Spatial statistics of atmospheric particulate matter in China

In this paper, the spatial dynamics of the atmospheric particulate matters (resp. PM$_{10}$ and PM$_{2.5}$) are studied using turbulence methodologies. It is found experimentally that the spatial correlation function $\rho(r)$ shows a log-law on the mesoscale range, i.e., $50\le r\le 500\,{km}$, with an experimental scaling exponent $\beta=0.45$. The spatial structure function shows a power-law behavior on the mesoscale range $90\le r\le 500\,{km}$. The experimental scaling exponent $\zeta(q)$ is convex, showing that the intermittent correction is relevant in characterizing the spatial dynamic of particulate matter. The measured singularity spectrum $f(\alpha)$ also shows its multifractal nature. Experimentally, the particulate matter is more intermittent than the passive scalar, which could be partially due to the \red{mesoscale movements} of the atmosphere, and also due to local sources, such as local industry activities.