On the dispersion of trace species in the atmospheric boundary layer: a re‐formulation of the governing equations for the turbulent flow of the compressible atmosphere

ABSTRACT

Since especially the parameterisation of the vertical dispersion of trace species in the atmospheric boundary layer has controversially been discussed in the literature, the 1st‐order balance equations for matter, momentum, and various energy forms were re‐formulated with Hesselberg's density‐weighted averaging calculus to point out that this problem arises from averaging the macroscopic balance equations of matter, momentum and various energy forms in the sense of Reynolds, rather than from the parameterisation of the vertical dispersion by 1st‐order closure principles, as this discussion seems to reflect. Results of the SANA field experiment "Eisdorf" presented here substantiate that in the case of chemically reactive trace constituents segregation effects owing to turbulence cannot generally be neglected as usually performed in Eulerian air pollution models. Modelling such segregation effects, however, requires, at least, 2nd‐order‐closure principles. Therefore, the 2nd‐order balance equations for 2nd moments like the eddy flux densities of matter and momentum as well as covariances of scalar quantities were also re‐formulated by considering Hesselberg's averaging procedure. This re‐formulated set of governing 1st‐order and 2nd‐order balance equations may be considered as most exact because the degree of simplification is reduced to a minimum. To distinguish between the Boussinesq approximated equation set for the turbulent atmospheric flow, denoted as Boussinesq fluid, and our re‐formulated one, the turbulent flow of the compressible atmosphere for which the re‐formulated governing balance equations are valid may be denoted as Hesselberg fluid. It is argued that averaging in the sense of Hesselberg reduces the risk to misinterpret turbulent atmospheric processes to a minimum. As exemplary shown on the basis of the balance equations for dry air, water vapour, and trace species, the so‐called Webb correction will become insignificant if Hesselberg's averaging calculus is considered. Based on the results obtained from the "Eisdorf" experiment and from sensitivity studies with a Seinfeld‐type kinetic mechanism for photochemical smog, it is argued that an evaluation and improvement of Eulerian air pollution models require directly measured 2nd‐order moments. Since the number of fast‐response physico‐chemical analysers for chemically reactive trace constituents is strongly limited, such fast‐response sensors have to be (further) developed to set‐up a true platform for model evaluation that implies not only a comparison of calculated and observed distributions of 1st moments (necessary condition), but also a comparison of the calculated and observed distributions of 2nd moments (sufficient condition).