In this study, we utilize a generalization of Monin–Obukhov similarity theory to construct first order turbulent closures for single-column models of the atmospheric boundary layer (ABL). A set of widely used universal functions for dimensionless gradients is evaluated. Two test cases based on Large-Eddy Simulations (LES) experimental setups are considered – weakly stable ABL (GABLS1; Beare et al. in Bound Layer Meteorol 118(2):247–272,2006), and very strongly stratified ABL (van der Linden et al. in Bound Layer Meteorol 173(2):165–192, 2019). The comparison shows that approximations obtained using a linear dimensionless velocity gradient tend to match the LES data more closely. In particular, the EFB (Energy- and Flux- Budget) closure proposed by Zilitinkevich et al. (Bound Layer Meteorol 146(3):341–373, 2013) has the best performance for the tests considered here. We also test surface layer “bulk formulas” based on these universal functions. The same LES data are utilized for comparison. The setup showcases the behavior of surface scheme, when one assumes that the velocity and temperature profiles in ABL are represented correctly. The advantages and disadvantages of different surface schemes are revealed.