## 1 Introduction  
As a vital component of terrestrial ecosystems, vegetation plays a pivotal role in indicating the quality of the surrounding ecological environment [1]. Consequently, the long-term monitoring of vegetation dynamics holds significant importance in various domains, including global climate change [2], climate regulation [3, 4], soil and water conservation [5, 6] and other aspects. The Normalized Difference Vegetation Index (NDVI), being one of the commonly employed indicators in the study of vegetation cover changes, effectively captures the growth status of regional vegetation [7]. Coal mining can result in varying degrees of surface subsidence, surface cracks, land damage [8], and groundwater pollution [9], factors that contribute to vegetation damage in different ways. Research utilizing MODIS NDVI data has found that the analysis of NDVI time-series trends is suitable for detecting changes in vegetation areas and identifying land degradation [10]. By analyzing NDVI time series and comparing the changes in the NDVI between mining and non-mining areas, it becomes evident that mining activities have a very noticeable negative impact on ecosystem vegetation [11]. Studies conducted on several large mining areas have shown that 40% of these areas exhibit reduced vegetation trends following mining, with 8.34% of them significantly impacted by human activities, leading to vegetation degradation [12]. Vegetation degradation can further lead to a decline in the ability of vegetation to absorb carbon [13]. Furthermore, existing research has indicated that there are still risks of overall vegetation degradation in reclaimed coal mining areas. All of the above discussions collectively emphasize the effectiveness of using the NDVI time series to monitor changes in vegetation conditions caused by mining activities [14,15]. The Yellow River Basin serves as a crucial ecological barrier in China and is also a significant economic region, often referred to as the \"energy basin\" [16]. Among China's 14 major coal bases, nine are situated within the Yellow River Basin [17]. Shanxi province holds a prominent position in the Yellow River Basin and is one of the country's most critical coal production areas, playing a vital role in ensuring China's energy security [18]. While large-scale coal mining has driven national and local economic and social development, it has also brought about a series of issues, including surface water and soil erosion, vegetation degradation, and damage to arable land. These problems have severely harmed the originally fragile ecological environment of the basin. According to relevant survey data, Shanxi province has witnessed the formation of a coal mining subsidence area covering 6500 square kilometers, which accounts for 4.20% of the province's total area. Within this subsidence area, the portion within the Yellow River Basin amounts to 4100 square kilometers, constituting 63.07% of the total coal mining subsidence area in the Shanxi province. Furthermore, the coal-mining subsidence area continues to expand at an annual rate of 50 square kilometers, significantly affecting the livelihoods and productivity of the local population [19]. Among the many scholars' studies, a considerable focus has been placed on monitoring the ecological environment across the entire Yellow River Basin [20,21]. Numerous research findings indicate favorable improvements in the vegetation conditions within the Yellow River Basin, with the most pronounced enhancements occurring in the central region. Overall, the changes have exhibited a degree of stability and sustainability. An analysis of the driving factors reveals that precipitation, humidity, and sunlight exert the most significant influence on vegetation cover. The relationship between these factors and changes in runoff and runoff coefficients is relatively complex, lacking clear correlations.