Recurrence of High Concentration Values in a Diffusing, Fluctuating Scalar Field

We propose a simple model for esimating the average number of occurrences per unit time η(co) that a threshold concentration co is exceeded. It is based on the joint probability density of the observed concentration c(t) and its time derivative ċ(t) under the assumption that c(t) is a stationary time series; this assumption leads to the hypothesis that c(t) and ċ(t) are statistically independent.

Adopting plausible forms of the frequency distributions of c and ċ, we apply the model to diffusion from an infinite area source and from an elevated point source, both in the neutral boundary layer, and obtain simple results for η(co) and the average duration of one excursion above co as functions of co, the mean and the standard deviation of the concentration, and surface-layer variables.