POD-based estimation of the flow field from free-surface velocity in the backward-facing step

With a view to "nowcasting" of depth-scale flow fields in rivers, estuaries, and the near-coast, this work develops empirical "measurement models" that correlate velocity at a water surface to subsurface flow fields. Free-surface flow over a backstep, as simulated by LES, is chosen as a test case. Proper Orthogonal Decomposition (POD) is first applied to both subsurface and surface velocity fields from a "training data set", whence we develop regression models between the vectors of surface and subsurface POD coefficients. These models are then applied to estimate the subsurface flow field outside the training data based on virtual "measurements" of streamwise velocity along a streamwise line at the water surface. Good predictive capability is obtained in a region some 20 step heights downstream of the step that is characterized by strong upwellings.