Optimal estimation of tidal open boundary conditions using predicted tides and adjoint data assimilation technique

Lateral tidal open boundary conditions which force tides in the internal region are estimated by an adjoint data assimilation system which assimilates predicted coastal tidal elevations into a two-dimensional Princeton Ocean Model for the East Coast of the United States. Control variables are the harmonic constants (amplitude and phase) of tidal constituents (M2, S2, N2, K1, O1) along the open boundary. The cost function is defined by the difference between predicted and model-simulated tidal elevations at coastal tide gauge locations. The limited memory Broyden–Fletcher–Goldfarb–Shanno quasi-Newton method for large-scale optimization is implemented to minimize the cost function. Identical twin experiments are performed to verify the adjoint model and to examine sensitivity of model results to the number and spatial distribution of tide gauge stations. The results from the predicted tidal elevation assimilation experiments show that the simulated tidal elevations forced by the optimal open boundary conditions are more accurate than those forced by the open boundary conditions derived from Schwiderskiʹs global tidal model. For M2 constituent, the maximum RMS error at tide gauge stations with data assimilation is generally 14 cm and the minimum correlation coefficient is 0.96. For the nine open coastal stations, the RMS errors are less than 5 cm. The results from the experiment in which five tidal constituents are considered together show that the RMS errors at the nine open coastal stations are less than 7 cm, and the correlation coefficients are greater than 0.99.