The statistics of chemical trace concentrations in the steady state

Abstract

The steady state probability distribution of chemical tracers in the atmosphere and in rain can be calculated from stochastic models, under explicit assumptions. We compare predictions from two such models, one based upon a linear stochastic equation in which random removal events … or storms … form a Poisson process, and the other based upon multiplicative random processes which produce a lognormal distribution. The two models predict different shapes for the resulting distributions of concentrations and fluxes of atmospheric tracers such as sulfates in ‘acid rain’. Consequently, estimates of the frequencies of extreme events, if based upon an assumed parametric form of a distribution function whose parameters are fitted by measurements of typical events, are model sensitive. To establish a preferred model for wet deposition, we have examined the statistics of sulfate deposition from the “European Network for the Study of Long Range Transport of Air Pollutants” (LRTAP), during the years 1973–1975. The shapes of the distributions of airborne sulfur species (SO 2+ SO 4 2−), and of raincarried sulfate fluxes to the ground, are between those predicted by the two models. Our results are of operational significance to efforts directed to establishing national standards for rain quality.