## 2 Materials and Methods
### IMAP-DOAS Retrieval  
Currently, various algorithms are employed for XCH\({}_{4}\) retrieval, including physical retrieval and data-driven methods. [PERSON] et al. (2023) compared two such methods, matched filter and IMAP-DOAS, through emission control experiments [32]. It is suggested that  
Figure 2: Instantaneous \(\Delta\)XCH\({}_{4}\) plume image for 10 m spatial resolution with an emission rate of 1000 kg/h, simulated by WRF-LES.  
the estimated results based on the IMAP-DOAS retrieval algorithm have better agreement with the true emissions. The matched filter is widely used for strong emissions where the plume occupies a small portion of the image, constructing a reference spectrum by averaging the radiance within the scene [33]. Given the limited experimental domain of this study, IMAP-DOAS was employed for pixel-by-pixel retrieval. The IMAP-DOAS algorithm, similarly to the conventional DOAS method, separates high-frequency spectral information from low-frequency spectral information, with the latter parameterized using Legendre polynomials. Within the SWIR spectrum, the absorption cross-section of methane is influenced by pressure and temperature. Additionally, maximum likelihood estimation was introduced into the algorithm, and the XCH\({}_{4}\) was obtained through a Gaussian Newton iterative optimization [34]. The forward model, as expressed in Equation (1), fitted low-frequency spectral information using Legendre polynomials [25]:  
\[F^{h}(x)=I_{0}(\lambda)\exp\left(-A\sum_{n=1}^{n}s_{n}\sum_{l=1}^{l}\tau_{n,l} \right)\cdot\sum_{k=0}^{K}a_{k}P_{k}(\lambda) \tag{1}\]  
In the formula, \(F^{h}(x)\) is the high spectral resolution spectrum as simulated by the forward model for a given state vector \(x\), \(I_{0}(\lambda)\) represents the solar intensity at different wavelength \(\lambda\). \(\tau_{n,l}\) denotes the optical depth of various trace gases at different vertical levels, based on profiles from the U.S. Standard Atmosphere. \(A\) is the air mass factor (AMF), which is defined as the ratio between the retrieved slant column and the atmospheric vertical column. \(s_{n}\) serves as the scale factor to the default optical depth in the retrieval. The term \(P_{k}\) is the kth Legendre polynomial, while \(a_{k}\) represents coefficients optimized in the retrieval. Subsequently, a Gauss-Newton iteration was applied, as depicted in Equation (2):  
\[x_{i+1}=x_{a}+\left(\mathbf{K}_{i}^{T}\mathbf{S}_{o}^{-1}\mathbf{K_{i}}+ \mathbf{S}_{a}^{-1}\right)^{-1}\mathbf{K}_{i}^{T}\mathbf{S}_{o}^{-1}\cdot[y- \mathbf{F}(x_{i})+\mathbf{K}_{i}(x_{i}-x_{a})] \tag{2}\]  
In this iterative process, \(x_{a}\) represents the priori state vector, including CH\({}_{4}\), H\({}_{2}\)O(g), and NO\({}_{2}\). We set the \(x_{a}\) to be very large, such that the retrieved parameters were almost entirely determined by the observation data. \(x_{i+1}\) represents the state vector during the iteration process. The observation error matrix \(\mathbf{S}_{o}\) was determined by the instrumental's SNR, while \(\mathbf{S}_{a}\) is the prior error covariance matrix. \(y\) is the observed backscatter top-of-atmosphere (TOA) radiance, \(\mathbf{F}(x)\) is the low-resolution spectrum convolved with the SRF in the forward model. \(\mathbf{K_{i}}\) represents the Jacobian matrix, and was calculated for each iteration i of the state vector. The retrieval process was performed with around 2.3 \(\upmu\)m, where CH\({}_{4}\) exhibits strong absorption features. Additionally, in this algorithm, it is also necessary to subtract the background value to derive \(\Delta\)XCH\({}_{4}\). The background concentration was determined by taking the pixels not included in the plume mask and taking a percentile [32].