Assessment of Complex Terminal Groundwater Aquifer for Different Use of Oued Souf Valley (Algeria) Using Multivariate Statistical Methods, Geostatistical Modeling, and Water Quality Index

: This research aims to assess the hydrogeochemical evolution of the groundwater in Oued souf valley for drinking and irrigation purposes. To achieve this, 49 groundwater samples from the complex terminal were examined and treated concurrently with multivariate statistical methods, geostatistical modeling and the WQI (water quality index). Focusing on the physico-chemical parameters, Q mode clustering analysis detected four major water groups, where the mineralization augmented from group 1 to group 4. The hydro-chemical type was the same, Ca-Mg-Cl-SO 4 for all the groups. Calcite, dolomite, anhydrite, and gypsum would be the dominant reactions with the undersaturation of evaporates minerals, based on geochemical modeling, while the carbonate minerals are precipitating. Geostatistical analysis using ordinary Kriging demonstrated the exponential semi-variogram model ﬁtted for EC (electrical conductivity), Ca 2+ (calcium), Mg 2+ (magnesium), K + (potassium), HCO 3 − (bicarbonate), Cl − (chloride), and SO 42 − (sulfate). At the same time, the rational quadratic model was the best-ﬁtted semi-variogram model for Na + (sodium) and NO 3 − (nitrate). EC, SO 42 − , and NO 3 − have a strong spatial structure, while Ca 2+ , Na + , K + , and HCO 3 − have a moderate spatial structure. Moreover, there was a weak spatial structure for Mg 2+ and Cl − . The WQI shows that CT (complex terminal groundwater aquifers) are not suitable for drinking and their quality for irrigation ﬂuctuates from excellent to moderate quality.


Introduction
Natural resources are very limited and continuously degraded due to climate change, rapid population growth, poor management, and misunderstanding of the resources' nature caused by the miscoordination and approaches' integration. Among all, water is the primary natural resource and the most vital one, which is responsible for nourishing and productivity functions of any ecosystem. Despite this natural resource being limited spatially and temporally to humans and other living beings, many problems related to its sustainability are due to humankind's competition over it [1]. The main agricultural activity in the Oued souf valley, depicted by a land use/land cover map published in [27], is irrigated agriculture, especially palm tree cultivation. However, in recent years, agriculture in Oued souf has extended to include other crops, such as pivot-irrigated potatoes [28], olives, maize, and other varieties of vegetables. However, all of these crops are irrigated from the uppermost aquifer (water table or phreatic aquifer) that runs underneath the entire Oued souf field. The local farmers have created an original method for palm tree cultivation called ghouts, which consists of digging on the dune's vast basins in which the palm trees are planted and consequently using the phreatic groundwater aquifer for growing. The majority of the existing crops need vast quantities of fertilizers and increased production, influencing groundwater quality. The potential source of pollution can also be represented by the urban areas that have been spreading since 1972. Consequently, the increase of wastewater discharges contributes to groundwater pollution [29]. However, to meet the needs for drinking water The main agricultural activity in the Oued souf valley, depicted by a land use/land cover map published in [27], is irrigated agriculture, especially palm tree cultivation. However, in recent years, agriculture in Oued souf has extended to include other crops, such as pivot-irrigated potatoes [28], olives, maize, and other varieties of vegetables. However, all of these crops are irrigated from the uppermost aquifer (water table or phreatic aquifer) that runs underneath the entire Oued souf field. The local farmers have created an original method for palm tree cultivation called ghouts, which consists of digging on the dune's vast basins in which the palm trees are planted and consequently using the phreatic groundwater aquifer for growing. The majority of the existing crops need vast quantities of fertilizers and increased production, influencing groundwater quality. The potential source of pollution can also be represented by the urban areas that have been spreading since 1972. Consequently, the increase of wastewater discharges contributes to groundwater pollution [29]. However, to meet the needs for drinking water and irrigation due to the economic and demographic development of the region, intensive pumping was applied on deep groundwater aquifers (complex terminal and continental intercalary) for different uses, but without sufficient treatment and discharge, these quantities return to the phreatic aquifer [30].
To save the region, it was necessary for the Algerian authorities to release a megaproject to stop the rising groundwater, however this project failed due to several problems [31]. The Oued souf region is diversified between a hot and dry summer and a mild winter, making it very similar to other regions of the Algerian Sahara [32]. The rainfall is typi-Water 2021, 13, 1609 4 of 26 fied by low, oscillatory, and infrequent precipitation, with an annual average of 5.90 mm, according to statistical analysis of meteorological data gathered from the meteorological station of Oued souf airport between 1978 and 2016. Evaporation, with an annual average of 181.18 mm, greatly outnumbers rainfall. The region's average maximum temperatures range from 20.76 • C in January to 45.31 • C in July, with average minimum temperatures ranging from 9.62 • C in January to 30.18 • C in August.

