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 language | English (US) |
|---|---|
| Pages (from-to) | 1756-1794 |
| Number of pages | 39 |
| Journal | Multiscale Modeling and Simulation |
| Volume | 16 |
| Issue number | 4 |
| DOIs | |
| State | Published - Jan 1 2018 |
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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 journal › Article
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TY - JOUR
T1 - Accuracy of some approximate Gaussian filters for the navier-stokes equation in the presence of model error
AU - Branicki, M.
AU - Majda, Andrew
AU - Law, K. J.H.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
AB - 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.
KW - 3DVAR
KW - data assimilation
KW - model error
KW - Navier-Stokes equation
KW - SPEKF
KW - stochastic parameterization
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U2 - 10.1137/17M1146865
DO - 10.1137/17M1146865
M3 - Article
AN - SCOPUS:85050304824
VL - 16
SP - 1756
EP - 1794
JO - Multiscale Modeling and Simulation
JF - Multiscale Modeling and Simulation
SN - 1540-3459
IS - 4
ER -