Nonlinear Time Series Analysis in the Geosciences: Applications in Climatology, Geodynamics and Solar-Terrestrial Physics [proof]

394 Pages·2008·24.052 MB·English

by  Reik Donner,  Susana Barbosa

Preface F
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The enormous progress over the last decades in ourPunderstanding 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
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of such data which are of special importance for studying the dynamical pro-
cesses in complex systems. Time series analysis theory and applications in
geo- and astrophysics have always been mutuEally stimulating, starting with
classical (linear) problems like the proper estimation of power spectra, which
hasbeenputforwardbyUdnyYule(studyTingthefeaturesofsunspotactivity)
and, later, by John Tukey.
In the second half of the 20th centuCry, more and more evidence has been
accumulated that most processes in nature are intrinsically non-linear and
thuscannotbesufficientlystudiedbylinearstatisticalmethods.Withmathe-
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maticaldevelopmentsinthefieldsofdynamicsystem’stheory,exemplifiedby
Edward Lorenz’s pioneering work, and fractal theory, starting with the early
fractalconceptsinferredbyHaroRldEdwinHurstfromtheanalysisofgeophys-
icaltimeseries,nonlinearmethodsbecameavailablefortimeseriesanalysisas
well.Overthelastdecades,thesemethodshaveattractedanincreasinginter-
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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 (EGUO) have reacted to these trends with the formation of
specialnonlinearfocusgroupsandtopicalsections,whichareactivelypresent
at the corresponding annual assemblies.
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Surprisingly, although nonlinear methods have meanwhile become an es-
tablished, but still developing toolbox for the analysis of geoscientific time
series,sofartherehasnotbeenabookgivinganoverviewovercorresponding
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applicationsofthesemethods.Theaimofthisvolumeisthereforetoclosethis
apparent gap between the numerous excellent books on (i) geostatistics and
the “traditionUal” (linear) analysis of geoscientific time series, (ii) the nonlin-
ear modelling of geophysical processes, and (iii) the theory of nonlinear time
series analysis.
VI Preface
Thisvolumecontainsacollectionofpapersthatwerepresentedinatopical
sessionon“ApplicationsofNonlinearTimeSeriesAnalysisintheGeosciences”
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
opportunitytopresentanddiscusstheirmostrecentresultsontheanFalysisof
time series from problems originated in the fields of climatology, atmospheric
sciences, hydrology, seismology, geodesy, and solar-terrestrial phOysics. Oral
and poster sessions included a total of 38 presentations, which attracted the
interestofmanycolleaguesworkingboththeoreticallyonandpracticallywith
nonlinearmethodsoftimeseriesanalysisinthegeosciences.ThOefeedbackfrom
bothpresentersandaudiencehasencouragedustopreparethisvolume,which
isdedicatedtobothexpertsinnonlineartimeseriesanalysisandpractitioners
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in the various geoscientific disciplines who are in need of novel and advanced
analysistoolsfortheirtimeseries.Inthisvolume,presentationsshownatthe
conference are complemented by invited contributionsPwritten 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
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this book in three parts that comprise typical applications from the fields of
climatology,geodynamics,andsolar-terrestrialphysics,respectively.However,
especially in the latter case, the assignment oEf 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
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application has already become very common for studying problems from
either of these fields.
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The first 7 chapters deal with problems from climatology and the atmo-
spheric sciences. A. Gluhovsky discusses the potential of subsampling for the
analysis of atmospheric time serieEs, which usually cannot be described by
a simple linear stochastic model. In such cases, traditional estimates of al-
readyverysimplestatisticscanRbesignificantlybiased,aproblemthatcanbe
solved by using subsampling methods. J. Mikˇsovsky´, P. Piˇsoft, and A. Raidl
report results on the spatial patterns of nonlinearity in simulations of global
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circulation models as well as reanalysis data. S. Hallerberg, J. Bro¨cker, and
H.Kantzdiscussdifferentmethodsforthepredictionofextremeevents,achal-
lenging problem of conteOmporary interest in various geoscientific disciplines.
