Ångstrom exponent is often used as a qualitative indicator of aerosol particle size. It is a slope of the wavelength dependence of the aerosol optical depth (extinction coefficient) in logarithmic coordinates. Basically, aerosol extinction coefficient is a function of aerosol size distribution and aerosol compositions which determines the refractive index. Different size distributions such as power law (Junge, 1955), gamma, lognormal distributions have been used to model atmospheric aerosols. For example, there is a simple relationship of the Ångstrom exponent (AE=v-2) for the Junge distribution (n=Cd _p^-v, where C is constant and d _p is particle diameter). Jung and Kim (2010) obtained the analytical relationship between the polydispersed aerosol size distribution with different refractive indices and the Ångstrom exponent under the assumption of the Junge aerosol size distribution. They applied the polynomial (Jung and Kim, 2006) and harmonic mean (Jung and Kim, 2007, 2008) approximations to the parameterization of the extinction coefficient. In the atmosphere, the aerosols continuously change their size distribution and composition through aerosol dynamic processes such as coagulation, condensation and deposition. The Ångstrom exponent also changes during the aerosol dynamic processes such as coagulation and condensation. For this reason, it is important to simulate aerosol dynamic processes in order to understand the optical properties and the effects of the atmospheric aerosol.

In this study, the change of the Ångstrom exponent for polydispersed aerosol size distribution during the aerosol dynamic processes was simulated as a function of time. Log-normal aerosol size distribution was assumed and moment method was used. Analytic solutions for coagulation and condensation are used and compared with numerical solution in estimating Ångstrom exponent. A sensitive analysis of the Ångstrom exponent during the coagulation and condensation process was performed. This study also estimated the change of the Ångstrom exponent under different real and imaginary parts of the refractive index during the coagulation and condensation processes. The results show that the Ångstrom exponent from the solution of both analytic and numerical methods agree well without much loss of accuracy. During the coagulation process, the total number concentration decreases, geometric mean diameter converges to the value around 1.32 and geometric mean diameter increases. On the other hand, during the condensation process, the geometric standard deviation approaches 1, which means particle size distribution converges to monodispersed size. The results also show how Ångstrom exponent can be changed during the aerosol dynamics processes with different refractive indices and compared their results with the simple analytic size distribution solutions.

Subsequently, this study shows how the Ångstrom exponent can be changed during the aerosol dynamics processes for a log-normal aerosol size distribution with different refractive indices and compared their results with simple analytic type solutions.

References

Junge, C. E. (1955) The size distribution and aging of natural aerosols as determined from electrical and optical measurements in the atmosphere, Journal of Meteorology, 12, 13–25.

Jung, C. H., and Y. P. Kim (2006) Numerical estimation of the effects of condensation and coagulation on visibility using the moment method, Journal of Aerosol Science, 37, 143-161.

Jung, C. H. and Y. P. Kim (2007) Particle extinction coefficient for polydispersed aerosol using a harmonic mean type general approximated solution, Aerosol Science and Technology, 41, 994-1001.

Jung, C. H. and Y. P. Kim (2008) Theoretical study on the change of the particle extinction coefficient during the aerosol dynamic processes, Journal of Aerosol Science, 39, 904-916.

Jung, C. H. and Y. P. Kim (2010) Simplified analytic model to estimate °Êngstrom exponent in Junge aerosol size distribution, Environmental Engineering Science, 27, 789-795.