Surface Delays for Gases Dispersing in the Atmosphere

Abstract

When a particle descends beneath the (nominal) lower boundary of the atmosphere, it may remain there for some time τ before it reemerges into the (resolved) flow. In particle trajectory models, τ is the random duration of unresolved trajectory segments, below the height zr at which an artificial reflection boundary condition is applied. By computing such paths, for realistic near-ground flows, it was found that the mean delay per reflection is τ ≈ 2.5zr/σw where σw is the standard deviation of the vertical velocity at zr. The corresponding mean alongwind displacement per reflection, due to the mean horizontal wind u(z) below zr, is δ ≈ ?u?|?zr? τ, where ?u?|?zr? is the height average of u in the waiting layer. The fluctuating component of the horizontal wind causes no mean drift but upon each reflection contributes a random drift whose root-mean-square value is σδ ≈ 2zr. From simulations on the continental scale, with a lower boundary placed at zr ≈ 25 m, it was found that a typical particle suffered about 15 reflections per day, resulting in a net delay on the order of 30 min per day.