D.B. Percivalpresentsanoverviewabouttheuseofthediscretewavelettrans-
formfortheanalysisofclimatologicaltimeseries,withaspecialconsideration
oficethicknessandoCxygenisotopedata.G.S.DuaneandJ.P.Hackerdescribe
aframeworkforautomaticparameterestimationinatmosphericmodelsbased
on the theory of synchronisation. W.W. Hsieh and A.J. Cannon report on
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recent improvements on nonlinear generalisations of traditional multivariate
methodslikeprincipalcomponentanalysisandcanonicalcorrelationanalysis,
whicharebasUedontheapplicationofneuralnetworksandallowtheextraction
ofnonlinear,dynamicallyrelevantcomponents.R.Donner,T.Sakamoto,and
N. Tanizuka discuss methods for quantifying the complexity of multivariate
Preface VII
timeseries,andhowsuchconceptscanbeusedtostudyvariationsandspatio-
temporal 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. FeFrnandes
discusstheissueofcharacterisingthelong-termvariabilityofsea-levelrecords
inthepresenceofnonstationarities,trends,orlong-termmemory.OA.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 lOinear 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. Gonza´lez,
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and A. Ferna´ndez describe a time-frequency analysis of GPS data from the
Deception Island Volcano (Southern Shetland Islands) for the estimation of
local crustal deformation. A. Jim´enez, A.M. Posadas,Pand 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.
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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 temEplate analysis, to study the in-
ternal structure of chaos in the Hide-Skeldon-Acheson dynamo, and com-
pares her results with those for the well-known Lorenz model. N.G. Mazur,
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V.A. Pilipenko, and K.-H. Glassmeier describe a framework for the analy-
sis of solitary wave signals in geophysical time series, particularly satellite
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observations of electromagnetic disturbances in the near-Earth environment.
M. Paluˇs and D. Novotna´ introduce a nonlinear generalisation of singular
spectrum analysis that can be usedEto derive dynamically meaningful oscilla-
torycomponentsfromatmospheric,geomagnetic,andsolarvariabilitysignals.
Finally, R. Donner demonstrateRs the use of phase coherence analysis for un-
derstandingthelong-termdynamicsofthenorth-southasymmetryofsunspot
activity.
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We would like to express our sincerest thanks to those people who made
theideaofthisbookbecomingreality:theauthors,whopreparedtheirexcel-
lentresultsforpublicatioOninthisbookandthenumerousreferees,whohelped
us evaluating the scientific quality of all contributions and making them be-
ing ready for publication. We also acknowledge the support of Springer at all
stagesduringthepreCparationofthisbook.Wedoverymuchhopethatitwill
inspire many readers in their own scientific research.
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Dresden / Porto, Reik Donner
January 2008 Susana Barbosa
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Contents F
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Part I Applications in Climatology and AtmosPpheric Sciences
Subsampling Methodology for the Analysis of Nonlinear

Atmospheric Time Series
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Alexander Gluhovsky ............................................. 3
Global Patterns of Nonlinearity in RealEand GCM-Simulated
Atmospheric Data
Jiˇr´ı Mikˇsovsk´y, Petr Piˇsoft, Aleˇs Raidl.............................. 17
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Prediction of Extreme Events
Sarah Hallerberg, Jochen Bro¨cker, HolgCer Kantz ..................... 35
Analysis of Geophysical Time Series Using Discrete Wavelet
Transforms: An Overview E
Donald B. Percival............................................... 61
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Automatic Parameter Estimation in a Mesoscale Model
Without Ensembles
Gregory S. Duane, Joshua PR. Hacker ............................... 81
Towards Robust Nonlinear Multivariate Analysis by Neural
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Network Methods
William W. Hsieh, Alex J. Cannon................................. 97
Complexity of SpaCtio-Temporal Correlations in Japanese Air
Temperature Records
Reik Donner, Takahide Sakamoto, Noboru Tanizuka ..................125
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X Contents
Part II Applications in Oceanography and Seismology
Time Series Analysis of Sea-Level Records: Characterising
Long-Term Variability F
Susana M. Barbosa, Maria Eduarda Silva, Maria Joana Fernandes ....157
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Empirical Global Ocean Tide and Mean Sea Level Modeling
