Saltwater intrusion management at different coastal aquifers bed slopes considering sea level rise and reduction in fresh groundwater storage

Coastal fresh groundwater management is a challenging research topic due to the relevance of these resources and the huge suffered risks due to global change and overpopulation. The geometrical features of coastal aquifers play a control role in saltwater intrusion (SWI). Seawater level rise and the reduction in aquifer fresh groundwater storage are promoting SWI. All these key factors are considered with two different numerical approaches defining schematic management criteria bottom using the numerical code SEAWAT. The former approach adopts the well-known Henry’s problem; the latter is based on the real study case of the Gaza aquifer (Palestine). Different aquifer bed slopes (ABS), and hydraulic and physical methods for SWI management are considered together with SLR, recharge reduction, and over pumping. The results showed that the land side ABS cases show more SWI than sea side and horizontal ABS. Cut-off walls and check dams are effective to manage SWI in horizontal ABS more than in other slopes, also the subsurface dams, earth fill and recharge of freshwater are good methods in land side ABS while the abstraction of brackish water and combination of recharge with abstraction are better to mitigate of SWI in sea side ABS. Useful comparing tables and considerations are defined with the purpose to guide the preliminary selections of new management solutions for reducing the effect of the global change on groundwater resources for different slopes aquifers around the coastal world.


Introduction
The influence of climate change (CC) on the availability of high-quality water resources is now widely recognized over the world (McDonald et al. 2011). In particular, investigation, management and mitigation of saltwater intrusion (SWI) in coastal regions are key issues for numerous coastal areas affected by water availability shortage and CC (Abd-Elaty et al. 2019;Polemio and Zuffianò 2020). Around 70% of the world's population lives in coastal areas where very high population density is observed; this percentage shows a widespread increasing trend causing the increase of freshwater demand (McDonald et al. 2011;Wada et al. 2016;Abd-Elaty et al. 2021a). Increasing freshwater demand and CC expose coastal groundwater to increasing salinization risks for SWI, especially in waterscarce regions (Polemio and Zuffianò 2020). It can get worse due to human activities and natural processes by reduction in groundwater recharge, over pumping, tidal effects, ocean and seismic waves, dispersion effects, and CC including sea level rise (SLR) (Bear et al. 1999;El Shinawi et al. 2022). SWI management becomes necessary for protection the coastal groundwater resources from salinization (Abd-Elaty et al. 2021b). Around 95% of the world's coastal areas will be severely affected by SLR by 2100, increasing the risk of flooding and SWI (Agren and Svensson 2017). The rise of the global mean sea level is expected to continue. The most recent best assessment is 0.28-0.55 cm by 2100 (IPCC 2021) while it was 18 to 58 cm in 2007 by the Intergovernmental Panel on Climate Change (IPCC 2007), with a rate of rising 8 to 16 mm/year from 2081 to 2100 (IPCC 2014). IPCC (2007) and (2014) indicated that the rainfall has increased in most mid-latitudes and high latitudes, while it has decreased in many mid-latitudes and subtropical arid regions in the 20th century. Abd-Elhamid et al. (2016) investigated the effect of different SLR scenarios on the coastal region of the Nile Delta, Egypt using the SEAWAT code. The results showed that the groundwater salinity has a significant impact by SLR. Mahmoodzadeh and Karamouz (2019) indicated that the storm surge has a shortterm SWI influence while the SLR has a relevant long-term SWI influence on fresh groundwater of a fully heterogenic coastal aquifer using the code SUTRA. Bear and Cheng (1999) presented that optimization of freshwater abstraction and management of salinization risks are the main management challenges for water supply decision-makers.
Abd-Elaty et al. (2020a) used a numerical model of SEAWAT for simulation the SWI in the Gaza Strip aquifer, Palestine using different methods and scenarios to control SWI. The results indicated that the artificial recharge using the treated wastewater could mitigate the SWI compared with the other method for the abstraction of brackish water while the combination of the two methods results the best choice. Abd-Elaty et al. (2021c) simulated the effects of groundwater abstraction and desalination brine deep injection on a coastal aquifer. The results showed that the salinization of the coastal aquifer can be mitigated by reducing the concentration of the water feeding the reverse osmosis plant, i.e., mixing the extracted brackish water with lower salinity water. Luyun et al. (2009) investigated the dynamics of residual saltwater by the construction of cut-off walls. Abdoulhalik et al. (2017) applied the mix of PSB by a semi-permeable subsurface dam and an impermeable cutoff wall; the results showed that mixing physical subsurface barriers (PSB) is effective to control SWI more than a single method. Abd-Elaty et al. (2022a) simulated the management of coastal aquifer salinity using inclined PSB; the results showed that the most positive impact in both cases was achieved for a slope of 1/4, indicating that a moderate vertical inclination of the PSB better preserve coastal groundwater resources. Jiao (2007 and) evaluated with simple calculations the effect of the landfill reclamation realised along the coastline on the groundwater heads and SWI. The results indicated a water table rise on old land and the seaward shift of the salt-fresh water interface. Abd-Elaty et al. (2022b) developed a numerical study using SEAWAT code to investigate the effect of different width of earth fill on the management of SWI in coastal aquifers considering SLR, showing the advantages of this solution.
In this current study, a new approach to retard SWI for sustainable fresh groundwater resources by examining the influence of ABS on SWI for different management methods including physical subsurface barriers, earth fill, check dam, abstraction, and natural or artificial recharge. The different scenarios are compared in terms of the position of the SWI interface, measured as the distance from the coastline at the aquifer bottom using the numerical code SEAWAT to provide a better understanding and a quantitative assessment of different management solutions for SWI in coastal aquifers. Simulations consider hydraulic or physical methods, together with SLR, recharge reduction, and or over pumping, with the different aquifer bed slopes (ABS), using two approaches. The former approach adopts the well-known Henry's problem; the latter is based on the real study case of the Gaza aquifer (Palestine). On these bases, the advantages of each solution are discussed. This study is useful examining the sensitivity of aquifer management under combination of SLR and decrease in aquifer storage for different coastal aquifers study slopes.