Geology and Hydrogeology
The Oued souf valley can be described as a synclinal layer formed on a pre-Cambrian tucked basement and filled discordantly by thick Meso-Cenozoic sedimentary formations, and ultimately by detrital, carbonate, or evaporate deposits. However, all of these sedimentary deposits are surrounded by dunes and are pebbly or gravely. Meanwhile, these formations are known as the eastern part of the Great Oriental Erg.
The tormented reliefs of the Great Oriental Erg are found on the basis of a quaternary structure made up of a number of dense and homogeneous tens of meters of eolian sand. This structure comprises the water table, with a descending substratum forwarded to the north. The groundwater of this formation with superficial runoff is expanding in the salty soil lagoons, where it will be evaporated and deposited as a superficial salt crust [8].
Lithostratigraphically, the study area consists primarily of limestone, marly clays, marls, gypsiferous marly clays, and gypsiferous marly clays with lagunal facies on top, from the Cretaceous to the Eocene (gypsum, anhydride, salts, and dolomitic passages). All of this is topped by the Neogene, which is composed of Oligocene conglomerates and shale, as well as Mio-Pliocene sub-horizontal red sandy clays and gypsiferous sandstone lentils. Meanwhile, Plio-Quaternary fine sands with limestone crusts cover everything in a single layer [33]. Furthermore, these sands contain 90% quartz crystals, gypsum, and silicates such as Feldspars and silicate accessories such as epidote zircon, rutile, tourmaline, and garnet, as well as limestone concretions; as a result, they are formatting the possible aquifer ( Figure 2) [34,35]. In terms of hydrogeology, the geomorphology and sedimentation of the basin have intensified permeation and subterranean flow of precipitated water on outcrops of concentric halos across the periphery. The alternation of permeable and impermeable deposits ensured their charging as they flowed into the depressed regions. Favorable paleogeographic and geological conditions that occurred during ancient rainy cycles are  In terms of hydrogeology, the geomorphology and sedimentation of the basin have intensified permeation and subterranean flow of precipitated water on outcrops of concentric halos across the periphery. The alternation of permeable and impermeable deposits ensured their charging as they flowed into the depressed regions. Favorable paleogeographic and geological conditions that occurred during ancient rainy cycles are the factors that contributed to groundwater formation [34]. The continental intercalary aquifer (CI), the terminal continental or complex terminal aquifers (CT), including the limestone aquifer (Senonian-Eocene), sand aquifer (Mio-Pliocene), and quaternary aquifer or water table, are the aquifers of Oued souf valley.

Piezometry
According to the data obtained from Agence Nationale des Ressources Hydraulique (ANRH) during 2015-2016, the covered study area is drilled by 49 wells, three of which are intended for irrigation and are located in the central city of El Oued, while the others are designed for drinking water supply, spreading over the other covered study area. However, 26 wells are from the Mio-Pliocene aquifer and 23 wells are from the Pontian aquifer. The most bottomless well is located in Guemmar municipality, with a depth of 398 m. This well belongs to the Mio-Pliocene aquifer. Additionally, the lower depth is 265 m in the same municipality, intended for drinking water. In the covered study area, the total abstraction is 67,820,480.64 m 3 /year.
In contrast, the biggest extraction is in W25, located in Guemmar for drinking water supply but from the Pontian aquifer. According to the piezometric map illustrated in Figure 3, the overexploitation of the complex terminal aquifer is represented by a high groundwater level in different municipalities and is clearly noted in the south to the middle part of the study area, in El Oued, Bayadha, Mih ouensa, Hassi khalfa, and Robbah. At the same time, the lowest levels are located in the northern part of the study area, in Magrane, Debila, Reguiba, and Guemmar. The piezometric level shows that the flow direction is from the south (recharge area) to the north (discharge area), towards Chott Melrhir and Chott Merouane in the north of the study area. Robbah. At the same time, the lowest levels are located in the northern part of the study area, in Magrane, Debila, Reguiba, and Guemmar. The piezometric level shows that the flow direction is from the south (recharge area) to the north (discharge area), towards Chott Melrhir and Chott Merouane in the north of the study area.

Sampling and Analysis
Forty-nine (49) groundwater samples were collected and analyzed by Agence Nationale des Ressources Hydrauliques (ANRH) of Oued souf from the complex terminal

Sampling and Analysis
Forty-nine (49) groundwater samples were collected and analyzed by Agence Nationale des Ressources Hydrauliques (ANRH) of Oued souf from the complex terminal aquifer of the Oued souf region during March 2019 (precisely, El Oued, Debila, Guemar, Kouinine, Ourmas, Reguiba, and Taghzout), including 26 groundwater samples from Mio-Pliocene aquifers and 23 samples from the Pontian, where these wells are intended for domestic and agricultural use. The sampling took place in March of this year. After a brief pumping time in polyethene bottles, the procedure was carried out. The physical parameters temperature, electrical conductivity, and pH were recorded on-site using a Multi-350 i. Multi-parameters. Analyses of the elements Cl − (chloride), HCO 3 − (bicarbonate), SO 4 2− (sulphate), Ca 2+ (calcium), Mg 2+ (magnesium), Na + (sodium), K + (potassium), and NO 3 − (nitrate) were performed by volumetry, UV-visible spectrometry, and flame spectrophotometry [36].
The validation of the analytical results has been carried out by the calculation of the charge balance errors (%E), which was <5% with a negative value, indicating the dominance of the anions in our groundwater samples. Microbiological analyses have also been performed by ANRH, including several parameters such as total germs, total and fecal coliforms, fecal streptococci, and clostridium sulfito reductor, with different areas for the cultivation.

Clustering Analysis
A method for classifying cases or variables based on their variance or resemblance is hierarchical cluster analysis. It is widely used, particularly for hydrochemistry investigations, to classify hydrogeochemical processes in groundwater by clustering collected water samples into distinct groups important in the geological and hydrogeological sense. Furthermore, this unsupervised grouping will distinguish water quality variables based on their similarity. Euclidean distances were used to classify parameters into initial clusters, whilst Ward's agglomeration method was used to link the resulting initial clusters [37][38][39][40][41][42][43].

