Model parameter estimation from data assimilation modeling: Temporal and spatial variability of the bottom drag coefficient

Acoustic Doppler current profiler (ADCP) data collected from a moving vessel are assimilated, using the adjoint method, into a tidal model of the lower Hudson estuary with the objective of estimating the bottom drag coefficient and residual upstream setup. An objective strategy for determining the weight given to prior estimates of the model parameters is shown to be necessary. The method of cross validation performs well for this purpose. Results of the assimilation experiments indicate that the drag coefficient increases by approximately 30% from neap tides to near-spring tides. Hydrographic data indicate that this increase is coincident with a decrease in vertical stratification. A point model of the vertical structure in an oscillatory boundary layer shows that the damping effect of stratification on turbulent mixing causes a reduction of the bottom drag coefficient. The assimilation results also indicate relatively large spatial variability in the drag coefficient, with higher values found in shallow regions flanking the estuary channel. This agrees with the results of the boundary layer model which show that a reduction in drag coefficient is associated with an increase of the ratio of water depth to bottom roughness.