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Web-based tool for analyzing the seawater-freshwater interface using analytical solutions and SEAWAT code comparison
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Abstract: Saltwater Intrusion (SI) poses a significant environmental threat to freshwater resources in coastal aquifers globally. The primary objective of this research is to illustrate the variations in the saltwater-freshwater interface using several established analytical solutions, integrated within a user-friendly web-based tool. Three case studies, including a hypothetical unconfined coastal aquifer, an experimental coastal aquifer, and a real-world coastal aquifer in Gaza, were applied to examine the interface dynamics using the developed tool, built with JavaScript. To simulate variable-density flow within the Gaza coastal aquifer, the public domain code SEAWAT was employed. The resulting lengths of seawater intrusion, as simulated by SEAWAT and the observed toe length, were compared with those obtained from the web-based analytical solutions under both constant head and constant flux boundary conditions. This comparison demonstrated a strong correlation between the experimental results, SEAWAT model outputs, and analytical solutions. This research provides valuable insights into SI in coastal aquifers, with a specific focus on the impact of Sea Level Rise (SLR) on the shifting position of the seawater intrusion toe. The outcomes are presented through an accessible web-based interface, thereby promoting broader dissemination and practical application of the research outcomes.
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Key words:
- Saltwater Intrusion /
- Numerical Simulation /
- Coastal Aquifers /
- Sea Level Rise /
- SEAWAT
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Figure 1. Saltwater intrusion wedge evolution over time (15, 30, 45, 60, 75, and 95 minutes) after increasing the freshwater head to 31.40 cm
Figure 3. Input parameters for calculating the seawater-freshwater interface for the hypothetical coastal aquifer using the analytical solutions Gyhben Herzberg, Glover, Rumer-Herleman, and Verruijt
Figure 4. Seawater-freshwater interface for a hypothetical coastal aquifer based on the analytical solutions of: (a) Gyhben Herzberg, (b) Glover, (c) Rumer-Herleman, and (d) Verruijt
Figure 5. Comparison between the simulated SW-FW interface for the hypothetical unconfined coastal aquifer (from Sun et al. 2021) and the analytical solutions of Gyhben-Herzberg, Glover, Rumer-Herleman, and Verruijt through the web-based interface model
Figure 6. Input Parameters for calculating the seawater-freshwater interface using the analytical solutions of Gyhben-Herzberg, Glover, Rumer-Herleman, and Verruijt for the experimental coastal aquifer
Figure 7. Seawater-freshwater interface for the experimental coastal aquifer based on the analytical solutions of: (a) Gyhben-Herzberg, (b) Glover, (c) Rumer-Herleman, and (d) Verruijt
Figure 8. Comparison between the experimental SW- FW interface for the experimental unconfined coastal aquifer (from Armanuos, 2017) and the analytical solutions for Gyhben-Herzberg, Glover, Verruijt, and Rumer-Herleman through the web-based interface
Figure 10. Calculated head versus observed head (Sirhan and Koch, 2013) for GCA
Figure 11. Simulated SI in Gaza aquifer for the base case. The contours represent the following concentration levels: 32,400 ppm for the 90% equi-concentration line, 18,000 ppm for the 50% equi-concentration line, and 3,600 ppm for the 10% equi-concentration line.
Figure 12. Input Parameters for calculating seawater intrusion wedge toe for the Gaza coastal aquifer using Ataie-Ashtiani et al. (2013) through the web-based interface tool for a constant flux boundary problem
Figure 13. Input parameters for calculating seawater intrusion wedge toe for the Gaza coastal aquifer using Ataie-Ashtiani et al. (2013) through the web-based interface tool for a constant head boundary problem
Figure 14. Seawater intrusion distribution in the Gaza coastal aquifer: (a) steady-state condition, (b) SLR = 0.5 m, (c) SLR = 1.0 m, (d) SLR = 1.5 m, and (e) SLR = 2.0 m
Table 1. Analytical Equations implemented in the Seawater (SW)-Freshwater (FW) Interface Web-Based Model
