Near-surface PM_2.5 estimates remain a global scientific research challenge due to their effect on human fitness and atmospheric environmental quality. However, practical near-surface PM_2.5 estimates are impeded by the incomplete monitoring data. In this study, we propose the trigonometric polynomial fitting (TPF) method to estimate near-surface PM_2.5 concentrations in south-central China during 2015. We employ 10-fold cross-validation (CV) to assess the reliability of TPF in estimating practical PM_2.5 values. When compared to alternative methods such as the orthogonal polynomial fitting (OBF) method based on Chebyshev basis functions, Kriging interpolation, and radial basis function (RBF) interpolation, our results show that utilizing TPF31, with a maximum order of 3 in the $x$ direction and a maximum order of 1 in the $y$ direction, leads to superior efficiency through error minimization. TPF31 reduces MAE and RMSE by 1.93%, 24%, 6.96% and 3.6%, 23.07%, 10.43%, respectively, compared to the other three methods. In addition, the TPF31 method effectively reconstructs the spatial distribution of PM_2.5 concentrations in the unevenly distributed observation stations of Inner Mongolia and the marginal regions of the study area. The reconstructed spatial distribution is remarkably smooth. Despite the non-uniform distribution of observation stations and the presence of missing data, the TPF31 method demonstrates exceptional effectiveness in accurately capturing the inherent physical attributes of spatial distribution. The theoretical and experimental results emphasize that the TPF method holds significant potential for accurately reconstructing the spatial distribution of PM_2.5 in China.

Changes in the climate system over recent decades have had profound impacts on the mean state and variability of ocean circulation, while the Nordic Sea overflow has remained stable in volume transport during the last two decades. The changes of the overflow flux depend on the pressure difference at the depth of the overflow outlet on both sides of the Greenland-Scotland Ridge (GSR). Combining satellite altimeter data and the reanalysis hydrological data, the analysis found that the barotropic pressure difference and baroclinic pressure difference on both sides of the GSR had a good negative correlation from 1993 to 2015. Both are caused by changes in the properties of the upper water, and the total pressure difference has no trend change. The weakening of deep convection can only change the temperature and salt structure of the Nordic Sea, but cannot reduce the mass of the water column. Therefore, the stable pressure difference drives a stable overflow. The overflow water storage in the Nordic Sea is decreasing, which may be caused by the reduction of local overflow water production and the constant overflow flux. When the upper interface of the overflow water body in the Nordic Sea is close to or below the outlet depth, the overflow is likely to greatly slow down or even experience a hiatus in the future, which deserves more attention.