Aerosol plays a very important role in affecting the earth-atmosphere radiation budget, and particle size distribution is an important aerosol property parameter. Therefore, it is necessary to determine the particle size distribution. However, the particle size distribution determined by the particle extinction efficiency factor according to the Mie scattering theory is an ill-conditioned integral equation, namely, the Fredholm integral equation of the first kind, which is very difficult to solve. To avoid solving such an integral equation, the BP neural network prediction model was established. In the model, the aerosol optical depth obtained by sun photometer CE-318 and kernel functions obtained by Mie scattering theory were used as the inputs of the neural network, particle size distributions collected by the aerodynamic particle sizer APS 3321 were used as the output, and the Levenberg–Marquardt algorithm with the fastest descending speed was adopted to train the model. For verifying the feasibility of the prediction model, some experiments were carried out. The results show that BP neural network has a better prediction effect than that of the RBF neural network and is an effective method to obtain the aerosol particle size distribution of the whole atmosphere column using the data of CE-318 and APS 3321.

Particle size distribution is one of the important microphysical parameters to characterize the aerosol properties. The aerosol optical depth is used as the function of wavelength to study the particle size distribution of whole atmospheric column. However, the inversion equation of the particle size distribution from the aerosol optical depth belongs to the Fredholm integral equation of the first kind, which is usually ill-conditioned. To overcome this drawback, the integral equation is first discretized directly by using the complex trapezoid formula. Then, the corresponding parameters are selected by the L curve method. Finally the truncated singular value decomposition regularization method is employed to regularize the discrete equation and retrieve the particle size distribution. To verify the feasibility of the algorithm, the aerosol optical depths taken by a sun photometer CE318 over Yinchuan area in four seasons, as well as hazy, sunny, floating dusty and blowing dusty days, were used to retrieve the particle size distribution. In order to verify the effect of truncated singular value decomposition algorithm, the Tikhonov regularization algorithm was also adopted to retrieve the aerosol PSD. By comparing the errors of the two regularizations, the truncated singular value decomposition regularization algorithm has a better retrieval effect. Moreover, to understand intuitively the sources of aerosol particles, the backward trajectory was used to track the source. The experiment results show that the truncated singular value decomposition regularization method is an effective method to retrieve the particle size distribution from aerosol optical depth.