Materials and methods
This chapter describes the general characteristics, hypotheses, main data, and boundary conditions concerning the numerical approach to the Henry's problem and to the selected study area of coastal aquifer.

SWI management methods
Different techniques were developed and applied for SWI management (Polemio and Zuffianò 2020). Figure 1 is presented Schematic sketch the SWI management techniques. The Physical Subsurface Barrier (PSB) methods use cut-off walls (CWs) or subsurface dams (SDs), also sheet piling and earth fill (see Fig. 1a and b). The barrier creates a discontinuity between the coastal brackish portion of the aquifer and the inland portion, where fresh groundwater can be safely discharged (Abd-Elaty et al. 2019b). Land reclamation in coastal zones usually occurs by extension of the shoreline towards the sea side using the artificial filling of appropriate soil (see Fig. 1c). The natural aquifer recharge by precipitation takes place over the reclaimed new land.
Hydraulic Barrier (HB) methods use injection by wells or infiltration by ponds of low-quality freshwater or abstraction of saltwater to permit the safe discharge of fresh groundwater of high quality (see Fig. 1d). The artificial recharge technique is man's planned operation used to increase the fresh groundwater heads (Bear 1999). This method is applied to the aquifer through infiltration by surface ponds or recharge wells (Roger 2010) (see Fig. 1e).

Variable density model
The use of numerical modelling supporting the design and selection of management criteria is a reliable choice in the case of groundwater at salinization risk. Modelling can be descriptive or prescriptive, assessing the effects of a specific utilisation scenario or guiding the choice of the optimal scenario respectively (Singh 2012). Tens of scientifically relevant modelling experiences were realised using descriptive or prescriptive models in more than 20 countries (Polemio and Zuffianò 2020).
The finite difference model of SEAWAT 2000 (version 4) was applied and simulated the SWI in the current coastal aquifers. This code couples flow and miscible variabledensity processes of MODFLOW (Harbaugh et al. 2000) and MT3DMS (Zheng and Wang 1999) into a single program.

