Calculate Peak to Mean Ratio

The peak-to-mean scaling

is important for understanding the response to wind-borne odours. Here Cm is the measure of mean concentration over an averaging time scale tm for which meteorological conditions are persistent, while Cp is the expected peak concentration, averaged over time tp, during the time tm. Cm is typically a ten-minute or one-hour average and is routinely and reliably modelled.

Peak concentrations Cp occur in relatively rare patches of poorly diluted odorous source material sensed by a ‘nose’ downwind of the source. The value of tp can vary from molecular diffusion timescales (sub-seconds) to seconds and minutes.

We have been able to relate these peak concentrations, the scaling properties, and the physical structure of the odour plumes to a recent prediction for the probability density function for an odour concentration (in fact, any passive tracer), which is characterised by a power law for the large-concentration rare-event tail. This so-called inertial-range behaviour extends from concentrations near the ensemble mean value, which is nominally small at any significant distance from the source, up to very large concentrations compared to the mean, limited only by the maximal initial source concentration and by molecular diffusion.

We find that for a point-source plume the exponent p is given by p = 6/17 ~0.35, and for a line-source plume, p = 3/14 ~0.21.

Both these values are already established empirical results, but we have shown that they are a consequence of modern turbulence theory and are universal properties independent of material and dispersion parameters.

See:

Borgas, M.S. (2000). The mathematics of whiffs and pongs. Presented at Enviro2000 Odour Conference, Sydney, 9-13 April 2000: Clean Air Society of Australia and New Zealand (see a slide presentation). Hibberd, M. F. (1998). Peak-to-mean ratios for isolated tall stacks (for averaging times from minutes to hours). In: Proceedings of the 14th International Clean Air and Environment Conference , Melbourne. Mitcham, Vic.: Clean Air Society of Australia and New Zealand. p. 255-260.

The code for the calculator can be viewed here. For more information, email: michael.borgas@csiro.au

Modified: May 22, 2008