Bred vectors, singular vectors, and Lyapunov vectors in simple and complex models

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dc.contributor.advisorKalnay, Eugeniaen_US
dc.contributor.authorNorwood, Adrienneen_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2015-09-18T05:57:06Z
dc.date.available2015-09-18T05:57:06Z
dc.date.issued2015en_US
dc.description.abstractWe compute and compare three types of vectors frequently used to explore the instability properties of dynamical models, Lyapunov vectors (LVs), singular vectors (SVs), and bred vectors (BVs). The first model is the Lorenz (1963) three-variable model. We find BVs align with the locally fastest growing LV, which is often the second fastest growing global LV. The growth rates of the three types of vectors reveal all predict regime changes and durations of new regimes, as shown for BVs by Evans et al. (2004). The second model is the toy ‘atmosphere-ocean model’ developed by Peña and Kalnay (2004) coupling three Lorenz (1963) models with different time scales to test the effects of fast and slow modes of growth on the dynamical vectors. A fast ‘extratropical atmosphere’ is weakly coupled to a fast ‘tropical atmosphere’ which is strongly coupled to a slow ‘ocean’ system, the latter coupling imitating the tropical El Niño–Southern Oscillation. BVs separate the fast and slow modes of growth through appropriate selection of the breeding parameters. LVs successfully separate the fast ‘extratropics’ but cannot completely decouple the ‘tropics’ from the ‘ocean,’ leading to ‘coupled’ LVs that are affected by both systems but mainly dominated by one. SVs identify the fast modes but cannot capture the slow modes until the fast ‘extratropics’ are replaced with faster ‘convection.’ The dissimilar behavior of the three types of vectors degrades the similarities of the subspaces they inhabit (Norwood et al. 2013). The third model is a quasi-geostrophic channel model (Rotunno and Bao 1996) that is a simplification of extratropical synoptic-scale motions with baroclinic instabilities only. We were unable to successfully compute LVs for it. However, randomly initialized BVs quickly converge to a single vector that is the leading LV. The last model is the SPEEDY model created by Molteni (2003). It is a simplified general atmospheric circulation model with several types of instabilities saturating at different time scales. Through proper selection of the breeding parameters, BVs identify baroclinic and convective instabilities. When the amplitude and rescaling period are further reduced, all BVs converge to a single vector associated with Lamb waves, something never before observed.en_US
dc.identifierhttps://doi.org/10.13016/M2164J
dc.identifier.urihttp://hdl.handle.net/1903/17071
dc.language.isoenen_US
dc.subject.pqcontrolledApplied mathematicsen_US
dc.subject.pqcontrolledAtmospheric sciencesen_US
dc.subject.pquncontrolledbred vectorsen_US
dc.subject.pquncontrolledchaotic systemsen_US
dc.subject.pquncontrolledLyapunov vectorsen_US
dc.subject.pquncontrolledsingular vectorsen_US
dc.titleBred vectors, singular vectors, and Lyapunov vectors in simple and complex modelsen_US
dc.typeDissertationen_US

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