High-resolution bathymetry estimates via X-band marine radar: 2. Effects of currents at tidal inlets

In this second of two papers, the high spatial resolution cBathy depth estimate algorithm is extended to account for the existence of currents aligned with the wave directions. The extended algorithm is applied using X-band radar image time series collected at two hydrodynamically and morphologically complex environments: an ebb-tidal shoal (New River Inlet, NC) and an estuarine river mouth (Columbia River, OR/WA). Even without accounting for Doppler effects, the depth estimates are capable of discerning the location of channels and shoals over domain sizes of 4km2 at the ebb-tidal shoal and 25km2 at the estuary mouth. However, the tidal currents at these sites are shown to strongly modulate depth estimate accuracy when only the intrinsic linear wave dispersion relation (neglecting Doppler shift effects) is inverted. Low-pass filtering of the depth estimate time series, via an uncertainty-weighted tidal average, explicitly attenuates the error oscillations beyond that of the uncertainty-weighted Kalman filter. This post-hoc method of compensating for the unmodeled Doppler term achieves 0.35m RMSE and 0.02m shallow bias at the shallow ebb tidal shoal as compared to a concurrent sounding survey, but substantial bias remains at the estuary mouth due to asymmetric Doppler effects for large following or opposing currents at large relative water depths. Simultaneous estimation of depth and currents via inversion of the dispersion relation including Doppler shifts is more effective at the deep estuary mouth, where currents more strongly affect the incident wave field. In the estuary channel with locations as deep as 27m, Kalman-filtered depths achieve 0.92m RMSE and 0.38m deep bias as compared to a concurrent sounding survey (95% of estimates are within 10% of those surveyed). Independent of the Doppler compensation technique, Kalman filtered depths can be used to more tightly constrain high-resolution current velocity estimates.