4.3.1. PCA (Principal Component Analysis)

Factor analysis is a statistical method used to effectively reduce the number of variables (dimensionality reduction) to minimize the loss of information in the original dataset, thus achieving a comprehensive analysis of data [27]. This statistical method has been widely used in various fields of research, including hydrogeological research. In this study, the factor analysis test was used to investigate the factors influencing the hydrochemical characteristics of groundwater.

It can be seen from the total variance explained that the first 4 principal components explained 87% of the total variance. In addition, the eigen values of the first 4 principal components were all greater than 1. Therefore, the first five principal components were selected. The main influencing factors were assessed to use the factors loading of the principal components (Table 2 and Figure 5). Factor loadings indicate the correlation between variables and principal components (PCs).


**Table 2.** Total variance explained by the factor analysis.

According to Tables 2 and 3, it can be seen that the variance contribution of Factor 1 (F1) accounted for 51.751% of the total variance, with strong positive loadings with HCO<sup>3</sup> <sup>−</sup>, Mg2+, TH, TDS, and mineralization (M), thus the findings indicate that these five parameters are the most important, representing the dissolution of calcite, dolomite carbonate and salt minerals, and silicate minerals. The results showed that F1 represents the main factors influencing the hydrochemical characteristics of shallow groundwater in the study area. The cumulative variance contribution of factor 2 (F2) was 68.716%. This factor revealed strong positive loadings with Na<sup>+</sup> and F−, which indicates that the high importance of these two parameters in F2. Therefore, it was suggested that F2 was related to the anthropogenic factors represented by F− concentrations in groundwater. On the other hand, Factor 3 (F3) and Factor 4 (F4) explained smaller proportions of variance of 9.562 and 9.009%, respectively. The result showed strong positive loadings of NO<sup>2</sup> − and As on F3, which indicates the high importance of these parameters in F3. Whereas NO<sup>3</sup> − and Fe2+ revealed strong positive and negative loadings on F4, respectively, which indicates the high importance of these two parameters in F4. The results suggested that F3 and F4 are related to industrial and agricultural pollution. The provincial-level industrial Park in Yongqing County, approved by the People's Government of Hebei Province in 2003, may affect the groundwater quality due to industrial wastewater discharges. Moreover, the agricultural area accounts for about 75% of the total area of the study area, which suggests a significant negative impact of agricultural activities on the groundwater quality in Yongqing County. 7 0.424 2.354 97.514 8 0.216 1.203 98.717 9 0.121 0.675 99.392 10 0.070 0.390 99.782 11 0.024 0.135 99.917 12 0.014 0.080 99.997 13 0.001 0.003 100.000 14 0.000 0.000 100.000 15 0.000 0.000 100.000 16 0.000 0.000 100.000 17 0.000 0.000 100.000 18 0.000 0.000 100.000

cates the high importance of these two parameters in F4. The results suggested that F3 and F4 are related to industrial and agricultural pollution. The provincial-level industrial Park in Yongqing County, approved by the People's Government of Hebei Province in 2003, may affect the groundwater quality due to industrial wastewater discharges. Moreover, the agricultural area accounts for about 75% of the total area of the study area, which suggests a significant negative impact of agricultural activities on the groundwa-

> **Initial Eigenvalue Total Variance Percentage Cumulative Percentage**

 9.315 51.751 51.751 3.054 16.966 68.716 1.721 9.562 78.279 1.622 9.009 87.288 0.831 4.618 91.906 0.586 3.254 95.160

*Water* **2022**, *14*, x FOR PEER REVIEW 9 of 17

ter quality in Yongqing County.

**PCs**

**Table 2.** Total variance explained by the factor analysis.

**Figure Figure 5. 5.** Factor loading Factor loading values between variable and principal components. values between variable and principal components.


Note: Extraction method: principal component analysis; Rotation method: Caesar normalized maximum variance method a; a. The rotation was converged after 6 iterations.

### 4.3.2. Gibbs Diagram Analysis 4.3.2. Gibbs Diagram Analysis

**Chemical Parameters**

HCO<sup>3</sup>

SO<sup>4</sup>

NO<sup>3</sup>

NO<sup>2</sup>

*Water* **2022**, *14*, x FOR PEER REVIEW 10 of 17

**Table 3.** Factor loading values between variables and principal components.

**PCs F1 F2 F3 F4**

TDS 0.934 0.323 −0.116 0.062 TH 0.975 −0.071 −0.158 −0.081 M 0.930 0.332 −0.130 0.020 pH −0.779 0.101 0.439 0.116 K<sup>+</sup> 0.142 −0.686 −0.277 0.258 Na<sup>+</sup> 0.520 0.806 −0.017 0.169 Ca2+ 0.836 −0.418 −0.248 −0.091 Mg2+ 0.970 0.114 −0.099 −0.069

<sup>−</sup> 0.900 0.345 −0.164 −0.090 Cl<sup>−</sup> 0.889 0.211 0.024 0.196

<sup>2</sup><sup>−</sup> 0.868 0.161 −0.062 0.271 F<sup>−</sup> 0.326 0.822 −0.232 0.154

<sup>−</sup> 0.184 0.193 0.019 0.743

<sup>−</sup> −0.212 −0.112 0.883 0.173 Mn 0.883 −0.067 0.041 −0.292 Fe2+ 0.199 0.265 0.019 −0.786 As −0.039 0.097 0.946 −0.125 SiO<sup>2</sup> 0.259 −0.478 −0.473 −0.575 Note: Extraction method: principal component analysis; Rotation method: Caesar normalized

Gibbs diagrams (Figure 6) have been widely used to reveal the ionic characteristics and determine the sources of the hydrochemical characteristics of river water [28,29]. In addition, they have been commonly used to analyze the hydrochemical characteristics of groundwater. Gibbs diagrams can be used to assess the relationship between TDS and Na+/(Na++Ca2+) and between TDS and Cl−/(Cl−+HCO<sup>3</sup> −) and identify the main sources of ions as well as the main factors influencing the hydrochemical characteristics of groundwater. Gibbs diagrams (Figure 6) have been widely used to reveal the ionic characteristics and determine the sources of the hydrochemical characteristics of river water [28,29]. In addition, they have been commonly used to analyze the hydrochemical characteristics of groundwater. Gibbs diagrams can be used to assess the relationship between TDS and Na<sup>+</sup> /(Na++Ca 2+) and between TDS and Cl<sup>−</sup> /(Cl−+HCO<sup>3</sup> − ) and identify the main sources of ions as well as the main factors influencing the hydrochemical characteristics of groundwater.

maximum variance method a; a. The rotation was converged after 6 iterations.

**Figure 6. Figure 6.** Gibbs diagrams, Gibbs diagrams, ( (**aa**) ) TDS versus Na/(Na+Ca), ( TDS versus Na/(Na+Ca), (**b b** ) ) TDS versus Cl/(Cl+HCO TDS versus Cl/(Cl+HCO3) 3 ).

It can be seen from Figure 6 that all water sampling points fall in the rock dominance control zone, which indicates that that rock dominance was the main influencing factor controlling the hydrochemical characteristics of groundwater in the study area. As shown in Figure 6a, Na<sup>+</sup> has a wide distribution and exhibit high proportions in some samples, indicating that sodium ions may be generated by a variety of sources. However, the proportion of Cl– is small and the distribution is concentrated, indicating that all Cl– is produced from the similar source or through the same geochemical process (Figure 6b). It should be noted that the Gibbs diagrams revealed only the natural factors influencing the groundwater chemical characteristics, while the human factors were not considered.
