Quantifying and improving sub‐grid diffusion in the boundary‐layer grey zone

Abstract

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.

Grey zone simulations of the morning convective boundary layer development

“…Potential temperature profiles match LES through the whole depth of the BL mainly during and after the rapid ML development. This is in accordance with the findings of Efstathiou and Beare [] which showed the ability of the bounding scheme in maintaining the resolved TKE and the characteristics of the coherent turbulence structures in agreement with the reference fields at grey zone resolutions. However, as the BOUND runs are unable to resolve TKE for Δ x / z h >2, the bounding scheme does not provide any significant improvement compared to the standard Smagorinsky scheme when the BL is shallow.…”

“…Efstathiou and Beare [] attempted to quantify subgrid diffusion in the grey zone, comparing coarse‐grained LES of a convective BL (CBL) with actual independent simulations for different grid resolutions. A new approach was developed based on bounding of the vertical diffusion to its effective values while adopting a mesoscale 2‐D treatment for horizontal diffusion.…”

“…Moreover, the partitioning of turbulent kinetic energy (TKE) when using the 3-D Smagorinsky closure depends on the choice of the turbulence mixing length [Efstathiou and Beare, 2015]. Increasing mixing length leads to the damping of any resolved motions, while reducing its magnitude results in enhanced convective overturning usually on the grid scale [Beare, 2014;Efstathiou and Beare, 2015]. In any case the Smagorinsky scheme is only a rough Journal of Geophysical Research: Atmospheres 10.1002/2016JD024860 approximation of the complete turbulent transport equations [Wyngaard, 2004] intended to model isotropic subgrid motions although using the appropriate mesoscale mixing length can be considered akin to a 1D local BL scheme.…”

Impact of urbanization patterns on the local climate of a tropical city, Singapore: An ensemble study

“…Therefore, the momentum and heat fluxes throughout the PBL may be partly resolved and partly parameterized. Several attempts have been made to tackle this issue by modifying traditional PBL schemes [e.g., Honnert et al, 2011;Boutle et al, 2014;Ito et al, 2015;Shin and Hong, 2015] or using LES [e.g., Zhou et al, 2014;Efstathiou and Beare, 2015]. Recently, more and more numerical studies at grey zone resolutions have been performed to study urban climate [e.g., Miao et al, 2009;Salamanca et al, 2012] and even tropical cyclone [Green and Zhang, 2015].…”

Key Elements of Turbulence Closures for Simulating Deep Convection at Kilometer‐Scale Resolution

“…Previous studies have shown that three‐dimensional LES‐type turbulence schemes in general perform better than one‐dimensional mesoscale‐model turbulence parameterization regarding the strength and/or organization of convection in simulations (Fiori et al, ; Machado & Chaboureau, ; Parodi & Tanelli, ; Verrelle et al, ). However, while much effort has been devoted to understanding and improving turbulence closures for the simulations of the dry convective boundary layer in the TI (Efstathiou & Beare, ; Ito et al, ; Kitamura, ; Shin & Dudhia, ; Zhou et al, ), relatively few studies have compared the validity of different LES‐type turbulence models for simulating moist convection at TI resolutions.…”