M2 tidal dissipation around Vancouver Island: an inverse approach

A representer approach is used to assimilate M2 tide gauge harmonics into a high-resolution two-dimensional finite element model of Puget Sound and the waters surrounding Vancouver Island. A preliminary model solution which employs a conventional drag coefficient for quadratic bottom friction is shown to produce elevation amplitudes and phases that differ significantly from the harmonics computed from an analysis of tide gauge observations. The assimilation procedure not only rectifies this problem but also shows that this better fit implies significant momentum equation residuals in regions where strong turbulent mixing and internal tide generation are known to occur. Thus, the assimilation identifies regions where dissipation beyond conventional bottom friction is required. Computed dissipation rates arising from these residuals reveal the largest energy sinks to be in the Gulf and San Juan Islands, Juan de Fuca Strait, and the channels off northeast Vancouver Island.