Michael Dowd

Assimilation of Data into Limited-Area Coastal Models

Thesis Approved January 1997

This thesis investigates assimilation of oceanographic data into limited-area coastal circulation models. The approach taken analyses coastal data using simple, process-oriented ocean dynamics which isolate the essential physics of the problem. It is first demonstrated that oceanographic data assimilation can be treated in the framework of regression, and its extension to the time dependent case. Commonly used techniques are reviewed in this context. Three studies are then carried out covering a range of oceanographic data and dynamics: (1) A statistical-dynamical method is proposed to extract the barotropic tide from a ship-borne acoustic Doppler current profiler (ADCP). A limited-area tidal model, posed in the frequency domain, is fit to the time-space series of ADCP velocity using a boundary control approach. The procedure is applied to ship ADCP data from the Western Bank region of the Scotian Shelf. ADCP derived tides were in good agreement with those from fixed current meters, and the tidal residual was also found to be consistent with a diagnostic calculation of the flow. (2) An approximate Kalman filter is derived for forecasting coastal circulation. The original ocean model is reformulated in terms of its dynamical modes, and a reduced model is obtained using a subset of the modes preferentially excited by forcing. This retains the dynamics necessary for model forecasts and error propagation, yet allows the Kalman filter to be efficiently implemented. The approximate filter was demonstrated using a prototype shallow water model of the Scotian Shelf and focused on the variability associated with wind and boundary driven flows. (3) The estimation of circulation from density data is investigated. In particular, the consequences of including a prognostic density equation, together with the usual set of diagnostic (thermal wind) equations, are considered. The advantage of this approach is that dynamically consistent density and velocity estimates can be obtained from hydrographic data. A unique limit, wherein the dynamics are treated as a strong constraint in the assimilation, is explored using an idealized coastal model. Buoyancy fluxes across the open boundaries into the model domain are determined from interior point observations of the density field. Numerical experiments are performed to illustrate the issues arising in this joint estimation problem. Application of the method to realistic ocean models is discussed.