| Summary: | Oceanographic observations are typically too sparse to provide a continuous picture of the evolving ocean state. However, the ability to accurately estimate the past, present, and future state of the ocean has many important applications including climate change research, fisheries management, weather forecasting, and marine pollution management. Data assimilation methods utilise knowledge of the ocean's governing physical processes to estimate the complete time-dependent ocean state. The goals of the thesis are to provide effective new approaches for assimilating Lagrangian measurements and to examine sub-optimal assimilation schemes based on a low-dimensional representation of the model state and dynamics. Four related studies address these goals: (1) Several issues pertaining to the assimilation of ocean drifter data are examined, including the effects of the velocity component unresolved by ocean models and the nonlinearity of the advection equation. For illustration, experiments are performed with a simplified ocean model developed to capture the basic nonlinear response to a tidal current over isolated coastal topography. (2) A method for extracting surface currents from sequential satellite images of an advected quantity (such as ice or sea surface temperature) is presented. The problem is formulated in a data assimilation context and successfully applied to both artificial data and a pair of real sea ice images from a region over the Labrador shelf. (3) An approach is developed for incorporating a low-dimensional representation of the forecast error statistics in a sequential assimilation system such that several of the typically imposed assumptions can be relaxed. Within the context of an operational numerical weather prediction system, the approach is shown to effectively resolve dynamical influences on the stationary error statistics. Certain aspects of this study may also be applicable to the newer field of operational ocean prediction. (4) A low-dimensional linear approximation of a nonlinear ocean model is obtained to formulate a sub-optimal assimilation scheme. The method avoids the manual coding of the linearised model and its adjoint by treating the model as a "black box". The effectiveness of the method is demonstrated with an identical twin experiment using an idealised configuration of a nonlinear primitive equation model. Taken together, the approaches examined in the thesis allow realistic ocean models to be effectively combined with remotely sensed Lagrangian data. This may represent a path for the future development of operational ocean prediction systems. Thesis (Ph.D.)--Dalhousie University (Canada), 2000.
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