Hydro-Chemical Analysis
The hydro-chemical recognition was performed by constructing diagrams such as the Piper diagram [44] and Chadha diagram [45], while Gibbs diagram [46] was also used to identify the main mechanisms governing the chemistry of groundwater.

Geostatistical Modeling
Geographical information system (GIS) applications are helpful tools to find the spatial distribution of groundwater quality parameters by integrating spatial data with other information to facilitate environmental protection and resource planning [47,48], and also for the evaluation of groundwater quality by the intervention of geostatistics [49,50]. Geostatistics is a mathematical tool concerned with spatial correlation schemes and the variogram, a quantitative spatial correlation measure commonly used in geostatistics [51]. Meanwhile, interpolation techniques such as Kriging will provide a neutral, best linear approximation of a regionalized vector in non-sampled locations [52][53][54].
Kriging, which can approximate the interpolation error of the values of the regionalized variable where there are no original measurements, is one of the best methods in geostatistics for interpolation at unsampled sites. Kriging is a method for estimating the spatial distribution of a variable's reliability and precision. A semi-variogram, which is mathematically defined by the equation below, can be used to quantify spatial dependence: γ (h) illustrates the semi-variogram as a function of the lag distance or separation vector, h, between two pints, N (h) represents the number of observation pairs divided by distance, h, and Z (Xi) represents the random variable at position Xi [55]. Ordinary Kriging is a linear appropriate interpolation technique that can produce predictive maps and was available in the ArcGIS (made by Environmental Systems Research Institute (Esri) in United States (California)) geostatistical extension. The spatial distribution, on the other hand, can be determined using the equation below [56]: where Z(X0) is the predictable value at X0 points, while n is the number of the sampled point, Z(Xi) is the recognized value at sampled Xi points, and λ is the weight assigned to the sampled point. The geostatistical analysis was performed using ArcGIS 10.4.1 software for generating spatial distribution maps.

Assessment for Drinking Purposes
The water quality index is a valuable tool for determining the quality of groundwater and whether it is suitable for drinking or irrigation [57,58]. Water quality index is a rating system that shows the cumulative impact of water quality parameters on total water quality. Furthermore, combining nuanced data and creating a score that describes water quality status is considered a convenient and easy way for decision-makers to gain a deeper understanding of the quality of surface/groundwater sources [59], where its formula is as follows [60]: The ith parameter's quality rating is Q i , and each parameter's W unit weight is n number of parameters.
where Vi is the ith parameter's observed value, V0 is the ith parameter's ideal value in pure water, V0 is zero for all parameters except pH = 7.0, and Si is the ith parameter's standard permitted value. Computation of unit weight, Wi, is contrarywise proportionate to the standard permissible value, Si, for water quality parameters: where K represents the weights' proportionality constant: When the WQI is less than 50, it is called excellent, decent (100-125), bad (125.1-150), very poor (150.1-175), and unfit for drinking when the WQI is greater than 175 (175-200).

Irrigation Suitability Assessment
The assessment of complex terminal groundwater samples for irrigation usage was performed by different ionic parameters in meq/L based on various indices, such as electrical conductivity (EC) (µS/cm) [61], total hardness (TH) [62], and alkalinity hazard (SAR), which is the fraction of Na+ ions in the water sample to Ca 2+ and Mg 2+ ions. As a result of constant usage of sodic water, the SAR is used to assess the potential for Na+ to build in the soil, predominantly (water flow) at the expense of Ca 2+ , Mg 2+ , and K + [61]. The percent Na is also employed in irrigation water classification. Na + is an important characteristic that aids in the classification of any water source for irrigation purposes. Na + binds to the soil chemically, reducing the soil's ability to transfer water. Alkaline soils are formed when Na + reacts with CO 3 2− , whilst saline soils are formed when Na + combines with chloride. Crop development is slowed by sodium-affected soil (alkaline/saline) [63].
Alkaline earths (Ca 2+ and Mg 2+ ) are usually in a condition of equilibrium in groundwater. Both Ca 2+ and Mg 2+ ions are associated with soil friability and aggregation, and both are important nutrients for crop growth. The presence of high concentrations of Ca 2+ and Mg 2+ in water can elevate soil pH (converting the soil to a saline state), reducing phosphorus availability. Magnesium in excess in groundwater degrades soil quality by turning it alkaline, resulting in lower agricultural yields. Excess Mg 2+ ions in water, according to agriculturists, degrade soil quality, resulting in low crop productivity, and this is expressed by MH (magnesium hazard) [64]. The RSC (residual sodium carbonate index) presents the amount of bicarbonate/carbonate and calcium/magnesium in irrigation water. Precipitation of Ca 2+ and Mg 2+ occurs when the concentrations of carbonate (CO 3 2− ) and bicarbonate (HCO 3 − ) ions surpass the concentrations of Ca 2+ and Mg 2+ ions. It details the leftover NaCO 3 that is missing if the carbonates are fewer than alkaline earths (Ca 2+ + Mg 2+ ).
An overabundance of CO 3 2− and HCO 3 − causes soil Ca 2+ and Mg 2+ to precipitate, affecting soil structure and potentially activating soil sodium [65]. The permeability index (PI) is a metric used to determine whether water is suitable for irrigation. The capacity of soil to transport water (permeability) is influenced by the long-term usage of irrigation water (with a high salt content), as well as the soil's Na + , Ca 2+ , Mg 2+ , and HCO 3 − ions [66]. The KR (Kelley ratio) is another indicator for determining the quality and classification of water for irrigation purposes, which is based on the ratio of Na + to Ca 2+ and Mg 2+ [67].
All indices are expressed by the following equations:

