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Volume 11, issue 7 | Copyright
Atmos. Meas. Tech., 11, 4477-4491, 2018
https://doi.org/10.5194/amt-11-4477-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 26 Jul 2018

Research article | 26 Jul 2018

Data inversion methods to determine sub-3 nm aerosol size distributions using the particle size magnifier

Runlong Cai1,2,*, Dongsen Yang3,*, Lauri R. Ahonen2, Linlin Shi3, Frans Korhonen2, Yan Ma3, Jiming Hao1, Tuukka Petäjä2, Jun Zheng3, Juha Kangasluoma2,4, and Jingkun Jiang1 Runlong Cai et al.
  • 1State Key Joint Laboratory of Environment Simulation and Pollution Control, School of Environment, Tsinghua University, 100084 Beijing, China
  • 2Institute for Atmospheric and Earth System Research/Physics Faculty of Science, University of Helsinki, P.O. Box 64, 00014 Helsinki, Finland
  • 3Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing University of Information Science & Technology, 210044 Nanjing, China
  • 4Aerosol and Haze Laboratory, Beijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical Technology, 100029 Beijing, China
  • *These authors contributed equally to this work.

Abstract. Measuring particle size distribution accurately down to approximately 1nm is needed for studying atmospheric new particle formation. The scanning particle size magnifier (PSM) using diethylene glycol as a working fluid has been used for measuring sub-3nm atmospheric aerosol. A proper inversion method is required to recover the particle size distribution from PSM raw data. Similarly to other aerosol spectrometers and classifiers, PSM inversion can be deduced from a problem described by the Fredholm integral equation of the first kind. We tested the performance of the stepwise method, the kernel function method (Lehtipalo et al., 2014), the H&A linear inversion method (Hagen and Alofs, 1983), and the expectation–maximization (EM) algorithm. The stepwise 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, respectively (Maher and Laird, 1985). In addition, Monte Carlo simulation and laboratory experiments were used to test the accuracy and precision of the particle size distributions recovered using four inversion methods. When all of the detected particles are larger than 3nm, the stepwise method may report false sub-3nm particle concentrations because an infinite resolution is assumed while the kernel function method and the H&A method occasionally report false sub-3nm particles because of the unstable least squares method. The accuracy and precision of the recovered particle size distribution using the EM algorithm are the best among the tested four inversion methods. Compared to the kernel function method, the H&A method reduces the uncertainty while keeping a similar computational expense. The measuring uncertainties in the present scanning mode may contribute to the uncertainties of the recovered particle size distributions. We suggest using the EM algorithm to retrieve the particle size distributions using the particle number concentrations recorded by the PSM. Considering the relatively high computation expenses of the EM algorithm, the H&A method is recommended for preliminary data analysis. We also gave practical suggestions on PSM operation based on the inversion analysis.

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We tested the performance of four inversion methods to recover sub-3 nm aerosol size distributions using the particle size magnifier (PSM). The PSM is widely used in new particle formation study; however, the inversion methods used in previous studies may report false particle concentrations. Due to the results, we suggest using the expectation–maximization algorithm to address the PSM inversion problem. We also gave practical suggestions on PSM operation based on the inversion analysis.
We tested the performance of four inversion methods to recover sub-3 nm aerosol size...
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