Which turbulence in atmospheric models at the kilometric scale ?

Turbulence is well-represented by mesoscale models for which the grid spacing is coarser than 2 km and the turbulence is entirely subgrid. It is also well-represented at very high grid spacing (10 to 100 m) by LES models for which turbulence is mainly resolved. However thanks to increasing computational resources, in a near future, limited area NWP models will reach grid spacing in the order of 1 km or even 500 m. In this range of scales, called “Terra Incognita“ by J. Wyngaard, turbulence is partly resolved and partly subgrid. The aim of this study is to develop a parameterization which provides adequate turbulence to the new generation, high resolution models.

The first goal of this study is to develop a new diagnostic based on LES, which clarifies which part of turbulence should be parameterized at kilometric scales. This reference is valid for any dry and cumulus-topped free convective boundary layer.

This LES reference is a precious tool for quantifying the errors made by atmospheric models when running at kilometric scales. These errors are quantified for the state-of-the-art mesoscale model MésoNH with several turbulence mixing options : a 1D or a 3D dimensionality, a Deardorf or a Bougeault-Laccarère mixing length and a K-gradient scheme or an EDMF (K-gradient with a mass-flux scheme). The mass-flux scheme activation has the most significant effect. K-gradient turbulence schemes are unable to reproduce the counter-gradient zone. In the grey-zone of turbulence, this characteristic has a disastrous effect : as the instability is too large and the subgrid mixing is too weak, the boundary layer is mainly mixed by the dynamic of the model. Then, the turbulent mixing is too strong and the structures too large. An EDMF can reproduce the counter gradient zone. However the mass-flux scheme in its original form only produced entirely subgrid thermals at a grid spacing for which boundary-layer thermals should be partly resolved. In this case, the subgrid mixing is too strong and no resolved structure is produced.

So the question arises as what is a subgrid thermal in the grey-zone of turbulence, when the mesh contains one thermal at the most and a part of the thermal has to be resolved by the advection scheme of the model. Conditional samplings make it possible to separate the thermals from their environment in LES. A conditional sampling has been adapted to detect the subgrid thermals in the grey zone of turbulence. This tool is used to test the traditional assumptions which lead to the mass-flux schemes. The wrongly neglected terms are then introduced in the mass-flux system of equations. The conditional sampling is then used to determine the entrainment/detrainment closure of this new scheme. Finally, the study furnishes a new parameterization valid in the grey zone.