## 2 Materials and Methods
### Data and Methods
#### 2.2.3 Multi-Source Time Series Remote Sensing Image Fusion Method Based on Space-Time Features  
The optimal weighted least squares fitting approach based on pixel, Multi-sensor Time-series correlation and Fusion (MulTiiFuse) [11], is employed to fuse the multi-source remote sensing image. The fused image is further corrected with spatial features. The corrected image time series is used for subsequent dynamic monitoring with the Mann-Kendall detection method and Theil Sen Slope Analysis. Finally, an accuracy assessment is performed to evaluate the monitoring results. The data processing and analysis procedure is shown in Figure 2.  
* Remote Sensing Image Fusion Based on Time Features  
When two time series remote sensing images from different sensors are combined, it is assumed that the time frames of the discrete time series extracted from the reference image sequence and the image sequence to be fused are inconsistent. As shown in Figure 3[11], the acquisition time intervals of time series \(X\) and \(Y\) are different, and there is an overlapping period. Firstly, linear interpolation is applied to interpolate the time points of \(X\) on \(Y\), and the interpolated time series \(X_{int}\) is obtained. Similarly, \(Y_{int}\) is also obtained. Then, in cases where linear interpolation may get singular values and the length of the time series is inconsistent, the amplitudes are introduced and normalized to obtain the weight of each acquisition time point. Finally, the fitting relationship between the interpolation time series \(X_{int}\) and \(Y_{int}\) is calculated with the weighted least square fitting regression method [23], as shown in the Equation below:  
\[Y_{int}=a+bX_{int} \tag{1}\]  
where \(a\) and \(b\) are constants. \begin{table}
\begin{tabular}{c c} \hline \hline
**Sensor** & **Acquisition Time** \\ \hline Landsat 7 ETM+ & 1999-10-01 \\ Landsat 7 ETM+ & 2000-09-01 \\ Landsat 7 ETM+ & 2002-09-07 \\ Landsat 5 TM & 2003-09-18 \\ Landsat 7 ETM+ & 2004-09-12 \\ Landsat 7 ETM+ & 2005-09-15 \\ Landsat 5 TM & 2006-08-09 \\ Landsat 7 ETM+ & 2007-09-21 \\ Landsat 7 ETM+ & 2008-09-23 \\ Landsat 7 ETM+ & 2009-08-25 \\ Landsat 7 ETM+ & 2010-08-28 \\ Landsat 7 ETM+ & 2011-06-28 \\ Landsat 7 ETM+ & 2013-06-17 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sensor and acquisition time of the Landsat images used in the study. * Fusion Image Correction Based on Spatial Features  
The above method provides a good idea for multi-source data fusion from the perspective of time characteristics. Based on this, we further uniformly select and modify singular pixels in spatial features of similar pixels to enhance the fusion effect of the multi-source remote sensing image data. Unsupervised classification refers to the clustering of pixels with similar spectral or spatial features in multispectral images. In this study, the unsupervised classification is uses to cluster image data as the basis to modify singular pixels. The common algorithms for clustering analysis include Iterative Self-Organizing Data Analysis (ISODATA), K-Means, chain method and so on. In ISODATA, the center of each cluster is determined by iteratively calculating the mean value of the sample pixels, which is similar to the K-Means algorithm. However, ISODATA is more advanced than K-Means with better classification results as the algorithm is self-organizing, i.e., being able to adjust the number of clusters according to intermediate results. This study applies ISODATA to perform cluster analysis on time series images to be corrected. Based on the results of unsupervised classification of multispectral images, the original image corresponding to the image to be corrected is classified, and then the Mahalanobis distance [24] is calculated to determine whether the pixel of the interpolation image belongs to a specific category.