The study of ionic balance (BI) can help to verify the accuracy of test results. The results of analyses can be considered good if this ionic balance is less than 5%, for a value of the balance between 5% and 10%, the results can be maintained and when the balance is greater than 10%, the analyzes are to be rejected [20].

The ionic balance is given by the following Equation (1):

BI ( % ) = ∑ cations − ∑ anions ∑ cations + ∑ anions × 100 (1)

where

BI (Ionic Balance);

∑cations: sum of major cations in water in milliequivalents;

∑anions: sum of major anions in water in milliequivalents.

The Piper diagram allows a classification of water. This classification is based on a representation of the chemical facies of water on a triangle of cations (left), anions (right) and an associated diamond giving a synthesis of the overall facies. The approximate location of an analytical result on each of these two triangles gives the first clarification on the anionic and cationic dominance [21]. This Piper hydrochemical diagram is mainly used in the literature to display the chemical facies of a set of water samples [22] [23].

The Piper diagram is used with the help of Diagramme software for the processing of hydrochemical data.

Changes in the chemical quality of water during its movement in the aquifer can be highlighted by the base exchange index (i.e.b.) [24] [25]. The i.e.b. expresses the relationship between the ions exchanged and the ions of the same nature originally existing in water. This index gives the nature of the ionic exchanges between water and the surrounding land using Equation (2) [22] [25]:

i .e .b . = [ Cl − ] − ( [ Na + ] + [ K + ] ) [ Cl − ] (2)

where:

[Cl⁻]: concentration in meq/l of chloride ions;

([Na⁺] + [K⁺]): concentration in meq/l of the sum of sodium and potassium ions.

So:

- if i.e.b. is negative, the Ca²⁺ and Mg²⁺ ions of the water are replaced by the K⁺ and Na⁺ ions of the surrounding formations;

- if i.e.b. is positive, the Na⁺ and K⁺ ions of the water are substituted by the Mg²⁺ and Ca²⁺ ions of the surrounding lands;

- if i.e.b. = 0, we have equilibrium between the chemical constitution of the water and the constitution of the surrounding land.

The influence of chemical elements in geochemical mineralization processes can be given by the state of saturation, determined by the saturation index. This saturation index provides information on the level of chemical equilibrium of water with the mineral in the aquifer matrix, in water-rock relationships, as a measure of the mechanism of dissolution and/or precipitation [26]. The saturation index is defined by the logarithm of the ionic activity ratio (PAI) to the equilibrium constant (K) (Equation (3)) [27]:

IS = log ( PAI K ) (3)

where:

PAI: ionic product of the solution;

K: equilibrium constant.

Three cases are possible:

IS < 0, the solution is undersaturated with respect to the mineral considered;

IS = 0, indicates saturation;

IS > 0, the solution is supersaturated.

Diagrams and PHREEQC Interactive software are used to calculate saturation indices with respect to minerals (calcite, aragonite, dolomite, anhydrite, gypsum and halite).

The binary diagrams show on a 2D figure the variation of the concentrations of the different ions or the representation of ion concentrations as a function of the chlorides considered as conservative halogens and not impacted by redox phenomena and minerals with reduced solubility [28] [29]. These binary diagrams can be used to analyze mineralization from correlations between the concentrations of major elements. These linear correlations between some of the chemical variables also aid in the study of the origin of mineralization according to the type of relationship [1]. For Faye, binary diagrams make it possible to distinguish the geochemical mechanisms responsible for the chemical evolutions noted, in addition to specifying the types of water [10]. The chloride ion indicates the origin of the salt in the water, it is a mixing tracer absent in exchanges between water and rock and is not lost [29] [30] [31].

Multivariate statistical analysis applied in the processing of hydrochemical data is based on the techniques of Ascending Hierarchical Classification (AHC) and Principal Component Analysis (PCA). These analysis techniques reduce and classify the information resulting from hydrochemical data with the aim of explaining the process of water governance [22] [32] [33] [34]. They show similarities or dissimilarities by grouping chemical elements (variables) or individuals (water point) according to their chemical compositions.

