The atmospheric boundary layer (ABL) plays a dominant role in the exchange of energy, water vapour, trace gases and momentum between the earth's surface and the overlying atmosphere. Consequently, the ABL is an important part of any numerical model in use for atmospheric and climate research, for operational weather forecasting, and for air-quality and wind-energy studies. For all these applications an overall representation is needed for boundary-layer turbulence and near-surface processes, as well as for vertical diffusion above the boundary layer. This representation is typically referred as the parametrization of vertical diffusion and turbulent mixing.It appears that models at various research groups and operational centres use rather different methods to represent turbulence and vertical diffusion and the reasons behind this diversity are not that easy to unravel. Most likely, this originates for historical reasons due to the outcome of various tuning exercises and to the number of models that have been evaluated against observations in the past. In addition, modellers often have different opinions on the complexity needed to represent atmospheric turbulence and vertical diffusion processes in weather forecast and climate models ). This directly affects the model performance of near-surface weather variables such as the 2-m air temperature and 10-m wind speed as well as boundary-layer depth, and the forecasting of low-level clouds and fog (e.g., Sandu et al. 2013Sandu et al. , 2014Zhang et al. 2014).The boundary-layer depth and the height variation of boundary-layer wind and turbulence also directly affect air quality and tracer concentrations near the surface (e.g, Karipot et al. 2008), the transport of aerosols and dust (e.g. Fiedler et al. 2013) and wind-energy applications (e.g., Storm et al. 2009). The ABL also plays an important role in the re-analysis (e.g., Tastula et al. 2013) and understanding of polar climates (e.g., Atlaskin and Vihma 2012;Sterk et al. 2013), as well as the so-called Arctic amplification (e.g., Esau et al. 2012). In addition, McNider et al. (2012) study the stable boundary layer over land and show that this coupled system can be very sensitive to changes in greenhouse gas forcing, surface roughness, heat capacity, and wind speed.