# A Kalman Filter-Based Method for Reconstructing GMS-5 Land Surface Temperature Time Series
## 4 Results and Discussion
### Error Analysis and Discussion  
The Kalman filter reconstruction results presented in Table 2 and the validation of the reconstruction results for the entire study area presented in Table 4 indicate that the reconstruction of the short-period land surface temperature time series and its application have good overall effects. However, the improvement in the accuracy is not significant at individual stations, which may be caused by the following errors:  
First, there could have been a satellite sensor calibration error. Japan's GMS-5 geostationary meteorological satellite was launched in 1995. It had been running beyond its intended service life, which was intended to end in 2002, or perhaps even in 2000. The functionality of the sensor declined continuously during its extended service life, resulting in its digit number (DN) values only being able to be used after complex calibration and adjustment. The land surface temperature product used in this study was calibrated against GMS-5 data prior to delivery. However, the data still exhibit errors.  
Figure 3: _Cont._Second, remote sensing inversion data are characterized by indirectness and morbidity. The signal received by the sensor is energy from a very complex land surface temperature process that includes atmospheric reflection, absorption, transmission to the land surface, and reflection back. Remote sensing inversion requires a large number of unknown parameters that are usually computed using empirical or semi-empirical formulas. Therefore, the inversion cannot achieve precise quantification. In addition, the parameters that were used in the subsequent atmospheric calibration and model selection are all uncertain, which could have affected the accuracy of the data to some degree.  
Third, there could have been an error in the in situ data from the meteorological stations, including systematic errors and accidental errors. In addition, the observations from the meteorological stations are point data, whereas the GMS-5 inversion yields area  
Figure 3: The spatial distribution of the land surface temperature in the Beijing–Tianjin–Hebei region in 2002 before and after reconstruction. (**a**,**b**) 15 February; (**c**,**d**) 15 May; (**e**,**f**) 15 August; and (**g**,**h**) 15 November.  
data. A comparison between the two reveals a fanning out problem from points to areas that neglects the scaling effect to some degree.  
Fourth, the method used in this study generates errors from two sources. During Kalman filter application, the initial value is uncertain and requires an empirical range. Thus, the accuracy of the initial value can impact the reconstruction results [37]. During the fitting of the reconstruction functions, according to previous research that found that the LST in situ data and satellite inversions exhibit a linear relationship, we built a simple first-order linear regression equation to spatially extend the reconstruction of the short-period land surface temperature time series that neglected the effects of scaling, complex topography, and environmental factors. Thus, this could have resulted in errors.