Particle filters are a class of data-assimilation schemes which, unlike current operational data-assimilation methods, make no assumptions about the linearity of the model equations or observation operators. This means They can potentially represent the full, possibly multi-modal, posterior probability density function (pdf). Unfortunately, the standard Sequential Importance Resampling (SIR) particle filter requires too many pal1icles to make it a viable operational data-assimilation scheme in high dimensional systems. This thesis explores an adaptation to the SIR filter, the equivalent-weights particle filter, designed to ensure an ensemble representation of the high probability region of the posterior pdf even in high dimensional systems. The formulation of the equivalent-weights particle filter involves various tuneable parameters. The first part of this thesis focusses on a theoretical and practical examination of the effect of the parameter choices on the ability of the equivalent-weights particle filter to represent the posterior pdf. Theoretically, the importance of ensuring equivalent weights for the majority of particles is shown and consequently the need to sample from a mixture proposal density al analysis time. Practically, the potentially large influence of the parameters is demonstrated and how this can be used to establish appropriate choices for some of the parameters is discussed. The second part of the thesis considers two areas related to the potential of the equivalent-weights particle filter as a viable data-assimilation scheme: the capacity to represent the posterior pdf and the effect on any model balances that may be present in the system. The ability of the equivalent-weights particle filter to represent the high probability region of the posterior pdf with relatively few particles in high dimensional systems is demonstrated. Changes in the observation distribution, frequency or error statistics result in minimal impact to this posterior representation. More distinctive effects are seen when the model error statistics are misrepresented in the ensemble. The final section on model balances relates to the use of the equivalent-weights pa11icle filter in atmosphere and ocean numerical models. The equivalent-weights par1icle filter is shown to have little effect on the model balances present in a simple ocean model and hence there is no evidence for the introduction of spurious gravity waves
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:603528 |
| Date | January 2013 |
| Creators | Ades, Melanie |
| Publisher | University of Reading |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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