One-dimensional turbulence (ODT) is a single-column simulation in which vertical motions are represented by an unsteady advective process, rather than their customary representation by a diffusive process. No space or time averaging of mesh-resolved motions is invoked. Molecular-transport scales can be resolved in ODT simulations of laboratory-scale flows, but this resolution of these scales is prohibitively expensive in ODT simulations of the atmospheric boundary layer (ABL), except possibly in small subregions of a non-uniform mesh. Here, two methods for ODT simulation of the ABL on uniform meshes are described and applied to the GABLS (GEWEX Atmospheric Boundary Layer Study; GEWEX is the Global Energy and Water Cycle Experiment) stable boundary-layer intercomparison case. One method involves resolution of the roughness scale using a fixed eddy viscosity to represent subgrid motions. The other method, which is implemented at lower spatial resolution, involves a variable eddy viscosity determined by the local mesh-resolved flow, as in multi-dimensional large-eddy simulation (LES). When run at typical LES resolution, it reproduces some of the key high-resolution results, but its fidelity is lower in some important respects. It is concluded that a more elaborate empirically based representation of the subgrid physics, closely analogous to closures currently employed in LES of the ABL, might improve its performance substantially, yielding a cost-effective ABL simulation tool. Prospects for further application of ODT to the ABL, including possible use of ODT as a near-surface subgrid closure framework for general circulation modeling, are assessed.