## 3 Results
### The Coupled Effect of Key Parameters on Methane Plume Retrieval  
This section will discuss the coupled effect of the three instrument parameters, as reflected in the estimated emission rates. Note that directly using the emission rates estimated results for parameter comparison may introduce errors from other factors, such as errors in \(U_{eff}\) and the estimation of the plume length. However, we contend that the overall trend in the estimated emission results could effectively indicate variations in the sensitivity of the instrument parameters. Due to the limitations of the simulation domain and the plume segmentation process, we restrict the spatial resolution from 10 m to 120 m. The total estimated results for three different emission levels are shown in Figure 8. It shows the estimation results clustered by different spatial resolutions (10 m, 30 m, 60 m, and 120 m). It can be seen that variations in instrument parameters lead to a certain degree of underestimation in the estimated emission rates, but such underestimations extend as methane emissions rate decrease. The estimated error for an emission rate of 10,000 kg/h is almost below 50%. As the emission rate decreases to 100 kg/h, the overall estimated error gradually increases, with the error even reaching up to 100%. A possible explanation is that higher emission rates lead to stronger \(\Delta\)XCH\({}_{4}\) signals, resulting in a sharper contrast with the background. Consequently, a more complete plume was detected. With an emission of 100 kg/h at the spatial resolution of 10 m, the most striking \(\Delta\)XCH\({}_{4}\) of the plume region remains below 100 ppb, and the weak concentration signal is easily submerged in the noise. In addition, changes in spatial resolution have the most marked impact on small emission rate plumes, and the underestimation gradually increases as spatial resolution degrades. Meanwhile, the estimated results also exhibit some changes with the other two instrument parameters. Since the estimated results of different emissions levels show similar trends across various instrument parameters, a detailed analysis was conducted at 1000 kg/h, as shown in Figure 9. Results for other emission rates are provided in the Supplementary Materials. As shown in the three-dimensional distribution plot of Figure 9a, degrading the spatial resolution from 10 m to 120 m has regular estimated results. Within this range of spatial degradation, \(\Delta\)XCH\({}_{4}\) remains easily distinguished from the background. At a high retrieval precision of a single pixel, characterized by a finer spectral resolution (2 nm or 5 nm) and higher SNR (from 400 to 800), plume emission rates were estimated more accurately, with less than 20% estimated error at all spatial resolutions. However, at a moderate spectral resolution (10 nm or 15 nm), the quantification results are underestimated generally. As mentioned in Section 3.1, the error in the single-pixel XCH\({}_{4}\) rises with coarser spectral resolution. Especially in low SNR scenarios, the plume signal is often overwhelmed by the noise, resulting in a greater degree of underestimation. For the estimation results of small emission rates (100 kg/h), see the Supplementary Materials Figure S2. When the  
Figure 8: Estimated results of plumes with varying emission rates under different instrument parameters: (**a**) 10,000 kg/h; (**b**) 1000 kg/h; (**c**) 100 kg/h. spatial resolution was coarsened to 120 m, both the spectral resolution and SNR were suboptimal, making it difficult to be effectively quantified under the current retrieval algorithm method. This indicates that spatial resolution is a critical prerequisite for detecting small emission plumes; whereas, for plumes with much higher emission rates, although the \(\Delta\)XCH\({}_{4}\) decreases with the change in spatial resolution, it remains greater than the background, and minor variations in spatial resolution (from 10 m to 120 m) have a negligible impact on plume quantification.