Geochemical Modeling
Geochemical modeling was performed using PHREEQC interactive software (made by United States Geological Survey (USGS) in united states) on our measured data for defining the chemical reactions and aqueous speciation in the aquifer system, and subsequently to assess the equilibrium state among groundwater and the existing minerals relating to the saturation index (SI) [68], which is calculated using the following equation: where SI is the saturation index of the mineral, while IAP is the ion activity product of the dissociated mineral, and Kt is equilibrium solubility at mineral temperature. The groundwater is being under-saturated when SI < 0 of a particular mineral (mineral dissolution condition). SI > 0 indicates the oversaturation of a particular mineral (precipitation condition), whilst S = 0 reflects the equilibrium state. Chloralkaline indices were computed to comprehend the cation exchange process incidence in the study area based on [69] the equations (meq/L): Table 1 shows a statistical description of the analyzed physicochemical parameters and measured groundwater samples. Meanwhile, a microbiological examination of the complex terminal groundwater aquifer reveals the absence of microbiological contamination. The pH levels range from 7.23 to 7.84, with a mean of 7.49. Whereas, in the study area, 100% of groundwater samples were in the range of 7.2-8.5, meaning low alkaline groundwater type, and all pH values were within the WHO (2011) acceptable range for drinking. The groundwater samples ranged in temperature from 11.8 to 35.1 • C. For the electrical conductivity devoted to the different salts dissolved in the groundwater samples, the results portray that the existence of wide variations of the electrical conductivity varied widely, from 2760 to 4730 µs/cm, the mean is 4131.48 µs/cm, and all the recorded values (100% of groundwater samples) exceeded the WHO standards for drinking purposes. A similar trend is observed for the total dissolved solids (TDS) and salinity. TDS in the study area varied from 1766 to 3027 mg/L, with a mean of 2650.918 mg/L, and 100% of groundwater samples were found to exceed the limit of WHO standards. The dissolved matter forms, which consist of inorganic salts, organic matter, and dissolved gases, are the responsible factors that contribute to TDS. However, TDS can classify the groundwater samples as 100% slightly saline, and all of them exceeded WHO standards for drinking purposes. Additionally, the salinity and dry residue are varied from 1.8% to 3% and from 1900 to 3980 mg/L respectively, and 3075.102 mg/L was the average value.