Using Satellite Altimetry Data Case Study: A New Empirical
Global Ocean Tide and Mean Sea Level Model Based on
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Jason-1 Satellite Altimetry Observations
Alireza A. Ardalan, Hassan Hashemi ...............................175
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Fourier, Scattering, and Wavelet Transforms: Applications to
Internal Gravity Waves with Comparisons to Linear Tidal
Data P
Jim A. Hawkins, Alex Warn-Varnas, Ivan Christov ..................223

Crustal Deformation Models and Time-Frequency Analysis of
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GPS Data from Deception Island Volcano (South Shetland
Islands, Antarctica)
Mar´ıa Eva Ram´ırez, Manuel Berrocoso, MarE´ıa Jos´e Gonz´alez,
A. Ferna´ndez....................................................245
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Describing Seismic Pattern Dynamics by Means of Ising
Cellular Automata
Abigail Jim´enez, Antonio M. Posadas,CKristy F. Tiampo..............273
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Part III Applications in Solar-Terrestrial Physics
Template Analysis of the HRide, Skeldon, Acheson Dynamo
Irene M. Moroz..................................................293
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Methods to Detect Solitons in Geophysical Signals: The Case
of the Derivative Nonlinear Schro¨dinger Equation
Nikolay G. Mazur, ViachOeslav A. Pilipenko, Karl-Heinz Glassmeier ....311
Detecting Oscillations Hidden in Noise: Common Cycles in
Atmospheric, GeoCmagnetic and Solar Data
Milan Paluˇs, Dagmar Novotn´a.....................................327
Phase CoherenNce Analysis of Decadal-Scale Sunspot Activity
on Both Solar Hemispheres
Reik Donner ....................................................353
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List of Contributors F AU: Please provide
e-mail(cid:160)id(cid:160)for(cid:160)all(cid:160)the
O missing(cid:160)contributions.
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Alireza A. Ardalan Alex J. CanPnon
Department of Surveying and Meteorological Service of Canada,
Geomatics Engineering, Environment Canada,

Center of Excellence in Surveying 201-401 BDurrard Street,
EngineeringandDisasterPrevention, Vancouver, BC,
Faculty of Engineering, Canada V6C 3S5,
University of Tehran, e-maiEl: [email protected]
Tehran-Iran,
e-mail: [email protected] IvTan Christov
Naval Research Laboratory,
CStennis Space Center,
Susana M. Barbosa MS 39529, USA;
Universidade do Porto, Northwestern University,
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Faculdade de Ciˆencias, Evanston, IL 60208, USA
e-mail: [email protected]
R Reik Donner
Institute for Transport and
Manuel Berrocoso
Economics,
Laboratorio de Astronom´ıa,R
Dresden University of Technology,
Geodesia y Cartograf´ıa.
Andreas-Schubert-Str. 23, 01062
Departamento de Matem´aticas.
O Dresden, Germany,
Facultad de Ciencias.
e-mail: [email protected];
Universidad de Ca´diz.
Graduate School of Science,
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Osaka Prefecture University,
Jochen Bro¨cker 1-1 Gakuen-cho, Naka-ku,
Max Planck Institute Sakai-shi, 599-8531 Japan
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for the Physics of Complex
Systems, Gregory S. Duane
N¨othnitzer StUr. National Center for Atmospheric
38, D 01187 Dresden, Research, Boulder, CO,
Germany e-mail: [email protected]
XII List of Contributors
AU: Please provide Maria Joana Fernandes Hassan Hashemi
full(cid:160)affiliation. Universidade do Porto, Department of Surveying and
Faculdade de Ciˆencias Geomatics Engineering,
Center of Excellence in Surveying
A. Fern´andez EngineeringandDisasterPreFvention,
Laboratorio de Astronom´ıa, Faculty of Engineering,
Geodesia y Cartograf´ıa. University of Tehran, O
Departamento de Matem´aticas. Tehran-Iran,
Facultad de Ciencias. e-mail: [email protected]
Universidad de Ca´diz. O
Jim A. Hawkins
Karl-Heinz Glassmeier
Planning SystemsRInc.,
Institut fu¨r Geophysik und extrater-
Slidell, LA 70458, USA,
restrische Physik,
e-mail: [email protected]
Technische Universit¨at P
Braunschweig, Germany,
e-mail: [email protected] William W . Hsieh
DepartmeDnt of Earth and Ocean
Alexander Gluhovsky Sciences,
Department of Earth & Atmospheric University of British Columbia 6339
Sciences, StoresEroad,
DepartmentofStatistics,andPurdue Vancouver, BC, Canada V6T 1Z4,
Climate Change Research Center e-mTail: [email protected]
(PCCRC), Purdue University,
West Lafayette,
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Indiana 47907, USA, Abigail Jim´enez
e-mail: [email protected] Department of Earth Sciences
EBiological and Geological Sciences,
Mar´ııa Jos´e Gonz´alez University of Western Ontario,
Laboratorio de Astronom´ıa, R London, Canada,
Geodesia y Cartograf´ıa. e-mail: [email protected]
Departamento de Matem´aticas.
