New Strategies for Prediction and Data Assimilation for Turbulent Dynamical Systems in Climate Science
Technical Report,25 Sep 2015,01 Jun 2018
New York University New York United States
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The climate is an extremely complex multi-scale turbulent dynamical system with an extremely large phase space with a large dimension of instabilities which strongly interact and influence the large scale state. Statistical uncertainty quantification UQ to the response to the change in forcing or uncertain initial data in such complex turbulent systems in a grand challenge with the fundamental difficulty that by necessity imperfect models model error are needed both for lack of physical understanding and the overwhelming computational demands of Monte Carlo simulation with a large phase space, the curse of ensemble size or the curse of dimension. One natural way to constrain the behavior of imperfect models is to use active data assimilation and data driven methods to constrain the dynamics but these approaches are also hampered by model error and the curse of ensemble size for complex turbulent dynamical systems. Three recently developed mathematical approaches are reported here for attacking these complex dynamical systems.
- Statistics and Probability
- Information Science