The shape of the probability density function of short-term concentration fluctuations of plumes in the atmospheric boundary layer

Abstract

The shape of the probability distribution of a set of high-resolution concentration fluctuation measurements from an ion plume is studied using order statistics and certain selected quantiles derived from them. A number of graphical techniques based on the order statistics are shown to be useful for the assessment of the symmetry and tailweight of the underlying distribution of concentration. These graphical techniques are applied, from both a descriptive and a computational point of view, to elucidate the underlying distributional shape of concentration and to assess the characterization efficacy of the probability distributions that have been proposed as models for concentration fluctuations. In this respect, a new probability distribution, namely, the g and h distribution, is introduced for describing concentration fluctuations and it is shown that this distribution is superior to the more commonly used models, namely, the log-normal, the exponential, and the clipped-normal distributions utilized by previous investigators. Except for the g and h distribution, it is found that none of the commonly used models for the concentration probability distribution is able to characterize accurately the extreme upper end of the concentration frequency distribution (i.e., the end of the distribution that is critical for the prediction of the probability of exposure to peak levels). However, the clipped-normal distribution is shown to provide a reasonably conservative model for the prediction of the exceedances of critical concentration levels. Finally, it is noted that the g and h distribution yields a bimodal form for the total probability density function for concentration whereas the clipped-normal distribution provides a unimodal form. It is shown that the bimodal form of the total concentration probability density function is consistent with both the data and certain theoretical results.