A velocity projection framework for inferring shallow water currents from surface tracer fields

To the extent that sea surface temperature and colors can be considered passive tracers, their motions can be tracked to estimate the current velocities, or a conservation equation can be invoked to relate their temporal variations to the velocities. We investigate the latter, the so-called tracer inversion problem, with a particular focus on (1) the conditions under which the problem can be rendered over-determined for least squares solutions, (2) the possibility of using the tracer conservation equation within the “velocity projection” framework to estimate subsurface current profiles in shallow coastal waters, and (3) the accuracy of the tracer inversion calculation in terms of the data resolution and noise. The velocity projection framework refers to relating surface motion, either measured directly or made visible by tracers, to the subsurface current motion through the equations of motion. The accuracy of the tracer inversion calculation is quantified in terms of the spatial and temporal resolution of the tracer distribution. In the presence of irreducible tracer noise, the accuracy of the inversion rapidly degrades, and it is shown that the inversion with velocity projection can help improve accuracy. The tracer inversion method developed in this study is applied to the satellite sea surface temperature data, and the velocity result is compared to the velocity measurements made with the shore-based HF Coastal Current Radar. The potential of improving the velocity estimation with the present approach is indicated.