Simple Model for the Vertical Transport of Reactive Species in the Convective Atmospheric Boundary Layer

• Published in: Boundary-layer meteorology Vol. 134; no. 2; pp. 195 - 221
• Main Authors: Kristensen, Leif, Lenschow, Donald H, Gurarie, David, Jensen, Niels Otto
• Format: Journal Article
• Language: English
• Published: Dordrecht Dordrecht : Springer Netherlands 01.02.2010; Springer Netherlands; Springer; Springer Nature B.V
• Subjects: Analysis; Animal behavior; Atmospheric boundary layer; Atmospheric chemistry; Atmospheric Protection/Air Quality Control/Air Pollution; Atmospheric Sciences; Boundary conditions; Boundary layer; Boundary layers; Chemical reactions; Convection, turbulence, diffusion. Boundary layer structure and dynamics; Convective boundary layer; Countergradient flux; Covariance; Damköhler number; Destruction; Differential equations; Dynamic meteorology; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Exact sciences and technology; External geophysics; Fluctuations; Fluxes; Geophysics. Techniques, methods, instrumentation and models; Mathematical models; Meteorology; Nitrogen dioxide; NO x -O₃ triad; Parametrization; Planetary boundary layer; Reactive species; Scalar-scalar covariance; Scalars; Surface temperature; Troposphere; Turbulence models; Wildlife conservation; NO; Convective boundary layer; Countergradient flux; triad; Reactive species; Damköhler number; Scalar–scalar covariance; O; Nitrogen oxide; Scalar-scalar covariance; Turbulent transfer; ozone; Closure model; Air biosphere interaction; one-dimensional models; Atmospheric boundary layer; Vertical profile; Convective layer; Gas exchange; Concentration distribution
• ISSN: 0006-8314; 1573-1472
• DOI: 10.1007/s10546-009-9443-x

We have developed a simple, steady-state, one-dimensional second-order closure model to obtain continuous profiles of turbulent fluxes and mean concentrations of non-conserved scalars in a convective boundary layer without shear. As a basic tool we first set up a model for conserved species with standard parameterizations. This leads to formulations for profiles of the turbulent diffusivity and the ratio of temperature-scalar covariance to the flux of the passive scalar. The model is then extended to solving, in terms of profiles of mean concentrations and fluxes, the NO x -O₃ triad problem. The chemical reactions involve one first-order reaction, the destruction of NO₂ with decay time τ, and one second-order reaction, the destruction of NO and O₃ with the reaction constant k. Since the fluxes of the sum concentrations of NO x = NO + NO₂ and O₃ + NO₂ turn out to be constant throughout the boundary layer, the problem reduces to solving two differential equations for the concentration and the flux of NO₂. The boundary conditions are the three surface fluxes and the fluxes at the top of the boundary layer, the last obtained from the entrainment velocity, and the concentration differences between the free troposphere and the top of the boundary layer. The equations are solved in a dimensionless form by using 1/(kτ) as the concentration unit, the depth h of the boundary layer as the length unit, the convective velocity scale w * as the velocity unit, and the surface temperature flux divided by w * as the temperature unit. Special care has been devoted to the inclusion of the scalar-scalar covariance between the concentrations of O₃ and NO. Sample calculations show that the fluxes of the reactive species deviate significantly from those of non-reactive species. Further, the diffusivities, defined by minus the flux divided by the concentration gradient may become negative for reactive species in contrast to those of non-reactive species, which in the present model are never negative.