Dynamic estimation of air pollution

The advection-diffusion model of air pollution over an urban area is developed. The region is subdivided into a grid and the three-dimensional partial differential equation of the pollution concentration is reduced to a linear vector difference equation. Along with this discrete equation, a stochastic model of air pollution is considered and pollution concentrations over the area are estimated from observed data generated by a few monitor points. High dimensionality of the resulting Kalman filter equation is avoided by using a discrete form of Chandrasekar-type equations. Diffusion coefficients in the advection-diffusion model, which are difficult to specify accurately, are also identified.