A note on peak-to-mean concentration ratios

Abstract

The peak-to-mean concentration ratio obtained from observations near a point source of pollution is a particular example of the ratio of any short-period concentration to the long-term mean. The value of this ratio may be obtained from the probability distribution function:

$$F(C) = F(0) exp [ - F(0) C/M]$$

whereF(C) is the probability or frequency that the ratio of a short-period average concentration (C) to the long-term mean (M) exceeds the valueC/M, andF(0) is a parameter dependent on the length of the short period and the position of the sampler relative to the centre-line of the plume. From (1) the peak-to-mean concentration ratio is shown to be related to the two averaging times by the expression

$$P/M = 1/F(0) [lnF(0) - lnt_M /t_P ]$$

wheret _M andt _P are, respectively, the averaging times of the long-term meanM and the short-term peakP.

Using recently published experimental data, Equation (1) and hence also (2) are shown to be valid for averaging timest _P from 5 s to 24 h and oft _M from 6 min to 5 yr providedt _P ≪t _M .