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Nonlinear Data Assimilation for high-dimensional systems

- with geophysical applications -
  • Peter Jan van Leeuwen
Part of the Frontiers in Applied Dynamical Systems: Reviews and Tutorials book series (FIADS, volume 2)

Abstract

In this chapter the state-of-the-art in data assimilation for high-dimensional highly nonlinear systems is reviewed, and recent developments are highlighted. This knowledge is available in terms of probability density functions, and the nonlinearity means that the shape of these functions is unknown a-priori. We focus on sampling methods because of they flexibility. Traditional Monte-Carlo methods like Metropolis-Hastings and its variants are discussed, including exciting new developments in this field. However, because of the serial nature of the sampling, and the possibility to reject samples these methods are not efficient in high-dimensional systems in which each sample is very expensive computationally. The emphasis of this chapter is on so-called particle filters as these are emerging as most efficient for these high-dimensional systems. Up to recently their profile has been low when the dimensions are high, or rather when the number of independent observations is high, because the area of state space when the observations are is decreasing very rapidly with system dimension. However, recent developments have beaten this curse of dimensionality, as will be demonstrated both theoretically and in high-dimensional examples. But it is also emphasized that much more needs to be done.

Notes

Acknowledgements

I thank the members Data Assimilation Research Centre (DARC) for numerous discussions on the topics of this paper, especially Melanie Ades, Javier Amezcua, David Livings, Phil Browne and Sanita Carvalho-Vetra. None of them is in anyway responsible for the contents. I also thank funding from the National Environment Research Council (NERC) via the National Centre of Earth Observation (NCEO) and via several other grants, and the EU FP7 project SANGOMA.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MeteorologyUniversity of ReadingReadingUK
  2. 2.The National Centre for Earth ObservationReadingUK

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