# Correlation Analysis between UBD and LST in Hefei, China, Using Luojia1-01 Night-Time Light Imagery
## 3 Methodology
### Geographically Weighted Regression  
Geography objects, such as a change in the pattern, the distribution of time and space, and the mutual coupling relationship, are scale-dependent, which means that a specific relationship within the geographical aspect may only be expressed on a certain scale [54]. The study area was divided into four spatial scales of \(0.5\times 0.5\) km, \(1\times 1\) km, \(1.5\times 1.5\) km, and \(2\times 2\) km, and the average UBD and average LST in each grid were determined. The UBD data were logarithmically transformed to make \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Temperature Class** & **Grading Basis** & **Temperature Range/\({}^{\circ}\)C** & **Area Percent/\%** \\ \hline low & \(\mu-SD>T\) & T \(<23.06\) & 9.04\% \\ sub-low & \(\mu-0.5 SD>T\geq\mu-SD\) & \(23.06\leq\) T \(<26.97\) & 33.87\% \\ middle & \(\mu+0.5 SD>T\geq\mu-0.5 SD\) & \(26.97\leq\) T \(\leq 30.88\) & 21.11\% \\ sub-high & \(\mu+SD>T\geq\mu+0.5 SD\) & \(30.88<\) T \(\leq 34.93\) & 25.77\% \\ high & \(T\geq\mu+SD\) & T \(>34.93\) & 10.21\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Temperature grading basis and temperature intervals. Figure 10: A sketch map of the overall LST distribution in the study area. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Data Sources** & **Maximum (\({}^{\circ}\)C)** & **Minimum (\({}^{\circ}\)C)** & **Average (\({}^{\circ}\)C)** & **Standard Deviation (\({}^{\circ}\)C)** \\ \hline RTE inversion value & 36.93 & 12.06 & 27.44 & 4.72 \\ MOD1A1 data & 34.07 & 15.62 & 26.31 & — \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Inversion accuracy verification of LST. the data population normally distributed. Then, the Pearson correlation coefficient between the UBD and LST was calculated, and a linear regression analysis using the bivariate regression model was used to explore the correlation between LST and UBD. As shown in Figure 11, UBD and LST showed a significant positive correlation at each of the four grid scales, the degree of correlation increased in pace with the spatial scale, and the correlation coefficient reached a maximum at the scale of 2 km. This shows that the distribution of the UBD has a warming effect on the LST at the fine-scale of the city, and the contribution UBD makes to the LST at the grid-scale of 2 km was greater than that at the other three scales. Due to the small scale of analysis and more complex factors affecting the LST, more variables need to be considered, such as local airflow and the regional surface three-dimensional structure. Therefore, the impact of LST decreases with increasing spatial scale, and the correlation between UBD and LST is stronger. The bivariate regression model (\(R^{2}\) = km 22) established on the 2 km grid-scale, although having certain interpretation and prediction capabilities, is not enough to express the spatial relationship between UBD and LST. We applied GWR and ordinary least squares (OLS) regression to further analyze the relationship between the UBD and LST. The traditional regression model is based on the use of OLS to estimate the parameters and is usually compared as a benchmark model with an improved model [55; 56; 57]. OLS can be expressed as:  
\[Y_{k}=\beta_{0}+\sum_{i=1}^{k}\beta_{i}X_{i}+\varepsilon_{k} \tag{15}\]  
where \(Y_{k}\) denotes the global dependent variable; \(X_{i}\) is the \(i\)th index of the independent variable; \(\beta_{0}\) represents the intercept value; \(i\) is the number of indicators; \(\beta_{i}\) is the slope coefficient; and \(\varepsilon\) denotes the random error term. Figure 11: Correlation between LST and UBD at four spatial scales: (**a**) UBD—LST at 0.5 km; (**b**) UBD—LST at 1 km; (**c**) UBD—LST at 1.5 km; and (**d**) UBD—LST at 2 km. GWR is characterized by incorporating the spatial characteristics of data into the model to create conditions for analyzing the spatial characteristics of the regression relationship [10; 47].