Seawater (SW)-Freshwater Interface Web-Based Model Analytical Equations Badon Ghyben (1888) & Herzberg (1901) $ \mathrm{z}=\dfrac{{\mathrm{\rho }}_{\mathrm{f}}}{{\mathrm{\rho }}_{\mathrm{s}}-{\mathrm{\rho }}_{\mathrm{f}}}{\mathrm{h}}_{\mathrm{f}} $ Glover (1959) $ {\mathrm{z}}^{2}=\dfrac{2{\mathrm{\rho }}_{\mathrm{f}}\mathrm{q}\mathrm{ }\mathrm{x}}{\mathrm{\Delta }\mathrm{\rho }\mathrm{ }\mathrm{K}}+{\left(\dfrac{{\mathrm{\rho }}_{\mathrm{f}}\mathrm{q}}{\mathrm{\Delta }\mathrm{\rho }\mathrm{ }\mathrm{K}}\right)}^{2} $ Rumer Jr and Harleman (1963) $ {\mathrm{z}}^{2}=\dfrac{2{\mathrm{\rho }}_{\mathrm{f}}\mathrm{q}\mathrm{ }\mathrm{x}}{\mathrm{\Delta }\mathrm{\rho }\mathrm{ }\mathrm{K}}+{0.55\left(\dfrac{{\mathrm{\rho }}_{\mathrm{f}}\mathrm{q}}{\mathrm{\Delta }\mathrm{\rho }\mathrm{ }\mathrm{K}}\right)}^{2} $ Verruijt (1968) $ \mathrm{Z}=-{\left({\left(\dfrac{\mathrm{q}}{\mathrm{\beta }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{K}}\right)}^{2}.\left(\dfrac{1-\mathrm{\beta }}{1+\mathrm{\beta }}\right)+2\left(\dfrac{\mathrm{q}}{\mathrm{\beta }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{K}}\right).\left(\dfrac{\mathrm{x}}{1+\mathrm{\beta }}\right)\right)}^{1/2} $ Where: $ {\rho }_{s} $ (M L−3) represents the seawater density, $ {\rho }_{f} $ (M L−3) represents the fresh groundwater density, $ {\textit{z}} $ (L) represents the depth to a point on the seawater-freshwater interface under the mean sea level, and $ {\mathrm{h}}_{\mathrm{f}} $ (L) represents the elevation of the water table in the aquifer measured above the mean sea level at the same point, q (L2 T−1) represents the rate of the fresh groundwater discharge, K (LT−1) denotes the hydraulic conductivity of the aquifer medium, $ \mathrm{\Delta }\mathrm{\rho }={\mathrm{\rho }}_{\mathrm{s}}-{\mathrm{\rho }}_{\mathrm{f}} $, x (L) represents the horizontal distance calculated from the shore line and $ \mathrm{\beta }=({\mathrm{\rho }}_{\mathrm{s}}-{\mathrm{\rho }}_{\mathrm{f}})/{\mathrm{\rho }}_{\mathrm{f}} $. 
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Table 2. Analytical equations for the influence of Sea Level Rise (SLR) on Toe of Seawater (SW)-Freshwater (FW) Interface (Ataie-Ashtiani et al. 2013)
Constant Flux Boundary Steady-state SI toe $ {X}_{T}=\left(\dfrac{q}{W}+L\right)-\sqrt{{\left(\dfrac{q}{W}+L\right)}^{2}-\dfrac{K\delta (1+\delta ){{{\textit{z}}}_{o}}^{2}}{W}} $ Impact of SLR on the toe of SW-FW interface ${ {X}_{T}^{{\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} } }=\left(\dfrac{q}{W}+L-\dfrac{\Delta {\textit{z} } }{s}\right)-\sqrt{ {\left(\dfrac{q}{W}+L-\dfrac{\Delta {\textit{z} } }{s}\right)}^{2}-\dfrac{K\delta (1+\delta )({ { {\textit{z} } }_{o}+\Delta {\textit{z} })}^{2} }{W}+}\dfrac{\Delta {\textit{z} } }{s}$ Constant Head Boundary Steady state SI toe $ q=\dfrac{K({\left({h}_{b}+{{\textit{z}}}_{o}\right)}^{2}-\left(1+\delta \right){{{\textit{z}}}_{o}}^{2})}{2L}-\dfrac{WL}{2} $ $ {X}_{T}=\left(\dfrac{q}{W}+L\right)-\sqrt{{\left(\dfrac{q}{W}+L\right)}^{2}-\dfrac{K\delta (1+\delta ){{{\textit{z}}}_{o}}^{2}}{W}} $ Impact of SLR on toe of SW-FW interface $ q=\dfrac{K\left({\left({h}_{b}+{{\textit{z}}}_{o}\right)}^{2}-\left(1+\delta \right)\left({\textit{z}}+\Delta {\textit{z}}\right)^{2}\right)}{2\left(L-\dfrac{\Delta {\textit{z}}}{s}\right)}-\dfrac{W\left(L-\dfrac{\Delta {\textit{z}}}{s}\right)}{2} $ ${ {X}_{T}^{{{\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} } } }=\left(\dfrac{q}{W}+L-\dfrac{\Delta {\textit{z} } }{s}\right)-\sqrt{ {\left(\dfrac{q}{W}+L-\dfrac{\Delta {\textit{z} } }{s}\right)}^{2}-\dfrac{K\delta (1+\delta )({ { {\textit{z} } }_{o}+\Delta {\textit{z} })}^{2} }{W}+}\dfrac{\Delta {\textit{z} } }{s}$ Where: $ {X}_{T} $ (L) represents the position of the toe calculated from the sea boundary, z (L) represents the mean sea level rise, $ {{X}_{T}^{{\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}}}} $ (L) represents the new position of the seawater-freshwater wedge toe calculated from the costal line boundary subsequently the Sea Level Rise (SLR), K (L T−1) represents the hydraulic conductivity of the groundwater aquifer system, L (L) represents the coastal aquifer length, q (L2 T−1) represents the fresh groundwater flow within the coastal aquifer boundary calculated per of the coastline aquifer unit width, zo (L) represents the coastal aquifer depth bottom calculated from the mean sea level, W (L T−1) represents the rate groundwater uniform recharge, and δ (−) represents the dimensionless value of the density term equal to (ρs–ρf)/ρf, where ρf (M L−3) is the density of the freshwater and ρs (M L−3) represents the density of the saltwater, s represents the slope of the seaward boundary of the aquifer. The public value of 0.025 is adopted for δ.