Hypothetical case study of Henry's problem
Henry's problem (Henry 1964) is used in the current simulation with the domain of 2 m in horizontal (X-direction) to 1 m in vertical (Z-direction) with a width of 0.10 m (Y-direction). The model was subdivided using 4 rows, 80 columns and 40 layers. The flow and contamination boundary conditions of this problem were assigned by a constant hydrostatic saline water pressure at the sea side of the model (right side) which represented the seaside by density (q s ) of seawater equal to 1025 kg m -3 at a constant salt concentration (C S ) of 35 kgm -3 . The aquifer land side (left side), which represents the inland boundary where the fresh groundwater is observed, corresponds to a recharge well with a constant inflow rate (Q in or Q f ) of 0.5702 m 3 day -1 at a constant salt concentration (C F ) by zero kg m -3 . The top and the bottom boundaries of the model are assumed to be no-flow boundaries (Fig. 2).
The seawater intrusion distance (SID) is usually represented by the 0.5 concentration contour line (isochlor) and measured along the bottom boundary from the aquifer seaside (Fig. 5d). The baseline case for the SID reached 64.50 cm in the case of SEAWAT. The results of the SEAWAT were compared with other codes by Henry (1964), Intera (1979), Voss and Souza (1987), Simpson and Clement (2004) and SVCHEM (2018) and given good agreement. Figure 3a shows the Gaza Strip (GS, Palestine), the selected case study for the sea side aquifer slope. The total area is of 365 km 2 , with a coastline length of 45 km along the Mediterranean Sea; the area width ranges from 6 at the north to 12 km at the south (Abu Heen and Muhsen 2016). GS is the most highly populated areas in the world (PCBS 2000), where the annual population growth is approximately 2.9% and the density reached about 4822 capita km -2 in 2015 (PCBS 2015). The climate of GS is semi-arid where the average precipitation ranges between 200 and 400 mm year -1 (PWA 2001(PWA , 2013, and the evaporation rate is about 1400 mm year -1 (SWIMED 2002). Figure 3b is presented the two formations of GS. The Tertiary ''Saqiya formation'' is located below of the GS aquifer and constitutes the aquifer bottom. It is composed by impervious clay shade rocks with thickness ranging from 400 to 1000 m. The Quaternary deposits, covering the Saqiya formation, constitute the Gaza aquifer, with thickness about equal to 160 m. These deposits include loose sand dunes (Holocene) and the Kurkar group (Pleistocene). The top of the Pleistocene deposits is covered by Holocene deposits with thickness of 25 m; the average thickness of the Kurkar Group sequence reaches from 200 to 120 m in the south and the north respectively (Abu Heen and Muhsen 2016;Abu Al Naeem et al. (2019).

The real case study of the Gaza aquifer, Palestine
The GCA transmissivity ranges between 700 and 5000 m 2 day -1 with the hydraulic conductivity of K x and K y are between 20 and 80 m day -1 . The aquifer effective porosity is 35%, the specific yield ranges between 0.15 and 0.30, and the specific storage is 10 -4 m -1 (PWA 2011(PWA , 2015. The longitudinal dispersivity (a L ) and transverse dispersivity (a T ) were 50 m and 0.10 m respectively (Qahman, 2004;(Sirhan and Koch 2013;and Abd-Elaty et al. 2021c). The SEAWAT model of GCA uses 180 columns, one row and 10 layers for active cells. The model is 9000 m in length in x-direction; topography range between ? 58 to -180 m above mean sea level (AMSL). The hydrostatic pressure is assigned at sea side to represent the saline water head while the groundwater flow on the inland side is assigned with freshwater flux using well modules to represent the freshwater recharge. The Lateral freshwater flux (q in ) was set 10 m 3 day 1 m -1 , the well abstraction rates 20.75 m 3 day 1 m -1 , and the vertical recharge and return flow 416.50 Mm year -1 . A constant concentration of 3500 ppm is fixed along the sea boundary while the inland boundary a value of zero ppm is applied. Figure 4 shows the distribution of aquifer salinity by Total dissolved solids (TDS) in the GCA for the current situation (base case). The current results are compared with Sarsak (2011) and Abd-elaty et al. (2020a;2021c). The results showed a good match between the other two models. The 0.5 isochlor reached a distance of 3177 m from the sea shoreline in the horizontal case. The calibrated model is used in the validation process to simulate different scenarios to control SWI intrusion. The total salt mass reached 5,718,820 kg.

