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Title: Four Dimensional Variational Data Assimilation for Hamiltonian Problems
Author: Watkinson, Laura
ISNI:       0000 0001 3564 0655
Awarding Body: University of Reading
Current Institution: University of Reading
Date of Award: 2006
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In this thesis we bring together two areas of mathematics; Hamiltonian dynamics and data assimilation. We construct a four dimensional variational (4d Var) data assimilation scheme for two Hamiltonian systems. This is to reflect the Hamiltonian behaviour observed in the atmosphere. We know, for example, that potential vorticity is conserved in atmospheric models. However, current data assimilation schemes do not explicitly include such physical relationships. In this thesis, by considering the two and three body problems, we demonstrate how such characteristic behaviour can be included in the data assimilation schemes. In our 4d Var schemes we add a weak constraint that imposes the conservation of the Hamiltonian, the total energy, at the initial time. This is effectively imposing an energy constraint from one data assimilation window to the next. Our results imply that these weak constraints affect the underlying geometry of the resulting data assimilation solution. We also demonstrate that this constraint reduces the error on this solution and the forecast. By imposing this constraint we are including additional information to the system. Due to the additional term in the cost function gradient, the analysis can only change in such a way as to satisfy this weak constraint. This thesis therefore demonstrates that the inclusion of similar weak con-straints, perhaps using the conservation of potential vorticity, could improve the analysis and forecast for atmospheric models.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available