*4.3. Geostatistical Analysis of the Study Area (Spatial Distribution)*

*4.3. Geostatistical Analysis of the Study Area (Spatial Distribution)*  The statistical and geostatistical analysis was done using ArcGIS 10.2, R, R studio, and MS Excel 2019. The spatial interpolators can easily predict the values of a specific attribute at locations unknown to the observer utilizing the values of sample locations known previously. The deterministic interpolators can utilize mathematical formulae to know the predicted values. This can be interpreted as similarity among the neighboring points and smoothing extent. The geostatistical interpolation techniques use certain statistical properties of the points previously measured to estimate the value of the surface locations. Depending on the spatial structure of the datasets framed, we can investigate the spatial dependence among the variables. The ordinary kriging method was selected based on a comparative analysis of interpolation methods. Models such as Circular (C), Spherical (S), Tetraspherical (T), Pentaspherical (P), Exponential (E), Gaussian (G), Rational Quadratic (RQ), Hole effect (H), K-Bessel (K), J-Bessel (J), and Stable (S\*) were used to arrive at appropriate semi variogram. The best-fitted models are RQ (Al and K), G (As), S\* (As, Cd, and Mn), H (Ba, NO3, Temp, Zn), P (Cr), C (Cu, Ni, and pH), and J (EC, HCO3, Pb, and TDS). Suppose the nugget ratio is less than 25%. In that case, we can assume that there is strong spatial dependence; 25 to 75% can be reflected as moderate spatial dependence. If greater than 75%, we can expect least or weak spatial dependence. After nugget analysis, it is obvious that Cd (0), K (7.38%), and SO4 (1.81%) variables exhibited strong spatial dependence. Al (27%), Ba (40.87%), Cr (63%), Cu (34%), EC (27%), HCO3 (56%), NO3(36%), Pb (64%), and TDS (53%) represented moderate spatial dependence. As (76%), Mn (79%), Ni (100%), pH (100%), Temp (93%), and Zn (100%) exhibited weak spatial de-The statistical and geostatistical analysis was done using ArcGIS 10.2, R, R studio, and MS Excel 2019. The spatial interpolators can easily predict the values of a specific attribute at locations unknown to the observer utilizing the values of sample locations known previously. The deterministic interpolators can utilize mathematical formulae to know the predicted values. This can be interpreted as similarity among the neighboring points and smoothing extent. The geostatistical interpolation techniques use certain statistical properties of the points previously measured to estimate the value of the surface locations. Depending on the spatial structure of the datasets framed, we can investigate the spatial dependence among the variables. The ordinary kriging method was selected based on a comparative analysis of interpolation methods. Models such as Circular (C), Spherical (S), Tetraspherical (T), Pentaspherical (P), Exponential (E), Gaussian (G), Rational Quadratic (RQ), Hole effect (H), K-Bessel (K), J-Bessel (J), and Stable (S\*) were used to arrive at appropriate semi variogram. The best-fitted models are RQ (Al and K), G (As), S\* (As, Cd, and Mn), H (Ba, NO3, Temp, Zn), P (Cr), C (Cu, Ni, and pH), and J (EC, HCO3, Pb, and TDS). Suppose the nugget ratio is less than 25%. In that case, we can assume that there is strong spatial dependence; 25 to 75% can be reflected as moderate spatial dependence. If greater than 75%, we can expect least or weak spatial dependence. After nugget analysis, it is obvious that Cd (0), K (7.38%), and SO<sup>4</sup> (1.81%) variables exhibited strong spatial dependence. Al (27%), Ba (40.87%), Cr (63%), Cu (34%), EC (27%), HCO<sup>3</sup> (56%), NO3(36%), Pb (64%), and TDS (53%) represented moderate spatial dependence. As (76%), Mn (79%), Ni (100%), pH (100%), Temp (93%), and Zn (100%) exhibited weak spatial dependence. Nugget analysis for selecting the appropriate model was presented in Table 5.

pendence. Nugget analysis for selecting the appropriate model was presented in Table 5. **Table 5.** The Spatial distribution and semi variogram element's observed sites.


The spatial distribution maps and semi variogram plots of essential variables were presented in Figures 6–12. Table 5 shows the specific locations of elements distribution in the area. *Water* **2022**, *14*, x FOR PEER REVIEW 12 of 20 *Water* **2022**, *14*, x FOR PEER REVIEW 12 of 20

**Figure 6.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Aluminum. **Figure 6.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Aluminum. **Figure 6.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Aluminum.

**Figure 7.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Barium. **Figure 7.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Barium. **Figure 7.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Barium.

*Water* **2022**, *14*, x FOR PEER REVIEW 13 of 20

**Figure 8.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Cadmium. **Figure 8.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Cadmium. **Figure 8.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Cadmium.

**Figure 9.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Chromium. **Figure 9. Figure 9.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Chromium. (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Chromium.

