A simple model for relating concentrations and fluctuations of trace reactive species to their lifetimes in the atmosphere

[1] By means of a simple analytical one-dimensional (1-D) model, we predict mean vertical structure and fluctuations in trace gas concentrations as a function of species lifetime in the atmosphere. The model assumes a well-mixed planetary boundary layer (PBL) overlain by a free troposphere with constant diffusivity separated by a jump in species concentration. A jump in concentration is also assumed across the tropopause, and an exponential increase in diffusivity with height is assumed through the stratosphere. This three-layer model is applied to species with surface sources that have lifetimes of the order of days to years and predicts that the standard deviations of the concentration fluctuations normalized by the mean concentration are approximately proportional to the lifetimes of the trace gases to a power between 1/2 and 1, depending on altitude and lifetime. Observations from several long-range aircraft field deployments, which collected gas samples from within the PBL up to 12 km altitude, generally agree with this prediction. A relation of this type is useful for estimating lifetimes of trace gases in the atmosphere or, conversely, if the lifetimes are known, average entrainment rates in the measurement region. The model also predicts a relationship among the surface emission, mean concentration, and lifetime, so that given any two of these quantities the third can be estimated.