Global Assessment of Scale and Significance; Earthscan: London, UK; International Water Management Institute (IWMI): Colombo, Sri Lanka, 2007; pp. 395–423. [Google Scholar]
- World Water Assessment Programme (United Nations). Water: A Shared Responsibility; the United Nations World Water Development Report 2; UN-HABITAT: Nairobi, Kenya, 2006. [Google Scholar]
- EPA. Guidelines for Delineation of Wellhead Protection Areas; EPA-440/5-93-001; United States Environmental Protection Agency: Washington, DC, USA, 1987; p. 212.
- Cleary, T.C.B.F.; Cleary, R.W. Delineation of Wellhead Protection Areas: Theory and Practice. Water Sci. Technol.
**1991**, 24, 239–250. [Google Scholar] [CrossRef] - Vassolo, S.; Kinzelbach, W.; Schafer, W. Determination of a well head protection zone by stochastic inverse modelling. J. Hydrol.
**1998**, 206, 268–280. [Google Scholar] [CrossRef] - Schleyer, R.; Milde, G.; Milde, K. Wellhead Protection Zones in Germany—Delineation, Research and Management. J. Inst. Water Environ. Manag.
**1992**, 6, 303–311. [Google Scholar] [CrossRef] - EPA. Handbook—Groundwater and Wellhead Protection; United States Environmental Protection Agency: Washington, DC, USA, 1994; p. 288.
- Harter, T. Delineating Groundwater Sources and Protection Zones; Rollins, L., Ed.; University of California at Davis: Davis, CA, USA, 2002. [Google Scholar]
- EPA. Literature Review of Methods for Delineating Wellhead Protection Areas; United States Environmental Protection Agency: Washington, DC, USA, 1998; p. 48.
- Rock, G.; Kupfersberger, H. Numerical delineation of transient capture zones. J. Hydrol.
**2002**, 269, 134–149. [Google Scholar] [CrossRef] - Piccinini, L.; Fabbri, P.; Pola, M.; Marcolongo, E.; Rosignoli, A. Numerical modeling to well-head protection area delineation, an example in Veneto Region (NE Italy). Rend. Online Soc. Geol. Ital.
**2015**, 35, 232–235. [Google Scholar] [CrossRef] - Harbaugh, A.W. MODFLOW-2005: The U.S. Geological Survey Modular Ground-Water Model—The Ground-Water Flow Process; US Department of the Interior, US Geological Survey: Reston, VA, USA, 2005.
- Forster, C.B.; Lachmar, T.E.; Oliver, D.S. Comparison of Models for Delineating Wellhead Protection Areas in Confined to Semiconfined Aquifers in Alluvial Basins. Groundwater
**1997**, 35, 689–697. [Google Scholar] [CrossRef] - Pollock, D.W. User Guide for MODPATH Version 7—A Particle-Tracking Model for MODFLOW; US Department of the Interior, US Geological Survey: Reston, VA, USA, 2016; p. 41.
- Evers, S.; Lerner, D.N. How uncertain is our estimate of a wellhead protection zone? Ground Water
**1998**, 36, 49–57. [Google Scholar] [CrossRef] - Theodossiou, N.; Fotopoulou, E. Delineating well-head protection areas under conditions of hydrogeological uncertainty. A case-study application in northern Greece. Environ. Process.
**2015**, 2, 113–122. [Google Scholar] [CrossRef] - Fadlelmawla, A.A.; Dawoud, M.A. An approach for delineating drinking water wellhead protection areas at the Nile Delta, Egypt. J. Environ. Manag.
**2006**, 79, 140–149. [Google Scholar] [CrossRef] [PubMed] - Stauffer, F.; Guadagnini, A.; Butler, A.; Franssen, H.J.H.; Van den Wiel, N.; Bakr, M.; Riva, M.; Guadagnini, L. Delineation of source protection zones using statistical methods. Water Resour. Manag.
**2005**, 19, 163–185. [Google Scholar] [CrossRef] - Schmoll, O.; World Health Organization. Protecting Groundwater for Health: Managing the Quality of Drinking-Water Sources; IWA Pub.: London, UK, 2006. [Google Scholar]
- Paradis, D.; Martel, R.; Karanta, G.; Lefebvre, R.; Michaud, Y.; Therrien, R.; Nastev, M. Comparative study of methods for WHPA delineation. Ground Water
