## 3 Results  
### Urban Expansion Dynamics in the Lanxi Urban Cluster  
#### 3.1.1 Overview of Lanxi from 2001 to 2021  
Over the past two decades, the major cities within the Lanxi urban cluster have undergone significant urban expansion. From 2001 to 2021, the built-up area increased from 183.50 km\({}^{2}\) to 294.30 km\({}^{2}\), a growth of 1.6 times. This growth trend illustrates the rapid development and sustained growth of the Lanxi urban cluster in the process of urbanization. The average annual growth rate of 2.39% indicates a relatively stable pace of urban land area expansion. Additionally, the expansion intensity index of 0.03 suggests that the rate of urban expansion relative to the total urban area is relatively low, indicating a gradual growth of urban expansion in proportion to the total urban area (Figure 3). From the perspective of land use change, the Lanxi urban cluster experienced several significant trends in land cover types between 2001 and 2021. First, the cropland area decreased from 14,660.30 km\({}^{2}\) in 2001 to 13,272.50 km\({}^{2}\) in 2021. This change is closely linked to urbanization and land development, indicating a shift of agricultural land towards urban and other land types. Meanwhile, forest area showed an increasing trend, rising from 2813.32 km\({}^{2}\) to 3243.09 km\({}^{2}\), an increase of about 15.3%. This growth may be attributed to reforestation and natural restoration activities, highlighting the effectiveness of ecological protection policies. Shrub area decreased from 1084.71 km\({}^{2}\) to 984.61 km\({}^{2}\), which may be related to adjustments in vegetation structure and pressures from land development. Grassland area saw a slight increase, from 73,833.90 km\({}^{2}\) to 74,126.35 km\({}^{2}\). This stable growth suggests that despite ongoing urban expansion and land development, the grassland ecosystem has been preserved to some extent. Additionally, the significant increase in water body area, from 3332.12 km\({}^{2}\) to 3716.10 km\({}^{2}\), may reflect changes in precipitation patterns due to climate change and improvements in water resource management. The reduction in snow/ice  
Figure 3: Urban expansion dynamics in the Lanxi urban cluster from 2001 to 2021.  
cover, from 3.11 km\({}^{2}\) to 1.96 km\({}^{2}\), indicates the impact of global warming on mountain ice cover. The barren land area increased from 3429.48 km\({}^{2}\) to 3700.02 km\({}^{2}\), likely due to intensified land development activities and natural erosion processes. (Figure 4, Table 1). The arrows in Figure 4 represent the conversion between different land types. For example, the arrow from yellow (cropland) to light green (grassland) indicates the area converted from cropland to grassland between 2001 and 2021. In the counterclockwise direction, arrows pointing between the same land types signify that there was no change in land type during this period. For instance, the arrow from yellow to yellow indicates that these areas of cropland remained unchanged from 2001 to 2021. Further analysis of land type transitions reveals that the conversion of cropland to grassland was the most prominent, with 4889.49 km\({}^{2}\) of cropland turning into grassland. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **2001 (km\({}^{2}\))** & **2021 (km\({}^{2}\))** \\ \hline Cropland & 14,660.31 & 13,272.51 \\ Forest & 2813.32 & 3243.09 \\ Shrub & 1084.71 & 984.61 \\ Grassland & 73,833.91 & 74,126.35 \\ Water & 3332.12 & 3716.11 \\ Snow/ Ice & 3.11 & 1.96 \\ Barren & 3429.48 & 3700.02 \\ Urban & 183.49 & 294.31 \\ Wetland & 0.59 & 2.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the land cover situation from 2001 to 2021. Figure 4: Land cover conversion from 2001 to 2021 (km\({}^{2}\)). This reflects the outcomes of agricultural restructuring and ecological restoration efforts.