one basis, as the location of the discharge points (including the stack height) matters -
all sources do not contribute to ambient air quality in the same manner. Their
contribution depends on each source's emission diffusion characteristics with respect to
each monitored receptor. This implies that one unit of extra reduction (over and above
the legislated level) by source ‘a’ may not necessarily be equivalent to one unit of
excess emission (over the legislated level) by source ‘b’ if the emission diffusion
characteristics or transfer coefficients for sources ‘a’ and ‘b’, associated with a given
receptor are not the same.
The cost effective allocation of a non-uniformly mixed assimilative3 pollutant is
that allocation which minimises the cost of pollution control subject to the constraint
that the target concentration level of pollutant in the ambient air is met at all receptors
in the airshed. This can be represented as4:
J
Min Σ Cj (rj
j=1
subject to
J
Ai ≥ Σ dij (ej - r)
j=1
rj ≥ 0
(1)
i = 1,...,I (2)
j = 1,.....,J (3)
Here Cj is the cost of emission reduction and rj is the amount of emission
reduction that the jth source has to achieve, and J is the number of sources (discharge
points) to be regulated. As rj increases, the marginal cost of control is expected to
increase. ej is the emission rate of the jth source that would prevail if the source failed
3 For assimilative pollutants, the capacity of the environment to absorb them is relatively large
compared to their rate of emission, such that the pollution level in any year is independent of the amount
discharged in the previous years. In other words, assimilative pollutants do not accumulate over time.
4 See Tietenberg (1985).
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