Cluster Analysis
All major ions (Ca 2+ , Mg 2+ , Na + , K + , Cl − , SO 4 2− , HCO 3 − , and NO 3 − ), EC, TDS, salinity, TH, TA, turbidity, temperature, and dry residue were regarded on the normalized data to establish potential hydro-chemical groups that occurred in the groundwater samples using hierarchical clustering analysis (Q-mode). To compute the similarity of water samples, Ward's linkage technique and Euclidean distance were used to execute HCA. A dendrogram of spatial HCA was generated in Figure 4.   Four groups of groundwater samples were created ( Figure 4). The most significant element in distinguishing these classes seems to be EC (Table 2). It is augmenting exponentially from group 1 to group 4. All these groups are plotted in a Piper plot to identify the geochemical evolution of water type. The physicochemical parameters of groundwater groups were compared to the World Health Organization (2011) for drinking water purposes, including statistical analyses.
Hydrochemistry of groundwater aquifers is one of the most difficult to interpret in more or less complex sedimentary environments because of the heterogeneity of the mineralogical chemical properties of the studied area [70]. The average EC of three wells in group 1 (W22, W13, and W5) is 3000 s/cm, indicating considerable mineralization and hence brackish water. A large number of wells are found in the recharge zone and are part of the Mio-Pliocene aquifer. The abundance of major ions is Na + + K + > Ca 2+ > Mg 2+ and Cl − > SO 4 2− > CO 3 2− + HCO 3 − > NO 3 − , in that order, Figure 5. The hydrochemical facies are characterized by Ca-Mg-Cl-SO 4 type, CaCl type, and chloride type, while one sample is of magnesium type, according to the piper plot in Figure 6. The dominance in this group is devoted to chloride (min = 631.06 mg/L, max = 787.06 mg/L, and mean = 706.7 mg/L), then calcium (min = 240.48 mg/L, max = 280.56 mg/L, and mean = 260.52 mg/L) and magnesium (min = 85.07 mg/L, max = 121.53 mg/L, and mean = 101.27 mg/L), and sulphates (min = 568.33 mg/L, max = 654.02 mg/L, and mean = 621.57 mg/L). In contrast, the concentration of nitrate has been lower compared to the other elements (min = 1.911 mg/L, max = 34.9 mg/L, and mean = 22.39 mg/L). Chloride, calcium, magnesium, and sulphates exceeded the desirable WHO 2011 standards for drinking water, while nitrate did not exceed the standards. Hydrochemistry of groundwater aquifers is one of the most difficult to interpret in more or less complex sedimentary environments because of the heterogeneity of the mineralogical chemical properties of the studied area [70]. The average EC of three wells in group 1 (W22, W13, and W5) is 3000 s/cm, indicating considerable mineralization and hence brackish water. A large number of wells are found in the recharge zone and are part of the Mio-Pliocene aquifer. The abundance of major ions is Na + + K + > Ca 2+ > Mg 2+ and Cl − > SO4 2− > CO3 2− + HCO3 − > NO3 − , in that order, Figure 5. The hydro-chemical facies are characterized by Ca-Mg-Cl-SO4 type, CaCl type, and chloride type, while one sample is of magnesium type, according to the piper plot in Figure 6.   Group 2 consists of wells (2, 20, 21, 8, 10, 17, 9, 4, 7, 16, 11, 18, 12, 14, 3, 28, and 44). These wells represent 34.69% of the water samples in the study area, where 20.41% of these wells are in El Oued municipality and consist of wells 2, 3, 4, 7, 8, 9, 10, 11, 12, and 14, that belong to the Mio-Pliocene aquifer, and 10.20% of water samples are in Debila (16, 17, 18, 20, and 21), belonging to the Mio-Pliocene aquifer. However, 2.04% of water samples divided between Guemar (W28) and Reguiba (W44) belong to Mio-Pliocene and Pontian, respectively. Extremely high salinity distinguishes this group (3650 < EC < 4430 µS/cm, mean = 4005.44 µS/cm), indicating brackish water. The order of major ions' abundance follows the same order as group 1 ( Figure 5), with hydro-chemical facies characterized by Ca-Mg-Cl-SO4 type, CaCl type, and chloride type ( Figure 6A). Chloride is simply the most dominant element in this group (min = 815.42 mg/L, max = 1240.86 mg/L, and mean = 976.9 mg/L).In this group Calcium and magnesium were dominated (min = 204.36 mg/L, max = 340.68 mg/L, and mean = 263.24 mg/L for calcium and min = 63.19 mg/L, max = 184.72 mg/L, and mean = 124.26 mg/L for magnesium) values being somewhat lower, while sulphates have been found also high (min = 602.39 mg/L, max = 978.26 mg/L, and mean = 764.12 mg/L). However, chloride, calcium, magnesium, potassium, and sulphates exceeded the desirable WHO 2011 standards for drinking water, while nitrate did not exceed the standards.  (Figure 5). Furthermore, the hydro-chemical facies are characterized by Ca-Mg-Cl-SO 4 type and CaCl type ( Figure 6A Group 4 consists of nineteen wells (6, 24, 40, 32, 33, 34, 42, 43, 46, 29, 37, 45, 39, 38, 23, 35, 26, 36, and 48), with a mean EC of 4348.95 µs/cm, indicating brackish water: 21.05% of the wells belong to the Mio-Pliocene aquifer (6, 23, 36, and 37) located in El Oued, Guemar, and Kouinine, while 78.95% belong to the Pontian aquifer and are distributed in Guemar, Ourmes, Kouinine, Reguiba, and Taghzout. The concentration of major ions is Na + > Ca 2+ > Mg 2+ and Cl − > SO 4 2− > HCO 3 − > NO 3 − , in that order ( Figure 5). The Piper plot also confirmed that hydro-chemical facies are Ca-Mg-Cl-SO 4 type, CaCl type, and chloride type ( Figure 6A). This group is dominated by chloride and sulfate (min = 730. 33  The Chadha plot in Figure 6B represents most of the samples (97.96%) in the 6th field (reverse ion-exchange Ca-Mg-Cl/SO 4 water type), revealing Ca-Mg-Cl type, Ca-Mgdominant Cl type, or Cl − -dominant Ca-Mg type waters (alkaline earth (Ca 2+ + Mg 2+ ) exceed alkali metals (Na + + K + ) and strong acidic anions (Cl − + SO 4 2− ) exceed weak acidic anions (HCO 3 − )), confirming the Piper diagram's results. On the other hand, 2.04% are plotted in the 7th field (seawater Na-Cl, which indicates that alkali metals exceed alkaline earth and strong acidic anions exceed weak acidic anions), which is more enhanced in (Ca 2+ + Mg 2+ ) and (Cl − + SO 4 2− ) than (HCO 3 − ).

Water Quality Index
In this study, the computation of WQI obtained values was compared to the WHO (2011) guidelines. Furthermore, ten parameters have been used in the calculation of the WQI for drinking purposes, EC, pH, Ca 2+ , Mg 2+ , Na + , K + , Cl − , SO 4 2− , HCO 3 − , and NO 3 − . All wells were classified above 50. Nevertheless, 10.20% of wells had good water quality (11.54% Mio-Pliocene and 8.70% from the Pontian), 24.49% of samples had poor quality (15.38% from Mio-Pliocene and 34.78% from the Pontian), while 55.10% had very poor quality (61.54% of Mio-Pliocene and 47.83% of Pontian). Furthermore, 4.08% are unfit for drinking purposes, including 7.69% of the Mio-Pliocene aquifer (Table 3).

