A New Inversion Method to Obtain Upper-Ocean Current-Depth Profiles Using X-Band Observations of Deep-Water Waves

Abstract

AbstractA new method for estimating current-depth profiles from observations of wavenumber-dependent Doppler shifts of the overlying ocean wave field is presented. Consecutive scans of marine X-band backscatter provide wave field measurements in the time–space domain that transform into the directional wavenumber–frequency domain via a 3D fast Fourier transform (FFT). Subtracting the linear dispersion shell yields Doppler shift observations in the form of (kx, ky, Δω) triplets. A constrained linear regression technique is used to extract the wavenumber-dependent effective velocities, which represent a weighted depth average of the Eulerian currents (Stewart and Joy). This new method estimates these Eulerian currents from the effective velocities via the inversion of the integral relationship, which was first derived by Stewart and Joy. To test the effectiveness of the method, the inverted current profiles are compared to concurrent ADCP measurements. The inversion method is found to successfully predict current behavior, with a depth-average root-mean-square (RMS) error less than 0.1 m s−1 for wind speeds greater than 5 m s−1 and a broad wave spectrum. The ability of the inversion process to capture the vertical structure of the currents is assessed using a time-average RMS error during these favorable conditions. The time-averaged RMS error is found to be less than 0.1 m s−1 for depths shallower than 20 m, approximately twice the depth of existing methods of estimating current shear from wave field measurements.