# 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
We applied the linear fitting functions with the coefficients listed in Table 3 to calculate the remote sensing inversion data for the corresponding sub-regions in the study area, thereby obtaining eight optimized spatial distribution maps of land surface temperature in the study area. Next, we used 15 February, 15 May, 15 August, and 15 November as examples of each of the four seasons in 2002 to optimize the remote sensing inversion of the land surface temperature of each sub-region in the study area. The reconstruction results are shown in Figure 3.  
With the exception of the land surface temperature observation stations used for the fitting equations, the other ground meteorological observation stations were used to validate the optimized results of the study area. We selected Langfang, Tangshan, Beijing, Qinglong, and Weichang as validation points; conducted a statistical analysis on the 2002 remote sensing inversion of the land surface temperature in these stations (before reconstruction), on the ground meteorological observations, and on the land surface temperature values after the reconstruction of the fitting functions; and obtained the average RMSE, Pearson's coefficient, and MAE, which are listed in Table 4.  
Figure 3 shows that the average and Pearson's coefficient of the land surface temperature values are all more similar after reconstruction than before reconstruction, and the MAE also decreased. In addition, regarding the RMSE, the majority of the land surface temperature observation stations exhibit RMSE values less than those obtained before reconstruction, indicating that the data dispersion decreases. Among the validation points, the RMSE value of the Langfang station after reconstruction is greater than that before reconstruction, but the change is small. This result may be caused by a systematic error. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Meteorological**} & **Mean after** & \multirow{2}{*}{**Mean of**} & **RMSE** & **RMSE of** & **Pearson’s** & **Mean** & **Pearson’s** & **Mean** \\
**Stations** & **LST Recon-** & **Mean** & **GMS-5** & **after** & **GMS-5** & **Coefficient** & **Absolute Error** & **Coefficient** \\
**Stations** & **struction** & **LST C’C** & **Derived** & **Recon-** & **Devired** & **before Reconstruction** & **after Recon-** & **after Recon-** \\  & (°C) & & **LST C’C** & **ST C’C** & **LST** & **construction** & **struction** & **struction** & **struction** \\ \hline Langfang & 13.720 & 13.818 & 12.839 & 7.428 & 4.682 & 0.907 & 3.633 & 0.919 & 3.422 \\ Tangshan & 12.677 & 13.201 & 12.356 & 3.824 & 4.436 & 0.915 & 3.414 & 0.933 & 2.928 \\ Beijing & 13.482 & 13.402 & 13.310 & 4.333 & 4.847 & 0.896 & 3.741 & 0.914 & 3.243 \\ Qinglong & 11.231 & 10.457 & 11.918 & 4.291 & 4.986 & 0.905 & 4.121 & 0.927 & 3.470 \\ Weichang & 9.443 & 6.569 & 9.539 & 4.689 & 5.203 & 0.929 & 4.324 & 0.948 & 3.217 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The mean and RMSE of the derived, the in situ, and the reconstructed surface temperature. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sub-Region**} & **Tianjin** & **Nangong** & **Xingtai** & **Chengde** & **Yuxian** \\  & **Sub-Region** & **Sub-Region** & **Sub-Region** & **Sub-Region** & **Sub-Region** \\ \hline A1 & 0.189 & 0.972 & 1.014 & 0.94 & 0.83 \\ B1 & 1.14 & 0.288 & \(-\)0.141 & 0.286 & 0.723 \\ A2 & 0.093 & 0.749 & 0.828 & 0.954 & 0.867 \\ B2 & 19.96 & 6.225 & 4.263 & 0.91 & 2.727 \\ A3 & \(-\)0.254 & 0.972 & 0.985 & 0.972 & 0.959 \\ B3 & 30.78 & 0.562 & 0.339 & 0.467 & 0.689 \\ A4 & \(-\)0.067 & 0.644 & 0.718 & 0.504 & 0.555 \\ B4 & 3.53 & 0.402 & 0.466 & \(-\)2.638 & \(-\)1.965 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fitting equation coefficients for each region and season in 2002.