## 3 Results and Discussion
### A Discussion of the Influential Elements on the OBD Results  
Although we can obtain a well-decomposed LST result from the OBD method, the elements determining the accuracy of the decomposed result should be analyzed. The radiance of the object and the weight of the subpixels or sub-objects are two main influential elements of the OBD method.  
The radiance error of an object is often due to the partial coverage of MODIS pixels by the edge areas of objects. If an LST image ranges between 300 K and 310 K, the radiance in the broadband would be approximately 164 Wm\({}^{-2}\) to 190 Wm\({}^{-2}\), under the assumption of a broadband emissivity (BBE) value of one. We hypothesize that the radiance errors of objects fall within the range of \(\pm\)5 Wm\({}^{-2}\) and \(\pm\)5%. Figure 8 illustrates the OBD LST error under different LST values with varying radiance errors. As shown in Figure 8a,b, the OBD LST error increases with the increasing radiance error. Additionally, the LST error varies depending on the LST value under the same radiance error. For instance, if the radiance error of an object is \(-\)4 Wm\({}^{-2}\), the LST error for a pixel with a true LST of 292 K ranges from \(-\)2.3 K to \(-\)1.7 K. Conversely, the LST error for a pixel with a true LST of 320 K ranges from \(-\)1.7 K to \(-\)1.1 K. The OBD LST error increases with the rising LST under a constant  
Figure 7: Influence of the object’s weight on OBD results.  
radiance error, as shown in Figure 8a. In contrast, the OBD LST error decreases with the rising LST under a constant radiance percentage error, as shown in Figure 8b. This occurs because higher LST values correspond to higher thermal radiance, resulting in greater radiance errors under the same percentage of radiance error.  
The initial LST estimation errors, influenced by the LST-RSI relationship, primarily affect the radiance of the object and the weighting of subpixels or sub-objects. Different land surface types may exhibit similar spectral characteristics in remote sensing images, despite having significantly different temperature values. To evaluate whether our OBD method improves the decomposed results compared to the initial LST, we hypothesize that an object, represented by high-spatial-resolution multispectral remote sensing data, consists of 5000 subpixels, with temperatures ranging from 290 K to 310 K. The initial LST errors for these subpixels were randomly generated within the ranges of \(\pm\)1 K, \(-\)4 to 0 K, and 0 to 4 K. We compared the mean error (ME), standard deviation (STD), and root mean square error (RMSE) between the initial LST errors and the OBD LST errors. This process was repeated 10,000 times to generate the comparative figures shown in Figure 9. Figure 9(a1-a3) presents the ME comparisons for the object under different initial LST error ranges. As shown in Figure 9(a1), the ME of the initial LST error within the \(\pm\)1 K range was reduced from \(\pm\)0.6 K to \(\pm\)0.1 K after applying the OBD method. In Figure 9(a2,a3), the initial LST ME for the ranges of \(-\)4 to 0 K and 0 to 4 K, representing low and high LST estimates, respectively, were significantly reduced to \(\pm\)0.1 K after applying the OBD method. The OBD method effectively reduces the ME, thereby preventing extreme LST estimations for subpixels. Figure 9(b1-b3) demonstrate that the OBD method does not significantly affect the STD of LST errors. However, as shown in Figure 9(c1-c3), the RMSE of the initial LST errors in the ranges of \(-\)4 to 0 K and 0 to 4 K was markedly reduced, indicating that the OBD downscaled LST results are much closer to the true LST.  
Figure 8: OBD LST error of (**a**) \(\pm\)5 Wm\({}^{-2}\) and (**b**) \(\pm\)5% under different radiance estimation errors.