In China, population growth and aging have partially negated the public health benefits of air pollution control measures, underscoring the ongoing need for precise PM_2.5 monitoring and mapping. Despite its prevalence, the satellite-derived Aerosol Optical Depth (AOD) method for estimating PM_2.5 concentrations often encounters significant spatial data gaps. Additionally, current research still needs better representation of PM_2.5 spatiotemporal heterogeneity. Addressing these challenges, we developed a two-stage model employing the Extreme Gradient Boosting (XGBoost) algorithm. By incorporating improved spatiotemporal factors, we achieved high-precision and full-coverage daily 1-km PM_2.5 mappings across China for the year 2020 without utilizing AOD products. Specifically, Model 1 develops improved temporal encodings and a terrain classification factor (DC), while Model 2 constructs an enhanced spatial autocorrelation term (Ps) by integrating observed and estimated values. Notably, Model 2 excelled in 10-fold sample-based cross-validation, achieving a coefficient of determination of 0.948, a mean absolute error of 3.792 μg/m³, a root mean square error of 7.144 μg/m³, and a mean relative error of 14.171%. Feature importance and Shapley Additive exPlanations (SHAP) analyses determined the relative importance of predictors in model training and outcome prediction, while correlation analysis identified strong links between improved temporal encodings, PM_2.5 concentrations, and significant meteorological factors. Two-way Partial Dependence Plots (PDPs) further explored the interactions among these factors and their impact on PM_2.5 levels. Compared to traditional methods, improved temporal encodings align more closely with seasonal variations and synergize more effectively with meteorological factors. Besides, the structured nature of DC aids in model training, while the improved Ps more effectively captures PM_2.5's spatial autocorrelation, outperforming traditional Ps. Overall, this study effectively represents spatiotemporal information, thereby boosting model accuracy and enabling seamless large-scale PM_2.5 estimations. It provides deep insights into variables and models, providing significant implications for future air pollution research.

Owing to a series of air pollution prevention and control policies, China’s PM_2.5 pollution has greatly improved; however, the long-term spatial contiguous products that facilitate the analysis of the distribution and variation of PM_2.5 pollution are insufficient. Due to the limitations of missing values in aerosol optical depth (AOD) products, the reconstruction of full-coverage PM_2.5 concentration remains challenging. In this study, we present a two-stage daily adaptive modeling framework, based on machine learning, to solve this problem. We built the annual models in the first stage, then daily models were constructed in the second stage based on the output of the annual models, which incorporated the parameter and feature adaptive tuning strategy. Within this study, PM_2.5 concentrations were adaptively modeled and reconstructed daily based on the multi-angle implementation of atmospheric correction (MAIAC) AOD products and other ancillary data, such as meteorological factors, population, and elevation. Our model validation showed excellent performance with an overall R² = 0.91 and RMSE = 9.91 μg/m³ for the daily models, along with the site-based cross-validation R²s and RMSEs of 0.86–0.87 and 12–12.33 μg/m³; these results indicated the reliability and feasibility of the proposed approach. The daily full-coverage PM_2.5 concentrations at 1 km resolution across China during the Three-Year Blue-Sky Action Plan were reconstructed in this study. We analyzed the distribution and variations of reconstructed PM_2.5 at three different time scales. Overall, national PM_2.5 pollution has significantly improved with the annual average concentration dropping from 33.67–28.03 μg/m³, which demonstrated that air pollution control policies are effective and beneficial. However, some areas still have severe PM_2.5 pollution problems that cannot be ignored. In conclusion, the approach proposed in this study can accurately present daily full-coverage PM_2.5 concentrations and the research outcomes could provide a reference for subsequent air pollution prevention and control decision-making.

The partial errors-in-variables (PEIV) model is an structured errors-in-variables (SEIV) model reformulated by collecting all the random elements of the coefficient matrix into an auxiliary random error vector to better treat the case where the coefficient matrix (or ‘data matrix’) A and observation vector y share common elements. In the usual PEIV model, the case of A and y sharing common elements has not been treated explicitly. However, in some cases, A and y do have common elements, taking the autoregressive problem as an example. To apply the PEIV model to SEIV problems with correlated matrix A and vector y, we propose an extended model named general PEIV (GPEIV). We also provide a corresponding algorithm for the total least-squares solution within the GPEIV model. A weight-matrix construction method, which is suitable for PEIV and GPEIV models, is also presented. The GPEIV model, the algorithm and the weight-matrix construction method are tested using two groups of numerical examples. The results show that the proposed model and corresponding algorithm can solve both uncorrelated and correlated SEIV problems, and the weight-matrix construction method is simple and efficient.

This paper presents a partial total-least-squares adjustment method for condition equations (PTLSC) in which the observation vector and coefficient matrix contain linearly correlated errors. In the proposed method, the functionally independent variables in the observation vector and the coefficient matrix of the condition equations are abstracted to form a collected observation vector. The PTLSC method is formulated by minimizing the sum of the weighted squared errors of the collected observation vector by the use of a Lagrangian multiplier algorithm. The estimation of the covariance matrix based on linear approximation for the collected observation vector is also derived. The proposed PTLSC method was tested in an example of rectangular building adjustment in a geographical information system (GIS). The results indicate that the proposed PTLSC method can adjust the interior angles of the digitized buildings so they are right angles, and it can be used to maintain the correlations among the elements in the observation vector and the coefficient matrix.

The sparsity regularization based on the L₁ norm can significantly stabilize the solution of the ill-posed sparsity inversion problem, e.g., azimuth super-resolution of radar forward-looking imaging, which can effectively suppress the noise and reduce the blurry effect of the convolution kernel. In practice, the total variation (TV) and TV-sparsity (TVS) regularizations based on the L₁ norm are widely adopted in solving the ill-posed problem. Generally, however, the existence of bias is ignored, which is incomplete in theory. This paper places emphasis on analyzing the partially biased property of the L₁ norm. On this basis, we derive the partially bias-corrected solution of TVS and TV, which improves the rigor of the theory. Lastly, two groups of experimental results reflect that the proposed methods with partial bias correction can preserve higher quality than those without bias correction. The proposed methods not only distinguish the adjacent targets, suppress the noise, and preserve the shape and size of targets in visual terms. Its improvement of Peak Signal-to-Noise Ratio, Structure-Similarity, and Sum-Squared-Errors assessment indexes are overall 2.15%, 1.88%, and 4.14%, respectively. As such, we confirm the theoretical rigor and practical feasibility of the partially bias-corrected solution with sparsity regularization based on the L₁ norm.