## 2 Methodology and Data
### Spatial Matching  
The GOSAT and Sentinel-5P satellites, as separate Earth observation platforms, possess unique design features and technical specifications, which directly impact their detection capabilities for the important greenhouse gas methane (CH\({}_{4}\)) in the atmosphere. Firstly, there is a significant difference in spatial resolution between the two satellites [46], which determines their level of detail in capturing the distribution of CH\({}_{4}\) in specific regions on the ground or in the troposphere. Secondly, their methods of observing CH\({}_{4}\) column concentrations in the troposphere are vastly different. GOSAT uses point-column scanning, while Sentinel-5P uses swath scanning, resulting in GOSAT having a much lower coverage of CH\({}_{4}\) concentration compared to Sentinel-5P. These two factors together result in spatial differences in their XCH\({}_{4}\) data products. To carry out subsequent fusion work, we need to first manually \"align\" the two datasets through spatial matching, ensuring that corresponding observations from both satellites fall on the same or closely adjacent geographic grid points to obtain data suitable for fusion and to eliminate spatial differences as much as possible.  
To achieve spatial matching, we use the boundaries of the grid and the interval between grid points for spatial matching [34; 47]. Taking a GOSAT data point as an example, we subtract its longitude from the left boundary of the grid longitude (column number 1), and then divide by the longitude interval between grid points to determine which two longitude grid points the point falls between. Next, we observe the decimal part; if it is greater than 0.5, it indicates that the point is closer to the right-side grid point, so the right-side grid point is chosen as the longitude matching point. If it is less than 0.5, it indicates that the point is closer to the left-side grid point, so the left-side grid point is chosen as the longitude matching point. A similar process is then applied to the latitude, with the difference being that the left boundary of the longitude grid (column number 1) is the minimum longitude of the study area, whereas the upper boundary of the latitude grid (row number 1) is the maximum latitude of the study area. Therefore, the difference between the upper boundary of the latitude grid and the latitude of the point to be matched is calculated, divided by the latitude interval, and if the decimal part is greater than 0.5, it indicates that it is closer to the lower grid point, so the lower grid point is chosen as the latitude matching point; if it is less than 0.5, it indicates that it is closer to the upper grid point, so the upper grid point is chosen as the matching point. This completes the spatial matching of longitude and latitude for a GOSAT data point. By repeating these operations  
Figure 1: Overview of the methodology workflow in this study.  
for each GOSAT data point, the spatial matching for all data points can be completed. The process of longitude matching for a GOSAT data point can be represented by Equation (1).  
\[\begin{array}{l}n\_lon=(lonG-min\_lonT)/interval;\\ decimal\_lon=n\_lon-floor(n\_lon);\\ decimal\_lon<0.5\to lonG\leftrightarrow lonT(,floor(n\_lon)+1);\\ decimal\_lon>0.5\to lonG\leftrightarrow lonT(,ceil(n\_lon)+1);\end{array}, \tag{1}\]  
where \(lonG\) represents the longitude of the point to be matched, \(min\_lonT\) represents the left boundary of the TROPOMI geographic grid (i.e., the minimum longitude of the study area, with column number 1), interval represents the interval between adjacent longitude grid points, and \(n\_lon\) represents the number of intervals between the longitude of the point to be matched and the left boundary, floor() is the floor function for rounding down, \(decimal\_lon\) represents the decimal part of \(n\_lon\), and ceil() is the ceiling function for rounding up.  
The latitude matching process is similar.