A Statistical Plume Model with First-Order Decay

Abstract

Many atmospheric contaminants decay or react in the atmosphere. in situations such as the diffusion of radioactive contaminants, certain chemical pollutants and viable microorganisms, a first-order decay rate is considered to be an appropriate model. The conventional method of estimating the downwind concentrations from a continuous point source of these decaying contaminants is to multiply the estimated concentration of an equivalent amount of a conserved pollutant by the factor exp(?kx/?) in which k is the first- order decay rate, x the downwind distance and ? the wind speed. In this paper, the statistical diffusion theory is extended to incorporate first-order decay. The statistical theory shows that there is a distribution of the local age of the contaminant at any point downwind. Since this distribution is skewed toward ages less than the travel lime x/?the proposed theory predicts higher concentrations than the conventional approach for a pollutant that decays at a first-order rate. The difference is a function of σx2k/x?. If this term is very small, the two approaches are in good agreement. If this term is large, the predictions of the proposed model are higher.