Geostatistical Modeling
The normalcy of the studied water parameters was taken into account, for performing the Kriging interpolation. On the basis of the mean error (ME) and root mean square normalized error (RMSSE) values, the best-fitted semi-variogram models were selected. The model is evaluated based on the precision of the predictions when ME is minimum, and RMSSE is close to unity.
The most important hydro-chemical parameters were fitted to the exponential semivariogram model, including EC, Ca 2+ , Mg 2+ , K + , Na + , HCO 3 − , Cl − , NO 3 − , and SO 4 2− . The rational quadratic model was the best-fitting semi-variogram model for Na + and NO 3 − . Depending on the nuggets' variance/sill ratio. Moreover, diverse classifications were accustomed to describ the spatial dependence of hydro-chemical groundwater parameters. There were three forms of spatial dependence considered in this study: strong when the ratio is less than 25%, mild when the ratio is between 25% and 75%, and weak when the ratio is greater than 75% (Table 5). In the study area, EC, SO 4 2− , and NO 3 − have a strong structure of spatial dependance, while Ca 2+ , Na + , K + , and HCO 3 − have a moderate spatial structure. Mg 2+ and Cl − both have a weak spatial structure of spatial dependance.
The spatial distribution of the EC (Figure 7) shows that the mineralization increases from the east of the study area towards the west and southwest part as a result of the local geology of the region in addition to the serious situation of some wells of the complex terminal, which present perforations in the level of casings, which favor the communication and the contact between the phreatic aquifer, which is also characterized by high mineralization. and Mg 2+ . Low values were found in the north of the study area around Sidi Aoun and Guemar, while the highest values were observed in the southwest of the study area. The lowest values of Mg 2+ were located near Guemar, southwest of Debila, south of El Oued, and Kouinine. Furthermore, a high value was also noted in the southwest, as shown in Figures 8B and 9C.  The spatial distribution maps for Ca 2+ , HCO3 − , Na + , K + , and Cl − show a hi heterogeneity due to the high geological variation areas as well as the depth of each we Ca 2+ concentrations are low to the south of El Oued, while the high values were found Debila, Sidi Aoun, and Kouinine. Ca increased in the south of the study area (Kouinin and in the northwest and around Debila and Sidi Aoun. At the same time, it was decreas from Guemar towards El Oued, until Bayadha. Additionally, HCO3 − increased from Oued (southeast) to the northwest and southwest, as shown in Figures 8A and 9B.
The existence of sodium is linked, in essence, to the dissolution of halite (evaporate Indeed, sodium, as for chlorides, displays high and non-homogeneous contents in t waters of the complex terminal (CT). The sodium levels in the CT groundwater samp decreased in the northeast of the study area, near Debila, and in the northwest. Figur  8C and 9A show that the chloride concentration increases from the west to the east.
Potassium comes mainly from evaporites, in this case, sylvite (KCl), or as a result an alteration of potassium clays in the phreatic and complex terminal aquifer. The stu The spatial distribution maps for Ca 2+ , HCO 3 − , Na + , K + , and Cl − show a high heterogeneity due to the high geological variation areas as well as the depth of each well. Ca 2+ concentrations are low to the south of El Oued, while the high values were found in Debila, Sidi Aoun, and Kouinine. Ca increased in the south of the study area (Kouinine) and in the northwest and around Debila and Sidi Aoun. At the same time, it was decreased from Guemar towards El Oued, until Bayadha. Additionally, HCO 3 − increased from El Oued (southeast) to the northwest and southwest, as shown in Figures 8A and 9B.
The existence of sodium is linked, in essence, to the dissolution of halite (evaporates). Indeed, sodium, as for chlorides, displays high and non-homogeneous contents in the waters of the complex terminal (CT). The sodium levels in the CT groundwater samples decreased in the northeast of the study area, near Debila, and in the northwest. Figures 8C and 9A show that the chloride concentration increases from the west to the east. and north of El Oued. The high values of nitrates confirm the dilution between th phreatic groundwaters and the complex terminal flows, resulting in considerable amount of nitrates in the complex terminal waters. The low values are registered in the ghout covered with reeds because of their use for the growth of reeds and at the level of th release of El Oued, where the oxygen necessary for the respiration of microorganisms i provided by the denitrification of nitrates.

Origin of Mineralization
Lithology influences groundwater mineralization in arid and semi-arid environments [71]. However, carbonate dissolution, evaporite dissolution, and silicat weathering are three major processes that contribute to the generation of solutes in groundwater systems [41]. The weathering concentrations of evaporites and carbonates on the other hand, are up to 80 and 12 times faster than those of silicates, respectively Consequently, even small amounts of carbonates and evaporites might have a big impac on water chemistry [72]. Figure 10A reveals that the dissolution of calcite is the main reaction in 40.81% of groundwater samples, with a ratio of 1 and 2, although 59.18% o Potassium comes mainly from evaporites, in this case, sylvite (KCl), or as a result of an alteration of potassium clays in the phreatic and complex terminal aquifer. The study area is characterized by high values of potassium, except for some zones where the potassium concentrations are very low, such as Debila, Guemar, and El Oued, as shown in Figure 8D.
Nitrate mainly comes from the contamination of wastewater in urban areas and fertilizers in agricultural lands. Figure 9D reveals that the high values of nitrates are found in the northwest and west of the study area, north of Guemar, north of Kouinine, and east and north of El Oued. The high values of nitrates confirm the dilution between the phreatic groundwaters and the complex terminal flows, resulting in considerable amounts of nitrates in the complex terminal waters. The low values are registered in the ghouts covered with reeds because of their use for the growth of reeds and at the level of the release of El Oued, where the oxygen necessary for the respiration of microorganisms is provided by the denitrification of nitrates.

