Improving Prediction Skill of Imperfect Turbulent Models Through Statistical Response and Information Theory

Turbulent dynamical systems with a large phase space and a high degree of instabilities are ubiquitous in climate science and engineering applications. Statistical uncertainty quantification (UQ) to the response to the change in forcing or uncertain initial data in such complex turbulent systems requires the use of imperfect models due to both the lack of physical understanding and the overwhelming computational demands of Monte Carlo simulation with a large dimensional phase space. Thus, the systematic development of reduced low order imperfect statistical models for UQ in turbulent dynamical systems is a grand challenge. This paper applies a recent mathematical strategy for calibrating imperfect models in a training phase and accurately predicting the response by combining information theory and linear statistical response theory in a systematic fashion. A systematic hierarchy of simple statistical imperfect closure schemes for UQ for these problems are designed and tested which are...

• Type: Journal
• Year: 2016
• Where: JNS
• Authors: Andrew J. Majda, Di Qi
• Keywords: JNS 2016