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

##### Original version

18th World IMACS/MODSIM Congress, Cairns, Australia 13-17 July 2009##### Abstract

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 sourceclasses,
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 w1, . . . ,wk in the meteorological
parameter space with associated probabilities p1, . . . , pk. 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 w1, . . . ,wk. 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.