Simple stochastic models for the sources and sinks of two aerosol types

Abstract

The statistical properties of two time-dependent and steady-state aerosol concentration distributions are derived from simple stochastic models of the particle sources and sinks. The analysis is applied to statistics of area averaged aerosol concentrations in two examples: (a) anthropogenic sulfate particles, for which the source is assumed constant in time, and removal is by precipitation at random times, and (b) windblown dust) for which we assume the sources are a constant background plus randomly occurring dust storms, and the sinks are time independent advection and dry deposition. The models are solved both analytically and by numerical simulation. For both models the time-lagged autocorrelation function of the pollutant is a simple exponential, and the ratio of the steady-state variance to the squared mean concentration varies inversely with the effective lifetime.

Application of data from the World Meteorological Organization to model (a) shows that the expected lifetimes for sulfates are between SO and 175 h, and the deposition distances are between 800 and 2000 km.