Impact of Advection Schemes on Tracer Interrelationships in Large-Eddy Simulations of Deep Convection

This study investigates the preservation of tracer interrelationships during advection in large-eddy simulations of an idealized deep convective cloud, which is particularly relevant to chemistry, aerosol, and cloud microphysics models. Employing the Cloud Model 1, advection is represented using third-, fifth-, and seventh-order weighted essentially non-oscillatory schemes. As a simplified analogy for cloud hydrometeors and aerosols, several inert passive tracers following linear and nonlinear relationships are initialized after the cloud reaches ∼6-km depth. Numerical mixing in the simulated turbulent convective clouds leads to significant deviations from the initial nonlinear relationships between tracers. In these simulations, a considerable fraction of the grid points where the tracers’ nonlinear relationships are altered from advection are classified as unrealistic (e.g., ∼13% for the environmental tracers on average), including errors from range-preserving unmixing and overshooting. Errors in the sum of three tracers are also relatively large, ranging between ∼1% and 16% for 5% of the grid points in and near the cloud. The magnitude of unrealistic mixing and errors in the sum of three tracers generally increase with the order of accuracy of the advection scheme. These results are consistent across model grid spacings ranging from 50 to 200 m, and across three different flow realizations for each combination of grid spacing and advection scheme tested. Tests employing a previously proposed scalar normalization procedure show substantially reduced errors in the sum of three tracers with a relatively small negative impact on other tracer relationships. This analysis, therefore, suggests efficacy of the normalization procedure when applied to turbulent three-dimensional cloud simulations. Significance Statement In nature, transporting several quantities through bulk motions of a fluid does not affect preexisting relationships between them. However, this is not always accomplished in numerical models of the atmosphere, because of intrinsic limitations in the transport algorithms employed. We aim to investigate how these errors behave in 3D realistic simulations of a cumulus cloud, where the turbulent flow constitutes a particular challenge. We show that relationships between quantities are significantly and frequently perturbed during bulk transport in the model. Moreover, our results suggest that increasing complexity of the bulk-transport algorithms (in a way that is conventionally employed for improving the representation of individual quantities) tends to worsen the representation of relationships between two or three quantities.