Abstract. The COVID-19 pandemic lockdowns led to a sharp drop in socio-economic activities in China in 2020, including reductions in fossil fuel use, industry productions, and traffic volumes. The short-term impacts of lockdowns on China's air quality have been measured and reported, however, the changes in anthropogenic emissions have not yet been assessed quantitatively, which hinders our understanding of the causes of the air quality changes during COVID-19. Here, for the first time, we report the anthropogenic air pollutant emissions from mainland China by using a bottom-up approach based on the near-real-time data in 2020 and use the estimated emissions to simulate air quality changes with a chemical transport model. The COVID-19 lockdown was estimated to have reduced China's anthropogenic emissions substantially between January and March in 2020, with the largest reductions in February. Emissions of SO2, NOx, CO, non-methane volatile organic compounds (NMVOCs), and primary PM2.5 were estimated to have decreased by 27 %, 36 %, 28 %, 31 %, and 24 %, respectively, in February 2020 compared to the same month in 2019. The reductions in anthropogenic emissions were dominated by the industry sector for SO2 and PM2.5 and were contributed to approximately equally by the industry and transportation sectors for NOx, CO, and NMVOCs. With the spread of coronavirus controlled, China's anthropogenic emissions rebounded in April and since then returned to the comparable levels of 2019 in the second half of 2020. The provinces in China have presented nearly synchronous decline and rebound in anthropogenic emissions, while Hubei and the provinces surrounding Beijing recovered more slowly due to the extension of lockdown measures. The ambient air pollution presented much lower concentrations during the first 3 months in 2020 than in 2019 while rapidly returning to comparable levels afterward, which have been reproduced by the air quality model simulation driven by our estimated emissions. China's monthly anthropogenic emissions in 2020 can be accessed from https://doi.org/10.6084/m9.figshare.c.5214920.v2 (Zheng et al., 2021) by species, month, sector, and province.

In this paper, a method is presented to obtain the analytical and approximate solutions of linear and nonlinear systems of second order boundary value problems. The analytical solution is represented in the form of series in the reproducing kernel space. In the mean time, the approximate solution u n (x) is obtained by the n-term intercept of the analytical solution and is proved to converge to the analytical solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.

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