Test models for improving filtering with model errors through stochastic parameter estimation

B. Gershgorin, J. Harlim, A. J. Majda

Research output: Contribution to journalArticlepeer-review


The filtering skill for turbulent signals from nature is often limited by model errors created by utilizing an imperfect model for filtering. Updating the parameters in the imperfect model through stochastic parameter estimation is one way to increase filtering skill and model performance. Here a suite of stringent test models for filtering with stochastic parameter estimation is developed based on the Stochastic Parameterization Extended Kalman Filter (SPEKF). These new SPEKF-algorithms systematically correct both multiplicative and additive biases and involve exact formulas for propagating the mean and covariance including the parameters in the test model. A comprehensive study is presented of robust parameter regimes for increasing filtering skill through stochastic parameter estimation for turbulent signals as the observation time and observation noise are varied and even when the forcing is incorrectly specified. The results here provide useful guidelines for filtering turbulent signals in more complex systems with significant model errors.

Original languageEnglish (US)
Pages (from-to)1-31
Number of pages31
JournalJournal of Computational Physics
Issue number1
StatePublished - Jan 1 2010


  • Data assimilation
  • Filtering turbulence
  • Kalman filter
  • Model error
  • Stochastic parameter estimation

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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