# XCO\({}_{2}\) Super-Resolution Reconstruction Based on Spatial Extreme Random Trees
## 1 Introduction
In the downscaling of carbon dioxide concentration, machine learning methods have also been widely applied, and scholars have conducted extensive research to enhance predictive performance [46; 47; 48]. Methods such as random forest, XGBoost, and gradient-boosting decision trees (GBDTs) have shown excellent applications in the high-resolution reconstruction of carbon dioxide. Random forest is an ensemble learning model that improves model robustness and accuracy by constructing multiple decision trees and combining their results [49]. XGBoost is a gradient-boosting algorithm that enhances the modeling capability of complex spatial relationships and optimizes downscaling effects by handling high-dimensional data, conducting feature selection, and through model optimization [50]. Gradient-boosting decision trees (GBDTs) gradually improve model predictive performance through the iterative training of decision trees [51]. Additionally, extreme random trees (ExtraTrees) have powerful feature dimension reduction capabilities. They introduce randomness in the feature selection and threshold determination process to increase model randomness and diversity, which help to reduce variance and the potential risks of overfitting [52]. By integrating multi-source data, these models handle high-dimensional information, optimize feature selection, enhance the modeling capability of complex spatial relationships, and provide strong support for the high-resolution monitoring of carbon dioxide concentrations. However, current popular machine learning methods rarely consider spatial information between carbon dioxide sources. Solely relying on changes in latitude and longitude values cannot adequately characterize and quantify the spatial position or relationships of geographic features, thus resulting in poor generalization performance of the established XCO\({}_{2}\) prediction models [53]. In summary, the aim of this study was to develop a machine learning model that takes into account spatial characteristics to elucidate the relationship between XCO\({}_{2}\) and its influencing factors. We considered the geographical and temporal heterogeneity of carbon dioxide. During model construction, a geographical spatial encoding strategy was employed to transform the latitude and longitude coordinates of each numerical point into Cartesian coordinates in a three-dimensional Cartesian coordinate system. This strategy ensures the smooth and uniform variation of spatial features to represent the positional relationships of geographic elements, i.e., spatial information. During model construction, spatial information was integrated with extreme random trees, resulting in a machine learning model called spatial extreme random trees (SExtraTrees). This model effectively addresses issues in respect of uneven changes in geographical and temporal location features and nonlinear relationship modeling. The contributions of this study are summarized as follows:  
1. Incorporating spatial information into the extreme random trees model, which integrates the advantages of machine learning methods and spatial features, enhancing the predictive performance of the model. This model can offer novel approaches for the high-resolution reconstruction of diverse geographical data. 2. Utilizing the constructed model to reconstruct a \(1\) km high-resolution XCO\({}_{2}\) dataset for China from 2016 to 2020. 3. Based on the predicted results, identifying and analyzing the spatiotemporal patterns of XCO\({}_{2}\) within the Chinese region. These long-term, high-resolution XCO\({}_{2}\) data contribute to our understanding of the spatiotemporal distribution characteristics of and variations in XCO\({}_{2}\), thus improving the formulation of policies and strategies for carbon emission reduction.