Using the large eddy simulation (LES) technique, the authors study a clear-air, stably stratified atmospheric boundary layer (ABL) as it approaches a quasi-steady state. The Beaufort Sea Arctic Stratus Experiment (BASE) dataset is used to impose initial and boundary conditions. The authors explore the parameter space of the boundary layer by varying latitude, surface cooling rate, geostrophic wind, inversion strength, and surface roughness. Recognizing the critical dependence of the results of LES on the subgrid-scale (SGS) model, they test and use a nonlinear SGS model, which is capable of reproducing the effects of backscatter of turbulent kinetic energy (TKE) and of the SGS anisotropies characteristic for shear-driven flows. In order to conduct a long-term LES so that an ABL can reach a quasi-steady state, a parallel computer code is developed and simulations with a spatial domain of up to 963 grid points are performed. The authors analyze the evolution of the mean wind, potential temperature, and turbulence profiles as well as the turbulence budgets. In their simulations, they observe the development of features that are characteristic of a stably stratified ABL: a two-layer ABL structure, an elevated inversion, and an associated inversion wind maxima. Good agreement is found between the LES results and the observations and with Nieuwstadt’s analytical model. The authors study the dependence of the boundary layer height on the flow parameters and determine model coefficients for a truncated Zilitinkevich–Mironov model.