## Nonlinear Time Series Analysis in the Geosciences: Applications in Climatology, Geodynamics and Solar-Terrestrial PhysicsReik V. Donner, Susana M. Barbosa The enormous progress over the last decades in our understanding of the mechanisms behind the complex system “Earth” is to a large extent based on the availability of enlarged data sets and sophisticated methods for their analysis. Univariate as well as multivariate time series are a particular class of such data which are of special importance for studying the dynamical p- cesses in complex systems. Time series analysis theory and applications in geo- and astrophysics have always been mutually stimulating, starting with classical (linear) problems like the proper estimation of power spectra, which hasbeenputforwardbyUdnyYule(studyingthefeaturesofsunspotactivity) and, later, by John Tukey. In the second half of the 20th century, more and more evidence has been accumulated that most processes in nature are intrinsically non-linear and thus cannot be su?ciently studied by linear statistical methods. With mat- matical developments in the ?elds of dynamic system’s theory, exempli?ed by Edward Lorenz’s pioneering work, and fractal theory, starting with the early fractal concepts inferred by Harold Edwin Hurst from the analysis of geoph- ical time series,nonlinear methods became available for time seriesanalysis as well. Over the last decades, these methods have attracted an increasing int- est in various branches of the earth sciences. The world’s leading associations of geoscientists, the American Geophysical Union (AGU) and the European Geosciences Union (EGU) have reacted to these trends with the formation of special nonlinear focus groups and topical sections, which are actively present at the corresponding annual assemblies. |

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### Contents

Subsampling Methodology for the Analysis of Nonlinear Atmospheric Time Series | 3 |

Global Patterns of Nonlinearity in Real and GCMSimulated Atmospheric Data | 17 |

Prediction of Extreme Events | 35 |

An Overview | 60 |

Automatic Parameter Estimation in a Mesoscale Model Without Ensembles | 81 |

Towards Robust Nonlinear Multivariate Analysis by Neural Network Methods | 96 |

Complexity of SpatioTemporal Correlations in Japanese Air Temperature Records | 125 |

Characterising LongTerm Variability | 157 |

Applications to Internal Gravity Waves with Comparisons to Linear Tidal Data | 223 |

Crustal Deformation Models and TimeFrequency Analysis of GPS Data from Deception Island Volcano South Shetland Islands Antarctica | 245 |

Describing Seismic Pattern Dynamics by Means of Ising Cellular Automata | 273 |

Template Analysis of the Hide Skeldon Acheson Dynamo | 292 |

The Case of the Derivative Nonlinear Schrodinger Equation | 311 |

Common Cycles in Atmospheric Geomagnetic and Solar Data | 327 |

Phase Coherence Analysis of DecadalScale Sunspot Activity on Both Solar Hemispheres | 354 |

387 | |

A New Empirical Global Ocean Tide and Mean Sea Level Model Based on Jason1 Satellite Altimetry Observations | 174 |

### Other editions - View all

Nonlinear Time Series Analysis in the Geosciences: Applications in ... Reik V. Donner,Susana M. Barbosa No preview available - 2010 |

Nonlinear Time Series Analysis in the Geosciences: Applications in ... Reik V. Donner,Susana M. Barbosa No preview available - 2008 |

### Common terms and phrases

amplitude applied approach areas average chaotic climate components computed considered continuous wavelet transform correlation corresponding cost functions curve cycle dataset Deception Island decomposition deﬁned deﬁnition detected diﬀerent dimension density discrete wavelet transform dynamics eﬀects eigenvalues equation estimated event ﬁeld ﬁltered ﬁnd ﬁrst forecast Fourier frequency Gaussian Geophys geophysical global ocean tide grid HadCM3 hemisphere inﬂuence internal wave Jason-1 matrix methods modes MODWT multivariate mutual information NCEP/NCAR NLCCA NLPCA noise nonlinear observations obtained ocean tide model oscillations overﬁtting parameter period phase synchronisation Phys prediction records recurrence plots reﬂection ROC curve satellite altimetry scale sea level Sect signal signiﬁcant solar activity soliton solution spatial speciﬁc spectrum spherical harmonics stations statistical stochastic subsampling sunspot sunspot numbers surrogate synchronization temperature tidal constituents tide gauge TOPEX/Poseidon trend upos values variability wavelet coeﬃcients wavelet transform wavelet variance