## 2 Methodology and Data
### High Precision and Wide Range XCH4 Fusion Dataset Construction
```
Input: - TROPOMI XCH\({}_{4}\) dataset \(T_{\text{Tropori}}\) - GOSAT XCH\({}_{4}\) dataset \(T_{\text{Gosat}}\) - Auxiliary variables \(V\)(longitude, latitude, aerosol optical depth, surface albedo, DEM, month) - Minimum number of training samples \(N_{0}=100\)
```  
Output: - Reconstructed high-precision and wide-coverage XCH\({}_{4}\) dataset \(T_{\text{reconstructed}}\) ```
**Procedure:**  
**For** each pixel location (\(x_{i}\),\(y_{i}\)) in \(T_{\text{tropomi}}\)**do**:  
1. Initialize spatial window \(W\) centered at (\(x_{i}\),\(y_{i}\)). 2. Set sample count \(N=0\). 3. **While**\(N<N_{0}\)**do**:  
1. Expand spatial window \(W\) (e.g., increase radius). 2. Collect matched samples within \(W\):  
- \(S=\{(x_{i}\),\(y_{i})\ |\ (x_{i}\),\(y_{i}\))\(\in\)\(W\), \(T_{\text{Tropomi}}(x_{i}\),\(y_{i}\)) and \(T_{\text{Gosat}}(x_{i}\),\(y_{i}\)) are available}. 3. Update sample count.\(W\):  
4. **End While**  
5. Prepare training data:  
1. Dependent variable \(Y=[T_{\text{Gosat}}(x_{i}\),\(y_{i}\))], \(\forall(x_{i}\),\(y_{i}\))\(\in\)S.  
2. Independent variables \(X=[T_{\text{Tropomi}}(x_{i}\),\(y_{i}\)), \(\forall(x_{i}\),\(y_{i}\))], \(\forall(x_{i}\),\(y_{i})\)\(\in\)S.  
6. Train a random forest model \(M\) using \(X\) and \(Y\). 7. Predict the XCH\({}_{4}\) value at (\(x_{i}\),\(y_{i}\)):  
1. Construct input features \(x_{i}\)\({}^{\text{input}}=[T_{\text{Tropomi}}(x_{i}\),\(y_{i}\)), \(V(x_{i}\),\(y_{i}\))]. 2. Compute predicted value \(\hat{Y}_{i}=M\).predict (\(x_{i}\)\({}^{\text{input}}\)). 8. Assign \(\hat{Y}_{i}\) to \(T_{\text{reconstructed}}(x_{i}\),\(y_{i}\)). End For Return\(T_{\text{reconstructed}}\). ```

**Algorithm 1** Pseudocode for Fusion Algorithm. ### Pre-Processing of GF-5 Data

Before utilizing the GF-5 imagery, it is essential to perform radiometric calibration, geometric correction, and other preprocessing steps, which are considered routine and will not be elaborated here. Additionally, it is necessary to exclude ground objects that could significantly affect the inversion results, such as clouds, shadows, and water bodies. In this study, the cloud mask was extracted based on the cloud detection method proposed by [PERSON] et al. [51]. This method involves calculating the equivalent apparent reflectance \(R_{1}\), \(R_{2}\), \(R_{3}\), \(R_{4}\) for each pixel in the 11 th to 20 th bands, 30 th to 60 th bands, 192 nd band, and 270 th to 272 nd bands of the imagery. A pixel is identified as a cloud pixel if it meets the following conditions:

\[\left\{ \begin{array}{l}R_{1}\cup R_{2}\textgreater{}0.3\\ R_{3}\textgreater{}0.04\cup R_{1}\textgreater{}0.15\\ \frac{R_{1}}{R_{4}}\textgreater{}7.5\cup\frac{R_{4}}{R_{3}}\textless{}1\end{array}  \right., \tag{2}\]

For shadow detection, this study employs a method based on the HSV color space. The HSV model is a hexagonal cone-shaped color space based on hue (H), saturation (S), and value (V). In this model, H represents the color information, indicating the position of the spectral color and is expressed in degrees; S represents the ratio between the selected color's purity and its maximum possible purity; V indicates the brightness level of the color. In the HSV model, shadow regions are characterized by three main features:

1. A higher hue value (H);
2. High saturation (S) due to scattered light mainly originating from shorter wavelength blue-violet light;
3. Lower value (V) as sunlight is blocked, reducing brightness. Therefore, we converted the RGB image to the HSV space using Equation (3):

\[\left\{ \begin{array}{l}V=\frac{1}{3}(R+G+B)\\ S=1-\frac{3}{R+G+B}\text{min}(R,G,B)\\ H=\left\{\begin{array}{l}\theta,B\leq G\\ 360^{\circ}-\theta,B\textgreater{}G\\ \end{array}\right.,\\ \theta=\arccos\left[\frac{\frac{1}{2}|(R-G)+(R-B)|}{\sqrt{(R-G)^{2}+(R-B)(G-B) }}\right]\end{array} \right., \tag{3}\]

Pixels where the hue (\(H\)) and saturation (\(S\)) values exceed certain thresholds and the value (\(V\)) is below a specific threshold are identified as shadow areas.