Filtering skill for turbulent signals for a suite of nonlinear and linear extended Kalman filters

M. Branicki, B. Gershgorin, A. J. Majda

Research output: Contribution to journalArticle

Abstract

The filtering skill for turbulent signals from nature is often limited by errors due to utilizing an imperfect forecast model. In particular, real-time filtering and prediction when very limited or no a posteriori analysis is possible (e.g. spread of pollutants, storm surges, tsunami detection, etc.) introduces a number of additional challenges to the problem. Here, a suite of filters implementing stochastic parameter estimation for mitigating model error through additive and multiplicative bias correction is examined on a nonlinear, exactly solvable, stochastic test model mimicking turbulent signals in regimes ranging from configurations with strongly intermittent, transient instabilities associated with positive finite-time Lyapunov exponents to laminar behavior. Stochastic Parameterization Extended Kalman Filter (SPEKF), used as a benchmark here, involves exact formulas for propagating the mean and covariance of the augmented forecast model including the unresolved parameters. The remaining filters use the same nonlinear forecast model but they introduce model error through different moment closure approximations and/or linear tangent approximation used for computing the second-order statistics of the augmented stochastic forecast model. A comprehensive study of filter performance is carried out in the presence of various moment closure errors which are enhanced by additional model errors due to incorrect parameters inducing additive and multiplicative stochastic biases. The estimation skill of the unresolved stochastic parameters is also discussed and it is shown that the linear tangent filter, despite its popularity, is completely unreliable in many turbulent regimes for both parameter estimation and filtering; moreover, regimes of filter divergence for the linear tangent filter are identified. The results presented here provide useful guidelines for filtering turbulent, high-dimensional, spatially extended systems with more general model errors, as well as for designing more skillful methods for superparameterization of unresolved intermittent processes in complex multi-scale models. They also provide unambiguous benchmarks for the capabilities of linear and nonlinear extended Kalman filters using incorrect statistics on an exactly solvable test bed with rich and realistic dynamics.

Original languageEnglish (US)
Pages (from-to)1462-1498
Number of pages37
JournalJournal of Computational Physics
Volume231
Issue number4
DOIs
StatePublished - Feb 20 2012

Fingerprint

Extended Kalman filters
Kalman filters
filters
forecasting
tangents
Parameter estimation
closures
storm surges
Statistics
statistics
multiscale models
moments
Tsunamis
test stands
Stochastic models
Parameterization
approximation
parameterization
contaminants
divergence

Keywords

  • Data assimilation
  • Extended Kalman Filter
  • Filtering turbulence
  • Gaussian closure filter
  • Model error
  • Stochastic parameter estimation

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

Filtering skill for turbulent signals for a suite of nonlinear and linear extended Kalman filters. / Branicki, M.; Gershgorin, B.; Majda, A. J.

In: Journal of Computational Physics, Vol. 231, No. 4, 20.02.2012, p. 1462-1498.

Research output: Contribution to journalArticle

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