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Shukla, Abhishek
Languages: English
Types: Doctoral thesis
Subjects: QA
Data assimilation schemes are methods to estimate true underlying state of the physical systems of interest by combining the theoretical knowledge about the underlying system with available observations of the state. However, in most of the physical systems the observations often are noisy and only partially available. In the first part of this thesis we study the case of sequential data assimilation scheme, when the underlying system is nonlinear chaotic and the observations are partial and noisy. We produce a rigorous and quantitative analysis of data assimilation process for fixed observation modes. We also introduce a novel method of dynamically rearranging observation modes, leading to the requirement of fewer observation modes while maintaining the accuracy of the data assimilation process.\ud \ud In the second part of the thesis we focus on 4DVAR data assimilation scheme which is a variational method. 4DVAR data assimilation is a method that solves a variational problem; given a set of observations and a numerical model for the underlying physical system together with a priori information on the initial condition to estimate the initial condition for the underlying model. We propose a hybrid data assimilation scheme where, we consider the 3DVAR scheme for the model as the constraint on the variational form, rather than constraining the variational form with the original model. We observe that this method reduces the computational cost of the minimization of the 4DVAR variational form, however, it introduces a bias in the estimate of the initial condition. We then explore how the results can be extended to weak constraint 4DVAR.

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