Proposed scenarios
This study was simulated three cases of ABS including the sloping towards the sea (seaside slope) with slope by 10 (horizontal) to 1(vertical); the horizontal bed and the sloping towards the land (landside slope) by 10:1 (Fig. 5a, c and e); the 0.5 isochlor for SID reached 59.50, 64.50 and 65.125 cm, respectively (Fig. 5b, d and f). The results showed that the bed slope of aquifer has a relevant effect on saltwater intrusion, in which the land side slope has more intrusion than horizontal and seaside slopes. The study was applied by changing the sea water level at the seaside by 3 cm, 6 cm, 9 cm, 12 and 15 cm while the freshwater flux was decreased by 5%, 10%, 15%, 20% and 25% compared with a rate of (Qin) 0.5702 m 3 day -1 m -1 at the base case for the Henry's problem. For Gaza aquifer, the SLR was assigned by 23.60 cm by 2050 while the natural recharge reduction by 25%. The total of natural recharge and return flow reached 136.60 MCM yr -1 at 2050 compared with a value of 102.68 MCM yr -1 at base case, while the groundwater abstraction reached 288.52 MCM yr -1 at 2050 compared with 175 MCM yr -1 at base case. The SWI for the Henry's problem and the real case of Gaza aquifer was managed by applying the hydraulic and physical methods including physical subsurface barriers, earth fill, abstraction, recharge, combination between abstractions and recharge methods and check dam.

Results and discussions
The model was applied to simulate the effect of SLR, reduction in fresh groundwater by recharge and over pumping.

Effect of SLR and reduction the freshwater recharge on SWI for Henry's problem
Tide log data showed that the sea level increases 1 mm per year over a period of 2 centuries before 1990, while the satellite and tide log data showed an increase of 3.2 mm per year after 1990 (Church and Clark 2013). The SLR trend, decreasing the recharge due to CC, and increasing abstraction (due to increasing population and pro capita water demand) affect large world regions, including the Mediterranean Sea (IPCC 2021). Figure 6a shows the results of combine SLR and reduction of the fresh groundwater storage for the three cases of aquifer bed slopes (ABS) for the seaside, horizontal and landside. The SEAWAT is used for the hypothetical case of Henry's problem to simulate the SWI for the three cases of ABS referred to the hypothetical steady or initial natural conditions. The sea level head was 100 cm at the ocean side and a constant flux to the aquifer by rate of (Qin) 0.5702 m 3 day -1 m -1 at the land side. The expected saline water rises were simulated by increasing sea water level at the seaside by 3 cm, 6 cm, 9 cm, 12 and 15 cm while the freshwater flux was decreased by 5%, 10%, 15%, 20% and 25%, the SID resulted was showed that SLR has a negative impact on aquifer salinity and increase SWI and the land side slope increases the SWI more than horizontal and sea side bed slope where the average percentage of increasing SWI was -57.99%, -52.12% and -50.05%.

Management of SWI for Henry's problem
Management of SWI was carried out using different hydraulic and physical methods including physical subsurface barriers, earth fill, abstraction, recharge and combination between abstractions and recharge methods and check dam to control the SWI due to combine of SLR and reduction in recharge and over pumping.

Effect of physical subsurface barriers
The simulated solution was applied on the three types of ABS using two physical subsurface barriers with the same parameters and boundary conditions at the base case. The former is a cut-off wall, while the latter is a subsurface dam.
Different scenarios were applied, analysing the SWI for different wall depths and dam heights by 15, 30, 45 and 60 cm, assessing the SWI improvement in terms of SID and salt repulsion or salinity reduction (see Fig. 6a and b).The groundwater salt repulsion (%) is    Fig. 6 Relationship between SWI and management techniques for different bed slopes of Henrys problem cutoff wall and subsurface dam for different bed slopes are presented in Fig. 6b and c.

Effect of land reclamation
The technique of earth fill is simulated by increasing the model width to 220 cm using 20 cm of fill with changing the fill hydraulic conductivity by 70%, 55%, 40% and 25% to reach 604.80 m day -1 , 475.20 m day -1 , 345.60 m day -1 and 216 m day -1 for the three bed slopes compare with 864 m day -1 for aquifer hydraulic conductivity (see Fig. 6c). The 0.  Figure 6d is presented the relations between the intrusion length (XT) and the fill earth methods for different bed slopes.

