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## The singular vector approach to the analysis of perturbation growth in the atmosphere

Buizza, Roberto; (1997) The singular vector approach to the analysis of perturbation growth in the atmosphere. Doctoral thesis (Ph.D), UCL (University College London).

## Abstract

This dissertation applies linear algebra to the study of perturbation growth in atmospheric flows. Maximally-growing perturbations are identified from singular vector analysis of the time-evolving flow. Given a system characterized by a linear propagator L(t0,t), which describes the time evolution of small perturbations x between time t0 and t around a time-evolving trajectory, an inner product (..;..)E on the tangent space of the perturbations defined by a matrix E and its associated norm ||..||E, the problem can be stated as: Find the phase space directions x for which ||x(t)||E/ ||x(t0)||E is maximum, where x(t)=L(t0,t)x(t0) Given the adjoint L*E of the forward propagator L, perturbation growth is gauged by computing the eigenvectors of an operator including L and L*E as factors. The eigenvectors with the largest eigenvalues define the directions with maximum growth. They are called the singular vectors of the tangent forward propagator L. First, the singular vector approach is described. Second, a barotropic model of the atmospheric flow is considered. The impact of underlying orography on singular vectors growing over different time intervals, and the role of singular vectors in explaining the maintenance of blocked flows during winter, are analyzed. Third, a 3-dimensional primitive equation model of the atmospheric flow is considered. Some aspects of the application of the singular vector technique to the study of perturbation growth in the whole atmosphere are analyzed. A physical interpretation of singular vector growth based on the application of the Eliassen-Palm theorem and on WKBJ theory is proposed. Finally, two examples of operational use of singular vectors are presented. Results show how the adjoint technique is a suitable methodology for the identification of atmospheric instabilities, and how it can be used to investigate predictability problems.

Type: Thesis (Doctoral) Ph.D The singular vector approach to the analysis of perturbation growth in the atmosphere An open access version is available from UCL Discovery English Thesis digitised by ProQuest. Earth sciences https://discovery.ucl.ac.uk/id/eprint/10097868