Climate models, numerical weather prediction (NWP) models, and atmospheric dispersion models often rely on parameterizations of planetary boundary layer height. In the case of a stable boundary layer, errors in boundary layer height estimation can result in gross errors in boundary-layer evolution and in prediction of turbulent mixing within the boundary layer. Ideally, observations would be used to determine the dependence of boundary layer height on parameters governing the flow in a boundary layer. However, observations of stably-stratified atmospheric boundary layers (ABLs) under idealized conditions which provide sufficient information about ABLs evolution under a wide range of conditions are either unattainable or rare. We therefore use controlled numerical experiments by performing numerical simulations of homogeneous, quasi-steady, stably-stratified ABLs which commonly occur in wintertime over sea-ice in polar regions.