Filtering Complex Turbulent Systems

Table of Contents

Preface
1. Introduction and overview: mathematical strategies for filtering turbulent systems
Part I. Fundamentals:
2. Filtering a stochastic complex scalar: the prototype test problem
3. The Kalman filter for vector systems: reduced filters and a three-dimensional toy model
4. Continuous and discrete Fourier series and numerical discretization
Part II. Mathematical Guidelines for Filtering Turbulent Signals:
5. Stochastic models for turbulence
6. Filtering turbulent signals: plentiful observations
7. Filtering turbulent signals: regularly spaced sparse observations
8. Filtering linear stochastic PDE models with instability and model error
Part III. Filtering Turbulent Nonlinear Dynamical Systems:
9. Strategies for filtering nonlinear systems
10. Filtering prototype nonlinear slow-fast systems
11. Filtering turbulent nonlinear dynamical systems by finite ensemble methods
12. Filtering turbulent nonlinear dynamical systems by linear stochastic models
13. Stochastic parameterized extended Kalman filter for filtering turbulent signal with model error
14. Filtering turbulent tracers from partial observations: an exactly solvable test model
15. The search for efficient skilful particle filters for high dimensional turbulent dynamical systems
References
Index.

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• Copyright Information Page (42 KB)
• Marketing Excerpt (505 KB)
• Front Matter (90 KB)
• Table of Contents (49 KB)
• Index (41 KB)