The Ascending Hierarchical Classification (AHC) is an analysis assessing the similarity or difference between samples to give an indication of class association [35]. This analysis allows multiple data to be grouped and ordered into distinct classes on a graph to facilitate their interpretations. On this graph, the individuals are distributed in succession of nesting forming a classification tree, called a dendrogram. According to Ahmed, it is a method of hierarchical classification of parameters, widely used in earth sciences and in the processing of hydrochemical results [22]. The Ascending Hierarchical Classification (AHC) method is powerful for processing hydrochemical data and for establishing geochemical models [32] [33].

Principal Component Analysis (PCA) is a descriptive statistical technique that displays on a graph much more information forming a database [24] [36]. It thus makes it possible, from a graphical representation, to distribute the chemical elements on the basis of their contents in the sampled water by reducing the number of variables. PCA is a method which decreases variables by representing the point cloud in a two-dimensional subspace generated by factor axes [32] [37] [38] [39]; this analysis determines the essential elements making it possible to interpret the phenomena involved from correlation with the variables [40]. According to Ahmed, PCA is used to study the mechanisms governing the physico-chemical constitution of water and/or their origins, and it is a new descriptive method recommended by Farnham, Johannesson et al. [22] [41].

The Ascending Hierarchical Classification (CHA) and Principal Component Analysis (PCA) methods are processed using the XLSTAT software.

The base exchange indices (i.e.b.) of the sampled waters vary between −3.47 and 0.73 (Figure 5). Most of these water points have positive values with 58.3% of the indices. These positive clues indicate that Mg²⁺ and Ca²⁺ ions replace Na⁺

and K⁺ ions in water. In contrast, negative core trade indices represent 41.7%. These negative indices indicate that the surrounding terrain releases Mg²⁺ and Ca²⁺ to fix the Na⁺ and K⁺ ions. The dominance of kaolinite-type clay is remarkable, over this cation exchange mechanism through clay minerals [11].

Box whisker (Figure 6) are represented from the calculation of the saturation indices. These boxes show that the waters are undersaturated with respect to all the minerals (calcite, aragonite, dolomite, anhydrite, gypsum, halite). Carbonate minerals (calcite, aragonite, dolomite) tend to approach saturation, while evaporitic minerals (anhydrite, gypsum, halite) are far from the saturation line.

The dissolution of these minerals would therefore participate in the mineralization of the water.

Figure 7 shows the cross diagrams of the concentrations of major elements (Na⁺, Ca²⁺, and Mg²⁺) with chlorides, (Ca²⁺, HCO 3 − ) with Mg²⁺ and ( HCO 3 − , SO 4 2 − ) with Ca²⁺. The distribution of points around the freshwater-saltwater mixing line can be adopted to determine other phenomena related to the mixing mechanism [31].

The representation of these major elements (Na⁺, Ca²⁺ and Mg²⁺) with (Cl⁻) indicates strong values of correlations. The correlation coefficients (r) are greater than 0.9 (Figures 7(a)-(c)). These correlation values would indicate a common source of these ions. This source could be marine and/or a dissolution of carbonate, evaporitic minerals. The high correlation between Na⁺ and Cl⁻ would be due to the same origin of a dissolution of halite and/or the presence of salt water [8]. The halite saturation index, undersaturated with respect to the water samples (Figure 6) could corroborate this. The representation of Na⁺ as a function

