Technical note: Particle extinction coefficient for polydispersed aerosol using a harmonic mean type general approximated solution

In the present study, an approximated expression for the single particle extinction efficiency (Q_ext) has been obtained, which was valid for a wide range of particle sizes. The approximate single particle extinction efficiency was obtained using the harmonic mean type approximation between the particle extinction efficiencies from the Rayleigh scattering and geometric scattering regions. The results were compared with the numerically calculated Mie's results, which showed that both the approximated and original Mie's results were comparable. The approximated polydispersity of the overall extinction coefficient (b_ext) obtained using the moment method was then tested and compared with the numerically integrated results. The approximated solution obtained showed how the b_ext effectively varied with the size distribution and greatly reduced computational time. Consequently, a simple and straightforward method for estimating the extinction coefficient for polydispersed aerosols, which can be widely applied in atmospheric aerosol models, has been developed in this study.