Origin of Mineralization
Lithology influences groundwater mineralization in arid and semi-arid environments [71]. However, carbonate dissolution, evaporite dissolution, and silicate weathering are three major processes that contribute to the generation of solutes in groundwater systems [41]. The weathering concentrations of evaporites and carbonates, on the other hand, are up to 80 and 12 times faster than those of silicates, respectively. Consequently, even small amounts of carbonates and evaporites might have a big impact on water chemistry [72]. Figure 10A reveals that the dissolution of calcite is the main reaction in 40.81% of groundwater samples, with a ratio of 1 and 2, although 59.18% of samples have a ratio greater than 2, suggesting a non-carbonated mineral source that could play a role in groundwater chemistry, most likely due to reverse cation exchange caused by clay adsorption of calcium and magnesium in the groundwater and/or gypsum dissolution [73]. Due to the pH variation, carbonates (calcite and dolomite) dissolve mostly in the form of HCO 3 − .
Water 2021, 13, x FOR PEER REVIEW 20 of 27 samples have a ratio greater than 2, suggesting a non-carbonated mineral source that could play a role in groundwater chemistry, most likely due to reverse cation exchange caused by clay adsorption of calcium and magnesium in the groundwater and/or gypsum dissolution [73]. Due to the pH variation, carbonates (calcite and dolomite) dissolve mostly in the form of HCO3 − . The majority of the points in Figure 10B are plotted on the right side, indicating that ion exchange dominates reverse ion exchange due to an excess of (SO4 2− + HCO3 − ). However, line 1:1 is very close to 47.37% of group 4 samples and 17.65% of group 2 samples, demonstrating that calcite, dolomite, anhydrite, and gypsum would be the primary reactions in the system for the concerned group. Group 1 has only one sample that is close to line 1:1 [74][75][76].
In Figure 11A [77], a Na + -normalized Ca 2+ vs. HCO3 − graph shows that the four group samples vary in their sensitivity to silicate weathering. The Na + -normalized vs. Mg 2+ plot in Figure 11B indicates that the four group samples range from being affected by silicate weathering with a weak tendency, to evaporates' dissolution. The majority of the points in Figure 10B are plotted on the right side, indicating that ion exchange dominates reverse ion exchange due to an excess of (SO 4 2− + HCO 3 − ). However, line 1:1 is very close to 47.37% of group 4 samples and 17.65% of group 2 samples, demonstrating that calcite, dolomite, anhydrite, and gypsum would be the primary reactions in the system for the concerned group. Group 1 has only one sample that is close to line 1:1 [74][75][76].
In Figure 11A [77], a Na + -normalized Ca 2+ vs. HCO 3 − graph shows that the four group samples vary in their sensitivity to silicate weathering. The Na + -normalized vs. Mg 2+ plot in Figure 11B indicates that the four group samples range from being affected by silicate weathering with a weak tendency, to evaporates' dissolution.

Controlling Mechanisms
Gibbs's diagrams signifying the variation of [Cl − /(Cl − /HCO 3 − )] and [Na + /(Na + /Ca 2+ )] ratios as a function of TDS. Precipitation, rock, and evaporation dominance are illustrations of these diagrams that are widely used to determine the structural origins of dissolved chemical components. Figure 12 shows the Gibbs plots of cation and anion ratios against TDS for each of the four groups. Chemical data from all the clustered groups are plotted in the evaporation-precipitation dominance part, suggesting that evaporation-precipitation has a strong influence on water quality. primary reactions in the system for the concerned group. Group 1 has only one sample that is close to line 1:1 [74][75][76].
In Figure 11A [77], a Na + -normalized Ca 2+ vs. HCO3 − graph shows that the four group samples vary in their sensitivity to silicate weathering. The Na + -normalized vs. Mg 2+ plot in Figure 11B indicates that the four group samples range from being affected by silicate weathering with a weak tendency, to evaporates' dissolution.

Controlling Mechanisms
Gibbs's diagrams signifying the variation of [Cl − /(Cl − /HCO3 − )] and [Na + /(Na + /Ca 2+ )] ratios as a function of TDS. Precipitation, rock, and evaporation dominance are illustrations of these diagrams that are widely used to determine the structural origins of dissolved chemical components. Figure 12 shows the Gibbs plots of cation and anion ratios against TDS for each of the four groups. Chemical data from all the clustered groups are plotted in the evaporation-precipitation dominance part, suggesting that evaporation-precipitation has a strong influence on water quality. For the assessment of ion exchange reactions between groundwater and its host rock [69,78], the chloro-alkaline indices (CAI) are widely used by suggesting two chloroalkaline indices (CAI I, II) for the interpretation of ion exchange between groundwater and host environment.
The exchange of Na + and K + from the water with Mg 2+ and Ca 2+ of the rocks is shown by the positivity of chloro-alkaline indices (base-exchange reaction). Meanwhile, negative chloro-alkaline indices mean that Mg 2+ and Ca 2+ from the water are exchanged with Na + and K + of the rocks. Figure 13 shows that most of the complex terminal groundwater aquifers have positive chloro-alkaline indices, explained by the substitution of Ca 2+ and Mg 2+ in groundwater with Na + and K + in the aquifer system. For the assessment of ion exchange reactions between groundwater and its host rock [69,78], the chloro-alkaline indices (CAI) are widely used by suggesting two chloroalkaline indices (CAI I, II) for the interpretation of ion exchange between groundwater and host environment.
The exchange of Na + and K + from the water with Mg 2+ and Ca 2+ of the rocks is shown by the positivity of chloro-alkaline indices (base-exchange reaction). Meanwhile, negative chloro-alkaline indices mean that Mg 2+ and Ca 2+ from the water are exchanged with Na + and K + of the rocks. Figure 13 shows that most of the complex terminal groundwater aquifers have positive chloro-alkaline indices, explained by the substitution of Ca 2+ and Mg 2+ in groundwater with Na + and K + in the aquifer system.

