Report: Low Frequency Predictive Skill Despite Structural Instability and Model Error
Abstract
The PI, Andrew Majda, the co-PI, Rafail Abramov, and the postdoctoral associates, Dimitris Giannakis, and Michal Branicki (funded by the DRI) have submitted the following papers all with the PI as author (and other collaborators listed) A) Mathematical Techniques for Quantifying Uncertainty in Complex Systems with Model Error with Prototype Applications Development of new uses of information theory to quantify uncertainty, irreducible impression, sensitivity, and long range forecasting skill (7,8,9,12, 4,6,1 ). This work includes explicit simple examples of irreducible imprecision where imperfect models can be tuned to match the climate mean and variance of the perfect model; nevertheless the response to external forcing has an intrinsic information barrier which cannot be improved within the class of imperfect models. The development and application of these ideas to unambiguous simple models for turbulent diffusion with complex features. The theoretical development of algorithms based on fluctuation dissipation theorems for sensitivity and long-range forecasting including intrinsic skill barriers for popular linear regression models. New non-Gaussian filtering algorithms for multi-scale filtering of turbulent signals (14,11,3,2). B) Nonlinear Laplacian Spectral Analysis (NLSA) for Time Series: Capturing intermittency and Low Frequency Variability Majda and Giannakis have developed novel NLSA algorithms and applied them to comprehensive climate models (13,10,5). Many processes in science and engineering develop multiscale temporal and spatial patterns, with complex underlying dynamics and time-dependent external forcings. Because of the importance in understanding and predicting these phenomena, extracting the salient modes of variability empirically from incomplete observations is a problem of wide contemporary interest.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 30, 2012
- Accession Number
- ADA590512
Entities
People
- Andrew J. Majda
Organizations
- New York University