**2007**, 45, 158–167. [Google Scholar] [CrossRef] [PubMed] - Landmeyer, J.E. Description and Application of Capture Zone Delineation for A Wellfield at Hilton Head Island, South Carolina. Water-Resour. Investig. Rep.
**1994**, 94, 4012. [Google Scholar] - ANWQMS. National Water Quality Management Strategies: Guidelines for Groundwater Protection in Australia; Agriculture and Resources Management Council of Australia and New Zealand: Canberra, Australia, 1995.
- DoELG. Groundwater Protection Schemes; Environmental Protection Agency and Geological Survey of Ireland, Department of Environment and Local Government: Dublin, Ireland, 1999.
- DVGW. Code of Practice W101 for Drinking Water Protection Areas Part 1, Protective Areas for Groundwater; German Association of Gas and Water Experts: Bonn, Germany, 1995. [Google Scholar]
- Government of Oman. Water Resources of the Sultanate of Oman; Ministry of Water Resources: Muscat, Oman, 1991.
- Bear, J.; Jacobs, M. On the movement of water bodies injected into aquifers. J. Hydrol.
**1965**, 3, 37–57. [Google Scholar] [CrossRef] - Todd, D.K.; Mays, L.W. 4.3 WELL IN A UNIFORM FLOW. In Groundwater Hydrology, 3rd ed.; Bill, Z., Ed.; John Wiley & Sons, Inc.: New York, NY, USA, 2004; p. 656. [Google Scholar]
- Haitjema, H.M.; Wittman, J.; Kelson, V.; Bauch, N. WhAEM: Program Documentation for the Wellhead Analytic Element Model; EPA/600/R-94/210 (NTIS PB95-167373); U.S. Environmental Protection Agency: Washington, DC, USA, 1994.
- Paradis, D.; Martel, R. HYBRID: A Wellhead Protection Delineation Method for Aquifers of Limited Extent; Geological Survey of Canada: Ottawa, ON, Canada, 2007; p. 5.
- Israel Ministry of Health. Public Health Regulations 2013—The Sanitary Quality of Drinking Water and Drinking Water Facilities; Collection of Regulations 7262; Department of Environmental Health, Public Health Services, Ministry of Health: Jerusalem, Israel, 2013; p. 34.
- Miller, C.; Chudek, P.; Babcock, S. A Comparison of wellhead Protection Area Delineation Methods for Public Drinking Water Systems in Whatcom County, Washington. J. Environ. Health
**2003**, 66, 17. [Google Scholar] [PubMed] - Loucks, D.P.; van Beek, E.; Stedinger, J.R.; Dijkman, J.P.M.; Villars, M.T. 9. Model Sensitivity and Uncertainty Analysis. In Water Resources Systems Planning and Management: An Introduction to Methods, Models and Applications; Springer International Publishing AG: Basel, Switzerland, 2005. [Google Scholar] [CrossRef]
- Guha, H. A Stochastic Modeling Approach to Address Hydrogeologic Uncertainties in Modeling Wellhead Protection Boundaries in Karst Aquifers1. JAWRA J. Am. Water Resour. Assoc.
**2008**, 44, 654–662. [Google Scholar] [CrossRef] - Weinberger, G.; Livshitz, Y.; Givati, A.; Zilberbrand, M.; Tal, A.; Weiss, M.; Zurieli, A. The Natural Water Resources Between the Mediterranean Sea and the Jordan River; Hydro Report 11/1; Israel Hydrological Service: Jerusalem, Israel, 2011; p. 63.
- Eriksson, E.; Khunakasem, V. Chloride concentration in groundwater, recharge rate and rate of deposition of chloride in the Israel Coastal Plain. J. Hydrol.
**1969**, 7, 178–197. [Google Scholar] [CrossRef] - Kass, A.; Gavrieli, I.; Yechieli, Y.; Vengosh, A.; Starinsky, A. The impact of freshwater and wastewater irrigation on the chemistry of shallow groundwater: A case study from the Israeli Coastal Aquifer. J. Hydrol.
**2005**, 300, 314–331. [Google Scholar] [CrossRef] - Nativ, R.; Weisbrod, N. Hydraulic Connections among Subaquifers of the Coastal-Plain Aquifer, Israel. Ground Water
**1994**, 32, 997–1007. [Google Scholar] [CrossRef] - Yosef, B. The Hydrogeology of the Coastal Plain of Western Galilee (in Hebrew); TAHAL: Tel Aviv, Israel, 1967. [Google Scholar]
- Wexler, A. Hydrogeological Plan for the Water Development, Production, and Utilization in the Kavri Basin; GSI/36/2001; Water Commission & Planning Department: Tel Aviv, Israel, 2001.
- Dvory, N. Hydrographic Survey in the Production Field of Nahariya Municipality Drilling Etgar Engineering LTD Report; Etgar: Tel Aviv, Israel, 2009. [Google Scholar]
- Yakirevich, A.; Kuznetsov, M.; Adar, E. Modeling Contaminant Migration in Coastal Aquifer (Givon Region)—Internal Report; Ben-Gurion University of the Negev: Beersheba, Israel, 2015. [Google Scholar]

