# Tourism-Induced Urbanization in Phuket Island, Thailand (1987-2024): A Spatiotemporal Analysis
## 2 Materials and Methods
### Urban Expansion Intensity and Diversity Analysis  
The methodology for analyzing Urban Expansion Intensity and Diversity in Phuket from 1987 to 2024 provided valuable insights into urban growth patterns [41]. Here, we are calculating UEII [42; 43] and Shannon Entropy [44; 45] and analyzing their changes and trends, offering a comprehensive understanding of urban expansion dynamics, crucial for effective urban planning and sustainable development.  
We adapted UEII to calculate the urban expansion, the average period rate relative to the total area; we used the following formula:  
\[\text{UEII}_{\text{ith}}=\frac{\left[\frac{ULA_{i,b}-ULA_{i,b}}{t}\right]}{TLA _{i}\times 100}, \tag{1}\]  
where  
\(\text{UEII}_{\text{ith}}\) is the mean Urban Expansion Intensity Index of the (ith) zone in period (t). \(\text{ULA}_{i,\text{a}}\) and \(\text{ULA}_{i,\text{b}}\) are the amount of urban area during time spans a and b in the (ith) spatial zone, respectively. \(\text{TLA}_{i}\) is the total area of Phuket (-543 square kilometers). The UEII values range from <0 to >1.92 and are divided into five categories (Table 1)  
Shannon Entropy, which measures the diversity and distribution of urban areas, was calculated using the following formula:  
\[H_{n}=\sum_{i}^{n}\text{P}_{i}\text{log}\left(\frac{1}{\text{P}_{i}}\right) \tag{2}\]  
where  
Pi is the probability of occurrence of the i period. Probabilities were determined by dividing each year's urban area by the total urban area over a 5-year period; the interpretation of Shannon Entropy is presented in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline
**UEII** & **Interpretation** \\ \hline Negative UEII & Decline in urban areas, potentially due to de-urbanization, land reclassification, or environmental impacts. \\ Low UEII (<0.5\%) & Slow growth or stagnation indicated mature urban areas with limited expansion. \\ Moderate UEII (0.5–2\%) & Steady and manageable urban growth. Indicates balanced development. \\ High UEII (>2\%) & Very high-speed development indicated significant urban expansion. \\
**Shannon Entropy** & High Entropy (4.5 to 5.25) \\ Moderate Entropy (2.5 to 4.5) & Balanced but not extreme diversity. \\ Low Entropy (0 to 2.5) & Low diversity and high concentration. \\ \hline \end{tabular}
\end{table}
Table 1: UEII and Shannon Entropy show the pace of urban expansion while explaining the diversity and concentration of urban development.  
Next, period-by-period UEII values were analyzed to identify significant fluctuations and trends in urban growth. High UEII values indicated periods of intense urban expansion, and high Shannon Entropy values reflected diverse and spread-out growth. Insights from UEII and Shannon Entropy trends informed strategic resource allocation for infrastructure and services [46]. The analysis helped plan for balanced and sustainable urban growth, ensuring that development did not exceed the region's carrying capacity. Policymakers could adjust urban development policies based on identified trends to manage growth effectively [47].  
Figure 4 presents the general framework of the study, outlining the key methodological steps undertaken. This framework provides a structured overview of the processes, including data collection, preprocessing, classification, and analysis, which collectively form the foundation for understanding land use dynamics and urban expansion in Phuket over the study period.