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Chaos 2017 Sep;27(9):093110

Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095-1565, USA.

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey, furthermore, a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled-provided the decay of temporal correlations is sufficiently well-resolved-within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.

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http://dx.doi.org/10.1063/1.4989400 | DOI Listing |

September 2017

Phys Rev E 2016 Aug 24;94(2-2):029904. Epub 2016 Aug 24.

This corrects the article DOI: 10.1103/PhysRevE.93.036201.

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http://dx.doi.org/10.1103/PhysRevE.94.029904 | DOI Listing |

August 2016

Phys Rev E 2016 Mar 16;93(3):036201. Epub 2016 Mar 16.

Department of Atmospheric and Oceanic Sciences, 405 Hilgard Ave., Box 951565, 7127 Math Sciences Bldg., University of California, Los Angeles, California 90095-1565, USA.

The comparison performed in Berry et al. [Phys. Rev. E 91, 032915 (2015)] between the skill in predicting the El Niño-Southern Oscillation climate phenomenon by the prediction method of Berry et al. and the "past-noise" forecasting method of Chekroun et al. [Proc. Natl. Acad. Sci. USA 108, 11766 (2011)] is flawed. Three specific misunderstandings in Berry et al. are pointed out and corrected.

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http://dx.doi.org/10.1103/PhysRevE.93.036201 | DOI Listing |

March 2016

Proc Natl Acad Sci U S A 2014 Feb 17;111(5):1684-90. Epub 2014 Jan 17.

Department of Atmospheric and Oceanic Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095.

Despite the importance of uncertainties encountered in climate model simulations, the fundamental mechanisms at the origin of sensitive behavior of long-term model statistics remain unclear. Variability of turbulent flows in the atmosphere and oceans exhibits recurrent large-scale patterns. These patterns, while evolving irregularly in time, manifest characteristic frequencies across a large range of time scales, from intraseasonal through interdecadal. Based on modern spectral theory of chaotic and dissipative dynamical systems, the associated low-frequency variability may be formulated in terms of Ruelle-Pollicott (RP) resonances. RP resonances encode information on the nonlinear dynamics of the system, and an approach for estimating them--as filtered through an observable of the system--is proposed. This approach relies on an appropriate Markov representation of the dynamics associated with a given observable. It is shown that, within this representation, the spectral gap--defined as the distance between the subdominant RP resonance and the unit circle--plays a major role in the roughness of parameter dependences. The model statistics are the most sensitive for the smallest spectral gaps; such small gaps turn out to correspond to regimes where the low-frequency variability is more pronounced, whereas autocorrelations decay more slowly. The present approach is applied to analyze the rough parameter dependence encountered in key statistics of an El-Niño-Southern Oscillation model of intermediate complexity. Theoretical arguments, however, strongly suggest that such links between model sensitivity and the decay of correlation properties are not limited to this particular model and could hold much more generally.

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http://dx.doi.org/10.1073/pnas.1321816111 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3918823 | PMC |

February 2014

Proc Natl Acad Sci U S A 2011 Jul 5;108(29):11766-71. Epub 2011 Jul 5.

Environmental Research and Teaching Institute, École Normale Supérieure, F-75230 Paris Cedex 05, France.

Interannual and interdecadal prediction are major challenges of climate dynamics. In this article we develop a prediction method for climate processes that exhibit low-frequency variability (LFV). The method constructs a nonlinear stochastic model from past observations and estimates a path of the "weather" noise that drives this model over previous finite-time windows. The method has two steps: (i) select noise samples--or "snippets"--from the past noise, which have forced the system during short-time intervals that resemble the LFV phase just preceding the currently observed state; and (ii) use these snippets to drive the system from the current state into the future. The method is placed in the framework of pathwise linear-response theory and is then applied to an El Niño-Southern Oscillation (ENSO) model derived by the empirical model reduction (EMR) methodology; this nonlinear model has 40 coupled, slow, and fast variables. The domain of validity of this forecasting procedure depends on the nature of the system's pathwise response; it is shown numerically that the ENSO model's response is linear on interannual time scales. As a result, the method's skill at a 6- to 16-month lead is highly competitive when compared with currently used dynamic and statistic prediction methods for the Niño-3 index and the global sea surface temperature field.

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http://dx.doi.org/10.1073/pnas.1015753108 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3141987 | PMC |

July 2011

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