Geochemical Modeling
Positive saturation index values suggest oversaturation and a tendency for the mineral to precipitate from the groundwater. Negative values all at once suggest undersaturation and, as a result, mineral dissolution into groundwater. The equilibrium condition occurs when the saturation index is between −0.5 and +0.5, and it indicates that the mineral in this groundwater is not dissolving or precipitating [79]. The dissolution of anhydrite, gypsum, and halite is identified in group 1, while aragonite, calcite, dolomite, and sylvite all have a supersaturation state. Aragonite, calcite, and dolomite are supersaturated in group 2 (precipitated). Anhydrite, gypsum, halite, and sylvite, on the other hand, are dissolved.
Aragonite, calcite, and dolomite were found to precipitate in group 3. Anhydrite, gypsum, halite, and sylvite were all dissolved during the process. In group 4, almost the same minerals are precipitating and dissolving. Figure 14 shows that evaporated minerals (anhydrite, gypsum, and halite) are undersaturated in most of the groups due to the dry environment and low precipitation in the study area, which leads to high evaporation in the surface water, making the uppermost aquifer (the phreatic aquifer) very mineralized compared to the complex terminal aquifer. The fact that evaporated minerals in groundwater samples are undersaturated shows that their soluble elements Na + , Cl − , Ca 2+ , and SO4 2− are not constrained by mineral equilibrium. Table 6 shows the outcomes from several minerals' saturation indices' computations (anhydrite, aragonite, calcite, dolomite, gypsum, halite, and sylvite).

Geochemical Modeling
Positive saturation index values suggest oversaturation and a tendency for the mineral to precipitate from the groundwater. Negative values all at once suggest undersaturation and, as a result, mineral dissolution into groundwater. The equilibrium condition occurs when the saturation index is between −0.5 and +0.5, and it indicates that the mineral in this groundwater is not dissolving or precipitating [79]. The dissolution of anhydrite, gypsum, and halite is identified in group 1, while aragonite, calcite, dolomite, and sylvite all have a supersaturation state. Aragonite, calcite, and dolomite are supersaturated in group 2 (precipitated). Anhydrite, gypsum, halite, and sylvite, on the other hand, are dissolved.
Aragonite, calcite, and dolomite were found to precipitate in group 3. Anhydrite, gypsum, halite, and sylvite were all dissolved during the process. In group 4, almost the same minerals are precipitating and dissolving. Figure 14 shows that evaporated minerals (anhydrite, gypsum, and halite) are undersaturated in most of the groups due to the dry environment and low precipitation in the study area, which leads to high evaporation in the surface water, making the uppermost aquifer (the phreatic aquifer) very mineralized compared to the complex terminal aquifer. The fact that evaporated minerals in groundwater samples are undersaturated shows that their soluble elements Na + , Cl − , Ca 2+ , and SO 4 2− are not constrained by mineral equilibrium. Table 6 shows the outcomes from several minerals' saturation indices' computations (anhydrite, aragonite, calcite, dolomite, gypsum, halite, and sylvite).

Conclusions
The techniques included in this study (hierarchical clustering analysis, geostatistical modeling, and the WQI) assisted in the identification of the factors that influence groundwater chemistry in the study area (Oued souf valley-southeast of Algeria).
A review of clustering based on groundwater quality datasets, using Q-mode (Ward's linkage method with the Euclidean distance), defined four major water types. In terms of electrical conductivity, all the groups reflected high to brackish water, with mean values of 3000, 4005.44, 4272, and 4348.95 µS/cm, respectively. At the same time, all the groups had the same hydro-chemical facies of Ca-Mg-Cl-SO 4 . In the first and second groups, however, chloride was the dominant ion (mean = 706.7 mg/L and 815.42 mg/L, respectively). Groups 3 and 4 were dominated by chloride and sulphates (mean = 817.62 mg/L for chloride and 800.88 mg/L for sulphates in group 3, where means for chloride and sulphate were 884.46 mg/L and 668.14 mg/L respectively in group 4).
Ordinary Kriging geostatistical analysis revealed a strong spatial structure for EC, SO 4 2− , and NO 3 − and a moderate spatial structure for Ca 2+ , Na + , K + , and HCO 3 − . Furthermore, Mg 2+ and Cl − have weak spatial structures. Owing to the high geological variation of the study area and the depth of each well, the spatial distribution maps for Ca 2+ , HCO 3 − , Na + , K + , and Cl − revealed high heterogeneity. El Oued to the south had low Ca +2 concentrations, while Debila, Sidi Aoun, and Kouinine had higher Ca 2+ concentrations.
The complex terminal groundwater's WQI values indicated unfitness for drinking uses. However, the irrigation indices showed that these groundwaters are of excellent to moderate irrigation quality. The dissolution of calcite controls 40.81% of groundwater samples, even though 59.18% of samples had a non-carbonate mineral origin, which may play a role in groundwater chemistry due to reverse cation exchange caused by clay adsorption and/or gypsum dissolution. Due to an excess of (SO 4 2− + HCO 3 − ), ion exchange was expected to dominate over reverse ion exchange. However, 47.37% of group 4 and 17.65% of group 2 samples showed the dominant reactions in the CT groundwater system. The geochemical evolution of the groundwater samples indicates an undersaturation of evaporated minerals in the study area, in contrast, the precipitation of the carbonate minerals has been occurred.
The study's key conclusion is that the agricultural and economic growth of the Oued souf region has directly resulted in overexploitation of deep groundwater aquifers, mainly the complex terminal aquifer, which has a long-term impact on their quantitative and qualitative aspects, particularly in some vulnerable areas.