A Physical Explanation of the Lognormality of Pollutant Concentrations

Abstract

Investigators in different environmental fields have reported that the concentrations of various measured substances have frequency distributions that are lognormal, or nearly so. That is, when the logarithms of the observed concentrations are plotted as a frequency distribution, the resulting distribution is approximately normal, or Gaussian, over much of the observed range. Examples include radionuclides in soil, pollutants in ambient air, indoor air quality, trace metals in streams, metals in biological tissue, calcium in human remains. The ubiquity of the lognormal distribution in environmental processes is surprising and has not been adequately explained, since common processes in nature (for example, computation of the mean and the analysis of error) usually give rise to distributions that are normal rather than lognormal. This paper takes the first step toward explaining why lognormal distributions can arise naturally from certain physical processes that are analogous to those found in the environment. In this paper, these processes are treated mathematically, and the results are illustrated in a laboratory beaker experiment that is simulated on the computer.

The German Environmental Survey 1990/1992 (GerES II): cadmium in blood, urine and hair of adults and children

“…Besides the 10th, 50th, and 90th percentiles, the 95th percentile was also specified to reflect the asymmetry of the distribution and to focus on persons with high exposure. Since statistical tests revealed that the data are log -normally distributed, which is in agreement with a general result concerning the distribution of environmental concentrations (Ott, 1990 ), the GM rather than the arithmetic mean was preferred to characterise the mean location of the data. Moreover, a 95% confidence interval for the GM (CI -GM ) was added to assess the estimation error of GM.…”

Doses and lung burdens of environmental tobacco smoke constituents in nonsmoking workplaces

“…An additional reason for using this convention was to estimate doses and lung burdens for NSWs in the same manner as those estimated for SWs in previous publications. Because chemical concentrations in studies of this nature tend to be lognormally distributed (Ott, 1990 ) , the Kolmogorov ±Smirnov goodness-of -fit test (Lilliefors option) was applied to determine whether the concentration data from NSWs followed the lognormal distribution. In the earlier work on cells 1 and 3, UVPM was shown to be lognormally distributed, and nicotine was lognormal in cell 3 but not in cell 1 ( LaKind et al, 1999c ) .…”

Application of the Bayesian approach for derivation of PDFs for concentration ratio values

“…We will assume that the CRs are log-normally distributed. This assumption is based on arguments of the log normality of concentrations of elements in the environment (Ott 1990(Ott , 1995, empirical observations of element concentrations in the environment that are used for calculation of CR values (Nordén et al, 2010) and the fact that the quotient of two log normal random variables is log normally distributed.…”

“…The underlying data for species with N>2 was assessed to be approximately log normally distributed by visual inspection of quantile-quantile plots. Based on these observations and also the theoretical consideration such as those addressed by Ott (1990Ott ( , 1995) the log normal assumption was also used for the two species with N=2. All statistical analyses for this example have been conducted using the BABAR software package which can be downloaded at no charge from the website: http://facilia.se/projects/babar.asp.…”