Developing a Mathematical Model to Assess the Liveablity in Blighted Mega City

Karachi (24° 37.38¢ N, 66° 54.42¢ E) is one of the mega cities of Pakistan. In general, deteriorating urban air quality in developing countries is a worsening environmental problem and causing damage to human health. The urban atmospheric pollution is several times higher than the limits set by the WHO. Being industrial city, the rate of increase of traffic volume has been exponential during the last decade in Karachi. More or less, 90% atmospheric pollution is related to vehicle emissions. To gauge and forecast future traffic volume and urban pollution level mathematical models are needed. This communication attempts to model the urban traffic population evolution and the atmospheric pollution levels during the past 25 years. The traffic model shows that total traffic volume in Karachi was 1 million in 1999. In 2008 it reached 2 million and in 2012 the traffic volume crossed 3 million verifying published data. According to this forecast model, it is also important to note that the total traffic volume in Karachi will go to 4 million, 5 million, and 6 million in the years 2015, 2018, and 2020 respectively. Auto Regressive Integrated Moving Average, ARIMA (2, 1, 2) model is found to be adequate model to capture Karachi urban atmospheric pollution variation. The model is the first of its kind for the region considered. As a further application, we develop an empirical model of local atmospheric pollution fluctuations as determined by urban traffic volume. The work should provide a basis for other applications, including urban planning,urban-regional air quality management, design of efficient energy programs, etc