Abstract:  As one of the important part of the atmospheric environment, the aerosol has a complex structure of size distribution. Fractal theory was applied to study the fractal characteristics of aerosol size distribution. First, it was proved that the functions of aerosol size distribution are of fractal invariance. Then, the fractal statistical models of aerosol particle and volume were established based on the fractal theory, and the validity and practicability were verified by the corresponding data from AERONET. Besides, sub-fractal approach was used to improve the aerosol volume fractal model. Finally, the practical significance of the fractal dimensions and its distributions were analyzed, and the relationship between the fractal dimension and aerosol size distribution was discussed. The results show that there is a linear relationship between the aerosol particle number and volume fractal dimensions. The fluctuation of the large aerosol particle fractal dimensions is smaller in the first half year than in the second half year. The distribution of the fine aerosol particle is concentrative in the study area, while that of the crude aerosol particle is dispersive. The fractal theory has a broad prospect of research and application as it provides a new method for the study of aerosol size distribution characteristics.

Key words: Size distribution, Fractal, Fractal Dimension, Atmosphere, aerosol, Spectral distribution, Fractal, Fractal dimension, Atmosphere, Aerosol