BAA: 11-26 Office of Naval Research FY2012 MURI Topic #16:

Extended-Range Environmental Prediction Using Low-Dimensional Dynamic Modes

Extended-Range Prediction with Low-Dimensional, Stochastic-Dynamic Models: A Data-driven Approach

Principal Investigator: Prof. Michael Ghil, University of California, Los Angeles

Columbia Team Coordinator: Dr. Michael K. Tippett, Columbia University

Abstract This project addresses the problem of using reduced-order models for the description, understanding and prediction of atmospheric, oceanic and sea ice variability on time scales of 1–12 months and beyond. The technical approaches include the use of linear and nonlinear, stochastic-dynamic models that capture the dominant and hopefully most predictable portion of the climate system’s variability. In particular, the low-order models we propose rely heavily on the proper identification and robust description of low-frequency modes (LFMs) of variability such as the Madden-Julian Oscillation (MJO), El Nino–Southern Oscillation (ENSO), North Atlantic Oscillation (NAO) and Pacific–North American (PNA) pattern. The expertise of the two teams participating in the project, at UCLA and at Columbia University (CU), includes pioneering work on the use of LFMs in extended-range prediction, as well as extensive experience with the operational performance of a variety of predictive models and methods on several time scales.

The major methodological problem we propose to address is the fact that in a nonlinear system there is a continuum of scales, from the fastest and shortest to the slowest and longest: Typically, there is no gap or separation between these scales. Recent ideas and methods from statistical physics and dynamical systems theory — associated with the names of H. Mori and R. Zwanzig — allow one to treat the effect of the larger scales on the smaller ones as memory effects. We propose numerically efficient methods for treating these effects, thus further improving a panoply of methods for model reduction and the application of the reduced models thus obtained to prediction.

The methods we propose to further develop, refine and test include linear inverse models, single- and multi-channel singular spectrum analysis (SSA), empirical model reduction (EMR) and past-noise forecasting (PNF), as well as various combinations thereof. We expect to obtain a better understanding of the predictive success of the SSA-EMR and EMR-PNF combinations in the light of Mori-Zwanzig theory, as well a substantial improvement in their predictive skill. Past close interactions between team members at the two participating institutions will allow us to bring out the tight couplings between (i) the advanced model-reduction methods; (ii) the innovative treatment of physical processes; and (iii) the operational aspects of testing, downscaling and forecasting.

The understanding and prediction of the climate system’s variability on seasonal-to-interannual scales has advanced most rapidly in the ENSO setting. We plan to exploit the experience gained in this area by carrying out research on the MJO, NAO and PNA. Each of these LFMs has specific properties that require better understanding of the LFM’s basic physics in order to properly apply the mathematical and numerical methodology to it. The proposing team has substantial strength in all of these areas and the anticipated outcomes include improved prediction of the physical environment for Navy operations in the mid-latitudes, as well as the polar regions. Furthermore, since the basic problem of noise interaction with nonlinear dynamics represents a major obstacle in many other settings of interest to DoD, the payoff may be quite high for other topics covered by the BAA.

Los Angeles and New York, 8 November 2011