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Facultad de Ciencias.
Holger Kantz
Universidad de Ca´diz.
Max Planck Institute for the Physics
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of Complex Systems,
Joshua P. Hacker
No¨thnitzer Str. 38,
National Center for Atmospheric
D 01187 Dresden, Germany,
Research, Boulder, CCO
e-mail: [email protected]
Sarah Hallerberg
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Max Planck Institute for the Physics Nikolay G. Mazur
of Complex Systems, Institute of the Physics of the Earth,
N¨othnitzer StUr. 38, Russian Academy of Sciences,
D 01187 Dresden, Moscow, Russia,
Germany e-mail: [email protected]
List of Contributors XIII
Ji´ı Mikˇsovsky´ Petr Piˇsoft
Department of Meteorology and Department of Meteorology and
Environment Protection, Environment Protection,
Faculty of Mathematics and Physics, Faculty of Mathematics and Physics,
Charles University, Charles University, F
Prague, Czech Republic, Prague, Czech Republic
e-mail: O
[email protected] Antonio M. Posadas
Department of Applied Physics,
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Irene M. Moroz University of Almer´ıa,
Mathematical Institute, Spain,
24-29 St Giles’, e-mail: [email protected]
Oxford OX1 3LB, UK
e-mail: [email protected] Aleˇs Raidl
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Department of Meteorology and
Environment Protection,
Dagmar Novotn´a
Faculty of Mathematics and Physics,
Institute of Atmospheric Physics,
Charles UDniversity, Prague, Czech
Academy of Sciences of the Czech
Republic
Republic,
Boˇcn´ı II/1401, E
141 31 Prague 4, Czech Republic, Mar´ıa Eva Ram´ırez
e-mail: [email protected] Laboratorio de Astronom’ıa,
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Geodesia y Cartograf’ıa.
Departamento de Matem´aticas.
Milan Paluˇs C
Facultad de Ciencias.
Institute of Computer Science,
Universidad de C’adiz.,
Academy of Sciences of the Czech
Ee-mail: [email protected]
Republic,
Pod voda´renskou vˇeˇz´ı 2,
Takahide Sakamoto
182 07 Prague 8, Czech RepubliRc,
Electrical Engineering Course,
e-mail: [email protected]
Osaka Municipal Ikuno Technical
R High School,
Donald B. Percival 2-3-66 Ikuno-higashi, Ikuno-ku,
Applied Physics Laboratory, Osaka-shi, 544-0025 Japan,
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University of Washington, e-mail:
Box 355640, Seattle, WA, taka [email protected];
98195–5640, USA, C Graduate School of Science,
e-mail: [email protected] Osaka Prefecture University,
1-1 Gakuen-cho, Naka-ku, Sakai-shi,
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Viacheslav A. Pilipenko 599-8531 Japan
Space Research Institute,
Russian AcadUemy of Sciences, Maria Eduarda Silva AU: Please provide
Moscow, Russia, Universidade do Porto, full(cid:160)affiliation.
e-mail: pilipenko [email protected] Faculdade de Ciˆencias
XIV List of Contributors
Noboru Tanizuka Kristy F. Tiampo
Graduate School of Science, Department of Earth Sciences
Biological and Geological Sciences,
Osaka Prefecture University,
University of Western Ontario,
1-1 Gakuen-cho,
London, Canada F
Naka-ku,
Sakai-shi,
Alex Warn-Varnas
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599-8531 Japan, Naval Research Laboratory,
e-mail: Stennis Space Center,
[email protected] MS 39529, USA O
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