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A New Mathematical Scheme for Approximating Overall Aerosol Extinction Coefficient during Brownian Coagulation

Category: Technical Note

Accepted Manuscripts
DOI: 10.4209/aaqr.2018.01.0021

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Yue Lai1, Yueyan Liu1, Mingzhou Yu 1,2, Lina Wang3, Jing Liu4, Qing Li1

  • 1 China Jiliang University, Hangzhou 310018, China
  • 2 Key Laboratory of Aerosol Chemistry and Physics, Chinese Academy of Science, Xi’an 710061, China
  • 3 State Environmental Protection Key Laboratory of Risk Assessment and Control on Chemical Processes, East China University of Science and Technology (ECUST), Shanghai 200237, China
  • 4 School of Municipal and Environmental Engineering, Harbin Institute of Technology (HIT), Harbin 150000, China


A new scheme for overall extinction coefficient was proposed.
The scheme is verified to be with acceptable accuracy and efficiency.
The new scheme has advantage over conventional method.


The approximation of overall aerosol extinction coefficient is conventionally achieved through integrating the single particle extinction efficiency over the whole size distribution, which consumes much computational time. In this work, a new approximated scheme with higher efficiency relative to the conventional scheme is proposed, in which the combination of polynomials for fitting Mie’s solution and the method of moments is to produce the overall extinction coefficient of an evolving nanoparticles. The closure of arbitrary moments is achieved by implementing the Taylor-series expansion method of moments. The new approximated scheme was verified by comparing it to a more exact referenced scheme under two different typical aerosol modes, namely nucleation mode and accumulation mode. The study verified the new scheme is a reliable method for approximating overall extinction coefficient during aerosol evolution with acceptable efficiency and accuracy, thus it is suitable to be used in some atmospheric aerosol models.


Overall extinction coefficient Method of moments Polynomial Taylor-series expansion Aerosol evolution

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