### Abstract

Data assimilation of turbulent signals is an important challenging problem because of the extremely complicated large dimension of the signals and incomplete partial noisy observations which usually mix the large scale mean flow and small scale fluctuations. Due to the limited computing power in the foreseeable future, it is desirable to use multiscale forecast models which are cheap and fast to mitigate the curse of dimensionality in turbulent systems; thus model errors from imperfect forecast models are unavoidable in the development of a data assimilation method in turbulence. Here we propose a suite of multiscale data assimilation methods which use stochastic Superparameterization as the forecast model. Superparameterization is a seamless multiscale method for parameterizing the effect of small scales by cheap local problems embedded in a coarse grid. The key ingredient of the multiscale data assimilation methods is the systematic use of conditional Gaussian mixtures which make the methods efficient by filtering a subspace whose dimension is smaller than the full state. The multiscale data assimilation methods proposed here are tested on a six dimensional conceptual dynamical model for turbulence which mimics interesting features of anisotropic turbulence including two way coupling between the large and small scale parts, intermittencies, and extreme events in the smaller scale fluctuations. Numerical results show that suitable multiscale data assimilation methods have high skill in estimating the most energetic modes of turbulent signals even with infrequent observation times.

Original language | English (US) |
---|---|

Pages (from-to) | 691-713 |

Number of pages | 23 |

Journal | Multiscale Modeling and Simulation |

Volume | 13 |

Issue number | 2 |

DOIs | |

State | Published - 2015 |

### Fingerprint

### Keywords

- Data assimilation
- Filtering
- Multiscale
- Superparameterization
- Turbulence

### ASJC Scopus subject areas

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

### Cite this

*Multiscale Modeling and Simulation*,

*13*(2), 691-713. https://doi.org/10.1137/140978326

**Multiscale methods for data assimilation in turbulent systems.** / Lee, Yoonsang; Majda, Andrew J.

Research output: Contribution to journal › Article

*Multiscale Modeling and Simulation*, vol. 13, no. 2, pp. 691-713. https://doi.org/10.1137/140978326

}

TY - JOUR

T1 - Multiscale methods for data assimilation in turbulent systems

AU - Lee, Yoonsang

AU - Majda, Andrew J.

PY - 2015

Y1 - 2015

N2 - Data assimilation of turbulent signals is an important challenging problem because of the extremely complicated large dimension of the signals and incomplete partial noisy observations which usually mix the large scale mean flow and small scale fluctuations. Due to the limited computing power in the foreseeable future, it is desirable to use multiscale forecast models which are cheap and fast to mitigate the curse of dimensionality in turbulent systems; thus model errors from imperfect forecast models are unavoidable in the development of a data assimilation method in turbulence. Here we propose a suite of multiscale data assimilation methods which use stochastic Superparameterization as the forecast model. Superparameterization is a seamless multiscale method for parameterizing the effect of small scales by cheap local problems embedded in a coarse grid. The key ingredient of the multiscale data assimilation methods is the systematic use of conditional Gaussian mixtures which make the methods efficient by filtering a subspace whose dimension is smaller than the full state. The multiscale data assimilation methods proposed here are tested on a six dimensional conceptual dynamical model for turbulence which mimics interesting features of anisotropic turbulence including two way coupling between the large and small scale parts, intermittencies, and extreme events in the smaller scale fluctuations. Numerical results show that suitable multiscale data assimilation methods have high skill in estimating the most energetic modes of turbulent signals even with infrequent observation times.

AB - Data assimilation of turbulent signals is an important challenging problem because of the extremely complicated large dimension of the signals and incomplete partial noisy observations which usually mix the large scale mean flow and small scale fluctuations. Due to the limited computing power in the foreseeable future, it is desirable to use multiscale forecast models which are cheap and fast to mitigate the curse of dimensionality in turbulent systems; thus model errors from imperfect forecast models are unavoidable in the development of a data assimilation method in turbulence. Here we propose a suite of multiscale data assimilation methods which use stochastic Superparameterization as the forecast model. Superparameterization is a seamless multiscale method for parameterizing the effect of small scales by cheap local problems embedded in a coarse grid. The key ingredient of the multiscale data assimilation methods is the systematic use of conditional Gaussian mixtures which make the methods efficient by filtering a subspace whose dimension is smaller than the full state. The multiscale data assimilation methods proposed here are tested on a six dimensional conceptual dynamical model for turbulence which mimics interesting features of anisotropic turbulence including two way coupling between the large and small scale parts, intermittencies, and extreme events in the smaller scale fluctuations. Numerical results show that suitable multiscale data assimilation methods have high skill in estimating the most energetic modes of turbulent signals even with infrequent observation times.

KW - Data assimilation

KW - Filtering

KW - Multiscale

KW - Superparameterization

KW - Turbulence

UR - http://www.scopus.com/inward/record.url?scp=84937412730&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937412730&partnerID=8YFLogxK

U2 - 10.1137/140978326

DO - 10.1137/140978326

M3 - Article

AN - SCOPUS:84937412730

VL - 13

SP - 691

EP - 713

JO - Multiscale Modeling and Simulation

JF - Multiscale Modeling and Simulation

SN - 1540-3459

IS - 2

ER -