## 2 Methodology and Data
### High Precision and Wide Range XCH4 Fusion Dataset Construction
GFEI uses national emissions data reported to the United Nations Framework Convention on Climate Change (UNFCCC) and maps it to infrastructure locations allocated to a 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\) grid, thus creating a methane emissions map for the oil, gas, and coal industries and sub-industries. As the spatial resolution sampling decreases, background noise becomes smoother. To adapt the ILMF inversion results to the accuracy of LRF (7 km), we upsample the 30 m resolution \(\Delta\)XCH4 image to a 1 km scale. The spatial resolution of the GFEI inventory is 0.1\({}^{\circ}\), which is sampled and reprojected to a 14 km grid. To establish the relationship between the LRF model, ILMF, and the prior GFEI, we define the convolution of the 1 km resolution \(\Delta\)XCH4 with the GFEI on a grid-by-grid basis to provide corresponding weight values for XCH4, as described by Equation (7):

\[P_{i}=\Delta XCH_{4_{i}}*GFEI_{i}, \tag{7}\]

The relationship between each 1 km grid cell's XCH4p and the output XCH4 LRF of the LRF model can be described by the following system of equations:

\[\left\{ \begin{array}{l}XCH^{1}_{4 LRF}=(\beta^{1}_{1}XCH^{1}_{4p}+\beta^{1}_ {2}XCH^{1}_{4p}+\ldots+\beta^{1}_{8}XCH^{1}_{4p})/\sum\beta^{1}+\varepsilon^{ 1}\\ XCH^{2}_{4 LRF}=(\beta^{2}_{1}XCH^{1}_{4p}+\beta^{2}_{2}XCH^{1}_{4p}+\ldots+\beta ^{2}_{8}XCH^{1}_{4p})/\sum\beta^{2}+\varepsilon^{2}\\ \ldots\\ XCH^{n}_{4 LRF}=(\beta^{n}_{1}XCH^{1}_{4p}+\beta^{2}_{2}XCH^{1}_{4p}+\ldots+ \beta^{n}_{8}XCH^{1}_{4p})/\sum\beta^{n}+\varepsilon^{n}\end{array} \right., \tag{8}\]where:

\[\beta_{i}=\
icefrac{{p_{i}}}{{\sum\limits_{i=1}^{\alpha}{p_{i}}}}, \tag{9}\]

To solve this model, we can consider it as a multiple linear regression process. Since this regression is rank-deficient, we use Lasso regression, which helps drive the regression coefficients towards zero, thus achieving sparsity in the features. The regression conditions are satisfied as follows:

\[argmin\Big{\{}\varepsilon^{T}\varepsilon+\alpha\big{\|}XCH_{4p}\big{\|}_{1} \Big{\}} \tag{10}\]

In Equation (10), the regularization coefficient \(\alpha\) is introduced to control model complexity and prevent overfitting by penalizing large regression coefficients. In our study, we set \(\alpha=0.1\) based on cross-validation experiments, which indicated this value achieved an optimal balance between accuracy and generalization. Specifically, we tested a range of \(\alpha\) values and found that values below 0.1 led to overfitting, increasing error on the validation set, while values above 0.1 resulted in underfitting. Thus, \(\alpha=0.1\) was selected to ensure a well-balanced trade-off between model precision and robustness. Ultimately, while ensuring high accuracy, we produce a 1 km spatial resolution XCH\({}_{4}\) dataset for the oilfield region. ## 3 Results

Located in Shandong Province, China, Dongying is home to the Shengli Oilfield, the second-largest oil production base in the country. Consequently, this study focuses on the Dongying area. The location of Dongying within China is shown in Figure 3. The image on the left shows the location of Shandong Province within China, while the image on the right indicates the location of Dongying City within Shandong Province. ### High Precision and Wide Range XCH\({}_{4}\) Dataset Fused by GOSAT and TROPOMI Data

After completing data filtering, spatiotemporal matching, and other preprocessing steps, we introduced independent variables such as latitude and longitude, surface albedo, and aerosol optical thickness. Using the LRF model, we fused TROPOMI and GOSAT data, combining TROPOMI's wide coverage with GOSAT's high precision, resulting in a high-precision global XCH\({}_{4}\) dataset. Figure 4 is a presentation of XCH\({}_{4}\) dataset fused by LRF model in Shandong Province.