*Water* **2022**, *14*, x FOR PEER REVIEW 14 of 20

**Figure 10.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Copper. **Figure 10.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Copper. **Figure 10.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Copper.

**Figure 11. Figure 11.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Potassium. (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Potassium.

**Figure 11.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Potassium.

**Figure 12.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Manganese. **Figure 12.** (**a**) Semi variogram, and (**b**) Spatial distribution mapping of Manganese.

**Table 5.** The Spatial distribution and semi variogram element's observed sites. **S. No Elements Low Moderate High**  1. Aluminum (Al) North west Western end Eastern end 2. Arsenic North west Western end South eastern 3. Barium Western end South western and north eastern South western 4. Cadmium Northern end North-south (extended) Western end 5. Chromium Northern end North-south (extended) Western end 6. Copper North-south (extended) Western end Eastern end 7. Potassium Western end Partially spotted all over the area North eastern 8. Manganese Western end South east North west The groundwater investigations in this area are expensive, and the sample locations were limited. Efforts are in progress to collect more samples with an increased temporal resolution to cross-validate the results obtained from the actual observations. Geostatistics in groundwater studies was never attempted for this study area. This study integrated physio-chemical, multivariate, and geostatistical analysis and water quality indices to analyze groundwater quality parameters. The parameters were correlated using correlation analysis, and both positive and negative correlations were found. To mention a few, Arsenic is positively correlated with nitrates, sulfates and EC and negatively correlated with pH and temperature. Lead is positively correlated with Al and As and negatively correlated with Ba and Zn. Ni positively correlated with As, Al, and Pb and negatively correlated with Zn. Chromium reflected a positive correlation with Ba and Cu and negatively correlated with As and Mn. Zinc is positively correlated with Al.

> The groundwater investigations in this area are expensive, and the sample locations were limited. Efforts are in progress to collect more samples with an increased temporal resolution to cross-validate the results obtained from the actual observations. Geostatistics A PCA was performed, and the results showed that there were five main components, PC1 through PC5, which represented a variance of 35% (PC1) and 12% (PC2), 10% (PC3), <10% (PC4 and PC5), respectively. Significant loadings on PC1 are As, Al, Pb, K, pH, sulfate, and nitrate. PC2 accommodates significant loadings of Ba and bi-carbonates with pH.

> in groundwater studies was never attempted for this study area. This study integrated physio-chemical, multivariate, and geostatistical analysis and water quality indices to analyze groundwater quality parameters. The parameters were correlated using correlation analysis, and both positive and negative correlations were found. To mention a few, Arsenic is positively correlated with nitrates, sulfates and EC and negatively correlated with The dataset was subjected to geostatistical analysis, and a suitable model was identified using standard kriging. The J-Bessel model was selected to represent Pb, TDS, HCO3, and EC. Pentaspherical model is employed to represent Cr. The circular model was used to show the distribution of Ni, Cu, and pH. The hole effect model was used to describe the spatial distribution of Zn, Temp, NO3, and Ba. A stable model was employed to reflect the

distribution of Mn, Cd, and As. The rational quadratic model was used to represent K and Al. Based on nugget analysis, it was observed that Zn, As, Mn, Ni, pH, and TDS exhibited weak spatial dependence. Moderate spatial dependence was exhibited by Al, Ba, Cr, Cu, Ec, HCO3, NO3, Pb, and TDS. Strong spatial dependence was observed in Cr, K, and SO4.

Groundwater quality deterioration has become a nightmare in this region, and this was due to limited surveillance and the never-ending injection of pollutants into this precious source. Most of the populace in this study area rely on this for industrial and drinking purposes after purification. Several studies were made to evaluate the potability of groundwater of Liwa aquifer mainly for agricultural needs; however, rigorous geostatistical methods were sparsely applied. This paper attempts to fill the void left in using geostatistics to represent groundwater quality. The variation among the sample clusters was studied previously using PCA. This paper uses optimal interpolation techniques and semivariogram analysis to produce statistically enriched results. Geological elements, and environmental and hydrological parameters were considered the core of these studies. Previous studies were made to emulate the subsurface hydrology characteristics with limited utilization of the geostatistics, and this work will add valuable inputs to the contemporary research on groundwater situation analysis and management. This paper presents a GIS-based approach with geostatistics in assessing groundwater quality at the Liwa region, UAE. The correlation matrix obtained supports PCA analysis. The results also shed light on groundwater quality deterioration due to anthropogenic activities. The exponential semivariogram model was systematically authenticated for each groundwater parameter. Analysis of groundwater samples reflects that cadmium, aluminum, and lead is in high proportions compared to other parameters like Cr, Cu, K, Mn, Ni, Zn, and Ba. The distribution maps are produced using the appropriate model of the kriging interpolation method for each variable.