Effect of combine abstraction and recharge
This technique used three cases to investigate the effect of the aquifer abstraction and recharge rates on SWI by (a) abstraction of saline groundwater, (b) recharge with wastewater or storm water, and (c) combination of both. Different settings of ABS were also examined, assessing the SWI improvement in terms of SID and salt repulsion. The recharge well was installed and located at 1 m from shoreline with depth -0.40 m form the model top, while the abstraction well was simulated at 0.40 m from shoreline with depth -0.85 from the model top surface with recharge and abstraction rates of 0.11404 m 3 per day per meter.  Fig. 6e-g. Fig. 6 h.

Effect of check dams
The results showed that the average values for SWI repulsion were 26.88%, 30.09%, and 28.66% using cut-off wall and ? 10.38%, ? 12.45% and ? 13.55% using the subsurface dam for ABS for the sea side, horizontal and land side respectively. The cut-off walls are more effective for horizontal bed slopes, while the subsurface dam for land side slopes. The use of land fill is an advantageous method in land side slopes where the SWI repulsion reached ? 15.92%, ? 18.90%, and ? 20.11% (see Table 1).
The use of hydraulic methods of the freshwater recharge led to repulsion of ? 30.13%, ? 30.27% and ? 30.57%, while the using of abstraction of brackish water reached ? 7.64%, ? 6.97% and ? 6.48% The combination of freshwater recharge and brackish water abstraction led to ? 34.55%, ? 34.38% and ? 34.41%. These results indicated that recharge methods are more effective in the case of land side bed slope while the abstraction and combination scenarios were more effective in the case of sea side bed slope. The check dam led to SWI repulsion of ? 44%, ? 46.70% and ? 43.82%, which indicates that check dams are effective in horizontal bed slopes (see Table 1).

Effect of SLR and reduction the freshwater recharge on SWI for the GCA
The effects of SLR and the reduction in fresh groundwater storage by decreasing in flow to the aquifer by recharge and increasing the wells abstraction rates on GCA were simulated by changing boundary conditions and hydrogeological parameters. SLR consists of a change of saline water head equal to 23.60 cm by 2050. The natural recharge reduction was simulated with reduction of precipitation and lateral flow by 25%. The practical effect of these hypothesis reduced the recharge contributions to 36.15 and 19.35 MCM yr -1 respect to 48.20 and 26.60 MCM yr -1 at base case (see Table 2). The aquifer return flow by leakage from the domestic, agriculture and wastewater sectors should increase to reach 62.56, 16 and 21.89 MCM yr -1 for each sector, to be compared with 28.50, 16 and 9.98 MCM yr -1 respectively. This should be done due to abstraction increase, which should be necessary to satisfy the increasing water demand by over population. The total return flow should reach 100.45 MCM yr -1 compare with 54.48 MCM yr -1 at base case.
The total of natural recharge and return flow could be considered equal to 136.60 MCM yr -1 at 2050 compared with 102.68 MCM yr -1 at base case.
The groundwater abstraction should increase reaching 288.52 MCM yr -1 at 2050 to be compared with 175 MCM yr -1 at base case. Table 2 summarizes the entire simulated modifications at 2050. The results of equi-concentration line 35,000 ppm are shown in Fig. 7, the intrusion length reached 6281 m from shore line measured at aquifer bottom and the salt mass is reached 1.04621 9 10 7 kg.

Management of SWI for Gaza aquifer
The GCA is an extremely interesting case study of real sea bed slope. The results of GCA simulations permit a deeper discussion and validation of the theoretical assessments realised with Henry's problem approach.

Effect of physical subsurface barriers
The physical subsurface barrier is installed at 3000 m from the shoreline with hydraulic conductivity equal to 1 9 10 -5 m day -1 , the bottom of the cut-off wall level is (-101.00) from MSL and (? 45.00) from the ground surface, while the top subsurface dam is carried out at level (-73.00) and the bottom at level (-176.00) above MSL. The SID reached 3,035 m and 3,002 m from shoreline, the salt mass is reached 9,999,650 and 10,453,700 kg for the two cases respectively (see Fig. 8a and b).

