## 2 Methodology and Data
### High Precision and Wide Range XCH4 Fusion Dataset Construction  
Due to variations in observation time, methods, and retrieval algorithms, there are discrepancies between the XCH4 products from TROPOMI and GOSAT. TROPOMI offers a wide range, while GOSAT provides higher precision [48; 49]. Recognizing their complementary strengths, we aim to merge these datasets to obtain an XCH4 dataset with both high precision and broad coverage. However, directly merging them is challenging due to inherent differences, often leading to reduced accuracy. Therefore, we use GOSAT's high-precision XCH4 product as the reconstruction target and employ machine learning models to correct the discrepancies, enhancing TROPOMI's precision. Based on spatial matching, we use the local random forest (LRF) model to integrate the two satellite products. Traditional modeling methods typically employ a global model [50], which is constant across all locations and struggles to account for spatiotemporal heterogeneity, especially in a rapidly changing global environment. In contrast, our LRF model varies with spatial location, adapting to the spatiotemporal heterogeneity of global XCH4 data distribution. The structure of the LRF model is illustrated in Figure 2.  
Considering the broader coverage of TROPOMI products, during the model training process, we used GOSAT XCH4 data as the dependent variable and TROPOMI XCH4 data as the independent variable. To enhance the model's accuracy, we also included longitude, latitude, aerosol thickness, surface albedo, DEM, and month as additional independent variables. Considering the spatial variability of  
Figure 2: Structure of the LRF model. spatially adaptive window for model training. Assuming the number of matched samples within the window is \(N\), the number of training samples within the window gradually increases as the window expands. Once the number of training samples within the window reaches a certain threshold (\(N\geq N_{0}\), where \(N_{0}\) is set to 100 in this study), the expansion stops. Then, the samples within the window are used to train the LRF model, yielding the XCH\({}_{4}\) for the given location (\(x_{i}\), \(y_{i}\)). To validate the performance of the LRF model and to ensure the proper organization of training and testing data, we employed a 5-fold cross-validation method within each local spatial window. Specifically, for each pixel (\(x_{i}\), \(y_{i}\)) to be reconstructed, we collected matching observations from TROPOMI and GOSAT within an adaptively expanding spatial window. When the number of matching samples reached at least 100 (\(N\geq N_{0}\)), where \(N_{0}\) is set to 100 in this study), we stopped expanding the window to ensure sufficient data for model training and validation. We then randomly divided the collected samples into five approximately equal subsets (folds). During cross-validation, four folds (accounting for 80% of the data) were used as the training set, which included independent variables and the dependent variable. The remaining one fold (accounting for 20% of the data) was used as the test set to evaluate the predictive performance of the model. By rotating the position of the test fold in each iteration, we ensured that every data point was used for testing, enhancing the reliability of the evaluation results. Algorithm 1 provides detailed pseudocode for the fusion of TROPOMI and GOSAT satellite data using the LRF model as employed in this work. This is intended to facilitate readers in reproducing the results by referencing Figure 2 along with the descriptions in this section.