## 2 Data and Methods
### Methods  
This research adopts the VDI index to assess the influence of urban expansion on vegetation quantitatively. Initially, the land cover area of built-up regions in key cities within the urban cluster is computed. The dynamic expansion of built-up areas within the Lanxi urban cluster from 2001 to 2021 was subsequently quantified by analyzing impervious areas' changes in and growth rates. This approach offers a tangible portrayal of urban transformations within the Lanxi urban cluster. With the use of GEE platform, we downloaded the maximum annual growing season EVI data from the MODIS database. Using this data, we performed pixel-level overlay calculations with rainfall data of the same resolution in ArcGIS software to obtain the pixel-level VDI data. By evaluating VDI values, this research discerns the varied impacts--both positive and negative--of urban expansion within the Lanxi urban cluster on vegetation. In addition, this study utilized a land use transfer matrix to investigate the evolution of different land cover types over the past two decades and analyzed the primary factors contributing to disturbances to vegetation. The specific process is shown in Figure 2.  
The VDI index integrates the EVI with rainfall data, effectively detecting vegetation disturbances while eliminating the impact of rainfall variations. [PERSON] et al. were the first to  
Figure 2: Workflow for assessing the impact of urban expansion on vegetation.  
use this method to quantify the impact of surface coal mining on vegetation disturbances in semi-arid areas, demonstrating its effectiveness in excluding the influence of rainfall in arid regions [60]. In 2024, [PERSON] et al. used VDI to study the dual impact of urban expansion on vegetation in the arid regions of northern China, and made certain suggestions for urban planning. The study found that urban expansion led to a reduction of 7736 km\({}^{2}\) in vegetation area but also promoted the growth of vegetation over 5011 km\({}^{2}\). Population growth and land use changes are the main factors of the negative impact, while economic growth is the main driving force of the positive impact [61]. Therefore, this method is highly reliable and applicable for evaluating the impact of urban expansion on vegetation in the Lanxi urban agglomeration. Thus, the research areas of this study encompass the changes in the VDI values of the urban expansion zones of the Lanxi area from 2001 to 2021. The impact of vegetation within the pixels was determined to be positive, negative, or neutral by comparing the magnitude of the VDI values.  
It is worth mentioning that the vegetation referred to in this paper includes cropland, grassland, forests, and shrubs in the context of land use. The main impact on the vegetation in the urban expansion areas is attributed to the city's expansion, such as environmental degradation caused by population growth and the increase in urban buildings at the expense of a reduction in vegetation. In arid regions, vegetation is extremely sensitive to the amount of rainfall; hence, this paper utilizes the VDI value as an indicator to eliminate the influence of rainfall.