Analysis of non-stationary vector fields using wavelet transforms

Fast Fourier transforms (FFT) and empirical orthogonal functions (EOF) have been widely applied to coastal zone current measurements. However riverine tides, estuarine outflows, and eddies, exhibit non-stationary characteristics which invalidate the basic assumptions of these methods. Wavelet analysis techniques can be used to determine the temporal evolution of ocean current variance over a range of frequency scales and therefore can provide an improved understanding of event-driven dynamics. To investigate the characteristics of this type of analysis, a simulated vortex was advected through a region consistent with a High-Frequency (HF) radar domain. Morlet continuous-wavelet transforms, bi-orthogonal discrete wavelet transforms, FFTs, EOPs and digital filtering techniques were applied to multiple vector time-series collected within the simulation domain. The stationary spectral analysis methods did not resolve the eddy well due to the distribution of the energy throughout the observation period. Band-pass filtering of each point created spurious anti-cyclonic eddy motions both preceding and following the simulated eddy. Morlet wavelets were shown to localize the vortex energy in both space and time, with a characteristic dipole pattern due to the axis of clockwise/counterclockwise rotational symmetry along the eddy path. Morlet and bi-orthogonal wavelet transforms were then applied to measurements from a HP Doppler radar deployed off the lower Florida Keys in May, 1994 when several sub-mesoscale eddies were observed. The wavelet energy demonstrated the characteristic dipole observed in the simulations, although little advection was observed in the real data.