A Kalman Filter-Based Method for Reconstructing GMS-5 Land Surface Temperature Time Series
Abstract
:1. Introduction
2. Summary of Study Area and Data Sources
2.1. Summary of Study Area
2.2. Data Source
3. Method
3.1. Kalman Filter-Based Reconstruction Algorithm
3.2. Study Procedure
- At the pixel scale, we obtained the daily average surface temperature of the ground observation stations at different sites and the GMS-5-based remote sensing inversion data for the surface temperature, applied the Kalman filter to reconstruct a short-period time series of the land surface temperature from the retrieved remote sensing inversion data, and analyzed the accuracy of the reconstruction.
- For the post-reconstruction land surface temperature of each station, we built a linear fitting function using the “sub-regional and per-seasonal” method and developed a technical scheme for reconstructing the land surface temperature time series. We assumed that the conditions in each zone, including the elevation, precipitation, dryness, and topography, were generally consistent and divided the study area according to its seasonal characteristics (spring, summer, autumn, and winter). According to the land surface temperature inverted by means of remote sensing during each season in 2002 in each zone and the Kalman filter reconstruction values, we applied the least squares method to build linear fitting functions to obtain the empirical coefficient for each season and to then build a first-order linear regression function based on the fitting functions between the remote sensing inversion data and refined value of each sub-region and season in 2002.
- We optimized the original remote sensing inversion of the land surface temperature in each sub-region of the study area, analyzed and compared the accuracy and rationality of the land surface temperatures of the representative stations before and after the reconstruction, and drew conclusions. We used the established fitting function of each zone and season to calculate the remote sensing inversion data using a raster calculator, obtaining the spatial distribution of the optimized land surface temperature in the study area and the refined values for the other stations. Regarding the optimized land surface temperature, we selected the representative stations in the area for validation to analyze and compare the accuracy and rationality of the land surface temperature before and after reconstruction and conducted an error analysis.
4. Results and Discussion
4.1. Station-Based Reconstruction of Land Surface Temperature
4.2. The Reconstruction of Land Surface Temperature Time Series on a Regional Scale
4.3. Error Analysis and Discussion
5. Conclusions
- 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 °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.
- 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.
- This study employed the Kalman filter, which is an auto-regression data processing algorithm for reconstruction, as the data assimilation algorithm. The Kalman filter has been widely used for more than 40 years and has yielded refined solutions for most of the problems that it has been applied in. Recently, numerous scholars have proposed improved algorithms for different applications. Future work can employ new data assimilation methods such as the improved Kalman filter algorithm and Gaussian kernel density estimation to achieve better reconstruction results.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Sub-Region Station | Mean Bias of GMS-5 (VISSR)-Derived LST (°C) | Mean Bias after Reconstruction LST (°C) | Accuracy Improvement | RMSE of GMS-5 (VISSR)-Derived LST (°C) | RMSE after Reconstruction | Accuracy Improvement | Pearson’s Coefficient | Mean Absolute Error |
---|---|---|---|---|---|---|---|---|
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 |
Yuxian | 2.163 | 1.680 | 22.3% | 5.349 | 4.920 | 8.02% | 0.912 | 3.882 |
Sub-Region Station | Mean of GMS-5 (VISSR)-Derived LST (°C) | Standard Deviations of GMS-5 (VISSR)-Derived LST (°C) | Mean of In Situ LST (°C) | RMSE | Correlation (R2) | Pearson’s Coefficient | Mean Absolute Error |
---|---|---|---|---|---|---|---|
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 |
Sub-Region | Tianjin Sub-Region | Nangong Sub-Region | Xingtai Sub-Region | Chengde Sub-Region | Yuxian Sub-Region |
---|---|---|---|---|---|
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 |
Meteorological Stations | Mean after LST Reconstruction (°C) | Mean of In Situ LST (°C) | Mean of GMS-5 (VISSR)-Derived LST (°C) | RMSE after Reconstruction | RMSE of GMS-5 (VISSR)-Derived LST | Pearson’s Coefficient before Reconstruction | Mean Absolute Error before Reconstruction | Pearson’s Coefficient after Reconstruction | Mean Absolute Error after Reconstruction |
---|---|---|---|---|---|---|---|---|---|
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 |
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Qin, R.; Chen, G.; Zhang, H.; Liu, L.; Long, S. A Kalman Filter-Based Method for Reconstructing GMS-5 Land Surface Temperature Time Series. Appl. Sci. 2022, 12, 7414. https://doi.org/10.3390/app12157414
Qin R, Chen G, Zhang H, Liu L, Long S. A Kalman Filter-Based Method for Reconstructing GMS-5 Land Surface Temperature Time Series. Applied Sciences. 2022; 12(15):7414. https://doi.org/10.3390/app12157414
Chicago/Turabian StyleQin, Rui, Genliang Chen, Haibo Zhang, Luo Liu, and Shaoqiu Long. 2022. "A Kalman Filter-Based Method for Reconstructing GMS-5 Land Surface Temperature Time Series" Applied Sciences 12, no. 15: 7414. https://doi.org/10.3390/app12157414
APA StyleQin, R., Chen, G., Zhang, H., Liu, L., & Long, S. (2022). A Kalman Filter-Based Method for Reconstructing GMS-5 Land Surface Temperature Time Series. Applied Sciences, 12(15), 7414. https://doi.org/10.3390/app12157414