Statistical Approach to Evaluation of Atmospheric Environment (I)

Basic Theorem of Dosage Model

Abstract

It is important to investigate the relations between the level of air pollutant concentration, its exposure time and their associated adverse effects on plant, animal and man.
We define “dosage” Dk (T) , which is the new measure of the level of air pollution, as follows,
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where x (t) is the air pollutant concentration at time t, x_c is the threshold concentration, T is the exposure time and U [x] is the unit step function.
The expectation and the variance of dosage are theoretically derived, when the probability density function of air pollutant concentration is approximated by log-normal distribution. The expected value of dosage is equivalent to the product of the k' th moment about origin and the exposure time when threshold value is zero.
The expected dosage is also calculated when the repair mechanism is considered. It is assumed in this dosage analysis that the adverse effect on plant and animal is related to the accumulation of tacit impairment, which is proportional to the square of concentration on the plant injury test and to the cube of concentration on the animal test.