Analysis of environmental quality data for decision making purposes (evaluation of compliance with standards, examination of environmental trends, determination of confidence intervals) generally requires a suitable univariate probability model. It sometimes is difficult, when many probability models are available, to select the most appropriate one for a given data set. The underlying physical laws which generate pollutant concentrations--diffusion processes--offer insight into which model may be most appropriate for a variety of situations. Treating the diffusion equation as a stochastic differential equation, the time series of pollutant concentration data from diffusion phenomena is shown to have a distribution that is best approximated by the censored, 3-parameter lognormal probability model (LN3C). The model is applied to 10 air quality data sets (SO2, O3, CO, particulate, hydrocarbons, and NO2 from the United States, France, West Germany, and Denmark) and 9 water quality data sets (BOD, coliform, chloride, and sulfate from the Ohio River). The authors conclude that the LN3C probability model offers data analysts a superior, general purpose model suitable for a large variety of environmental phenomena.