# Correlation Analysis between UBD and LST in Hefei, China, Using Luojia1-01 Night-Time Light Imagery
## 3 Methodology
### LST Retrieval from Landsat8  
Conventional methods based on Landsat8 TIRS surface temperature inversion include the radiative transfer equation (RTE) method, single-channel method, and split-window algorithm. Some scholars have carried out quantitative comparison analysis on the inversion precision of the different algorithms. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Density Class** & **Density Range/\%** & **Area Percent/\%** \\ \hline low & 0–5 & 38.77 \\  & 5–10 & 8.29 \\ \hline sub-low & 10–15 & 4.34 \\  & 15–20 & 10.66 \\ \hline middle & 20–25 & 13.01 \\  & 25-30 & 11.59 \\ \hline sub-high & 30–35 & 5.86 \\  & 35–40 & 3.11 \\ \hline high & 40–45 & 2.58 \\  & 45–50 & 1.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The UBD levels in the study area. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Sample** & **Average NTL** & **Actual UBD (\%)** & **Estimated UBD (\%)** & **Absolute Error (\%)** \\ \hline
1 & 0.034940 & 30.24 & 36.63 & 5.29 \\
2 & 0.001009 & 0.52 & 0.57 & 0.05 \\
3 & 16.683639 & 16.97 & 19.2 & 2.23 \\
4 & 0.008449 & 9.08 & 13.57 & 4.49 \\
5 &  
The results showed that the radiation transfer equation method has the highest precision [27]. The basic principle of the radiation transfer equation method can be illustrated as follows: firstly, the influence of the atmosphere on the surface heat radiation is estimated, then these effects are subtracted from the total heat radiation amount observed by the satellite sensor, and the surface heat radiation intensity is finally obtained and converted into the LST. The Landsat8 TIRS has two thermal infrared bands (bands 10, 11), but the calibration parameters for the TIRS band 11 are not stable; thus, we selected the Landsat8 TIRS band 10 on which to use the RTE method to invert the surface temperature. The calculation formula is as follows. The thermal infrared radiation brightness value \(L_{\lambda}\) received by TIRS consists of three parts: the atmospheric transmissivity (\(\tau\)), the atmospheric upward radiation (\(L\uparrow\)), and the atmospheric downward radiation (\(L\downarrow\)). We use the atmospheric correction parameter calculator website provided by NASA ([[https://atmcorr.gsfc.nasa.gov/](https://atmcorr.gsfc.nasa.gov/)]([https://atmcorr.gsfc.nasa.gov/](https://atmcorr.gsfc.nasa.gov/))) to get these values, where \(\tau\) is 0.47, \(L\uparrow\) is 4.93 \(W/\left(\text{m}^{2}\text{-}\upmu\text{m}\cdot\text{sr}\right)\), and \(L\downarrow\) is 7.18 \(W/\left(\text{m}^{2}\text{-}\upmu\text{m}\cdot\text{sr}\right)\). The RTE of the thermal infrared radiance L received by the TIRS is as follows:  
\[L_{\lambda}=L\uparrow+[\varepsilon B(T_{s})+(1-\varepsilon)L\downarrow]\tau \tag{8}\]  
where \(\varepsilon\) is the land surface emissivity; \(T\) is the real temperature of the surface; \(B(T_{s})\) is the radiance of the blackbody at temperature \(T\) in the thermal infrared band; and \(\tau\) is the atmospheric transmittance in the thermal infrared band. Remote sensing estimation of Vegetation Fractional Cover (VFC) refers to the vertical projected area of vegetation as a percentage of the total area of the study area. It reflects the degree of vegetation and the size of the photosynthesis area of the plant. At present, the more mature VFC estimation method is dimidiate pixel mode, which is estimated by the Normalized Difference Vegetation Index (NDVI). NDVI can be expressed as:  
\[NDVI=\frac{NIR-R}{NIR+R} \tag{9}\]  
\[VFC=\left(NDVI-NDVI_{S}\right)/\left(NDVI_{V}-NDVI_{S}\right) \tag{10}\]  
where \(NIR\) is for near-infrared reflectivity; \(R\) is red band reflectivity; \(NDVI_{S}\) is the \(NDVI\) value of bare land; and \(NDVI_{V}\) is the \(NDVI\) value of vegetation. On the scale of pixels, surface features are mainly divided into three types: natural surface, water body, and urban building. The natural surface is the main body in the composition of the ground, so the natural surface is the main body of temperature inversion.