# XCO\({}_{2}\) Super-Resolution Reconstruction Based on Spatial Extreme Random Trees
## 2 Materials and Methods
### Spatial Extreme Random Trees  
China is a vast territory, with significant differences in urbanization levels, industrial conditions, energy structures, and climate conditions among different regions, resulting in \begin{table}
\begin{tabular}{c c c c} \hline \hline
\begin{tabular}{c} Resource and Environmental \\ Science Data Center \\ \end{tabular} & [[https://www.resdc.cn](https://www.resdc.cn)]([https://www.resdc.cn](https://www.resdc.cn)) (accessed on 10 February 2024) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Independent variables and corresponding sources. typical spatial distribution patterns of carbon dioxide concentration. There is evident spatial heterogeneity between carbon dioxide concentration and influencing factors. Although the extreme random trees method can increase the randomness and diversity of models and reduce the risk of overfitting by randomizing feature selection and threshold selection processes, better capture the nonlinear relationships between data, and further improve the robustness of the model, it cannot effectively address the spatial heterogeneity of XCO\({}_{2}\). Therefore, by considering spatial features and incorporating spatial information into the extreme random trees model, we can inherit the advantages of extreme random trees and effectively address the uneven changes in geographical and temporal location characteristics. In this study, by adopting a geographic spatial encoding strategy (Equation (1)), latitude and longitude polar coordinates were converted into Cartesian coordinates in a three-dimensional Cartesian coordinate system to characterize the positional characteristics of geographical elements (Figure 2), resulting in feature variables that uniformly change within the range \([-6371,6371]\), i.e., spatial relationships. This spatial information exhibits smooth and uniform changes, effectively addressing the spatial heterogeneity issue of XCO\({}_{2}\). \[g_{i}= \begin{bmatrix}g_{xi}\\ g_{yi}\\ g_{zi}\end{bmatrix} = \begin{bmatrix}Rsin\varphi_{i}cos\theta_{i}\\ Rsin\theta_{i}\\ Rcos\varphi_{i}cos\theta_{i}\end{bmatrix}  \tag{1}\]  
In the equation, \(g_{i}\) represents the geographic spatial information encoding feature of point \(i\), \(\varphi_{i}\) represents the longitude of point \(i\), \(\theta_{i}\) represents the latitude of point \(i\), and \(R\) represents the radius of the Earth (approximately 6371 km). The spatial extreme random trees model was used to establish the relationship between XCO\({}_{2}\) and influencing factors at a resolution of 10 km. The specific principles of the spatial extreme random trees are illustrated in Figure 3. Initially, the pre-processed annual scale environmental factor data set with a spatial resolution of 1 km from 2016 to 2020 was resampled to an annual scale data set with a spatial resolution of 10 km by the nearest neighbor method, and aligned with the original XCO\({}_{2}\) annual scale data set with a spatial resolution of 10 km. The XCO\({}_{2}\) data of each point has corresponding environmental factor data, which establishes the corresponding relationship between the model-independent variables and some dependent variables, and this process is called data fusion. Subsequently, spatial information computed based on latitude and longitude was aggregated into the aligned dataset to form a training dataset. The model computation for the relationship between independent variables and dependent variables based on the spatial extreme random trees is represented by Equation (2). XCO\({}_{2}\) data serve as the dependent variable, while factors such as DEM, GPP, and spatial features are used as independent variables for modeling. Leveraging this established relationship, the dataset of influencing factors at 1 km resolution was inputted into the trained spatial extreme random trees model to reconstruct China's high-resolution (1 km) XCO\({}_{2}\) dataset. \[XCO_{2}=SExtraTrees(DEM,GPP,NDVI,NTL,POP,Wnd,Pre,Tem,Rh,Spatial Features) \tag{2}\]  
Figure 2: Geospatial encoding schematic.