Application of a direct inverse data assimilation method to the M-2 tide on the Newfoundland and southern Labrador Shelves

The barotropic M-2 tide over the Newfoundland and southern Labrador Shelves and adjacent deep ocean is studied using a linear harmonic finite-element model and a newly developed direct inverse method for data assimilation. Th e dataset includes harmonic tidal constituents from TOPEX/Poseidon altimetr y, coastal tide gauges, bottom pressure gauges, and moored current meters. Three modeling approaches are taken: a conventional modeling approach with boundary conditions specified from along-boundary observations; a full inte rior data assimilative approach, which provides an optimal domain-wide solu tion; and a sensitivity study in which the roles of various data subsets an d the frictional parameters are investigated. The optimal solution from the full assimilative approach has rms misfits of 3.5 cm and 1.3 cm s(-1) for elevation and current, respectively (in terms of distances on the complex plane), compared to overall rms amplitudes of 3 0 cm and 6 cm s(-1). These misfits are reduced by more than 40% and 70% fro m those in the conventional solution. Formal confidence limits for the opti mal solution can be estimated but depend on assumptions about the spatial c ovariance of the observational residuals. The sensitivity study provides qu antitative indications of the importance of the quantity and location of th e observational data and indicates little sensitivity to the specified fric tional fields within a reasonable range. In particular, the inclusion of a fraction of the velocity data in the assimilation results in a significant improvement in the model fit to the velocity observations.