Abstract
The most frequently used boundary-layer turbulence parameterization in numerical weather prediction (NWP) models are turbulence kinetic energy (TKE) based-based schemes. However, these parameterizations suffer from a potential weakness, namely the strong dependence on an ad-hoc quantity, the so-called turbulence length scale. The physical interpretation of the turbulence length scale is difficult and hence it cannot be directly related to measurements or large eddy simulation (LES) data. Consequently, formulations for the turbulence length scale in basically all TKE schemes are based on simplified assumptions and are model-dependent. A good reference for the independent evaluation of the turbulence length scale expression for NWP modeling is missing. Here we propose a new turbulence length scale diagnostic which can be used in the gray zone of turbulence without modifying the underlying TKE turbulence scheme. The new diagnostic is based on the TKE budget: The core idea is to encapsulate the sum of the molecular dissipation and the cross-scale TKE transfer into an effective dissipation, and associate it with the new turbulence length scale. This effective dissipation can then be calculated as a residuum in the TKE budget equation (for horizontal sub-domains of different sizes) using LES data. Estimation of the scale dependence of the diagnosed turbulence length scale using this novel method is presented for several idealized cases.
Highlights
The parametrization of turbulence processes in the Atmospheric Boundary Layer (ABL) is an essential component of numerical weather prediction (NWP) and global circulation (GC) models.The parametrizations are based on broad physical understanding from observations, as well as on the statistical properties of resolved-turbulence flows from finer-scale model simulations
The turbulence kinetic energy (TKE) dissipation rate, e, is set to the value of the effective dissipation rate of the whole domain, whose scale is assumed to be above the energy-containing range
We have derived and presented a new turbulence length scale diagnostic based on Large Eddy Simulation (LES) data that contains the influence of the sub-grid cross-scale TKE transfer
Summary
The parametrizations are based on broad physical understanding from observations, as well as on the statistical properties of resolved-turbulence flows from finer-scale model simulations. The grid spacing determines the extent to which the turbulent motions are resolved. In the traditional NWP and GC models all turbulent motions are sub-grid and turbulence needs to be fully parametrized. Large Eddy Simulation (LES) models have a smaller grid spacing and resolve a part of the turbulent motions, namely the large energy-containing anisotropic turbulent eddies. Between the range of grid-sizes of classical NWP/GC models and LES lies the gray zone of turbulence [1,2,3], where turbulence parametrization is more difficult, because the anisotropic turbulent eddies are only partly resolved and the other part of their impact needs to be parametrized
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