Noise filtering, data predicting, and unmonitored data interpolating are important to dam deformation data analysis. However, traditional methods generally process single point monitoring data separately, without considering the spatial correlation between points. In this paper, the Space-Time Kalman Filter (STKF), a dynamic spatio-temporal filtering model, is used as a spatio-temporal data analysis method for dam deformation. There were three main steps in the method applied in this paper. The first step was to determine the Kriging spatial fields based on the characteristics of dam deformation. Next, the observation noise covariance, system noise covariance, the initial mean vector state, and its covariance were estimated using the Expectation Maximization algorithm (EM algorithm) in the second step. In the third step, we filtered the observation noise, interpolated the whole dam unmonitored data in space and time domains, and predicted the deformation for the whole dam using the Kalman filter recursion algorithm. The simulation data and Wuqiangxi dam deformation monitoring data were used to verify the STKF method. The results show that the STKF not only can filter the deformation data noise in both the temporal and spatial domain effectively, but also can interpolate and predict the deformation for the whole dam.

Current reported spatiotemporal solutions for fusing multisensor aerosol optical depth (AOD) products used to recover gaps either suffer from unacceptable accuracy levels, i.e., fixed rank smooth (FRS), or high time costs, i.e., Bayesian maximum entropy (BME). This problem is generally more serious when dealing with multiple AOD products in a long time series or over large geographic areas. This study proposes a new, effective, and efficient enhanced FRS method (FRS-EE) to fuse satellite AOD products with uncertainty constraints. AOD products used in the fusion experiment include Moderate Resolution Imaging SpectroRadiometer (MODIS) DB/DT_DB_Combined AOD and Multiangle Imaging SpectroRadiometer (MISR) AOD across mainland China from 2016 to 2017. Results show that the average completeness of original, initial FRS fused, and FRS-EE fused AODs with uncertainty constraints are 22.80%, 95.18%, and 65.84%, respectively. Although the correlation coefficient (R = 0.77), root mean square error (RMSE = 0.30), and mean bias (Bias = 0.023) of the initial FRS fused AODs are relatively lower than those of original AODs compared to Aerosol Robotic Network (AERONET) AOD records, the accuracy of FRS-EE fused AODs, which are R = 0.88, RMSE = 0.20, and Bias = 0.022, is obviously improved. More importantly, in regions with fully missing original AODs, the accuracy of FRS-EE fused AODs is close to that of original AODs in regions with valid retrievals. Meanwhile, the time cost of FRS-EE for AOD fusion was only 2.91 h; obviously lower than the 30.46 months taken for BME.

The spatio-temporal random effect (STRE) model, a type of spatio-temporal Kalman filter model, can be used for the fusion of the Global Navigation Satellite System (GNSS) and Interferometric Synthetic Aperture Radar (InSAR) data to generate high spatio-temporal resolution deformation series, assuming that the land deformation is spatially homogeneous in the monitoring area. However, when there are multiple deformation sources in the monitoring area, complex spatial heterogeneity will appear. To improve the fusion accuracy, we propose an enhanced STRE fusion method (eSTRE) by taking spatial heterogeneity into consideration. This new method integrates the spatial heterogeneity constraints in the STRE model by constructing extra-constrained spatial bases for the heterogeneous area. The effectiveness of this method is verified by using simulated data and real land surface deformation data. The results show that eSTRE can reduce the root mean square (RMS) of InSAR interpolation results by 14% and 23% on average for a simulation experiment and Los Angeles experiment, respectively, indicating that the new proposed method (eSTRE) is substantially better than the previous STRE fusion model.

Ground PM _2.5 mapping method based on aerosol optical depth (AOD) is universal. However, since the modeling samples for hourly PM _2.5 mapping are usually very large, and it also lacks an efficient spatiotemporal model to describe the strong spatiotemporal correlation existed in the large hourly PM _2.5 modeling samples, most of the existing studies focus on the daily, monthly, and annual average scales. In this study, a model coupled with spatiotemporal Kalman filter and linear mixed effect (LMESTKF) is proposed. Based on the hourly seamless 1-km AOD data generated by fusing multiple satellite products and numerical model data products, we realize efficient and accurate hourly seamless 1-km PM _2.5 mapping in the Beijing-Tianjin-Hebei urban agglomeration region. Results show the R ² , RMSE, Bias and MAPE metrics based on sample-based and site-based 10-fold cross validation method are (0.91, 14.37 μg/m ³ , -0.41 μg/m ³ , 28.91 %) and (0.87, 16.98 μg/m ³ , -0.32 μg/m ³ , 34.62 %) respectively, the accuracy is higher than those of the existed PM _2.5 mapping models in Beijing-Tianjin-Hebei urban agglomeration region. In addition, the time and memory consumption required to construct the LMESTKF model for hourly PM _2.5 mapping at monthly scale is only around 10 minutes and 4 GB respectively, indicating that the LMESTKF model proposed in this study is not only high in accuracy but also fast in efficiency. These results prove the proposed LMESTKF model can efficiently generate accurate hourly PM _2.5 maps, which can further promote the prevention and control of PM _2.5 pollution in China.