A physical explanation of the lognormality of pollutant concentrations

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.