Mathematical Modeling of Air Pollutants: An Application to Indian Urban City

Continuous development and increase of population in the urban areas, a series of problems related to environment such as deforestation, release of toxic materials, solid waste disposals, air pollution and many more, have attracted attention much greater than ever before. The problem of air pollution in cities has become so severe that there is a need for timely information about changes in the pollution level. The air pollution dispersion is a complex problem. It covers the pollutant transport and diffusion in the atmosphere. The pollutant dispersion in the atmosphere depends on pollutant features, meteorological, emission and terrain conditions. Physical and mathematical models are developed to describe the air pollution dispersion. Physical models are small scale representations of the atmospheric flow carried out in wind tunnels. Mathematical models are divided in to statistical and deterministic models. Statistical models are based on analysis of past monitoring air quality data. Deterministic models are based on a mathematical description of physical and chemical processes taking place in the atmosphere. These models are based on mathematical equations, express conservation laws of mass, momentum and energy. Both the models are discussed in this chapter. Statistical models are also divided into linear and non-linear models. Several studies based on the statistical models have been carried out in different regions to identify local meteorological conditions, most strongly associated with air pollutants concentration to forecast the air quality (McCollister & Willson, 1975; Aron & Aron, 1978; Lin, 1982; Aron, 1984; Katsoulis, 1988; Robeson & Steyn, 1990). Many of the previous studies (Sanchez et. al., 1990; Mantis et al., 1992; Milionis & Davies, 1994) analyzed the meteorological conditions associated with high pollutant concentration. These studies usually produced qualitative or semi quantitative results and shed light on the relation between the meteorological conditions and pollutant concentrations. Shi & Harrison, 1997 developed a linear regression model for the prediction of NOx and NO2 in London. A linear regression model was used by Cogliani, 2001 for air pollution forecast in cities by an air pollution index highly correlated with meteorological variables. Since the relation between air pollutants and meteorological variables is not linear, some non-linear models i.e., Neural Network can also be used to forecast the pollutant concentrations (Bozner et al., 1993; Comrie, 1997). The deterministic models are divided in to Eulerian, Lagrangian and Gaussian models. In this chapter we discuss only the Eulerian analytical models. The atmospheric diffusion