## 1 Introduction  
Land surface temperature (LST) products generated from a Moderate-Resolution Imaging Spectroradiometer (MODIS) are significant for various studies of surface processes, including land-air interactions [1, 2], water resource management [3, 4], agricultural drought [5], and environmental biogeochemistry [6], primarily due to their relatively high revisit time. However, the relatively low spatial resolution, of 1000 m, of the MODIS LST product limits its applicability in studies requiring high temporal and spatial resolutions to identify detailed variations in the thermal heat flux across the study region [7, 8, 9, 10, 11, 12]. Therefore, downscaling the MODIS LST to higher spatial resolutions is crucial to meet the needs of many studies, such as argon-drought monitoring and urban heat island monitoring, which require pixel-level detail to capture LST variations in complex environments [13, 14, 15, 16]. Downscaling involves enhancing the spatial resolution of data [17]. LST downscaling in remote sensing typically leverages the relationships between different spatial resolutions in the form of regression models to predict the LST at finer resolutions. These methods can be broadly categorized into two types: direct LST downscaling and thermal radiance (TR) downscaling [18, 19, 20]. Many researchers have conducted studies on direct LST downscaling methods, which typically utilize the regression relationship between the LST and remote sensing indices (RSIs) [21, 22, 23, 24, 25]. The DisTrad method is a typical approach that utilizes a linear regression relationship between the LST and the NDVI to downscale the MODIS LST to finer spatial resolutions [26]. [PERSON] found that a regression model using only the LST and the NDVI was insufficient to capture the LST spatial distribution in urban areas and proposed an enhanced Disaggregation of Thermal Radiometry (DisTrad) method incorporating 15 remote sensing indices [27]. [PERSON] and [PERSON] decomposed the pixels of MODIS LST images using the relationship between LST and principal components within a moving window over a high-resolution auxiliary image [28]. [PERSON] et al. further explored the impact of varying the size of the moving window on the regression relationship between the LST and the RSI [29]. TR downscaling methods generate downscaled LSTs using the physical thermal properties of different landcovers, rather than relying directly on LST and RSI relationships [30, 31, 32, 33, 34]. [PERSON] and [PERSON] developed a physical method to decompose low-spatial-resolution TR for sub-pixel LST retrieval by employing a scale-invariant model on MODIS TR and the statistical relationship between MODIS TR and different landcover fractions using high-resolution auxiliary data [30]. [PERSON] and [PERSON] downscaled MODIS TR through a nonlinear transformation to maximize the correlation between MODIS TR and various VNIR bands [35]. [PERSON] et al. introduced a two-step pixel decomposition method that transitions from TR decomposition to LST downscaling, ensuring that the thermal radiance of parent pixels in the MODIS LST image remains unchanged [36, 37]. Beyond these two categories of downscaling methods, efforts have also been made to apply artificial neural networks [38] and spectral unmixing models [39] for disaggregating Landsat TM thermal data and airborne, hyperspectral remote sensing data from the DAIS [40, 41, 42]. However, most existing LST downscaling methods are based on pixel-by-pixel image analysis, which has inherent limitations. Pixel-based approaches often struggle to capture spatial patterns and contextual information, particularly in heterogeneous landscapes, leading to the so-called \"salt and pepper effect\" [43]. These methods also fail to account for the spatial relationships between neighboring pixels, which are crucial for accurately representing land surface processes. Given these limitations, there is a need to explore alternative approaches that can better capture spatial and contextual information [15, 16].