**Figure 1.**Illustration of comparative index ${\mathrm{C}}_{\mathrm{i}}$ (modified according to Paradis et al. [21]).

**Figure 2.**Location, representative aquifer cross-section of the two study areas and the well distribution map of the multi-well pumping site in Rehovot: (

**a**) location of two study areas; (

**b**) example hydrogeological cross-section of coastal aquifer in Israel; (

**c**) distribution pattern of eight pumping wells in the Rehovot wellfield.

**Figure 3.**Level-B and Level-C WHPAs of the Nahariya pumping site delineated by different methods: (

**a**) Level-B (TOT = 100 days) WHPAs; (

**b**) Level-C (TOT = 400 days) WHPAs.

**Figure 4.**2D numerical model domain and boundary conditions of the Nahariya site: yellow lines represent the simulated groundwater heads.

**Figure 5.**3D numerical model domain of the Rehovot pumping field: (

**a**) Model domain and boundary conditions; (

**b**) Representative cross-section A-A’ of the model after calibration.

**Figure 6.**Level-B and Level-C WHPAs of the Rehovot wellfield pumping site delineated by different methods: (

**a**) Level-B (TOT = 400 days) WHPAs; (

**b**) Level-C (TOT = 15 years) WHPAs.

**Figure 7.**Probabilistic maps produced by stochastic modeling that reflects the uncertainty of WHPAs at the Rehovot wellfield pumping site: (

**a**) Level-B probabilistic map; (

**b**) Level-C probabilistic map. The red shapes represent the WHPAs from the normal deterministic numerical modeling method.

**Figure 8.**Recommended procedure for selecting a WHPA delineation based on data availability and delineation expectation.

Analytical Methods | Equations | Note |
---|---|---|

CFR | $\mathrm{r}=\sqrt{\frac{\mathrm{Qt}}{\mathsf{\pi}\mathrm{nH}+\mathrm{N}\mathsf{\pi}\mathrm{t}}}$ | r (L): radius of the circular WHPA, Q (L ^{3}/T): pumping rate,t (T): time of travel, n (-): aquifer porosity, H (L): aquifer thickness, N (L/T): infiltration rate. |

Uniform flow equation | ${\mathrm{X}}_{\mathrm{L}}=-\frac{\mathrm{Q}}{2\mathsf{\pi}\mathrm{Kbi}}$ ${\mathrm{Y}}_{\mathrm{L}}=\pm \frac{\mathrm{Q}}{2\mathrm{Kbi}}$ ${\mathrm{t}}_{\mathrm{x}}=\frac{\mathrm{n}}{\mathrm{Ki}}{[\mathrm{r}}_{\mathrm{x}}-(\frac{\mathrm{Q}}{2\mathsf{\pi}\mathrm{Kbi}}\left)\mathrm{ln}\right\{1+(\frac{2\mathsf{\pi}\mathrm{Kbi}}{\mathrm{Q}}{)\mathrm{r}}_{\mathrm{x}}\left\}\right]$ | X_{L} (L): down-gradient flow boundary,Y _{L} (L): max. width of up-gradient zone,t _{x} (T): time of travel,r _{x}(±) (L): distance to up-gradient boundary (+), or to down-gradient boundary (−),K (L/T): hydraulic conductivity, b (L): aquifer thickness, i (-): hydraulic gradient, n (-): aquifer porosity, Q (L ^{3}/T): pumping rate. |

HYBRID | ${\mathrm{t}}_{\mathrm{x}}=\frac{\mathrm{n}}{\mathrm{Ki}}{[\mathrm{r}}_{\mathrm{x}}-(\frac{\mathrm{Q}}{2\mathsf{\pi}\mathrm{Kbi}}\left)\mathrm{ln}\right\{1+(\frac{2\mathsf{\pi}\mathrm{Kbi}}{\mathrm{Q}}{)\mathrm{r}}_{\mathrm{x}}\left\}\right]$ $\frac{\mathrm{d}}{2}=\frac{{\mathrm{r}}_{\mathrm{x}}(+){+\mathrm{r}}_{\mathrm{x}}(-)}{2}$ $\mathsf{\pi}\frac{\mathrm{w}}{2}\frac{\mathrm{d}}{2}=\frac{\mathrm{tQ}}{\mathrm{bn}}$ | w/2 (L): vertical dimension of ellipse, d/2 (L): horizontal dimension of ellipse, other parameters are the same as the parameters from uniform flow equation method. |

