10th International Aerosol Conference September 2 - September 7, 2018 America's Center Convention Complex St. Louis, Missouri, USA
Abstract View
Data Inversion Methods to Determine Sub-3 nm Particle Size Distributions Using the Particle Size Magnifier
RUNLONG CAI, Dongsen Yang, Lauri R. Ahonen, Linlin Shi, Frans Korhonen, Yan Ma, Tuukka Petäjä, Jun Zheng, Juha Kangasluoma, Jingkun Jiang, Tsinghua University
Abstract Number: 244 Working Group: Instrumentation
Abstract Measuring particle size distribution accurately down to approximately 1 nm is needed for studying atmospheric new particle formation. The scanning particle size magnifier (PSM) using diethylene glycol as the working fluid has been used for measuring sub-3 nm atmospheric aerosols. A proper inversion method is required to recover the particle size distribution from PSM raw data. However, the performance of PSM inversion methods, especially considering the influence of random errors, has not been systematically examined. Similar to many other aerosol spectrometers and classifiers, PSM inversion can be deduced to a problem described by the Fredholm integral equation of the first kind. The inversion methods used in other aerosol instruments can possibly be applied to solve the PSM inversion problem. Among them, those methods requiring with less prior information on the particle size distribution are more preferable.
We tested the performance of the step-wising method, the kernel function method (Lehtipalo et al., 2014), the H&A method (Hagen and Alofs method, 1983), and the expectation-maximization algorithm. The step-wising method and the kernel function method were used in previous studies on PSM. The H&A method and the expectation-maximization algorithm were used in data inversion for the electrical mobility spectrometers and the diffusion batteries (Maher and Laird., 1985), respectively. In addition, Monte Carlo simulation was used to test the accuracy and precision of the particle size distributions recovered using different inversion methods. The relative random errors estimated from atmospheric observation and laboratory study were added in the simulated particle concentration detected by the PSM. Laboratory experiments were conducted to test the sizing accuracies of different inversion methods and to verify the results predicted by the simulation.
The step-wising method may report false sub-3 nm particle concentrations when there are no sub-3 nm particles because it does not account for the influence of particles large than 3 nm. The kernel function method and the H&A method may lead to relatively large uncertainties in the recovered particle size distribution because of using the unstable least square method. Sometimes they report false sub-3 nm concentrations due to the large uncertainties. Compared to the kernel function method, the H&A method lead to smaller uncertainties while having similar computational expenses. Among all the tested inversion methods, the expectation-maximization algorithm has the highest accuracy and stability. We suggest using the expectation-maximization algorithm to retrieve the particle size distributions from PSM raw data. The H&A method is recommended for preliminary analysis considering the computational expenses of the expectation-maximization algorithm.
Based on the inversion analysis, we also provided practical suggestions on PSM operations. The uncertainties of the recovered size distributions of particles smaller than 1.3 nm or larger than 3 nm may be large due to the incomplete kernel function curves, the low resolutions, and/or the low detection efficiencies. The measuring uncertainties in the scanning mode may also increase the uncertainties of the recovered size distribution. Thus, the scanning scheme of the saturator flow rate is suggested to be improved to reduce the measuring uncertainties. In addition, one should carefully distinguish the false inversion results from the true sub-3 nm particle concentrations.