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1. Introduction
Fine particulate matter (PM2.5) is particulate matter with aerodynamic diameter less than 2.5 μm in ambient air [1]. Hazy weather will form if PM2.5 concentration is too high, which has adverse impacts on human health, traffic, and outdoor activities [2], and it will also produce other indirect inestimable economic losses [3]. Therefore, many countries attach great importance to the monitoring and forecasting of PM2.5 concentration. A large number of ground-based monitoring stations have been established. For example, 1500 monitoring stations have been set up in the United States. In China, around 1500 stations have been set up in 454 cities by 2018, and a new national ambient air quality standard for PM2.5 was introduced in 2012 [1, 2]. Generally, it is believed that high PM2.5 concentration has become a prominent challenge for air pollution control in China, which is mainly caused by the industrial combustion of coal and gasoline, traffic emissions, and long-distance transport [4, 5]. The North China Plain, especially the Beijing-Tianjin-Hebei region (Figure 1(a)), is one of the regions most severely affected by the hazy weather [4, 6]. To monitor air pollution, many urban environmental stations have been built in this region, and many researchers have analyzed the causes and behavior of high PM2.5 concentration recently [3, 7].
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There have been many studies on PM2.5 concentration data analysis methods, such as real-time data space interpolation of monitoring points, weighted regression models, and mixed models [1, 8]. The application of the preceding methods mostly depends on the complete and continuous monitoring data provided by local monitoring stations. However, problem arises when original spatiotemporal PM2.5 concentration data are incomplete, which hinders further analysis and modelling, such as aerosol-related haze control and environmental health risk assessment [9, 10].
In practice, missing values and data gaps always exist in the original spatiotemporal observation records due to various factors. For example, satellite-based remote sensing may be affected by clouds, rain, aerosols, or incomplete track coverage in atmospheric research [11, 12]; in situ observations from land-based stations, shipborne monitoring, offshore...
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; Lv, Xianqing 1
1 Physical Oceanography Laboratory, Qingdao Collaborative Innovation Center of Marine Science and Technology (CIMST), Ocean University of China, Qingdao, China; Qingdao National Laboratory for Marine Science and Technology, Qingdao, China
2 Ocean College, Zhejiang University, Zhoushan, China





