Application of a Direct Inverse Data Assimilation Method to the M2 Tide on the Newfoundland and Southern Labrador Shelves

Abstract

The barotropic M2 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. The dataset includes harmonic tidal constituents from TOPEX/Poseidon altimetry, 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 interior data assimilative approach, which provides an optimal domain-wide solution; and a sensitivity study in which the roles of various data subsets and 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 30 cm and 6 cm s?1. These misfits are reduced by more than 40% and 70% from those in the conventional solution. Formal confidence limits for the optimal solution can be estimated but depend on assumptions about the spatial covariance of the observational residuals. The sensitivity study provides quantitative indications of the importance of the quantity and location of the observational data and indicates little sensitivity to the specified frictional 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.