The Inversion of Vertical Current Shear from X-Band Observations of the Wavefield

Ocean surface waves propagate according to a dispersion relationship, which defines the relationship between a wave’s wavenumber and its frequency. In the presence of underlying currents, waves are accelerated or decelerated, and this dispersion relationship is augmented by an additional Doppler shift. Furthermore, if the underlying currents are not depth-uniform, the Doppler shift-wavenumber relationship is non-linear. This dissertation focuses on the development of an inversion method to estimate current-depth profiles from a collection of wavelength-dependent Doppler shift measurements. This process leverages Gaussian quadrature along with multiple least squares techniques to supply constraints to the otherwise inherently noisy inversion. To measure Doppler shifts to be used as inputs into the inversion process, this work takes advantage of the sensitivity of marine X-band backscatter to space-time wavefield properties. Sequential images of backscatter are collected and, using a Fast Fourier Transform, are transformed into wavenumber-frequency space for current extraction.X-Band backscatter (along with supporting wind and current measurements) was collected during two unique field campaigns. The first took place in June, 2013 as a part of the Riverine and Estuarine Transport Experiment 2 (RIVET2) field campaign in the Mouth of the Columbia River (MCR), Oregon. The second data set was collected from R/P FLIP in the Southern California bight in November 2013 as a part of the SoCal2013 experiment. From the strong, polarized currents in the MCR to the weaker, wind- and tide-driven currents of the deeper water off of California, the contrast between the data sets from the perspective of wave-current interaction is significant. The results of the new inversion method from both data sets are compared to those measured by ADCPs. The depth- and time-dependence of the comparisons show that inverted currents successfully capture important geophysical phenomena such as depth