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Linear theory for filtering nonlinear multiscale systems with model error.

Tyrus Berry1, John Harlim2

  • 1Department of Mathematics , The Pennsylvania State University , University Park, PA 16802, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|July 9, 2014
PubMed
Summary
This summary is machine-generated.

This study develops optimal filtering methods for multiscale dynamical systems with model error. Online parameter estimation simultaneously improves filtering and statistical prediction, outperforming offline methods.

Keywords:
covariance inflationfiltering multi-scale systemsmodel errorparameter estimationstochastic parameterizationuncertainty quantification

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Area of Science:

  • Dynamical systems theory
  • Stochastic processes
  • Data assimilation

Background:

  • Model error in multiscale systems arises from unresolved small-scale processes.
  • Accurate filtering requires accounting for these model limitations.
  • Noisy observations of slow variables are available.

Purpose of the Study:

  • Develop and analyze filtering techniques for multiscale systems with model error.
  • Investigate parameter estimation strategies for reduced models.
  • Compare online and offline parameter estimation methods.

Main Methods:

  • Higher-order asymptotic expansion of conditional measure moments.
  • Analysis of continuous-time linear and nonlinear models.
  • Numerical experiments using the two-layer Lorenz-96 model.

Main Results:

  • A unique parameter choice optimizes filtering and statistical estimation in linear models.
  • Nonlinear models show similar behavior with correct stochastic parametrization.
  • Online parameter estimation yields superior filtering and prediction compared to offline methods.

Conclusions:

  • Simultaneous online estimation of parameters is crucial for accurate filtering and statistical prediction in multiscale systems.
  • Inappropriate stochastic parametrization can lead to conflicting performance metrics.
  • Online methods demonstrate robustness, especially when slow variables are not fully observed.