Effect of land reclamation
The land fill depth is ranged from level (-9.30) to (-20.70) from MSL with a length of 1200 m from the shoreline, the fill hydraulic conductivity is 0.10 m day -1 . The SID reached 5510 m, as presented in Fig. 8c. The aquifer salt mass reached 9,116,411 kg.

Effect of combine abstraction and recharge
Abstraction well and recharge well to manage the SWI in the case of GCA were simulated. Three cases are considered: the first is the recharge of treated wastewater, the second is the abstraction of brackish water and the third is a combination of recharge and abstraction. The total expected production from wastewater in the Gaza strip will be reached 109.47 MCM yr -1 and the leakage is 21.89 MCM yr -1 so the total volume of wastewater will be 87.58 Mm 3 /year at 2050. Production of treated wastewater increases gradually by an increment of 2 MCM yr -1 (Sirhan 2013). The actual value of wastewater treatment could be assessed as equal to 80 MCM yr -1 by 2050. The excess quantity of untreated wastewater is disposed to the Mediterranean Sea; the volume is assessed equal to 31.90 and 7.58 MCM yr -1 by 2010 and 2050 respectively. The recharge well was located at 6000 m from shore line with a depth -60.00 form MSL. The SID reached 3,350 m with a salt mass of 6,028,400 kg.
The future desalination volume is expected to 129.74 MCM yr -1 by 2035 for the long term (PWA 2011). This modification was simulated using the same value by 2050 and installing abstraction wells from brackish water. The abstraction well was simulated at 3000 m from shore line with depth -160.00 from MSL. SID reached 2990 m with salt mass of 1.00089 9 10 7 kg. Combining recharge and abstraction wells, SID reached 2,933 m with a salt mass is 6,413,380 kg (see Fig. 8d-f).

Effect of check dams on SWI
In this scenario the GCA was simulated adding check dam. The head of dam is (? 7.00) AMSL and distance from 1400 to 1800 m from shore line. The results of this scenario are presented in Fig. 8g; the SID reached 4,203 m from shore line with the aquifer salt mass is 7,918,470 kg (Table 4).
Considering as reference the base case (Run 1, Table 3) of the Gaza aquifer, the global change scenario, describes huge effects with increases in terms of SID, equal to 3,104 m, and salt volume, equal to 4,743,280 kg. In terms of management initiatives, the worst solution seems the earth fill (Run 5), without improvements both in terms of SID and total salt volume. Very low is the SID improvement with cut-off wall (Run 3) and subsurface dam (Run 4) solutions, which are unable to avoid a huge increase of total salt volume.The use of recharge (Run 6) with or without abstraction (Run 8) offers the best results. Referring to the base case, the SID variation is 173 and -244 m and the salt total volume variation is 309,580 and 694,560 for recharge and recharge with abstraction respectively.

Conclusion
Saltwater intrusion in coastal aquifers is a natural phenomenon which can cause increasing groundwater quality degradation due to the global change. This study was assessed numerically the efficiency of different management solutions in terms of salt repulsion and SID modifications using a conceptualised aquifer and a real aquifer. The coastal aquifers or the portion of those with a side bed slope resulted in more proneness to SWI than sea side and horizontal bed slope cases. The cut-off walls and check dams reach the best efficiency with horizontal bed coastal aquifers. The efficiency of the subsurface dams, earth fill, and recharge of freshwater prevails for aquifers with land bed slopes while the abstraction of brackish water and the combination of freshwater recharge with brackish water abstraction are prevail in the case of sea side slopes. The efficiency of these solutions was tested for the Gaza coastal aquifer, a real sea bed slope aquifer, the type more prone to SWI. The main results showed the huge relevance of global change effects on this aquifer but also highlighted the optimal management solutions, mainly focused on the recharge with treated wastewater. Future research efforts will concern a real aquifers with different slopes bed and efforts to enlarge the research to the effects of the third dimension, operating with tank laboratory experiments and real aquifers.
Acknowledgements The authors are thankful to the Department of Water and Water Structures Engineering, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt, for constant support during the study.
Authors' contributions IA-E conceptualization, software; data curation; writing; IA-E and MP reviewing and editing methodology, original draft preparation; MP supervision.
Funding Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB). This study did not receive any funding.
Data availability Upon request.
Code availability Upon request.

Declarations
Conflict of interest The authors declare no conflict of interest.

Consent for publication Yes
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