## 1 Introduction  
The atmospheric boundary layer (ABL) is the lowest part of the atmosphere where the Earth's surface strongly influences the wind, temperature, and humidity through turbulent transport of air mass. Due to its superior importance for the atmosphere system, an appropriate representation of the ABL is essential for both operational numerical weather prediction (NWP) and climate models as well as for a wide range of practical applications, such as air pollution forecast and wind energy yield estimates. In contrast to the ABL, the stable boundary layer (SBL) is typically one order of magnitude shallower and can reach a vertical extent as low as 10 m. Turbulence in the SBL is typically much weaker or intermittent and is mainly produced by vertical wind shear, whereas buoyancy inhibits vertical motion. Furthermore, a number of nonturbulent motions, such as wave-like motions, solitary modes, microfronts or drainage flows, become important [1]. The principal problem in representing turbulence in those models correctly is that the length scales of the turbulent processes are typically far below model resolution and therefore need to be parameterized. While the corresponding parameterization schemes, e.g., reference [2], generally work very well for near-neutral and unstable conditions, they show significant shortcomings for the SBL, e.g., by systematically overestimating turbulent mixing rates and the height of the ABL (\(h_{ABL}\)) [3; 4; 5; 6]. In the context of weather forecasting, this leads to, amongst others, significant errors in the prediction of near surface parameters, such as the 2-m temperature and 10-m wind speed for situations with clear skies and low wind typically occurring at night or during winter [6]. Errors in \(h_{ABL}\) might also induce considerable uncertainties in the forecast of wind profiles and the location of low-level jets (LLJ), which are crucial parameters for applications such as wind energy. Furthermore, this also leads to a typical warm bias for SBL conditions in NWP models [4; 7; 8], which is also of importance under the aspects of climate and climate change. One of the most dominant signals in climate records is the accelerated warming of the polar regions during wintertime and the increase in nighttime temperatures at lower latitudes [9]. This observed polar amplification may be partly related to the shallow SBL with a corresponding small heat capacity. Hence, a certain heat gain results in a relatively large temperature increase [10]. In addition, this dampens the temperature inversion infrared cooling to space [11; 12]. A systematic overestimation of turbulent mixing and the ABL height thus complicates the proper attribution of the mechanisms of Arctic climate change [12; 13; 14]. Monin-Obukhov similarity theory (MOST) provides dimensionless relationships between the surface fluxes of heat and momentum, the variance and the mean gradients of temperature, moisture, and wind in the atmospheric surface layer (SL). These dimensionless relationships are a function of the height (\(z\)) above the surface, which is made dimensionless with the Monin-Obukhov length scale (\(L\)). Strictly speaking, these relationships apply only for stationary and homogeneous surface conditions. In practice, however, there is a strong need for wider application, and as such, field observations in a variety of circumstances are needed to evaluate the dimensionless relationships. Most of the surface parameterization schemes in NWP and climate models are based on the traditional MOST, which is known for its shortcomings in characterizing the SBL [15; 16; 17; 18; 19; 20; 21]. Under such conditions, continuous turbulence may break down and become intermittent e.g., [22], so that non-local features,such as the stability at higher levels and the Coriolis effect, gain relative importance [23; 24]. This may imply the occurrence of upside-down events, in which turbulence is mainly generated by the vertical wind shear associated with LIJ [23; 25].