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

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.