**Table 2.**Hydrogeological parameters used in different methods for the Nahariya and Rehovot pumping sites.

Method | Pumping Rate (m^{3}/day) | Saturated Thickness (m) | Porosity (%) | Recharge Rate (mm/year) | Conductivity (m/day) | Hydraulic Gradient |
---|---|---|---|---|---|---|

Nahariya site | ||||||

CFR | 6600 | 15.5 | 30 | 250 | - | - |

Uniform flow equation | 6600 | 15.5 | 30 | - | 250 | 0.0025 |

WhAEM2000 | 6600 | 15.5 | 30 | 250 | 250 | - |

HYBRID | 6600 | 15.5 | 30 | 250 | 250 | 0.0025 |

MODFLOW-MODPATH | 6600 | 15.5 | 30 | 250 | 250 | - |

Rehovot site | ||||||

CFR | 1000–3000 | 4.9–18.5 | 30 | 208 | - | - |

WhAEM2000 | 1000–3000 | 85 | 30 | 208 | 10.5 | - |

HYBRID | 1000–3000 | 4.9–18.5 | 30 | 208 | 10.5 | 0.0019–0.0068 |

MODFLOW-MODPATH | 1000–3000 | 4.9–18.5 | 30 | 0.1–475 | 0.006–30 | - |

**Table 3.**Calculation results of Level-B and Level-C WHPAs in the Rehovot pumping site by analytical methods.

Well Number | Analytical Methods | ||||||||
---|---|---|---|---|---|---|---|---|---|

CFR | Uniform Flow Equation | HYBRID | |||||||

Level-B WHPA | |||||||||

r (m) | S (km^{2}) | X_{L} (m) | Y_{L} (m) | r_{x} (m) | S (km^{2}) | w/2(m) | d/2 (m) | S (km^{2}) | |

Well 1 | 397 | 0.49 | 3002 | 9431 | 415 | - | 398 | 397 | 0.50 |

Well 2 | 335 | 0.35 | 1173 | 3686 | 367 | - | 334 | 336 | 0.35 |

Well 3 | 295 | 0.27 | 462 | 1450 | 361 | - | 292 | 298 | 0.27 |

Well 4 | 238 | 0.18 | 374 | 1176 | 291 | - | 236 | 241 | 0.18 |

Well 5 | 221 | 0.15 | 323 | 1014 | 274 | - | 219 | 224 | 0.15 |

Well 6 | 367 | 0.42 | 707 | 2223 | 433 | - | 365 | 370 | 0.42 |

Well 7 | 152 | 0.07 | 160 | 505 | 203 | - | 148 | 156 | 0.07 |

Well 8 | 231 | 0.17 | 289 | 907 | 296 | - | 227 | 235 | 0.16 |

Level-C WHPA | |||||||||

Well 1 | 1467 | 6.76 | 3002 | 9431 | 1715 | - | 1457 | 1477 | 6.76 |

Well 2 | 1236 | 4.80 | 1173 | 3686 | 1704 | - | 1120 | 1275 | 4.48 |

Well 3 | 1089 | 3.72 | 462 | 1450 | 2069 | - | 941 | 1260 | 3.72 |

Well 4 | 880 | 2.43 | 374 | 1176 | 1670 | - | 761 | 1018 | 2.43 |

Well 5 | 817 | 2.10 | 323 | 1014 | 1613 | - | 692 | 965 | 2.10 |

Well 6 | 1356 | 5.77 | 707 | 2223 | 2330 | - | 1229 | 1497 | 5.78 |

Well 7 | 560 | 0.98 | 160 | 505 | 1336 | - | 420 | 748 | 0.99 |

Well 8 | 852 | 2.28 | 289 | 907 | 1833 | - | 685 | 1060 | 2.28 |

**Table 4.**Statistical characteristics of the hydraulic conductivities to be randomly sampled at two pumping sites.

Parameters | Mean(Starting) Value | Value Range | Distribution Pattern |
---|---|---|---|

Nahariya Site | |||

K (m/day) | 200 | 100–300 | Lognormal |

Rehovot Site | |||

K_{west} (m/day) | 10.43 | 5.0–15.0 | Lognormal |

K_{east} (m/day) | 7.30 | 3.5–10.5 | Lognormal |

_{west}is the hydraulic conductivity of the western part sandstone of Rehovot pumping site MODFLOW model; K

_{east}is the hydraulic conductivity of the eastern part sandstone of Rehovot pumping site MODFLOW model.

