New approach to handle gas-particle transformation in air pollution modelling using fractional derivatives

Özet

In this study, a new fractional advection–diffusion equation is developed that governs the formation of a secondary pollutant (sulphur dioxide in sulphate) and considers the removal processes of the pollutant from the atmosphere. The equation is solved using a Laplace transform technique considering a vertically inhomogeneous planetary boundary layer. The simulations performed in this study show the influence of dry and wet deposition, including the order of the derivative used (memory effect), on the concentrations of the primary and secondary pollutants. The numerical experiment performed using the proposed semi-analytical solution shows that the numerical results are consistent with the physical aspects of the dispersion process and that the proposed model is representative of the pollutant dispersion process considering the gas-particle transformation. It is observed that the effect of the fractional derivative is related to anomalous dispersion, with the concentration of the pollutant decreasing or increasing according to the order of the derivative.