## 1 Introduction
Various geostatistical methods can enhance the spatiotemporal coverage of XCO2 data. For example, traditional ordinary Kriging [14; 15], sliding window Kriging [16], empirical Bayesian Kriging [17], precision-weighted Kriging [18], fixed-rank Kriging [19], among others, have proved effective in obtaining large-scale spatial distributions of XCO2. The spatiotemporal Kriging algorithm, an extension from spatial to spatiotemporal domains, takes the temporal trend and spatial correlation within the data into account at the same time, thereby improving the accuracy of interpolation [20]. However, the resolution of the results obtained by such interpolation methods is limited, especially when the satellite data are very sparse, making it challenging to obtain full-coverage results with high temporal and spatial resolution. Moreover, this method may inadvertently smooth the spatial characteristics of XCO2, which should not be ignored in applied researches like atmospheric pollution source studies [21]. In addition to the various Kriging methods, researchers have used the Bayesian Maximum Entropy (BME) [22] and the High-Accuracy Surface Modeling (HASM) [23] to attain precise XCO2 distribution results, which have high computational complexity and require substantial computational power when handling large datasets. In recent years, with the development of artificial intelligence technology and the advent of the big data era, data-driven machine learning methods have rapidly evolved in the field of remote sensing. Many scholars have already explored the potential of machine learning methods to apply to the XCO2 gap-filling problem [24; 25; 26]. Based on multi-source remote sensing datasets such as elevation, nighttime light, vegetation indices, meteorology, land use, and socioeconomic data like population density as modeling independent variables, they used XCO2 retrieval data and existing XCO2 datasets simulated by atmospheric physicochemical models (such as Carbon Tracker XCO2 and CAMS XCO2) to construct machine learning models including Random Forest (RF), Extreme Random Forest, XGBoost, LightGBM and CatBoost to obtain full-coverage XCO2 datasets for different study areas. The experiments indicate that machine learning models have satisfactory performances in XCO2 data interpolation, especially the RF model. Furthermore, some researchers made efforts to use deep learning methods. [PERSON] [27] constructed a Deep Neural Network (DNN) model based on OCO-2 XCO2, CAMS XCO2, and auxiliary datasets, such as meteorology datasets and vegetation indices, to generate a long-term daily full-coverage XCO2 dataset with high accuracy (\(R^{2}\) = 0.866) compared to TCCON measurements. [PERSON] and [PERSON] [28] developed a Convolutional Neural Network (CNN) model based on XCO2 data from the SCIAMACHY sensor, GOSAT satellite, OCO-2 satellite, and Carbon Tracker dataset, along with multi-source remote sensing datasets as auxiliary variables. This model produced a long-term monthly XCO2 dataset for China, and accuracy validation results demonstrate its strong generalization ability and good agreement with TCCON observations, with an average bias of \(-\)0.60 ppm, \(MAE\) of 0.95 ppm, and \(RMSE\) of 1.18 ppm. Machine learning models can automatically capture complex surface features and patterns, enabling the achievement of high-precision parameter extractions and spatiotemporal predictions for quantitative problems caused by the lack of precise description through traditional mechanisms. Although machine learning models have problems related to poor interpretability, these models can provide full-coverage XCO2 datasets with high consistency with ground-based measurements, showcasing significant practical utility. For deep learning models, a substantial number of training samples are typically required, posing a challenge in obtaining a sufficient quantity of high-quality labeled training datasets.