Accuracy of some approximate Gaussian filters for the navier-stokes equation in the presence of model error

M. Branicki, Andrew Majda, K. J.H. Law

Research output: Contribution to journalArticle

Abstract

Bayesian state estimation of a dynamical system from a stream of noisy measurements is important in many geophysical and engineering applications where high dimensionality of the state space, sparse observations, and model error pose key challenges. Here, three computationally feasible, approximate Gaussian data assimilation/filtering algorithms are considered in various regimes of turbulent 2D Navier-Stokes dynamics in the presence of model error. The first source of error arises from the necessary use of reduced models for the forward dynamics of the filters, while a particular type of representation error arises from the finite resolution of observations which mix up information about resolved and unresolved dynamics. Two stochastically parameterized filtering algorithms, referred to as cSPEKF and GCF, are compared with 3DVAR-a prototypical time-sequential algorithm known to be accurate for filtering dissipative systems for a suitably inflated "background" covariance. We provide the first evidence that the stochastically parameterized algorithms, which do not rely on detailed knowledge of the underlying dynamics and do not require covariance inflation, can compete with or outperform an optimally tuned 3DVAR algorithm, and they can overcome competing sources of error in a range of dynamical scenarios.

Original languageEnglish (US)
Pages (from-to)1756-1794
Number of pages39
JournalMultiscale Modeling and Simulation
Volume16
Issue number4
DOIs
StatePublished - Jan 1 2018

Fingerprint

Gaussian Filter
Model Error
Navier-Stokes equations
Navier-Stokes equation
Navier Stokes equations
Navier-Stokes Equations
filter
filters
Filtering
Parameterized Algorithms
Data Assimilation
Sequential Algorithm
Dissipative Systems
Reduced Model
Bayesian Estimation
State Estimation
state estimation
Engineering Application
Navier-Stokes
Inflation

Keywords

  • 3DVAR
  • data assimilation
  • model error
  • Navier-Stokes equation
  • SPEKF
  • stochastic parameterization

ASJC Scopus subject areas

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

Accuracy of some approximate Gaussian filters for the navier-stokes equation in the presence of model error. / Branicki, M.; Majda, Andrew; Law, K. J.H.

In: Multiscale Modeling and Simulation, Vol. 16, No. 4, 01.01.2018, p. 1756-1794.

Research output: Contribution to journalArticle

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