Nonlinear time series analysis in the geosciences

LECTURE
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IN EARTH
Reik V.
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SCIENCES
D o n n e r
Susana M .
Barbosa
Editors
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Applications i n Climatology,
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Physics
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Geodynamics
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R e i k V. D o n n e r •
Susana M . Barbosa
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Geodynamics
Physics
W i t h 151 Figures
DAI HQC THAI NGUYEN
B U N G T i l l HOC L I E U
S p r i n g e r
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Editors
Dr. Reik V. Donner
TU Dresden
Institut fiir Wirtschaft und
Verkehr
Andreas-Schubert-Str. 23
01062 Dresden
Germany
donner@vwi.tu-dresden.de
Dr. Susana M. Barbosa
Universidade do Porto
Fac. Ciencias
Depto. Matematica Aplicada
Rua do Campo Alegre 687
4169-007 Porto
Portugal
"For all Lecture Notes in Earth Sciences published till now please see final pages of the book"
ISBN: 978-3-540-78937-6 e-ISBN: 978-3-540-78938-3
Lecture Notes in Earth Sciences ISSN: 0930-0317
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Preface
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 processes 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
has been put forward by Udny Yule (studying the features of sunspot activity)
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 sufficiently studied by linear statistical methods. With mathematical developments in the fields of dynamic system's theory, exemplified by
Edward Lorenz's pioneering work, and fractal theory, starting with the early
fractal concepts inferred by Harold Edwin Hurst from the analysis of geophysical time series, nonlinear methods became available for time series analysis as
well. Over the last decades, these methods have attracted an increasing interest 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.
Surprisingly, although nonlinear methods have meanwhile become an established, but still developing toolbox for the analysis of geoscientific time
series, so far there has not been a book giving an overview over corresponding
applications of these methods. The aim of this volume is therefore to close this
apparent gap between the numerous excellent books on (i) geostatistics and
the "traditional" (linear) analysis of geoscientific time series, (ii) the nonlinear modelling of geophysical processes, and (iii) the theory of nonlinear time
series analysis.
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VI
Preface
This volume contains a collection of papers that were presented in a topical
session on "Applications of Nonlinear Time Series Analysis in the Geosciences"
at the General Assembly of the European Geosciences Union in Vienna from
April 15-20, 2007. More than 30 colleagues from various countries used this
opportunity to present and discuss their most recent results on the analysis of
time series from problems originated in the fields of climatology, atmospheric
sciences, hydrology, seismology, geodesy, and solar-terrestrial physics. Oral
and poster sessions included a total of 38 presentations, which attracted the
interest of many colleagues working both theoretically on and practically with
nonlinear methods of time series analysis in the geosciences. The feedback from
both presenters and audience has encouraged us to prepare this volume, which
is dedicated to both experts in nonlinear time series analysis and practitioners
in the various geoscientific disciplines who are in need of novel and advanced
analysis tools for their time series. In this volume, presentations shown at the
conference are complemented by invited contributions written by some of the
most distinguished colleagues in the field.
In order to allow the interested reader to easily find methods that are
suitable for his particular problems or questions, we have decided to arrange
this book in three parts that comprise typical applications from the fields of
climatology, geodynamics, and solar-terrestrial physics, respectively. However,
especially in the latter case, the assignment of the different subjects has not
always been unique, as there are obvious and rather strong links to the two
other fields. Moreover, we would like to note that there are methods whose
application has already become very common for studying problems from
either of these fields.
The first 7 chapters deal with problems from climatology and the atmospheric sciences. A. Gluhovsky discusses the potential of subsampling for the
analysis of atmospheric time series, which usually cannot be described by
a simple linear stochastic model. In such cases, traditional estimates of already very simple statistics can be significantly biased, a problem that can be
solved by using subsampling methods. J. Miksovsky, P. Pisoft, and A. Raidl
report results on the spatial patterns of nonlinearity in simulations of global
circulation models as well as reanalysis data. S. Hallerberg, J. Brocker, and
H. Kantz discuss different methods for the prediction of extreme events, a challenging problem of contemporary interest in various geoscientific disciplines.
D.B. Percival presents an overview about the use of the discrete wavelet transform for the analysis of climatological time series, with a special consideration
of ice thickness and oxygen isotope data. G.S. Duane and J.P. Hacker describe
a framework for automatic parameter estimation in atmospheric models based
on the theory of synchronisation. W.W. Hsieh and A.J. Cannon report on
recent improvements on nonlinear generalisations of traditional multivariate
methods like principal component analysis and canonical correlation analysis,
which are based on the application of neural networks and allow the extraction
of nonlinear, dynamically relevant components. R. Donner, T. Sakamoto, and
N. Tanizuka discuss methods for quantifying the complexity of multivariate
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Preface
VII
time series, and how such concepts can be used to study variations and spatiotemporal dependences of climatological observables. As a particular example,
the case of Japanese air temperature records is considered.
The next 5 chapters describe the analysis of time series in the fields of
oceanography and seismology. S.M. Barbosa, M.E. Silva, and M.J. Fernandes
discuss the issue of characterising the long-term variability of sea-level records
in the presence of nonstationarities, trends, or long-term memory. A. Ardalan
and H. Hashemi describe a framework for the empirical modelling of global
ocean tide and sea level variability using time series from satellite altimetry.
