Abstract
Spaceborne Along-Track Interferometric Synthetic Aperture Radar (along-track InSAR) has been used successfully to produce estimates of the surface current velocity field on a number of occasions. Along-track InSAR data are comprised of two complex images with a very short time lag, with each pixel containing an amplitude and phase. The phase difference allows a direct measurement of the line-of-sight velocity of the Bragg scattering ripples, which includes contributions of the horizontal surface current as well as the phase velocity of the Bragg ripples and orbital motions of longer waves. To calculate the surface current field, the complicated wave-related contributions to the measured radar velocity need to be estimated and subtracted. Previously, either a single mean velocity correction was used or a spatially varying correction was computed using a relatively simple numerical current-wave interaction model. In areas with large current gradients and spatial depth changes, the resulting complicated surface wave field, such as at our test location at the Columbia River, requires a sophisticated method to estimate the complex corresponding velocity corrections. In this location, the near-shore hindcast model Delft3D with the wave model SWAN, is used to produce 2-D theoretical current and wave fields. To determine the location and magnitude of the wave-related motion contributions, we calculate the Doppler velocity anomaly by subtracting the 1-D component of the theoretical surface current velocities parallel to the radar from the Doppler velocities. Comparing the Doppler velocity anomaly to the SWAN predicted wave height, wave breaking and wave steepness, we confirm the expectation that the Doppler velocity anomaly is closely related to wave breaking and wave steepness. To calculate the required Doppler anomaly correction, we first use the SAR imaging model M4S to simulate ATI-SAR data for wavenumber spectra converted from the SWAN frequency spectra. Unfortunately, the Delft3D implementation of SWAN is unable to output spectral information at the high frequencies that correspond to the high wave numbers to which the radar is sensitive, the gravity-capillary waves. We continue this work by investigating the change in image statistics between areas of high and low Doppler anomaly. We calculate the spatially changing probability density function of the interferogram amplitude and the associated higher order moments: variance, skewness, and kurtosis. We develop an empirical model that relates changes of the image statistics, to the wave motions and the resulting Doppler correction. We apply the empirical model to our data set at the Columbia river as well as to new images and show that we improve the Doppler velocity estimates universally and are able to account for 45%-80% of the required Doppler correction, referenced against the Delft3D model results.