## 3 Results and Discussion  
### Downscaling of MODIS LST with ASTER and ETM+ VNIR Data  
Following the downscaling procedure outlined in Figure 3, the MODIS LST product was successfully downscaled to a 90 m pixel scale using the ASTER and ETM+ VNIR data. Figure 5(a1,a2) illustrates the LST obtained from the ASTER LST product and the corresponding downscaled result from the MODIS LST product using the ASTER VNIR data. Both images display high LSTs in urban areas and lower LSTs in the suburban regions of York and Lancaster. This similar LST distribution suggests that the downscaled LST from the coarser MODIS LST image is applicable. Simultaneously, the MODIS LST product was downscaled to 90 m using the ETM+ VNIR data, given that the Landsat series represents the world's longest continuously acquired remote sensing data collection and is freely accessible. If the OBD downscaled result proves accurate, this method could be used to generate high-spatial-resolution and high-temporal-resolution thermal remote sensing datasets utilizing MODIS and Landsat series data. The downscaled results were validated through a comparative analysis with the ASTER LST product, rather than the ETM+ LST product, due to the temporal discrepancy between the MODIS and ETM+ imaging times. Figure 5(b1-b3) present the OBD results in a complex region containing urban areas, large rivers, and forests. Similar distributions are observed between the OBD downscaled result (Figure 5(b3)) and the ASTER LST product (Figure 5(b2)) across the entire image. However, the decomposed LST in the Susquehanna River appears more uniform in Figure 5(b3), while the true LST product shows higher LST fragments near the riverside. Figure 5(c1-c3) display the OBD results for urban and suburban areas, demonstrating similar color distributions and locations of high- and low-LST areas, indicating that the OBD method is suitable for these environments. To evaluate the similarity between the OBD downscaled results and the ASTER LST product, a scatter plot and a statistical chart were generated, as shown in Figure 6. Figure 6 presents the overall comparison scatter plot of the OBD and ASTER LST products, revealing a fitted line slope of 0.76, which is very close to a 1:1 line. Furthermore, the red area in the scatter plot is concentrated along the 1:1 line, indicating that many of the OBD results closely align with the ASTER LST product. This finding is further supported by the LST error statistics between the OBD LST and ASTER LST presented in Figure 6b. Figure 6b is the statistics plot of the OBD LST result minus the ASTER LST product. Most pixels fall within an LST error range of \([0,1]\) K. Approximately 80% of the total pixels demonstrate the OBD LST error within \(\pm 3\) K.  
To demonstrate the accuracy of the approach, Table 3 presents a comparison of the downscaled LST errors between the OBD and PBA methods across different landcover types in various areas. For the entire image in the ASTER natural terrain, the mean error (ME) of the OBD method is \(-0.96\) K, indicating that the decomposition result is, on average, \(0.96\) K lower than the true LST. The RMSE is \(2.12\) K, indicating an average error of \(2.12\) K in the decomposition, despite its general applicability. In comparison, the ME and RMSE of the PBA method are higher, with values of \(3.13\) K and \(2.48\) K, respectively. In region B, the predominant landscape is characterized by natural surfaces, such as vegetation, with fewer  
Figure 5: A comparison of the downscaling results: (**a1**) The ASTER LST image from the AST_08 product. (**a2**) The corresponding downscaled result of the MODIS LST into the pixel scale of \(90\) m by the OBD method with the ASTER VNIR data. (**b1**) The ETH+ data of area B, RGB: 432. (**b2**) The ASTER LST image of area B. (**b3**) The downscaled result of the MODIS LST image of area B by the OBD approach with the ETH+ VNIR data. (**c1**) The ETH+ data of area C, RGB: 432.