Linear theory for filtering nonlinear multiscale systems with model error
1Department of Mathematics , The Pennsylvania State University , University Park, PA 16802, USA.
Proceedings. Mathematical, Physical, and Engineering Sciences
|July 9, 2014
Summary
This study develops optimal filtering methods for multiscale dynamical systems with model error. Online parameter estimation simultaneously improves filtering and statistical prediction, outperforming offline methods.
Area of Science:
- Dynamical systems theory
- Stochastic processes
- Data assimilation
Background:
- Model error in multiscale systems arises from unresolved small-scale processes.
- Accurate filtering requires accounting for these model limitations.
- Noisy observations of slow variables are available.
Purpose of the Study:
- Develop and analyze filtering techniques for multiscale systems with model error.
- Investigate parameter estimation strategies for reduced models.
- Compare online and offline parameter estimation methods.
Main Methods:
- Higher-order asymptotic expansion of conditional measure moments.
- Analysis of continuous-time linear and nonlinear models.
- Numerical experiments using the two-layer Lorenz-96 model.
Main Results:
- A unique parameter choice optimizes filtering and statistical estimation in linear models.
- Nonlinear models show similar behavior with correct stochastic parametrization.
- Online parameter estimation yields superior filtering and prediction compared to offline methods.
Conclusions:
- Simultaneous online estimation of parameters is crucial for accurate filtering and statistical prediction in multiscale systems.
- Inappropriate stochastic parametrization can lead to conflicting performance metrics.
- Online methods demonstrate robustness, especially when slow variables are not fully observed.
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