J.A. Hawkins, A. Warn-Varnas, and I . Christov use different linear as well as
nonlinear Fourier-type techniques for the analysis of internal gravity waves
from oceanographic time series. M.E. Ramirez, M . Berrocoso, M.J. Gonzalez,
and A. Fernandez describe a time-frequency analysis of GPS data from the
Deception Island Volcano (Southern Shetland Islands) for the estimation of
local crustal deformation. A. Jimenez, A . M . Posadas, and K.F. Tiampo use
a cellular automaton approach to derive a simple statistical model for the
spatio-temporal variability of seismic activity in different tectonically active
regions.
The final 4 chapters discuss problems related to dynamical processes on
the Sun and their relationship to the complex system "Earth". I . M . Moroz
uses a topological method, the so-called template analysis, to study the internal structure of chaos in the Hide-Skeldon-Acheson dynamo, and compares her results with those for the well-known Lorenz model. N.G. Mazur,
V.A. Pilipenko, and K.-H. Glassmeier describe a framework for the analysis of solitary wave signals in geophysical time series, particularly satellite
observations of electromagnetic disturbances in the near-Earth environment.
M . Palus and D. Novotna introduce a nonlinear generalisation of singular
spectrum analysis that can be used to derive dynamically meaningful oscillatory components from atmospheric, geomagnetic, and solar variability signals.
Finally, R. Donner demonstrates the use of phase coherence analysis for understanding the long-term dynamics of the north-south asymmetry of sunspot
activity.
We would like to express our sincerest thanks to those people who made
the idea of this book becoming reality: the authors, who prepared their excellent results for publication in this book and the numerous referees, who helped
us evaluating the scientific quality of all contributions and making them being ready for publication. We also acknowledge the support of Springer at all
stages during the preparation of this book. We do very much hope that it will
inspire many readers in their own scientific research.
Reik Donner
Susana Barbosa
Dresden / Porto,
January 2008
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Contents
P a r t I A p p l i c a t i o n s i n C l i m a t o l o g y and A t m o s p h e r i c Sciences
Subsampling M e t h o d o l o g y f o r the Analysis o f N o n l i n e a r
A t m o s p h e r i c T i m e Series
Alexander Gluhovsky
3
Global Patterns of Nonlinearity in Real and GCM-Simulated
Atmospheric Data
Jifi Miksovsky, Petr Pisoft, Ales Raidl
17
Prediction of Extreme Events
Sarah Hallerberg, Jochen Brocket,
35
Holger Kantz
Analysis of Geophysical Time Series Using Discrete Wavelet
Transforms: A n O v e r v i e w
Donald B. Percival
61
Automatic Parameter Estimation in a Mesoscale Model
W i t h o u t Ensembles
Gregory S. Duane, Joshua P. Hacker
81
Towards Robust Nonlinear Multivariate Analysis by Neural
Network Methods
William W. Hsieh, Alex J. Cannon
97
Complexity of Spatio-Temporal Correlations in Japanese Air
T e m p e r a t u r e Records
Reik Donner, Takahide Sakamoto, Noboru Tanizuka
125
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X
Contents
P a r t I I A p p l i c a t i o n s i n Oceanography and Seismology
Time Series Analysis of Sea-Level Records: Characterising
Long-Term Variability
Susana M. Barbosa, Maria Eduarda Silva, Maria Joana Fernandes
157
Empirical Global Ocean Tide and Mean Sea Level Modeling
U s i n g Satellite A l t i m e t r y D a t a Case S t u d y : A N e w E m p i r i c a l
G l o b a l Ocean T i d e and M e a n Sea Level M o d e l Based o n
Jason-1 Satellite A l t i m e t r y Observations
Alireza A. Ardalan, Hassan Hashemi
1*»
Fourier, Scattering, and Wavelet Transforms: Applications to
I n t e r n a l G r a v i t y Waves w i t h Comparisons t o Linear T i d a l
Data
James A. Hawkins, Alex Warn-Varnas, Ivan Christov
223
Crustal Deformation Models and Time-Frequency Analysis of
GPS D a t a f r o m D e c e p t i o n Island Volcano ( S o u t h S h e t l a n d
Islands, A n t a r c t i c a )
Maria Eva Ramirez, Manuel Berrocoso, Maria Jose Gonzalez,
Alberto Fernandez
245
Describing Seismic Pattern Dynamics by Means of Ising
Cellular A u t o m a t a
Abigail Jimenez, Antonio M. Posadas, Kristy F. Tiampo
273
P a r t I I I A p p l i c a t i o n s i n Solar-Terrestrial Physics
Template Analysis of the Hide, Skeldon, Acheson Dynamo
Irene M. Moroz
293
Methods to Detect Solitons in Geophysical Signals: The Case
of the D e r i v a t i v e N o n l i n e a r Schrodinger E q u a t i o n
Nikolay G. Mazur, Viacheslav A. Pilipenko, Karl-Heinz Glassmeier
. . . . 311
Detecting Oscillations Hidden in Noise: Common Cycles in
A t m o s p h e r i c , Geomagnetic and Solar D a t a
Milan Palus, Dagmar Novotnd
327
Phase Coherence Analysis of Decadal-Scale Sunspot Activity
on B o t h Solar Hemispheres
Reik Donner
355
Index
387
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