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Table 3. Numerical model parameters for the hypothetical unconfined coastal aquifer (from Sun et al. 2021)
Parameter Description Value Units L Aquifer length 500 m H Aquifer depth 50 m n Porosity 0.30 -- K The hydraulic conductivity 30 m/d $ {\alpha }_{l} $ The longitudinal dispersivity 1.0 m $ {\alpha }_{t} $ The transverse dispersivity 0.1 m $ {\rho }_{f} $ The density of the fresh groundwater 1,000 Kg/m3 $ {\rho }_{s} $ The density of saline water 1,025 Kg/m3 Boundary condition hs Seawater hydraulic head 50 m qf Freshwater inflow 0.2 m/d Cs Saltwater concentration 35,000 mg/L Cf The concentration of the freshwater 1,000 mg/L
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Table 4. Boundary conditions and hydraulic parameters used for Gaza aquifer model
Boundary condition Value Unit The flux of the lateral freshwater 10 m3/d/m Well abstraction rates 20.75 m3/d/m Vertical recharge rate and the return flow 416.5 mm/year The head of the saltwater hs Zero m The concentration of the seaside boundary 35000 mg/L The concentration of the land side boundary 1000 mg/L Hydraulic parameters Confined aquifer Unconfined aquifer Unit The hydraulic conductivity in the horizontal (Kh) 0.2 34 m/d The hydraulic conductivity in the vertical direction (Kv) 0.02 3.4 m/d The value of the Effective porosity (ne) 0.3 0.25 - Total Porosity (nt) 0.45 0.35 - The density of the fresh groundwater 1000 1000 Kg/m3 The density of the saline water 1025 1025 Kg/m3 Specific storage 0.00001 0.0001 - Longitudinal dispersivity 50 12 - Transverse dispersivity 5 1.2 - Molecular diffusion coefficient (D) 0.0001 0.0001 m2/d
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Table 5. Parameters for the Gaza Coastal Aquifer and comparison of SW-FW web-based toe position (for Zo = 100 m) with Ataie-Ashtiani et al. (2013)
No. K
(m/d)W
(mm/a)Zo (m) L (m) ∆Z S Flux BC Head BC Q (m2/d) XT
Ataie-Ashtiani et al. (2013)XT
Current
studyhb
(m)XT
Ataie-Ashtiani et al. (2013)XT
Current
study1 15 58 100 10,000 0 - 1. 7 593 592.8 16.5 593 593.34 2 0.1 638 637.75 704 703.81 2 0.01 823 823.34 878 877.71 2 15 31 100 10,000 0 - 3.4 454 454.34 23.9 454 454.20 2 0.1 493 492.97 529 529.49 2 0.01 675 674.70 702 702.15 3 15 31 100 10,000 0 - 1.8 734 734.06 15 734 732.19 2 0.1 785 784.59 885 884.99 2 0.01 969 969.14 1055 1054.59
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Table 6. Parameters for the Gaza Coastal Aquifer and comparison of SW-FW web-based toe position with SEAWAT results (for 90% concentration = 32,400 mg/L at Zo = 180 m) under various SLR scenarios
No. K (m/d) W (mm/a) Zo (m) L (m) ∆Z S Flux BC Q (m2/d) SEAWAT XT
Current
Study
(m)1 15 58 180 9,000 0 - 1.7 2,208 2,101 0.5 0.1 2,216 2,119 1.0 0.1 2,229 2,137 1.5 0.1 2,243 2,155 2.0 0.1 2,252 2,173
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