The Development and Application of an Inversion Technique to Extract Vertical Current Profiles from X-Band Observations of the Wavefield in both Shallow and Deep Water Environments

Recent interest in submesoscale upper ocean dynamics has grown with the understanding of the importance of processes such as Langmuir circulation, wave breaking, and upper ocean currents in both air entrainment and upper ocean mixing. This interest has stimulated the development of emerging observational technology for modelling support and experimental upper ocean studies. X-Band radar has proven to be a valuable tool for the study of upper ocean phenomena, as radar backscatter supplies directional phase-resolved wave information out to O(5km). This work uses time series of wave-modulated radar backscatter maps to extract underlying current information. Current-depth profiles are extracted from X-Band wavefield observations for depths O(10m) by taking advantage of the unique effect the vertical structure of underlying currents has on the wavenumber-Doppler shift relationship of the wavefield. First, a 3 dimensional Fast Fourier Transform (FFT) organizes the space-time backscatter observations into the directional wavenumber – frequency domain from which the current-induced wavenumber-Doppler shift profile is estimated. Current-depth profiles are then estimated via the inversion of an Laplace-type integral expression using inversion tools such as Gauss-Legendre quadrature and multiple constrained least squares techniques. The inversion method is applied using X-Band backscatter collected in both shallow and deep water environments. The shallow water application uses land-based X-Band observations in the energetic, tidally forced mouth of the Columbia River where current magnitude and vertical current shear signals are strong and directionally constrained by the inlet. Inverted depth-current profiles show good agreement with concurrent ADCP measurements, correctly capturing subsurface current reversals as the tide changes. The deep water example uses sea-based X-Band observations near Santa Catalina Island, CA. Despite lower current magnitudes and the increased complexity of directional processing, inverted currents capture the evolution of depth-current structures in agreement with ADCP observations.