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Title: Accuracy of Some Approximate Gaussian Filters for the Navier--Stokes Equation in the Presence of Model Error

Journal Article · · Multiscale Modeling & Simulation
DOI: https://doi.org/10.1137/17m1146865 · OSTI ID:1866715
 [1];  [2];  [3]
  1. Univ. of Edinburgh, Scotland (United Kingdom); Alan Turing Institute for Data Science, London (United Kingdom)
  2. New York Univ. (NYU), NY (United States)
  3. Univ. of Manchester (United Kingdom)
+ Show Author Affiliations

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. In this work, 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.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
US Department of the Navy, Office of Naval Research (ONR); USDOE
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1866715
Journal Information:
Multiscale Modeling & Simulation, Journal Name: Multiscale Modeling & Simulation Journal Issue: 4 Vol. 16; ISSN 1540-3459
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (1)

Conditional Gaussian Systems for Multiscale Nonlinear Stochastic Systems: Prediction, State Estimation and Uncertainty Quantification journal July 2018

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Related Subjects

97 MATHEMATICS AND COMPUTING
EDVAR
Navier-Stokes equation
SPEKF
data assimilation
model error
stochastic parameterization