New Strategies for Prediction and Data Assimilation for Turbulent Dynamical Systems in Climate Science
Abstract
The objective of this proposal is to develop new mathematical approaches for complex systems. To approach the objective the PI will (1) improve prediction performance by applying statistical response theory and information theory to complex dynamical systems; (2) develop new algorithms for multi-scale data assimilation in complex systems; and (3) detect causality in data-driven models based on nonlinear Laplacian spectral analysis. New Strategies for Prediction and Data Assimilation for Turbulent Dynamical Systems in Climate Science Abstract 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, Òthe curse of ensemble sizeÓ or Òthe curse of dimension.Ó 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 proposed here for attacking these complex turbulent dynamical systems. I. Improving Prediction Skill of Forced Imperfect Turbulent Dynamical Systems through Statistical Response Theory and Information Theory II. Novel Algorithms for Multi-scale Data Assimilation in Complex Turbulent Systems III. Detecting Causality in Data Driven Models based on Nonlinear Laplacian Spectical Analysis (NLSA) A natural way to make progress on I) and II) is by studying passive tracers in turbulent dynamical systems by both direct Eulerian methods as well as Lagrangian tracers, a natural way to probe the atmosphere and ocean through sensors or small drones. There are several reasons for this; Passive tracers with uncertain sources approximate the leading behavior of greenhouse gases and have intermittent extreme events and involve many spatio-temporal scales of dynamics so imperfect models are a necessity and accurate statistical prediction, data assimilation, and UQ remain major challenges. Also, a natural way to attack the extremely difficult challenge of closed loop adaptive stochastic control of the climate is to utilize Eurlerian and Lagrangian tracers as sensors to rapidly probe the system.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 12, 2017
- Source ID
- W911NF1510636
Entities
People
- Andrew Majda
Organizations
- Army Contracting Command
- New York University
- Office of the Secretary of Defense