Robert J. Beare

A Length Scale Defining Partially-Resolved Boundary-Layer Turbulence Simulations

Numerical weather prediction (NWP) model forecasts at horizontal grid lengths in the range of 100 m to 1 km are now possible. Within this range of grid lengths, the convective boundary layer (CBL) is partially resolved and thus in the so-called ‘grey zone’. For simulations in the grey zone, numerical dissipation sources from both the advection scheme and the subgrid model are likely to be significant. Until now, these effects have not been incorporated fully into our understanding of the grey zone. In order to quantify these effects, a dissipation length scale is defined based on the second moment of the turbulent kinetic energy (TKE) spectrum. An ensemble of simulations of a CBL are performed using a large-eddy model across the grey-zone resolutions and for a range of subgrid model, advection scheme and vertical grid configurations. The dissipation length scale distinguishes the effects of the different model configurations in the grey zone. In the middle of the boundary layer, the resolved TKE is strongly controlled by the numerical dissipation. This leads to a similarity law for the resolved TKE in the grey zone using the dissipation length scale. A new definition of the grey zone emerges where the inversion depth and dissipation length scale are the same size. This contrasts with the typical definition using the horizontal grid length. At the inversion, however, the variation of the dissipation length scale with grid length is less predictable, reflecting significant challenges for modelling entrainment in the grey zone. The dissipation length scale is thus a simple diagnostic to aid both NWP and large-eddy modellers in understanding the grey zone.

A note on boundary layer friction in baroclinic cyclones

The interaction between extratropical cyclones and the underlying boundary layer has been a topic of recent discussion in papers by Adamson et al. (2006) and Beare (2007). Their results emphasise different mechanisms through which the boundary layer dynamics may modify the growth of a baroclinic cyclone. By using different sea-surface temperature distributions and c omparing the low-level winds, the differences are exposed and both of the proposed mechanisms appear to be acting within a single simulation. Copyright c 2007 Royal Meteorological Society

Diagnosis of boundary-layer circulations

Diagnoses of circulations in the vertical plane provide valuable insights into aspects of the dynamics of the climate system. Dynamical theories based on geostrophic balance have proved useful in deriving diagnostic equations for these circulations. For example, semi-geostrophic theory gives rise to the Sawyer–Eliassen equation (SEE) that predicts, among other things, circulations around mid-latitude fronts. A limitation of the SEE is the absence of a realistic boundary layer. However, the coupling provided by the boundary layer between the atmosphere and the surface is fundamental to the climate system. Here, we use a theory based on Ekman momentum balance to derive an SEE that includes a boundary layer (SEEBL). We consider a case study of a baroclinic low-level jet. The SEEBL solution shows significant benefits over Ekman pumping, including accommodating a boundary-layer depth that varies in space and structure, which accounts for buoyancy and momentum advection. The diagnosed low-level jet is stronger than that determined by Ekman balance. This is due to the inclusion of momentum advection. Momentum advection provides an additional mechanism for enhancement of the low-level jet that is distinct from inertial oscillations.

Simulating Dispersion in the Evening-Transition Boundary Layer

We investigate dispersion in the evening-transition boundary layer using large-eddy simulation (LES). In the LES, a particle model traces pollutant paths using a combination of the resolved flow velocities and a random displacement model to represent subgrid-scale motions. The LES is forced with both a sudden switch-off of the surface heat flux and also a more gradual observed evolution. The LES shows ‘lofting’ of plumes from near-surface releases in the pre-transition convective boundary layer; it also shows the subsequent ‘trapping’ of releases in the post-transition near-surface stable boundary layer and residual layer above. Given the paucity of observations for pollution dispersion in evening transitions, the LES proves a useful reference. We then use the LES to test and improve a one-dimensional Lagrangian Stochastic Model (LSM) such as is often used in practical dispersion studies. The LSM used here includes both time-varying and skewed turbulence statistics. It is forced with the vertical velocity variance, skewness and dissipation from the LES for particle releases at various heights and times in the evening transition. The LSM plume spreads are significantly larger than those from the LES in the post-transition stable boundary-layer trapping regime. The forcing from the LES was thus insufficient to constrain the plume evolution, and inclusion of the significant stratification effects was required. In the so-called modified LSM, a correction to the vertical velocity variance was included to represent the effect of stable stratification and the consequent presence of wave-like motions. The modified LSM shows improved trapping of particles in the post-transition stable boundary layer.

Grey zone simulations of the morning convective boundary layer development

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.

A Framework for Convection and Boundary Layer Parameterization Derived from Conditional Filtering

AbstractA new theoretical framework is derived for parameterization of subgrid physical processes in atmospheric models; the application to parameterization of convection and boundary layer fluxes ...