## 3 Results
### Urban Expansion Dynamics in the Lanxi Urban Cluster
#### 3.1.2 Statistical Expansion Information of the Key Cities  
During the study period, Lanzhou, the hub city within the Lanxi urban cluster, experienced the most significant urban expansion, with an area increase of 47.93 km\({}^{2}\). Despite the large expansion, Lanzhou's expansion intensity index was relatively low at 0.02, indicating a stable growth pattern. Baiyin followed with an urban expansion of 25.02 km\({}^{2}\). Interestingly, Baiyin's expansion intensity index was 0.05 higher than Lanzhou's, suggesting more concentrated growth over a shorter period. Xining, starting with a smaller initial area, saw the most significant proportional growth, with its urban land area increasing by 2.84 times at an annual growth rate of 5.35%. The total expansion area for Xining was 9.01 km\({}^{2}\), and its expansion intensity index was notably higher at 0.09, making it the city with the fastest total area growth within the cluster.  
The rapid development of these cities can be attributed to their roles as central cities within the Lanxi urban cluster. The development of the Lanxi region mainly relies on these cities, and the influx of population tends to prioritize these cities for work and settlement, leading to faster development and urban expansion.  
From the expansion rate perspective, Haidong expanded by 2.59 times, with an annual growth rate of 2.59%. However, due to Haidong's smaller urban land base, its total expansion area was only 7.39 km\({}^{2}\). Dingxi also experienced rapid development, with its urban land area increasing from 14.68 km\({}^{2}\) to 30.07 km\({}^{2}\) over the past twenty years, an increase of 15.38 km\({}^{2}\) and an annual growth rate of 3.64%. Multiple factors, including economic development, population growth, industrial distribution, and policy differences, influence the varying expansion rates among cities. Larger cities tend to have higher industrial integration and more policy preferences, leading to larger expansion in big cities and smaller expansion in smaller cities. We have summarized the specific data on urban expansion in Table 2 and Figure 5. Table 2 compiles the expansion information of major cities within the Lanxi urban cluster, while Figure 5 shows the urban expansion areas.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Urban Expansion Dynamics**} & \multicolumn{4}{c}{**Impact on Vegetation**} \\ \cline{2-10}  & \multicolumn{2}{c}{**Urban Land Area (km\({}^{2}\))**} & \multicolumn{2}{c}{**Expanded**} & \multicolumn{2}{c}{**Annual**} & \multicolumn{2}{c}{**Expansion Rate**} & \multicolumn{2}{c}{**Positive Impacts**} & \multicolumn{2}{c}{**Negative Impacts**} \\ \cline{2-10}  & **2001** & **2021** & **Area (km\({}^{2}\))** & **UEI** & **Growth Rate** & & **Area** & **Area** & **Area** & **Greenage** \\ \hline Lanzhou & 121.80 & 169.73 & 47.93 & 0.02 & 1.67\% & 1.39 & 15.94 & 33.25\% & 25.38 & 52.94\% \\ Baiyin & 27.43 & 52.45 & 25.02 & 0.05 & 3.29\% & 1.91 & 11.75 & 46.96\% & 9.75 & 38.96\% \\ Dingxi & 14.68 & 30.07 & 15.38 & 0.05 & 3.65\% & 2.05 & 4.88 & 31.69\% & 6.44 & 41.84\% \\ Linxia & 11.72 & 20.41 & 8.69 & 0.04 & 2.81\% & 1.74 & 2.50 & 28.76\% & 5.56 & 63.99\% \\ Xining & 4.91 & 13.92 & 9.01 & 0.09 & 5.35\% & 2.84 & 2.56 & 28.43\% & 4.56 & 50.59\% \\ Haidong & 2.86 & 7.39 & 4.53 & 0.08 & 4.87\% & 2.59 & 1.94 & 42.75\% & 1.81 & 39.99\% \\ \hline Total & 2184.40 & 2314.97 & 110.56 & 0.03 & 2.39\% & 1.60 & 39.57 & 35.71 & 53.5 & 48.28 \\ \hline \hline \end{tabular} Note: UEI refers to the Urban Expansion Intensity Index.  
\end{table}
Table 2: Urban expansion dynamics in the Lanxi urban cluster from 2001 to 2021.