Prognosis of qualitative behavior from time series: low-dimensional stochastic modeling of ENSO phenomena
Abstract
The majority of natural systems (climate system including) are known to be both high-dimension and open, i.e., subject to numerous external forcings. Hence in many cases they produce complex multi-scale behavior which cannot be modeled in deterministic way by direct analysis of observed processes. A basic idea underlying the suggested stochastic approach is that the robust dynamic properties of the system evolution can be described by a few variables, while other features may be considered as a stochastic disturbance. Models in a form of random dynamical systems (RDS) present a necessary and important step towards reconstructing the observed systems when their adequate first-principle mathematical models are either unknown or subjected to further verification. Note that, even for deterministic systems, the construction of a deterministic model from the observed time series and use of this model for prediction has quite a number of principal restrictions connected with high embedding dimension and overembedding problem. Reconstruction in the form of RDS (stochastic model) removes these restrictions, thus making the proposed approach more universal. In this report a stochastic modeling approach is applied to analysis of ENSO system behavior. Research during the past 30 years has shown that the El-Niño/Southern-Oscillation (ENSO) dynamics is governed, by and large, by the interplay of several nonlinear mechanisms that can be studied in forced delay differential equations (DDE). These models provide a convenient paradigm for explaining interannual ENSO variability and shed new light on its dynamical properties. Recently, Ghil et al. (2008) have performed a detailed analysis of a DDE model of ENSO variability over its entire, three-dimensional parameter space; they discovered a sharp separation of the parameter space into a “smooth” and a “rough” domain, where the latter exhibits sensitive dependence on parameters. We compliment this model by both dynamical noise reflecting influences of external forcings on its parameters, and slow trend of control parameter making this system weakly non-autonomous. The time series obtained from this model were used for construction of low dimensional stochastic model of evolution operator. Applicability of reconstructed model for prognosis of qualitative changes (critical transitions) of system behavior is demonstrated for time interval greater than “observation” period. Workability of the approach for analysis and prognosis of real-measured ENSO dynamics is investigated. Ghil, M., I. Zaliapin, and S. Thompson (2008) A delay differential model of ENSO variability: parametric instability and the distribution of extremes. Nonlin. Proc. Geophys., 15, 417-433.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2010
- Bibcode:
- 2010AGUFMNG43H1463M
- Keywords:
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- 3238 MATHEMATICAL GEOPHYSICS / Prediction;
- 3270 MATHEMATICAL GEOPHYSICS / Time series analysis;
- 4425 NONLINEAR GEOPHYSICS / Critical phenomena