The asymptotic moments of the concentration of a pollutant subject to rainout and dry removal are given. Both the lengths of the wet and dry periods and the wet and dry removal rates are allowed to be random, although the removal rate is assumed to be fixed within any one wet or dry period. The results hold in a more general setting than removal processes, so its is hoped that they will be applicable to other problems.

The purpose of this paper is to study simple mathematical models for the variation of the concentration of atmospheric pollutants. The particles are assumed to be emitted into the atmosphere with constant intensity and removed from the atmosphere with an intensity proportional to the precipitation intensity. The precipitation intensity is assumed to be a stationary stochastic process with no spatial variation. The mean, variance and covariance function of the concentration are calculated for some precipitation models. Under certain general assumptions it is shown that the concentration of ‘long-lived' particles is approximately described by an Ornstein–Uhlenbeck process. Finally, the different models are compared by means of Swedish precipitation data.