## 3 Results and Analysis
### Response of the NDVI in Shanxi Section of the Yellow River Basin to Climatic Factors  
Figure 6 illustrates the interannual variations in the NDVI, annual mean temperature, and annual cumulative precipitation in the Shanxi section of the Yellow River Basin. From 2001 to 2020, the highest annual mean temperature reached 11.46 \({}^{\circ}\)C, while the lowest was 10.09 \({}^{\circ}\)C, showing relatively little variation. In contrast, the annual cumulative precipitation ranged from a maximum of 679.37 mm to a minimum of 391.24 mm, with a significant difference of 288.13 mm between the maximum and minimum values. Overall, precipitation showed an increasing trend, while the annual mean temperature remained relatively stable. By calculating the correlation coefficients between the NDVI and these two climate variables, it was observed that the NDVI exhibited a significant positive correlation with annual cumulative precipitation (r = 0.464; \(p\) = 0.039 \(<\) 0.05), whereas the correlation between NDVI and annual mean temperature was positive but not statistically significant (R = 0.185,  
Figure 4: NDVI fluctuation changes in the Shanxi Section of the Yellow River Basin and mining areas. It is divided into five levels based on the magnitude of the CV: low fluctuation change (CV \(\leq\) 0.05), lower fluctuation change (0.05 \(<\) CV \(\leq\) 0.10), medium fluctuation change (0.10 \(<\) CV \(\leq\) 0.15), higher change (0.15 \(<\) CV \(\leq\) 0.20), and high volatility change (0.20 \(<\) CV). \(p\) > 0.05). Comparing the correlation coefficients, it was evident that the NDVI had a stronger correlation with annual cumulative precipitation in the study area. Furthermore, from Figure 6, it can be observed that in the years 2007, 2013, and 2016, when the annual cumulative precipitation reached a small peak, the NDVI also exhibited a corresponding small peak. Therefore, increased precipitation in the study area had a more significant impact on vegetation cover. To further investigate the intrinsic connection between the NDVI and climate factors in the study area, this paper conducted a quantitative study on the relationship between climate factors and the NDVI. It calculated the partial correlation coefficients between the NDVI and annual mean temperature, as well as between the NDVI and annual cumulative precipitation at the pixel level. Significance tests were also performed and, based on the magnitude of the partial correlation coefficients and their significance, the results were categorized, leading to the generation of Figures 7 and 8. Figure 5: The Hurst Index and change trend forecast of Shanxi Section of the Yellow River Basin: (a) Spatial distribution of the Hurst Index; it is classified into five categories: strong anti-persistence (0 < H \(\leq\) 0.2), weak anti-persistence (0.2 < H \(\leq\) 0.4), random uncertainty (0.4 < H \(\leq\) 0.6), weak persistence (0.6 < H \(\leq\) 0.8), and strong persistence (0.8 < H \(\leq\) 1). (b) Variation trend prediction of the Hurst index. The classification criteria are shown in Table 1.  
The research results indicate that, in the Shanxi section of the Yellow River Basin, 66.01% of the region shows a positive correlation between the NDVI and annual mean temperature, while 27.84% of the region exhibits a negative correlation. The areas with a positive correlation are widespread, primarily concentrated in the southern and eastern parts, whereas the regions with a negative correlation are mainly found in the central areas of the hilly terrain in the western part of the Shanxi Plateau, the city area of Taiyuan, and near the Yuncheng Basin. From the perspective of the distribution within mining areas, each mining area has certain regions with a negative correlation, primarily located in the southeastern parts of the Liulin mining area, the Hebopiao mining area, and the southeastern part of the Jincheng mining area.