## 3 Results
### Spatial Homogeneity in Correlation Analysis  
The degree to which the detected heatwave metrics from \(T_{\rm air}\) and LST align is demonstrated in Table 4. It presents the cumulative'median' of [PERSON]'s correlation coefficient (\(r\)) for the 10 meteorological stations and 10 LST grids that match the heatwave indices. Our LST modeling outperforms the existing MOD11A1 and MYD11A1 products during daytime heatwaves, notably for HWN at \(r=0.55,0.62\), and HWF at \(r=0.66,0.71\), respectively. It is evident that the derived in situ temperature largely follows the retrieved LST anomalies. For other indices, their associations are slightly moderate: HWD \(r=0.48\), HWM \(r=0.32\) to \(0.39\), and HWA \(r=0.35\). In contrast to daytime heatwaves, nighttime heatwaves demonstrate a weaker link between all heatwave characteristics. It is evident that the derived in situ temperature largely follows the retrieved LST anomalies.  
Figure 4 illustrates the distribution of the correlation coefficient (Pearson's \(r\)) at \(p<0.05\) corresponding to heatwave indices, considering pixel-by-pixel observations of \(T_{\rm air}\) and LST. In rural, peri-urban, and urban areas, the link between \(T_{\rm max}\) and MOD11A1 and \(T_{\rm max}\) and MYD11A1 is positively strong, with \(r\) values larger than 0.60 and up to 0.90, respectively; the highest correlated MOD11A1 result is observed in P07 (located in Ayutthaya province as a rural context). In addition, the association between \(T_{\rm max}\) and MYD11A1, particularly in rural regions in Lopburi province, P08 and P09, remains more robust than in other places (\(r=0.80\)) for HWN, HWF, and HWD. At \(r=0.60\), however, peri-urban and urban stations are strongly related to HWM and HWA. In a peri-urban area, the connection between nighttime heatwaves corresponding to \(T_{\rm min}\) and MOD11A1 is highest for HWN (\(r=0.85\)) and HWF (\(r=0.75\)) in Suvarambhumi Airport (P05). In contrast, HWD shows the strongest link in the urban region (P03 Bang Na, Bangkok) with a correlation coefficient of 0.75, while P01 (Khlong Toei, Bangkok) displays the highest HWM (\(r=0.65\)) and HWA (\(r=0.62\)). The \(T_{\rm min}\) against the MYD11A1 product indicates that P05, as the outskirt area, has the strongest link with all heatwave indices at \(r=0.60\) to 0.85, with the exception of P02 as the urban area, which has a smaller magnitude. Nighttime heatwaves are discovered to have a negative correlation in more regions than daytime heatwaves, particularly in rural areas.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Data**} & \multicolumn{5}{c}{**Pearson’s Correlation Coefficient (\(r\))**} \\ \cline{2-6}  & **HWN** & **HWF** & **HWD** & **HWM** & **HWA** \\ \hline \(T_{\rm max}\) vs. MOD11A1 (day) & 0.55 & 0.66 & 0.48 & 0.32 & 0.35 \\ \(T_{\rm max}\) vs. MYD11A1 (day) & 0.62 & 0.71 & 0.48 & 0.39 & 0.40 \\ \(T_{\rm min}\) vs. MOD11A1 (night) & 0.31 & 0.26 & 0.10 & 0.02 & 0.07 \\ \(T_{\rm min}\) vs. MYD11A1 (night) & 0.36 & 0.45 & 0.26 & 0.08 & 0.13 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Cumulative median [PERSON]’s correlation coefficient (\(r\)) for linear relationship between 10 Observed \(T_{\rm air}\) points and 10 valid LST grids, coinciding with heatwave indices at \(p<0.05\).  
Figure 4: The distribution of pixel-wise correlation coefficients (\(r\)) between observed \(T_{\rm air}\) and observed MODIS-LST; \(T_{\rm max}\) and MOD11A1 Day (**a,e,i,m,q**), \(T_{\rm max}\) and MYD11A1 Day (**b,f,j,n,r**), \(T_{\rm min}\) and MOD11A1 Night (**c,g,k,o,s**), \(T_{\rm min}\) and MYD11A1 Night (**d,h,l,p,r**).