# A Kalman Filter-Based Method for Reconstructing GMS-5 Land Surface Temperature Time Series
## 4 Results and Discussion
### The Reconstruction of Land Surface Temperature Time Series on a Regional Scale  
After applying the Kalman filter, we obtained the refined values of the inversed remote sensing data for the land surface temperature time series. However, this algorithm cannot be extended spatially. The remote sensing inversion of the land surface temperature represents the value of a land surface unit with an area of approximately 25 km\({}^{2}\). Table 1 indicates that it is possible to build a good linear correlation between the land surface \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{\begin{tabular}{c} **Sub-Region** \\ **Station** \\ \end{tabular} } & \begin{tabular}{c} **Mean Bias of** \\ **GMS-5** \\ **(VISSR)-** \\ **Derived** \\ **LST (°C)** \\ \end{tabular} & \begin{tabular}{c} **Mean Bias** \\ **after** \\ **Reconstruction** \\ **LST (°C)** \\ \end{tabular} & \begin{tabular}{c} **Accuracy** \\ **Improvement** \\ **LST (°C)** \\ \end{tabular} & \begin{tabular}{c} **RMSE of** \\ **(VISSR)-** \\ **Reconstruction** \\ **LST (°C)** \\ \end{tabular} & \begin{tabular}{c} **RMSE after** \\ **Reconstruction** \\ **LST (°C)** \\ \end{tabular} & \begin{tabular}{c} **Accuracy** \\ **Improvement** \\ **LST (°C)** \\ \end{tabular} & \
\begin{tabular}{c} **Pearson’s** \\ **Coefficient** \\ \end{tabular} &
\begin{tabular}{c} **Mean** \\ **Absolute Error** \\ \end{tabular} \\ \hline Tianjin & 0.375 & 0.266 & 29.1\% & 4.716 & 4.393 & 6.85\% & 0.919 & 3.389 \\ Nangong & 0.572 & 0.399 & 30.2\% & 4.895 & 4.869 & 0.53\% & 0.904 & 3.693 \\ Xingtai & 1.541 & 1.117 & 27.5\% & 4.906 & 4.719 & 3.81\% & 0.903 & 3.675 \\ Chengde & 2.678 & 2.024 & 24.4\% & 5.643 & 4.613 & 18.25\% & 0.927 & 3.558 \\ Yuxin & 2.163 & 1.680 & 22.3\% & 5.349 & 4.920 & 8.02\% & 0.912 & 3.882 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The statistics of the optimized surface temperature data compared to the original data from five stations in the Beijing–Tianjin–Hebei region in 2002. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{\begin{tabular}{c} **Sub-Region** \\ **Station** \\ \end{tabular} } & \begin{tabular}{c} **Mean of** \\ **(VISSR)-** \\ **Derived** \\ **LST (°C)** \\ \end{tabular} & \begin{tabular}{c} **Standard** \\ **Deviations of** \\ **GMS-5** \\ **(VISSR)-** \\ **CIVSSR-** \\ **LST (°C)** \\ \end{tabular} & \begin{tabular}{c} **Standard** \\ **Deviations of** \\ **GMS-5** \\ **(VISSR)-** \\ **Situ LST (°C)** \\ \end{tabular} & \begin{tabular}{c} **Mean of In** \\ **Situ LST (°C)** \\ \end{tabular} & \begin{tabular}{c} **RMSE** \\ **Stu LST (°C)** \\ \end{tabular} & \
\begin{tabular}{c} **Correlation (R2)** \\ **Coefficient** \\ \end{tabular} &
\begin{tabular}{c} **Pearson’s** \\ **Absolute Error** \\ \end{tabular} \\ \hline Tianjin & 13.152 & 10.497 & 13.528 & 10.502 & 0.815 & 0.899 & 3.761 \\ Nangong & 13.686 & 10.688 & 14.258 & 10.553 & 0.840 & 0.895 & 3.799 \\ Xingtai & 13.833 & 10.363 & 15.374 & 10.033 & 0.835 & 0.896 & 3.741 \\ Chengde & 11.847 & 10.841 & 9.169 & 11.708 & 0.851 & 0.896 & 4.696 \\ Yuxian & 11.364 & 10.938 & 9.201 & 11.437 & 0.831 & 0.905 & 4.348 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlation analysis of the remote sensing-retrieved data and the in situ values at five stations in the Beijing–Tianjin–Hebei region. observations from the five stations in the Beijing-Tianjin-Hebei region and the image pixels with a certain area. We used the remote sensing inversion of each observation station, including those in Tianjin, Nangong, Xingtai, Chengde, and Yuxian, and the values after Kalman filter reconstruction to build a linear fitting function for each station. The obtained function coefficients are listed in Table 3. We built a fitting equation between the remote sensing inversion value and the refined value for 2002 for each sub-region and season and applied the fitting function to the sub-region in which the station is located to obtain the refined value of the land surface temperature for each season and sub-region.