## 3 Results  
### Performance of Different Spectral Resolutions  
At the same spectral sampling rate, a finer spectral resolution improves the detection of methane absorption features, thereby improving the identification of subtle variations in XCH4. The \(k\) spectrum represents the absorptive capacity of atmospheric CH4 for radiance at specific wavelengths. As shown in Figure 4a, different spectral resolutions affect the absorption coefficient \(k\) in distinct ways. Figure 4b exhibits the methane absorption coefficient \(k\) calculated by the majority of hyperspectral imagers at varying spectral resolutions. It is evident that the instruments with coarser spectral resolution tend to blur certain spectral absorption features, leading to a smoother variation in the \(k\) spectrum. Capturing delicate methane absorption details enables the mitigation of interference from low-frequency spectral information during retrieval to a certain extent [27], which is particularly important for enhancing subsequent retrieval precision.  
Figure 4: (**a**) \(k\) spectrum convolved with different spectral resolution; (**b**) same as (**a**), but convolved with different satellite sensors.  
Figure 3: Schematic representation of satellite radiance received at different spatial resolutions.  
At the 1000 kg/h emission rate, Figure 5a-d show the retrieved \(\Delta\)XCH\({}_{4}\) results, subtracting the background XCH\({}_{4}\). The finer spectral resolutions reveal a more distinct transient morphology of the plume at the same spatial resolution of 10 m and SNR of 800, with the \(\Delta\)XCH\({}_{4}\) signal more prominently differentiated from the background. The retrieval capabilities are comparable at 2 nm and 5 nm spectral resolutions. However, an underestimation of the retrieval results is observed at coarser spectral resolutions, making regions with low \(\Delta\)XCH\({}_{4}\) visually difficult to identify in the images. This underestimation is caused by an overall overestimation of the background and an underestimation of the plume regions. It may be attributed to the fact that as the spectral resolution decreases, it is difficult to accurately distinguish between methane absorption and other factors that influence the spectrum under the current algorithm. Also, since the retrieval was performed within a specific spectrum, limited spectral information could be one of the reasons for the poor performance obtained with coarse spectral resolution. However, this is beyond the scope of this article.  
Figure 5e-h present a comparison of the simulated and the retrieved \(\Delta\)XCH\({}_{4}\). Each plot includes linear regression lines and reference lines with a slope of 1, alongside the corresponding scatter points. Additionally, the relevant statistical variables are displayed. Meanwhile, it can be seen from the statistical variables that if the spectral resolution is 2 nm, the root mean square error (RMSE) is as low as 4.91 ppb. However, when the spectral resolution decreases to 15 nm, the RMSE increases significantly to 24.48 ppb, while the other two instrument parameters remain unchanged. Similarly, the mean absolute error (MAE) rises with coarser spectral resolutions, ranging from 3.44 ppb at 2 nm to 13.59 ppb at 15 nm. Notably, at spectral resolutions of 2 nm and 5 nm, the correlation coefficient (R\({}^{2}\)) remains comparable, indicating that the two spectral resolutions perform equally well in such little noise. These results highlight the significant impact of spectral resolution on retrieval performance.