A single‐column model of the dry, shear‐free, convective boundary layer is presented in which non‐local transports by coherent structures such as thermals are represented by the partitioning of the fluid into two components, updraught and environment, each with a full set of prognostic dynamical equations. Local eddy diffusive transport and entrainment and detrainment are represented by parametrizations similar to those used in eddy diffusivity mass flux schemes. The inclusion of vertical diffusion of the vertical velocity is shown to be important for suppressing an instability inherent in the governing equations. A semi‐implicit semi‐Lagrangian numerical solution method is presented and shown to be stable for large acoustic and diffusive Courant numbers, though it becomes unstable for large advective Courant numbers. The solutions are able to capture key physical features of the dry convective boundary layer. Some of the numerical challenges posed by sharp features in the solution are discussed, and areas where the model could be improved are highlighted.

Recent increases in computing power mean that atmospheric models for numerical weather prediction are now able to operate at grid spacings of the order of a few hundred meters, comparable to the dominant turbulence length scales in the atmospheric boundary layer. As a result, models are starting to partially resolve the coherent overturning structures in the boundary layer. In this resolution regime, the so‐called boundary layer “gray zone,” neither the techniques of high‐resolution atmospheric modeling (a few tens of meters resolution) nor those of traditional meteorological models (a few kilometers resolution) are appropriate because fundamental assumptions behind the parameterizations are violated. Nonetheless, model simulations in this regime may remain highly useful. In this paper, a newly formed gray zone boundary layer community lays the basis for parameterizing gray zone turbulence, identifies the challenges in high‐resolution atmospheric modeling and presents different gray zone boundary layer models. We discuss both the successful applications and the limitations of current parameterization approaches, and consider various issues in extending promising research approaches into use for numerical weather prediction. The ultimate goal of the research is the development of unified boundary layer parameterizations valid across all scales.

Operational high‐resolution numerical weather prediction models are now able to partially resolve turbulent motions due to increased computing power. The partitioning of resolved and parametrized fluxes becomes important in the representation of turbulent transfer that determines the state of the atmospheric boundary layer. In this study, successive simulations of a convective boundary layer using the Met Office Large Eddy Model from the large‐eddy simulation to the mesoscale limit are compared with the corresponding coarse‐grained fields to examine model behaviour over the grey zone. The differences in the turbulent kinetic energy partitioning between coarse‐grained (reference) and actual fields are identified and used to quantify sub‐grid diffusion in the grey zone under different atmospheric forcings and surface heat flux. It is shown that the excessive mixing due to the large values of mixing length at coarse resolutions results in the cut‐off of resolved turbulence in the grey zone. The damping of resolved motions comes earlier for wind shear runs. In contrast, coarse‐grained fields exhibit a smooth transition of the resolved turbulent kinetic energy across the scales. Decreasing numerical dissipation through the sub‐grid scheme leads to the increase of resolved turbulence, but fails to reproduce the reference transition pattern that imposes some physical limitations to the partially resolved turbulence simulations. Pragmatic blending of mixing length values maintains a more realistic turbulent kinetic energy transition from fine to coarse resolutions and potential temperature profiles in the grey zone. Bounding vertical diffusion to its effective values, an approach based on maintaining inherent properties of the flow across the scales, is able to match the coarse‐grained fields from the highly resolved to the almost unresolved state, regardless of the forcing. Finally, the complexity of modelling in the grey zone is exhibited in the dependence of turbulence onset on time and vertical resolution.

Numerical simulations of two cases of morning boundary layer development are conducted to investigate the impact of grid resolution on mean profiles and turbulent kinetic energy (TKE) partitioning from the large eddy simulation (LES) to the mesoscale limit. Idealized LES, using the 3‐D Smagorinsky scheme, is shown to be capable of reproducing the boundary layer evolution when compared against measurements. However, increasing grid spacing results in the damping of resolved TKE and the production of superadiabatic temperature profiles in the boundary layer. Turbulence initiation is significantly delayed, exhibiting an abrupt onset at intermediate resolutions. Two approaches, the bounding of vertical diffusion coefficient and the blending of the 3‐D Smagorinsky with a nonlocal 1D scheme, are used to model subgrid diffusion at grey zone resolutions. Simulations are compared against the coarse‐grained fields from the validated LES results for each case. Both methods exhibit particular strengths and weaknesses, indicating the compromise that needs to be made currently in high‐resolution numerical weather prediction. The blending scheme is able to reproduce the adiabatic profiles although turbulence is underestimated in favor of the parametrized heat flux, and the spin‐up of TKE remains delayed. In contrast, the bounding approach gives an evolution of TKE that follows the coarse‐grained LES very well, relying on the resolved motions for the nonlocal heat flux. However, bounding gives unrealistic static instability in the early morning temperature profiles (similar to the 3‐D Smagorinsky scheme) because model dynamics are unable to resolve TKE when the boundary layer is too shallow compared to the grid spacing.

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