# XCO\({}_{2}\) Super-Resolution Reconstruction Based on Spatial Extreme Random Trees
## 3 Results  
### Model Comparison  
To assess the effectiveness of the proposed model, we compared the predictive results of the spatial extreme random trees model with those of Kriging interpolation and extreme random trees model predictions. The fitting results of each model are shown in Table 2. Kriging interpolation, as the most classical interpolation method, infers values at unknown locations by leveraging the spatial correlation between known observation points. Previous studies have demonstrated its effectiveness in CO\({}_{2}\)-related research [37]. Since the data initially used for this method are XCO\({}_{2}\) data with a resolution of 10 km, and the known points are evenly distributed, the fitting results are relatively good, with an R\({}^{2}\) of 0.961, MAE of 0.697 ppm, and RMSE of 0.699 ppm. However, this method can only model  
Figure 3: Structure and specific principles diagram of the spatial extreme random trees model.  
and interpolate single variables, which ignores the spatiotemporal correlation between XCO\({}_{2}\) and other influencing factors. It may oversmooth the data, fail to capture local variability, exhibit a poor ability to predict nonlinear relationships, and have low efficiency and accuracy when computing large amounts of data. Although the extreme random trees model considers the complex relationships between XCO\({}_{2}\) and other influencing factors and performs well in capturing nonlinear relationships and improving efficiency when processing large amounts of data, it ignores the spatial heterogeneity of XCO\({}_{2}\). The fitting results for the extreme random trees model are as follows: R\({}^{2}\) = 0.939, MAE = 0.726 ppm, and RMSE = 0.866 ppm. In contrast, the spatial extreme random trees model demonstrates strong nonlinear modeling capabilities. When spatial features were integrated into the machine learning method, this model's ability to capture spatial geographical relationships was enhanced, leading to significantly improved fitting accuracy with an R\({}^{2}\) of 0.985, MAE of 0.407 ppm, and RMSE of 0.434 ppm. Hence, we opted to employ spatial extreme random trees for the high-resolution reconstruction of XCO\({}_{2}\).  
Figure 4 illustrates the spatial distribution of the initial XCO\({}_{2}\) data at a 10 km resolution in 2016, along with the reconstructed XCO\({}_{2}\) results at a 1 km resolution using different methods. Because Kriging interpolation infers the values at unknown points based on the numerical values of known points, and XCO\({}_{2}\) generally exhibits a gradual trend, visually, the Kriging interpolation results show a clear smoothing trend. By ignoring spatial heterogeneity, the extreme random trees model theoretically underestimates the complexity of XCO\({}_{2}\) spatial distribution, leading to the phenomenon of underestimation in the predicted XCO\({}_{2}\) values, particularly in eastern coastal areas. The spatial distribution of XCO\({}_{2}\) predicted by the spatial extreme random trees model is most similar to the original data, indicating that our reconstructed XCO\({}_{2}\) data possess higher precision and accuracy.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **R\({}^{2}\)** & **MAE (ppm)** & **RMSE (ppm)** \\ \hline Kriging & 0.961 & 0.697 & 0.699 \\ ExtraTrees & 0.939 & 0.726 & 0.866 \\ SExtraTrees & 0.985 & 0.407 & 0.434 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of predictive performance with different methods.  
Figure 4: Spatial distribution of the original XCO\({}_{2}\) data in 2016 at a resolution of 10 km, as well as the predicted XCO\({}_{2}\) results at a resolution of 1 km via Kriging interpolation, the extreme random trees model, and the spatial extreme random trees model.