of Cl⁻ (Figure 7(a)) (r = 0.98) indicates an important part of the points located on the mixing line and some placed above. The alignment of the points is made on the mixing line between two poles formed for a mixture of two waters, i.e. when the water is contaminated by salt water, on the sea water dilution line [42]. This representation shows a weak growth in sodium ion (Na⁺). Enrichment/depletion of Na⁺ in fresh water would result from exchange of bases ensuring the progression of facies from Ca-Cl or Na-Cl or Ca-HCO₃ to Na-Cl or Na-HCO₃ [10] [11]. The relationship between Ca²⁺ and Mg²⁺ (Figure 7(d)) shows a good correlation with r = 0.91. On this relation, the arrangement of the points with respect to the mixing line favors an enrichment in magnesium (Mg²⁺) compared to calcium (Ca²⁺). The movements of the freshwater and seawater compositions are ensured by ion exchange reactions largely resulting from the enrichments and depletion of magnesium and calcium, respectively [22]. Thus, the representation of Ca²⁺ with Cl⁻ (Figure 7(b)) (r = 0.92) would show this depletion of Ca²⁺ by a large part of the points placed at the bottom of the mixing line. The diagrams HCO 3 − with Ca²⁺ and HCO 3 − with Mg²⁺ (Figure 7(e) and Figure 7(f)) indicate correlation coefficients respectively r = 0.55 and r = 0.65.

For these representations, calcium and magnesium are better correlated with chlorides (Figure 7(b) and Figure 7(c)) (r = 0.92 and r = 0.95) than with bicarbonates. These results seem to confirm a common, marine origin of Ca²⁺ and Mg²⁺, especially in the northern and western parts of the area. However, calcium and magnesium would come from a dissolution of dolomite and/or calcite, since the waters are undersaturated with respect to these minerals (Figure 6). The degradation of minerals would lead, from a dissolution of calcite and/or feldspar to the presence of Ca²⁺ [14]. The enrichment in calcium relative to bicarbonate (Figure 7(e)) would be due to a dissolution of calcite in the presence of CO₂. In the group of fresh waters that are not contaminated by salty waters, the waters are often of calcium bicarbonate facies (Ca-HCO₃) [8]. This type of Ca-HCO₃ facies occurs largely in the center, south and east of the southern Saloum area and is a characterization of freshwater. The relationship between Ca²⁺ and SO 4 2 − (Figure 7(g)) (r = 0.71) and the saturation index (Figure 6) of undersaturated water compared to gypsum indicate that calcium and sulfate ions would be bound to the dissolution of gypsum formations.

Principal Component Analysis (PCA) is applied to major elements ( HCO 3 − , Cl⁻, SO 4 2 − , NO 3 − , Ca²⁺, Mg²⁺, Na⁺, K⁺), conductivity (EC) and pH. This analysis gives the results of Table 2, Table 3 and Figure 8. The correlation matrix (Table 2)

shows a strong correlation of electrical conductivity with major elements except HCO 3 − and NO 3 − . This correlation varies between 0.716 and 0.988. These strong correlation values express the contribution of major elements in electrical conductivity. The correlations of Cl⁻ with SO 4 2 − , Ca²⁺, Mg²⁺, Na⁺ and K⁺ are strong.

The correlation coefficient varies between 0.714 and 0.988. These correlations corroborate the common origin of these major elements which could be marine and/or by a dissolution of carbonate, evaporitic minerals.

From the eigenvalues (Table 3), two principal components (F1 and F2) are retained. These components represent 85.49% of the total variance. The choice of the components (1 and 2) is based on the criterion of Kaiser (1960), according to which, factors with eigenvalues greater than or equal to 1 are considered as possible sources of variance. The factor 1 (F1) expresses 68.69% of the total variance, and is represented positively by EC, Na⁺, K⁺, Mg²⁺, Ca²⁺, Cl and SO 4 2 − . This factor appears as a factor of mineralization. It would reflect the dissolution of carbonate, evaporite formations and/or a saline intrusion. On the other hand, the second factorial axis (F2) represents 16.80% of the total variance. This factor is characterized positively by HCO 3 − and pH, and negatively by NO 3 − . The opposition of these two anions in the space of variables, reflects two different origins of these elements. This difference could be explained by an anthropogenic origin (domestic and agricultural activities) of nitrates ( NO 3 − ), and bicarbonates ( HCO 3 − ) would come from the dissolution of carbonates.