Modeling the diurnal cycle of conserved and reactive species in the convective boundary layer using SOMCRUS

Abstract. We have developed a one-dimensional second-order closure numerical model to study the vertical turbulent transport of trace reactive species in the convective (daytime) planetary boundary layer (CBL), which we call the Second-Order Model for Conserved and Reactive Unsteady Scalars (SOMCRUS). The temporal variation of the CBL depth is calculated using a simple mixed-layer model with a constant entrainment coefficient and zero-order discontinuity at the CBL top. We then calculate time-varying continuous profiles of mean concentrations and vertical turbulent fluxes, variances, and covariances of both conserved and chemically reactive scalars in a diurnally varying CBL. The set of reactive species is the O₃–NO–NO₂ triad. The results for both conserved and reactive species are compared with large-eddy simulations (LES) for the same free-convection case using the same boundary and initial conditions. For the conserved species, we compare three cases with different combinations of surface fluxes, and CBL and free-troposphere concentrations. We find good agreement of SOMCRUS with LES for the mean concentrations and fluxes of both conserved and reactive species except near the CBL top, where SOMCRUS predicts a somewhat shallower depth, and has sharp transitions in both the mean and turbulence variables, in contrast to more smeared-out variations in the LES due to horizontal averaging. Furthermore, SOMCRUS generally underestimates the variances and species–species covariances. SOMCRUS predicts temperature–species covariances similar to LES near the surface, but much smaller magnitude peak values near the CBL top, and a change in sign of the covariances very near the CBL top, while the LES predicts a change in sign of the covariances in the lower half of the CBL. SOMCRUS is also able to estimate the intensity of segregation (the ratio of the species–species covariance to the product of their means), which can alter the rates of second-order chemical reactions; however, for the case considered here, this effect is small. The simplicity and extensibility of SOMCRUS means that it can be utilized for a broad range of turbulence-mixing scenarios and sets of chemical reactions in the planetary boundary layer; it therefore holds great promise as a tool to incorporate these processes within air quality and climate models.