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Title: Instability and regularization for data assimilation
Author: Moodey, Alexander J. F.
Awarding Body: University of Reading
Current Institution: University of Reading
Date of Award: 2013
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The process of blending observations and numerical models is called in the environmental sciences community, data assimilation. Data assimilation schemes produce an analysis state, which is the best estimate to the state of the system. Error in the analysis state, which is due to errors in the observations and numerical models, is called the analysis error. In this thesis we formulate an expression for the analysis error as the data assimilation procedure is cycled in time and derive results on the boundedness of the analysis error for a number of different data assimilation schemes. Our work is focused on infinite dimensional dynamical systems where the equation which we solve is ill-posed. We present stability results for diagonal dynamical systems for a three-dimensional variational data assimilation scheme. We show that increasing the assumed uncertainty in the background state, which is an a priori estimate to the state of the system, leads to a bounded analysis error. We demonstrate for general linear dynamical systems that if there is uniform dissipation in the model dynamics with respect to the observation operator, then regularization can be used to ensure stability of many cycled data assimilation schemes. Under certain conditions we show that cycled data assimilation schemes that update the background error covariance in a general way remain stable for all time and demonstrate that many of these conditions hold for the Kalman filter. Our results are extended to dynamical system where the model dynamics are nonlinear and the observation operator is linear. Under certain Lipschitz continuous and dissipativity assumptions we demonstrate that the assumed uncertainty in the background state can be increased to ensure stability of cycled data assimilation schemes that update the background error covariance. The results are demonstrated numerically using the two-dimensional Eady model and the Lorenz 1963 model.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available