Multiscale Methods for Data Assimilation in Turbulent Systems

@article{Lee2015MultiscaleMF,
  title={Multiscale Methods for Data Assimilation in Turbulent Systems},
  author={Yoonsang Lee and Andrew J. Majda},
  journal={Multiscale Model. Simul.},
  year={2015},
  volume={13},
  pages={691-713}
}
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… 

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References

SHOWING 1-10 OF 37 REFERENCES

Ensemble Kalman filters for dynamical systems with unresolved turbulence

Mathematical test models for superparametrization in anisotropic turbulence

  • A. MajdaM. Grote
  • Environmental Science
    Proceedings of the National Academy of Sciences
  • 2009
TLDR
The main result here is the systematic development of simple test models that are mathematically tractable yet capture key features of anisotropic turbulence in applications involving statistically intermittent fluctuations without local statistical equilibration, with moderate scale separation and significant impact on the large-scale dynamics.

Stochastic superparameterization in a one-dimensional model for wave turbulence

Superparameterization is a multiscale numerical method wherein solutions of prognostic equations for small scale processes on local domains embedded within the computational grid of a large scale

Conceptual dynamical models for turbulence

  • A. MajdaYoonsang Lee
  • Environmental Science, Physics
    Proceedings of the National Academy of Sciences
  • 2014
TLDR
Conceptual dynamical models of turbulence are developed which capture key statistical features of vastly more complex anisotropic turbulent systems in a qualitative fashion and potentially provide a useful test bed for algorithms for prediction, uncertainty quantification, and data assimilation for anisotrop turbulent systems.

Test Models for Filtering with Superparameterization

TLDR
This paper considers the Fourier domain Kalman filter for filtering regularly spaced sparse observations of the large-scale mean variables and finds high filtering and statistical prediction skill with superpara-superparameterization.

Stochastic superparameterization in quasigeostrophic turbulence

Blended particle filters for large-dimensional chaotic dynamical systems

TLDR
Test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations.

A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks

Abstract. We study catastrophic filter divergence in data assimilation procedures whereby the forecast model develops severe numerical instabilities leading to a blow-up of the solution. Catastrophic

An Introduction to Estimation Theory

Despite the explosive growth of activity in the eld of Earth System data assimilation over the past decade or so there remains a substantial gap between theory and practice The present article