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Spectral characteristics of the oceanic boundary-layer response to wind stress forcing are assessed by comparing surface drifter observations from the Southern Ocean to a suite of idealized models that parameterize the vertical flux of horizontal momentum using a first-order turbulence closure scheme. The models vary in their representation of vertical viscosity and boundary conditions. Each is used to derive a theoretical transfer function for the spectral linear response of the ocean to wind stress. <br></br> The transfer functions are evaluated using observational data. The ageostrophic component of near-surface velocity is computed by subtracting altimeter-derived geostrophic velocities from observed drifter velocities (nominally drogued to represent motions at 15-m depth). Then the transfer function is computed to link these ageostrophic velocities to observed wind stresses. The traditional Ekman model, with infinite depth and constant vertical viscosity is among the worst of the models considered in this study. The model that most successfully describes the variability in the drifter data has a shallow layer of depth O(30–50 m), in which the viscosity is constant and O(100–1000 m<sup>2</sup> s<sup>−1</sup>), with a no-slip bottom boundary condition. The second best model has a vertical viscosity with a surface value O(200 m<sup>2</sup> s<sup>−1</sup>), which increases linearly with depth at a rate O(0.1–1 cm s<sup>−1</sup>) and a no-slip boundary condition at the base of the boundary layer of depth O(10<sup>3</sup> m). The best model shows little latitudinal or seasonal variability, and there is no obvious link to wind stress or climatological mixed-layer depth. In contrast, in the second best model, the linear coefficient and the boundary layer depth seem to covary with wind stress. The depth of the boundary layer for this model is found to be unphysically large at some latitudes and seasons, possibly a consequence of the inability of Ekman models to remove energy from the system by other means than shear-induced dissipation. However, the Ekman depth scale appears to scale like the climatological mixed-layer depth.