**Table 5.**Level-B protection areas and comparison index ${\mathrm{C}}_{\mathrm{i}}$ of different delineation methods at the Nahariya and the Rehovot pumping site.

Pumping Sites | Surface Area (S) | CFR | Uniform Flow Equation | WhAEM2000 | HYBRID | MODFLOW-MODPATH |
---|---|---|---|---|---|---|

$\mathbf{Index}\left({\mathbf{C}}_{\mathbf{i}}\right)$ | ||||||

Nahariya Site (Level-B: 100 days) | ||||||

Nahariya well | S (km^{2}) | 0.14 | 0.29 | 0.097 | 0.14 | 0.073 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 43.1 | 25.0 | 58.6 | 51.7 | Reference | |

Rehovot Site (Level-B: 400 days) | ||||||

Well 1 | S (km^{2}) | 0.49 | - | 0.05 | 0.51 | 0.09 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 18.4 | - | 43.3 | 17.7 | Reference | |

Well 2 | S (km^{2}) | 0.35 | - | 0.02 | 0.33 | 0.06 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 17.1 | - | 33.3 | 18.2 | Reference | |

Well 3 | S (km^{2}) | 0.27 | - | 0.02 | 0.25 | 0.07 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 25.9 | - | 28.6 | 28.00 | Reference | |

Well 4 | S (km^{2}) | 0.18 | - | 0.02 | 0.18 | 0.05 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 27.8 | - | 40.0 | 27.8 | Reference | |

Well 5 | S (km^{2}) | 0.15 | - | 0.02 | 0.15 | 0.05 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 33.3 | - | 16.7 | 33.3 | Reference | |

Well 6 | S (km^{2}) | 0.42 | - | 0.04 | 0.41 | 0.13 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 31.0 | - | 30.8 | 31.7 | Reference | |

Well 7 | S (km^{2}) | 0.07 | - | 0.02 | 0.06 | 0.05 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 51.2 | - | 40.0 | 33.3 | Reference | |

Well 8 | S (km^{2}) | 0.17 | - | 0.02 | 0.15 | 0.05 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 29.4 | - | 40.0 | 33.3 | Reference | |

Average | S (km^{2}) | - | - | - | - | - |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 28.8 | - | 34.1 | 27.03 | Reference | |

Sum | S (km^{2}) | 2.00 | - | 0.21 | 1.91 | 0.55 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | - | - | - | - | - |

**Table 6.**Level-C protection areas and comparison index ${\mathrm{C}}_{\mathrm{i}}$ of different delineation methods at the Nahariya and Rehovot pumping sites.

Pumping Sites | Surface Area (S) | CFR | Uniform Flow Equation | WhAEM2000 | HYBRID | MODFLOW-MODPATH | |
---|---|---|---|---|---|---|---|

$\mathbf{Index}\left({\mathbf{C}}_{\mathbf{i}}\right)$ | |||||||

Nahariya Site (Level-B: 100 days) | |||||||

Nahariya well | S (km^{2}) | 0.56 | 0.75 | 0.37 | 0.55 | 0.29 | |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 25.1 | 38.6 | 54.3 | 53.2 | Reference | ||

Rehovot Site (Level-B: 400 days) | |||||||

Entire wellfield | S (km^{2}) | 14.38 | - | 2.62 | 16.04 | 5.66 | |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 30.2 | - | 40.6 | 35.3 | Reference |

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**MDPI and ACS Style**

Liu, Y.; Weisbrod, N.; Yakirevich, A. Comparative Study of Methods for Delineating the Wellhead Protection Area in an Unconfined Coastal Aquifer. *Water* **2019**, *11*, 1168.
https://doi.org/10.3390/w11061168

**AMA Style**

Liu Y, Weisbrod N, Yakirevich A. Comparative Study of Methods for Delineating the Wellhead Protection Area in an Unconfined Coastal Aquifer. *Water*. 2019; 11(6):1168.
https://doi.org/10.3390/w11061168

**Chicago/Turabian Style**

Liu, Yue, Noam Weisbrod, and Alexander Yakirevich. 2019. "Comparative Study of Methods for Delineating the Wellhead Protection Area in an Unconfined Coastal Aquifer" *Water* 11, no. 6: 1168.
https://doi.org/10.3390/w11061168