Meteorological data assimilation by adaptive Bayesian optimization
The principal aim of this research is the elucidation of the Bayesian statistical principles that underlie the theory of objective meteorological analysis. Emphasis is given to aspects of data assimilation that can benefit from an iterative numerical strategy. Given special consideration are statistical validation of the covariance profiles and nonlinear initialization. A new economic algorithm is presented, based on the imposition of a sparse matrix structure for all covariances and precisions held during the computations. Very large datasets may be accommodated using this structure and a good linear approximation to the analysis equations established without the need to unnaturally fragment the problem. It is a relatively straight-forward matter to extend the basic analysis algorithm to one that incorporates a check on the plausibility of the statistical model assumed for background errors-the so-called validation problem. Two methods of validation are described within the sparse matrix framework: a direct extension of the Bayesian principles to embrace, not only the regular analysis variables, but also the parameters that determine the precise form of the covariance functions; the non-Bayesian method of generalized cross validation adapted for use within the sparse matrix framework. This study is concerned with the establishment of a consistent dynamical balance within a forecast model - the initialization problem. The formal principles of the modern theory of initialization are reviewed and a critical examination is made of the concept of the slow manifold. Even within a simple three-mode linearized system, the notion that a universal slow manifold exists is untenable. It is argued that a consistent treatment of the initialization problem should strictly be guided by statistics as much as by dynamics; a new methodology to accomplish the unification of analysis and initialization within The Bayesian paradigm is proposed.
- Research Organization:
- Wisconsin Univ., Madison, WI (United States)
- OSTI ID:
- 7162948
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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