Theoretical study on the change of the particle extinction coefficient during the aerosol dynamic processes

Abstract

In this study, the effects of aerosol dynamics on the aerosol optical properties were analytically investigated using an approximated expression for the overall extinction coefficient $(b_{\mathrm{ext}})$, which was valid for a wide range of particle size. The processes of both coagulation and condensation in the continuum region were considered using the moment method, with an overall extinction coefficient obtained from the harmonic mean between the overall particle extinction coefficient of the Rayleigh scattering and geometric scattering regions. The derived analytical expressions were compared with the asymptotic expressions of the extinction coefficient, which showed that the obtained expressions ultimately approached the asymptotic expressions.

Subsequently, this study showed a simple and straightforward method for estimating the changes in the extinction coefficient and visibility of polydispersed aerosols during aerosol dynamic processes. The accuracy of the approximated overall coefficient was dependent on a given aerosol refractive index and size parameter. Usually, the error was less than 8% for an average size parameter range of 0–80.

Introduction

It is important to quantify the optical properties of aerosols as they have an affect on global radiative forcing and atmospheric visibility degradation phenomena. Impairment of atmospheric visibility is mainly attributed to the scattering and absorption of visible light by suspended fine particles. Also, light extinction is used in many aerosol measurement devices (Friedlander, 2000).

The physical relationship between the light extinction and atmospheric particulate constituents can be established if both the particulate concentration and size distribution for all chemical species are known (Sloane, 1988, Sloane et al., 1991). Theoretically, the overall extinction coefficient can be calculated using the Mie's theory (Seinfeld & Pandis, 1998) as follows:

$$b_{\mathrm{ext}}={\int }_0^{d_{\mathrm{p}}^{\max }}\frac{\pi d_{\mathrm{p}}^2}{4}{Q}_{\mathrm{ext}}(d_{\mathrm{p}},\lambda ,m)n(d_{\mathrm{p}}){\mathit{dd}}_{\mathrm{p}}={\int }_0^{d_{\mathrm{p}}^{\max }}\frac{{\lambda }^2}{4\pi }{p}^2{Q}_{\mathrm{ext}}(m,p)n(d_{\mathrm{p}}){\mathit{dd}}_{\mathrm{p}}\text{.}$$

Here, $Q_{\mathrm{ext}}(d_{\mathrm{p}},\lambda ,m)$ is the single particle extinction efficiency for a particle with a diameter, $d_{\mathrm{p}}$, and refractive index, m, for light with wavelength, $\lambda$, $p(=\pi d_{\mathrm{p}}/\lambda )$ the size parameter, $n(d_{\mathrm{p}})$ the size distribution and $b_{\mathrm{ext}}$ the overall extinction coefficient.

Aerosols within the atmosphere continuously change their particle size and composition and thus, their optical properties. In order to quantify the effect of the particle size distribution change on the optical properties of aerosols, the changes in the overall extinction coefficient and visibility during the processes of both coagulation and condensation should be simulated.

Jung and Kim (2006) approximated the single particle extinction efficiency using 6th order polynomials within the particle diameter range of $0.01–2.5\mathrm{\mu }\mathrm{m}$ for three kinds of aerosols, namely, hazy, urban and clean aerosols, for application of the moment method to estimate changes in the optical properties. However, their results could not be applied to obtain a general type of single particle extinction efficiency since the polynomial expression should be fitted and, thus, the coefficients for the polynomials should be calculated repeatedly for different refractive indices. Furthermore, the derived expression was valid only for the fine particle range.

Later, Jung and Kim (2007) developed general expressions for the single particle extinction efficiency and an overall extinction coefficient without the limitations of specific refractive indices or an applicable particle size range, based on the harmonic mean between the Rayleigh scattering and geometric scattering regions.

In this study, the changes to the overall extinction coefficient and visibility during coagulation and condensation were obtained analytically using the harmonic mean approximation developed by Jung and Kim (2007) to evaluate the influence of aerosol dynamics on the optical properties. The derived analytical expressions obtained for the extinction coefficient for the continuum region were compared with the numerical or exact solutions for the coagulation and condensation processes. Finally, the asymptotic expressions for the extinction coefficient during coagulation and condensation were derived and compared with the derived analytical expressions.