Fluxes and Concentrations of Non-Conserved Scalars in the Atmospheric Surface Layer

Abstract

We have carried out a theoretical study of the simplest possible, second-order, chemical destruction process in the atmospheric surface layer. The model describes the destruction of two gases emanating from the surface with the same molecular flux. Although this situation seems artificial with no counterpart in the real atmosphere, the results shed light on some fundamental problems. For example, it is possible to specify boundary conditions, with the concentrations and the fluxes at a given height away from the surface, which lead to unrealistic solutions with infinite surface fluxes. A method to describe and separate the consistent solutions for this process was developed. It is in general of particular interest from an experimental point of view since it is not possible to measure fluxes right at the surface: if a measurement of flux and concentration in a given height requires infinite surface fluxes there is something wrong with the data. We expect that such problems will be inherent in more complex reactions schemes, such as the NO-NO₂-O₃ triad. Just as in first-order destruction processes, the Damköhler ratio will enter the turbulent diffusivity, but where this ratio is concentration independent for first-order processes, the present second-order model implies that the Damköhler ratio is proportional to the concentration. In the study of first-order processes it was found that the Damköhler correction to the turbulent diffusivity is of minor importance from an experimental point of view. We arrive at the same conclusion in this particularly simple study of second-order destruction. In other words, this work may be considered a further development of a previous study of the first-order destruction of a passive scalar. The model and the method we develop to solve the corresponding nonlinear differential equations are considered a preliminary study for developing tools to deal with more complicated atmospheric processes. Also, the results obtained may serve as a “calibration case” for more elaborate simulations.