The development of the planetary boundary layer (PBL) is related to the exchange of momentum, energy, and water between the atmosphere and the land surface as well as to the resulting feedback processes in the land-atmosphere (L-A) system (Santanello et al., 2018). The representation and the parametrization of surface fluxes in models is crucial in weather and climate models for reliable forecasts and simulations. The surface layer (SL) is the direct connection between the land-surface and the atmosphere. The behavior of SL profiles depends on the vertical stability in the atmosphere as well as the soil and the land cover properties and their heterogeneities.In order to describe the dependence of SL profiles on the surface fluxes, flux-gradient relationships have been developed. These relationships are fundamental for the parameterization of fluxes in weather forecast, climate and earth system models. The most prominent and widely used scheme is the Monin-Obukhov similarity theory (MOST; e.g., Monin & Obukhov, 1954;Obukhov, 1971). It relates the vertical gradients of wind, potential temperature and specific humidity in the SL to fluxes of momentum, heat and moisture in combination with dimensionless similarity functions. These similarity functions depend on the atmospheric stability and are typically classified by the bulk Richardson number R b . The height z above the canopy is scaled with the Monin-Obukhov length L. MOST is used for the parameterization of surface turbulent fluxes in almost all weather forecast and climate models such as in the SL scheme of the Weather Research and Forecast (WRF) model (Jiménez et al., 2012). However, MOST is not the only option for the description of flux-gradient relationships in the SL. Another approach relates the fluxes and the gradients in a similar way as in MOST but uses a similarity function, which is dependent on R b (Lee & Buban, 2020). With increasing numbers and different kinds of observations, machine