Surf zone bathymetry inversion during storms

An ability to measure nearshore bathymetry from remote sensing would be invaluable for studying nearshore morphodynamics, and has been a longstanding goal of the community. To date, the most robust methods involve inverting wave celerity measurements using the linear wave dispersion relationship. During storms, however, it is well known that linear theory loses accuracy (due to large wave amplitude) and the remote sensing signatures involved in measuring wave celerity become more complex (e.g., water surface reflectivity changes rapidly as waves transition to breaking). Hence during storms -- when bathymetry changes most rapidly -- it would be useful to have methods for estimating bathymetry that do not rely on wave celerity alone. In this study, we apply a variational data assimilation algorithm to obtain bathymetry from inversion of three observation types: wave height, longshore current, and wave dissipation. An extensive validation has been conducted using data collected from five different storms at the Field Research Facility in Duck, NC, which featured onshore and offshore sandbar migration events. The results show that different observation types give different accuracy for bathymetry: For example, assimilating wave height tended to produce better results compared to longshore current. Finally, we propose and test algorithms for improving estimates of time-dependent intra-storm bathymetry by combining statistical and physical constraints in a Kalman Filter and a Kalman Smoother.