A multiple-source air quality control model achieving a stan-dard, defined by a vector-valued function

Sven-˚ Gustafson
2009 18 th World IMACS/MODSIM Congress   unpublished
Earlier papers by Gustafson, Kortanek, Sweigart and others describe models for controlling air pollution, consisting of chemically inert pollutants like sulphur dioxide. It was assumed that the concentration contributions from the sources added up at each receptor point. The goal was to achieve acceptable air quality for each receptor point, generally defined by the annual mean concentration of the pollutant under study. The set of polluting sources was split in n source-classes, where the
more » ... ses, where the sources in each class were regulated in the same way and independently of the other source-classes. One such class could be motor vehicles which are required to use the same quality of fuel, since it is of course not possible to regulate the pollution output from each vehicle separately. The idea was to determine the relation between the strength of each source-class and its contribution to the annual mean concentration at each receptor point in the air quality control area. Then one calculates how the strengths of sources need to be reduced to achieve the desired air quality. Generally, there are many reductions policies which achieve this goal and one seeks to calculate the policy which achieves this at the lowest total regulation cost. This model requires large amounts of data, since one needs to have lists of all source-classes as well as meteorological information in order to calculate the contributions to the mean concentration. Here we propose to discretise the set of weather states as well. Each weather situation is defined by meteorological parameters like wind speed, wind direction, mixing height and so on. The idea is to represent the set of all possible weather situations in the control area by k points w 1 ,. .. , w k in the meteorological parameter space with associated probabilities p 1 ,. .. , p k. Thus the climate in the air quality control area is represented by this discrete probability distribution. Next we introduce standards for each weather state defined by the functions w 1 ,. .. , w k. These standards are determined such that the permissible pollution has a desirable distribution, e.g. such that the probability of very high concentrations is low. It is assumed that it is known which weather states give the highest pollution concentrations. Hence we get k constraints at each receptor point and we may calculate , using semi-infinite programming, the reductions policy which satisfies these constraints at minimum control costs. Similar models may be developed for water pollution problems.