# Monitoring Water Area Dynamics in Kashgar (2003-2023) Using Multi-Source Remote Sensing Data
## 2 Materials and Methods
### Methods
#### 2.3.2 Data Analysis Methods  
This study employed the Theil-Sen slope estimator [32] and the Mann-Kendall (MK) test [33] to analyze temporal trends in water area changes within the Kashgar region. These non-parametric methods are widely utilized for trend analysis due to their robustness and flexibility. The Theil-Sen estimator provides a robust measure of trend magnitude, exhibiting resilience to outliers and measurement errors, making it particularly suitable for long-term time series data. The MK test, on the other hand, assesses the significance of monotonic trends in time series data without requiring assumptions of normality or linearity [34]. Furthermore, the MK test possesses the capability to identify abrupt shifts or change points within the data [35].  
This study employed visual interpretation and kernel density analysis to investigate the spatiotemporal dynamics of water bodies in the Kashgar region from 2003 to 2023. The visual interpretation provided a qualitative assessment of water body changes, while the kernel density analysis offered a quantitative evaluation of their spatial distribution patterns, particularly for dispersed water bodies such as lakes. Kernel density estimation, a non-parametric technique, constructs a smoothed probability density function by convolving a kernel function with each data point, assigning weights based on distance [36]. This approach enables the quantification of spatial clustering or dispersion of point features.  
This study investigated the seasonal trends and changes in water area extent in the Kashgar region from 2003 to 2023, utilizing water inundation frequency (_WIF_) data. WIF, defined as the ratio of inundation occurrences at a given location to the total number of inundation events within a specified period, serves as an indicator of regional inundation patterns. WIF is calculated by dividing the number of times a pixel is inundated by the total number of inundation events across the time series [37]. Mathematically, WIF can be expressed as:  
\[WIF=\frac{\sum_{j=1}^{N}W_{i,j}}{\sum_{j=1}^{N}O_{i,j}}\times 100\% \tag{3}\]  
where \(N\) denotes the total number of valid observed pixels; \(W_{i,j}\) is a binary variable representing the inundation status of the ith pixel in the jth image (1 indicating inundation, 0 indicating no inundation); and \(O_{i,j}\) denotes the observation status of the ith pixel in the jth image (1 indicating observed, 0 indicating unobserved).  
To mitigate noise artifacts arising from cloud cover, shadowing, and resolution constraints, the 25 th and 75 th percentiles of water inundation frequency (WIF) are adopted as primary segmentation thresholds, consistent with established methodologies [6; 38]. Pixels with WIF values below the 25 th percentile were classified as non-water bodies. Pixels exceeding the 25 th percentile were further categorized into two classes: permanent water bodies (characterized by year-round presence and insensitivity to seasonal variations, with WIF values ranging from 0.75 to 1) and seasonally fluctuating water bodies (exhibiting inundation extent variations across seasons, with WIF values ranging from 0.25 to 0.75).