# 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.