## 4 Discussion  
Although the statistical data (Table 2) and vertical distributions of heavy metals (Figure 2) can reflect changes in PTEs as a whole, clustering analysis can provide an objective grouping method for PTEs [55; 56]. In general, most studies apply cluster analysis to PTEs examine the relationship between  
Figure 2: Vertical variations of \({}^{137}\)Cs, PTEs and magnetic susceptibility (MS) in lake sediments from North Aral Sea. variables. However, Figure 3 shows the two-way dendrogram for the clustering of PTEs and sample layers generated with two-way cluster analysis. The connection distance shown on the graph is a standardized Euclidean distance and represents the relative similarity between the sample layers and the PTEs. Differences between the clusters can be used to distinguish sample layers and PTEs. Judging from the distances between the sample horizons, there is a huge difference between the first layer (0-21 cm) and the second layer (22-30 cm). If the first layer (0-21 cm) were further divided, it could be divided into three secondary layers (0-1 cm), (2-9 cm) and (10-21 cm), which are consistent with the stages noted in the vertical distribution plots (Figure 2). The cluster analysis showed that separation of the sediment core into layers based on the characteristics of PTEs achieves good results. In addition to sample horizons, the cluster analysis also allows for easier determination of the affinity between PTEs. Clustering between PTEs indicated that the nine PTEs could be divided into three clusters. The first PTE cluster includes Cd and As, which are  
Figure 3: Cluster dendrogram for samples and PTE concentrations. also the elements with the largest toxicity coefficients among the nine PTEs studied. The second group includes Ni, Zn, Pb and Cu, and the third group includes V, Cr and Co. The elements in the second and third groups are more closely related compared with the elements of the first group. The results show the usefulness of micro-geochemical features that may not be identifiable by comprehensive statistical data alone. Temporal changes in the geo-accumulation index of each PTE are depicted in Figure 4. The geo-accumulation index of all nine PTEs was less than 0 before 1970, indicating that the status of all PTEs was practically unpolluted. From 1970 to 1975, PTEs became significantly enriched. After 1975, with the exception of as (0-1), the geo-accumulation index of the PTEs was greater than 1, reflecting a moderately polluted status. What factors have caused this obvious change? The high-frequency MS and low-frequency MS of the Aral Sea sediments are significantly correlated, which is a typical characteristic of lake sediments [57]. In lacustrine sediments, the correlation between magnetic susceptibilities measured at different frequencies is very good, and the correlation coefficient (r) can exceed 0.99 (\(p<0.001\)), indicating that increasing magnetic susceptibility is related to an increase in the content of magnetic minerals. Previous studies have shown that MS can be used to reflect the variations in the intensity of human activities [58; 59; 60]. The intensification of human activities has led to the enrichment in ferromagnetic materials of surface materials entering the lake, which has led to a significant increase in magnetic susceptibility since 1970 AD. Figure 5 shows changes over time in magnetic susceptibility, temporal changes in surface area of irrigated Land in Aral Sea basin [61], and the volume of import and export trade between the former Soviet Union and the United States. Temporal changes in surface area of irrigated Land (million hectares) in the Aral Sea basin, to a certain extent, reflect changes in agricultural intensity. The area of irrigated Land in Aral Sea basin was slowly increasing before the 1970s but showed a drastic increase during the 1970s (Figure 5). A sudden change  
Figure 4: Time-varying curves of PTE geo-accumulation indexes (I\({}_{\text{geo}}\)).