# Modeling and Simulation of Air Quality in Bamako

The air pollution is one of the biggest killers in the world [WHO]. Since the monitoring of urban pollutants is very expensive, the modeling of the pollutants dispersion is an alternative that offers good results in the study of air quality [Kumar] and covers the pollution transport and diffusion in the atmosphere, its dry and wet deposition and chemical reactions and depends on pollutant properties, meteorological conditions, emission data and terrain parameters.

Let $c$ be a vector of concentration fields, where each element $c_i$ corresponds to the scalar field of concentration of the chemical species (pollutant) labelled by $i$ in the air. The spatio-temporal evolution of the concentration $c_i$ is described by the following advection-diffusion-reaction model:

$\dfrac{\partial c_i}{\partial t} = - \underbrace{\nabla \cdot \left ( \mathbf{u} c_i \right)\ }_{\text{advection}} + \underbrace{\nabla \cdot \left ( \rho K \nabla \left ( \dfrac{c_i}{\rho} \right) \right )}_{\text{diffusion}} + \underbrace{\chi_i (c)}_{\text{chemistry}} - \underbrace{\Lambda_i(x,t)c_i}_{\text{deposit}} + \underbrace{S_i(x,t)}_{\text{volumic sources}}$

where

• $\rho$: air density

• $K$: diffusion coefficient

• $\mathbf{u}$: wind velocity

• $\chi_i$: chemical source term that describes the chemical reactions

• $\Lambda_i$: scavenging coefficient

• $S_i$: source terms

• $x$: spatial coordinates

• $t$: time coordinates

The advection corresponds to transport by the wind field, and the diffusion describes the turbulent mixing. The reaction corresponds to the physical and chemical processes of transformation of pollutants.

The model is based on the assumption that there is no feedback between the chemical species and the flow fields (wind velocity, turbulent diffusivity, temperature). We assume that the flow is incompressible, which means the variations in density $\rho$ are assumed to be constant.

## 4. Bibliography

• [WHO] W.H.Organization, Air pollution, www.who.int/phe, 2020.

• [Kumar] S.Kumar, R.Kumar, Air Quality: Monitoring and Modeling, BoD-Books on Demand, 2012.