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Model Error, Information Barriers, State Estimation and Prediction in Complex Multiscale Systems
Andrew J Majda1,2, Nan Chen1
1Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study introduces an information-theoretic framework and nonlinear modeling for complex multiscale systems. It improves predictions and quantifies uncertainty, especially for extreme events in climate and ocean science.
Area of Science:
- Complex systems science
- Information theory
- Nonlinear dynamics
- Climate science
- Atmosphere and ocean science
Background:
- Complex multiscale systems are prevalent across scientific disciplines.
- Understanding and predicting these systems presents significant challenges due to their intricate nature.
- Existing methods often struggle with uncertainty quantification and capturing extreme events.
Purpose of the Study:
- To develop and apply an information-theoretic framework for analyzing complex multiscale systems.
- To introduce novel reduced-order nonlinear modeling strategies for enhanced prediction capabilities.
- To address limitations in current approaches for state estimation, data assimilation, and model error quantification.
Main Methods:
- Application of an information-theoretic framework to quantify model fidelity, sensitivity, and information barriers.
- Integration of information theory into data-driven nonlinear stochastic modeling.
- Development of efficient reduced-order nonlinear modeling strategies combined with information theory for model calibration.
Main Results:
- The information-theoretic framework successfully assesses prediction skills and overcomes shortcomings of traditional path-wise measurements, particularly for extreme events.
- A systematic data-driven nonlinear stochastic modeling framework enables effective predictions of nonlinear intermittent time series.
- New modeling strategies provide skillful predictions of intermittent extreme events in spatially-extended complex dynamical systems.
Conclusions:
- The developed framework and modeling strategies offer a rigorous approach to understanding and predicting complex multiscale systems.
- This research enhances the ability to handle model errors, quantify uncertainty, and predict extreme events.
- The findings have direct applications in climate, atmosphere, and ocean science, improving forecasting and analysis.
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