Ekman currents in the Antarctic circumpolar current
thesisposted on 2023-05-27, 14:04 authored by Roach, C
The action of wind on the ocean surface results in the formation of Ekman spirals, as proposed by V.W. Ekman in 1905. The spirals display exponential decay of current speed and anticyclonic rotation with increasing depth. Observations of Ekman spirals are extremely rare, and there are few studies that test Ekman theory against observations. Here we present a unique array of velocity profiles from EM-APEX profiling floats, which we use to examine the nature of Ekman spirals in the Southern Ocean and test how well they are described by theory. Classical Ekman theory assumes the momentum mixing within the upper ocean is set by a constant eddy viscosity. However, previous observational studies have found Ekman spirals to be compressed, with different viscosities estimated from current speed and rotation. This behaviour has been linked to surface trapping of Ekman currents (Price et al. 1987) or could arise due to a failure to consider depth varying geostrophic currents (Polton et al. 2013). We use 1400 profiles of velocity from EM-APEX floats, collected at the northern Kerguelen Plateau as part of the Southern Ocean FINE-structure (SOFINE) expedition during the Austral summer of 2008-9, to investigate whether a constant viscosity parameterization is the best way to represent momentum mixing in the upper ocean, or whether other methods such as a depth-varying viscosity or a mixing scheme linked with stratification (e.g. Price et al., 1986) are more effective. Previous studies of Ekman layer observations have examined either the raw observations, or models of momentum input in the spectral domain or in the time domain. In this study we use all three approaches to build a robust picture of Ekman spirals in the Southern Ocean and their response to wind forcing. Ekman velocities were isolated from inertial and geostrophic currents in the absolute velocity profiles. Estimates of eddy viscosity and Ekman layer depth were separately obtained from profiles of current speed and heading. Assuming a vertically-uniform geostrophic current the Ekman layer depths from current heading were approximately twice as large as those from current speed decay. This degree of spiral compression has been observed in prior studies. Assuming a linear geostrophic shear, constant viscosity estimates from current heading and speed decay converged towards a common value, implying a significant reduction in the compression of the Ekman spirals. Including geostrophic shear through the Ekman layer also increased the number of EM-APEX profiles displaying Ekman spiral-like behaviour from 224 to 441, and reduced the RMS velocity residual between fitted and observed spirals. There was no clear relationship between the observed viscosities and mixed layer depth or strength of stratification. This suggests that the compressed spirals observed in previous studies are due to aliasing the geostrophic current into the Ekman spiral (Polton et al. 2013), rather than surface trapping of Ekman currents associated with stratification. Nine conceptual Ekman models were fitted to the observations in the spectral domain using the method of Elipot and Gille (2009). Application of the spectral technique to shipboard ADCP and in situ wind data indicated a constant viscosity model with a finite boundary layer depth (BLD) was the best performing model. Eddy viscosities agreed with Elipot's results for the same latitude bands but the optimal BLD was found to be deeper for the SOFINE region. Examination of Elipot's results indicate that within the latitude band of our study bootstrap, estimates of summer BLDs displayed a greater range of variability than the year round or winter BLDs. This suggests that the deeper BLDs observed in our study were principally due to the timing of SOFINE. A similar analysis using EM-APEX float data and blended reanalysis-scatterometer winds was inconclusive. To test for the effects of time-varying wind forcing and stratification in the mixed layer, we ran linear and stratified Ekman models with the Price Weller and Pinkel (1986) mixing scheme, forced by both in situ shipboard winds and a variety of reanalysis wind data. Model time mean skill was analysed by comparing the correlation between the simulated and observed mean current profiles. Time varying performance was assessed using a two-sample Kolmogorov-Smirnov test and quantile-quantile plots. For the model runs with the shipboard winds, the classical linear time-varying Ekman model offered the best performance. Model runs using 6 hourly reanalysis winds interpolated onto the float tracks performed poorly, preventing a proper assessment of skill of the stratified models relative to the linear Ekman models. The combined evidence in this thesis suggests that the classical constant viscosity Ekman model offers an adequate representation of the near surface response to wind forcing with a minimal number of parameters.
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