Physics-Informed Estimation of Tidal and Subtidal Flow Fields From ADCP Repeat Transect Data

Acoustic Doppler current profilers (ADCPs) are a global standard in observing flow fields in rivers, estuaries and the coastal ocean. To date, it remains a labor intensive challenge to isolate mean flow fields governed by river discharge, tides and atmospheric forcing on the one hand, from small-scale turbulence, positioning imprecision, Doppler noise and erroneous backscatter, on the other hand. Here, we introduce a generic, new method of combining raw shipborne ADCP transect data with continuity and smoothness constraints to obtain better estimates of turbulence-averaged three-dimensional flow velocities in any type of open water body. The physical constraints are enforced with variable relative importance via generalized Tikhonov regularization. We demonstrate that in complex estuarine flow, this procedure allows for more reliable estimates of tidal amplitudes, phases and their gradients than what is possible with a purely data-based approach, by testing the method's generalization capabilities and robustness to turbulence and measurement noise on a data set retrieved at a tidal channel junction. The increased adherence to mass conservation and robustness to noise of various kinds allows for more reliable and verifiable estimates of Reynolds-averaged flow components, and subsequently, of terms in the Navier-Stokes equations.