# A Kalman Filter-Based Method for Reconstructing GMS-5 Land Surface Temperature Time Series
## 5 Conclusions  
To solve problems associated with missing data in the time series of remote sensing-inversed energy parameters, this study uses a new method to reconstruct land surface temperature time series based on a data assimilation approach, designs a refined assimilation algorithm that is validated and calibrated in the study area, and develops a technique that is able to reconstruct the remote sensing inversion of the daily land surface temperature to provide more comprehensive and consistent long-term time series data sets for land surface process modeling and related research. The main conclusions are as follows:  
1. At the site-pixel scale, based on the data assimilation approach, it is possible to effectively improve the accuracy and consistency of the entire data set using reconstruction algorithms such as the Kalman filter. We selected representative stations from the study area, used the Kalman filter as the assimilation algorithm, and continuously introduced the daily average LST in situ into the Kalman filter as the \"true value\" to optimize the remote sensing inversion data. After Kalman filter reconstruction, the average RMSE, Pearson's coefficient, and MAE of the land surface temperature were significantly improved. As indicated in Table 1, the average temperature of the Chengde area was 0.65 \({}^{\circ}\)C greater than it was before reconstruction, showing an increase of 24.4%. The maximum increase in the RMSE was 18.25%. In addition, the changes in the time series are very consistent with those of the land surface observations. Furthermore, when there is a large number of missing data and poor accuracy, the algorithm is able to reconstruct the missing data, improve the quality of the entire data set, and recover the trends of the original time series. These results indicate that the Kalman filter performs well when optimizing short-period land surface temperature time series. 2. Based on the site-scale results, we proposed a \"sub-elevation-per season segmentation fitting\" scheme that is able to extend the site-based reconstruction method to the entire study area. We performed time series reconstruction and reconstruction on the daily remote sensing inversion data for the land surface temperature over the course of a whole year in the study area and achieved satisfactory application results. This method is based on the following three assumptions: the relationship between the remote sensing inversion data and ground meteorological observations is linear; conditions such as the precipitation, dryness, and topography are generally consistent within each sub-region; and the Kalman filter reconstruction results are reliable. We selected one land surface temperature ground meteorological observation station in each sub-region of the study area, divided the data into four seasons (spring, summer, autumn, and winter), and built linear regression equations based on the relationship between the remote sensing inversion data and the Kalman filter-refined value to optimize each sub-region in the study area. Our validation results reveal that with the exception of Langfang, where the RMSE of the land surface temperature observation station is greater than that before reconstruction, the average and RMSE of the land surface temperatures at the other stations are all closer to the observational averages than they were before reconstruction. The Pearson's coefficient and MAE of the land surface temperature were significantly improved compared with before reconstruction. The changes in the optimized year-round land surface temperature time series are more consistent with those observed in the ground meteorological observations, and the land surface temperature data are more comprehensive spatially and more continuous temporally. 3. This study employed the Kalman filter, which is an auto-regression data processing algorithm for reconstruction, as the data assimilation algorithm.