As an important cause of global warming, CO₂ concentrations and their changes have aroused worldwide concern. Establishing explicit understanding of the spatial and temporal distributions of CO₂ concentrations at regional scale is a crucial technical problem for climate change research. High accuracy surface modeling (HASM) is employed in this paper using the output of the CO₂ concentrations from weather research and forecasting-chemistry (WRF-CHEM) as the driving fields, and the greenhouse gases observing satellite (GOSAT) retrieval XCO₂ data as the accuracy control conditions to obtain high accuracy XCO₂ fields. WRF-CHEM is an atmospheric chemical transport model designed for regional studies of CO₂ concentrations. Verified by ground- and space-based observations, WRF-CHEM has a limited ability to simulate the conditions of CO₂ concentrations. After conducting HASM, we obtain a higher accuracy distribution of the CO₂ in North China than those calculated using the classical Kriging and inverse distance weighted (IDW) interpolation methods, which were often used in past studies. The cross-validation also shows that the averaging mean absolute error (MAE) of the results from HASM is 1.12 ppmv, and the averaging root mean square error (RMSE) is 1.41 ppmv, both of which are lower than those of the Kriging and IDW methods. This study also analyses the space-time distributions and variations of the XCO₂ from the HASM results. This analysis shows that in February and March, there was the high value zone in the southern region of study area relating to heating in the winter and the dense population. The XCO₂ concentration decreased by the end of the heating period and during the growing period of April and May, and only some relatively high value zones continued to exist.

Dissolved oxygen (DO) is a direct indicator of water pollution and an important water quality parameter that affects aquatic life. Based on the fundamental theorem of surfaces in differential geometry, the present study proposes a new modeling approach to estimate DO concentrations with high accuracy by assessing the spatial correlation and heterogeneity of DO with respect to explanatory variables. Specifically, a regularization penalty term is integrated into the high-accuracy surface modeling (HASM) method by applying geographically weighted regression (GWR) with some covariates. A modified version of HASM, namely HASM_MOD, is illustrated through a case study of Poyang Lake, China, by comparing the results of HASM, a support vector machine (SVM), and cokriging. The results indicate that HASM_MOD yields the best performance, with a mean absolute error (MAE) that is 38%, 45%, and 42% lower than those of HASM, the SVM, and cokriging, respectively, by using the cross-validation method. The introduction of a regularization penalty term by using GWR with respect to covariates can effectively improve the quality of the DO estimates. The results also suggest that HASM_MOD is able to effectively estimate nonlinear and nonstationary time series and outperforms three other methods using cross-validation, with a root-mean-square error (RMSE) of 0.20 mg/L and R² of 0.93 for the two study sites (Sanshan and Outlet_A stations). The proposed method, HASM_MOD, provides a new way to estimate the DO concentration with high accuracy.