Data assimilation of tides in the Bohai Sea using the adjoint method

The two-dimensional data assimilation model of the tides in the Bohai Sea was established using the a joint method to study the tides of the Bohai Sea. The adjoint equations were derived from the two-dimensional tidal equations by Lagrange multiplier method. The observation data were from the tidal gauge stations and the satellite altimetry data. To evaluate the role of the altimetry data and the tidal gauge data in the data assimilation of the tides in the Bohai Sea, three numerical experiments were carried out. Experiment 1 only assimilates the tidal gauge data, Experiment 2 only assimilates the altimetry data, and Experiment 3 assimilates the combined data of the tidal gauge stations and the satellite altimetry. The tidal constituents M₂, S₂, K₁ and O₁ of the Bohai Sea were simulated. The results show that it is better when assimilating the tidal gauge data and the altimetry data simultaneously than assimilating any one separately. The mean absolute differences of the amplitude and phase-lag are 1.52 cm and 2.22° for M₂, 1.26 cm and 3.30° for S₂, 1.19 cm and 2.72° for K₁, 0.55 cm and 1.93° for O₁, respectively. The results reflect the tidal system of the Bohai Sea well, especially for the outer sea area since the altimetry data were assimilated.