Spectral characterization of Ekman velocities in the Southern Ocean based on surface drifter trajectories

Velocity time series from surface drifter data are exploited in a novel way to study the Southern Ocean surface circulation response to wind forcing. The ageostrophic component of the drifter velocities at 15 m is approximated by subtracting altimeter-derived geostrophic velocities from the drifter velocities. The resultant ageostrophic velocity time series are studied in the frequency domain jointly with contemporaneous time series of local wind stress from atmospheric reanalysis data.Rotary spectral analysis indicates that both wind stresses and ocean velocities are predominantly anticyclonic. Cross-spectral analysis shows that the upper ocean responds preferentially to anticyclonic winds not only at the inertial frequency but also at subinertial frequencies. The phase of the cross-spectra which is interpreted as a geometric angle indicates that the component of velocity that is coherent with the wind stress is to the left of the wind at subinertial frequencies and to the right at supra-inertial frequencies, and is seen as evidence of Ekman-type currents.A first order closure of the oceanic vertical turbulence, where the oceanic stress is equal to a viscosity coefficient K times the velocity vertical shear, is used to interpret the cross-spectrum. In this framework, the real part of the cross-spectrum of the wind stress and ocean surface ageostrophic velocity is shown to be a measure of the wind energy input rate to the Ekman layer. This energy input is therefore estimated across the Southern Ocean.The observed transfer function, which is the cross-spectrum divided by the auto-spectrum of the wind stress, is compared to the theoretical transfer functions arising from 10 different Ekman-type boundary layer models. These models differ in the dependence of K on the vertical coordinate and in the bottom boundary condition. The most dynamically consistent model has a vertical viscosity that is finite at the surface and increases linearly to the bottom of the boundary layer depth. Results of the comparison to models provide in situ seasonal estimates of zonally averaged near-surface viscosities and boundary layer depths across the Southern Ocean