ALBERT

Note: Inhalt: 1 Einleitung. - 1.1 Alltägliche Probleme. - 1.2 Uni- und multivariate Daten. - 1.3 Wege ins Statistiklabyrinth. - 2 Statistische Grundlagen. - 2.1 Einführung in die Terminologie. - 2.2 Datentypen -Skalenniveaus. - 2.3 Korrelation. - 2.4 Regression. - 2.5 Lineare Regression. - 2.6 Multiplelineare Regression. - 2.7 Unimodale Modelle - die Gauß'sche Regression. - 2.8 Logistische und Gauß'sche logistische Regression. - 2.9 Interaktionen. - 2.10 Gewichtetes Mittel. - 2.11 Partielle Analysen. - 3 Datenmanipulationen. - 3.1 Normalverteilung und Transformationen. - 3.2 Standardisierungen. - 3.3 Transponieren, Umkodieren und Maskieren. - 4 Ähnlichkeits- und Distanzmaße. - 4.1 Qualitative Ähnlichkeitsmaße. - 4.2 Quantitative Ähnlichkeitsmaße. - 4.3 Distanzmaße. - 4.4 Vergleich der geschilderten Koeffizienten. - 5 Ordinationen - das Prinzip. - 5.1 Dimensionsreduktion als Analysestrategie. - 5.2 Polare Ordination. - 6 Korrespondenzanalyse (CA). - 6.1 Das Prinzip. - 6.2 Mathematische Artefakte - Probleme der CA. - 6.3 DCA {Detrended Correspondence Analysis). - 6.4 Zusammenfassendes zu Problemen der CA und DCA. - 7 Interpretation von CA und DCA. - 7.1 Zur Skalierung und Interpretation der Ordinationsdiagramme. - 7.2 Umweltvariablen-Interaktionen von Effekten. - 7.3 Ordination und Umweltdaten. - 8 Kanonische Ordination (constrained ordination). - 8.1 Prinzip der Kanonischen Korrespondenzanalyse (CCA). - 8.2 Interpretation eines CCA-Diagramms. - 8.3 Forward selection bei kanonischen Ordinationen. - 8.4 Überprüfung einer CCA. - 9 Hauptkomponentenanalyse (PCA). - 9.1 Das Prinzip - geometrische Herleitung. - 9.2 Das Prinzip - der mathematische Ansatz. - 9.3 Optionen bei einer PCA. - 9.4 Stärken und Schwächen der PCA. - 9.5 Faktorenanalyse. - 10 Lineare Methoden und Umweltdaten: PCA und RDA. - 10.1 Indirekte Ordination. - 10.2 Kanonische Ordination - Prinzip der Redundanzanalyse. - 10.3 Interpretation einer RDA. - 11 Partielle Ordination und variance partitioning. - 11.1 Kovariablen. - 11.2 Partielle PCA, CA, DCA. - 11.3 Partielle kanonische Ordination. - 11.4 Variance partitioning. - 12 Multidimensionale Skalierung. - 12.1 Der andere Weg zum Ziel. - 12.2 Metrische Multidimensionale Skalierung - Hauptkoordinatenanalyse. - 12.3 Nichtmetrische Multidimensionale Skalierung. - 12.3.1 Das Prinzip. - 12.3.2 NMDS - Optionen und Probleme. - 12.3.3 Ablauf einer NMDS. - 13 Klassifikation - das Prinzip. - 13.1 Das Wesen von Klassifikationen. - 13.2 Die wichtigsten Klassifikationsstrategien. - 14 Agglomerative Klassifikationsverfahren. - 14.1Clusteranalyse - Grundlagen. - 14.2 Auswertung von Dendrogrammen. - 15 Divisive Klassifikationsverfahren. - 15.1 Ordination Space Partitioning. - 15.2 TWINSPAN. - 15.3 Ablauf einer TWINSPAN-Analyse. - 15.4 Kritik an der TWINSPAN-Analyse. - 16 Sonstige Verfahren zur Beschreibung von Gruppenstrukturen. - 16.1 Nichthierarchische agglomerative Verfahren. - 16.2 Nichthierarchische divisive Verfahren. - 16.3 Numerische "treue"-basierte Verfahren. - 16.4 Diskriminanzanalyse. - 16.4.1 Das Prinzip. - 16.4.2 Voraussetzungen. - 16.4.3 Gütekriterien/Prüfung der Ergebnisse. - 17 Permutationsbasierte Tests. - 17.1 Das Prinzip von Permutationstests. - 17.2 Test auf Signifikanz von Ordinationsachsen. - 17.3 Mantel-Test. - 17.4 Gruppenvergleiche - Mantel-Tests und MRPP. - 17.5 Procrustes-Analysen. - 17.6 Indicator Species Analysis. - 17.7 Ausblick Randomisierungsverfahren. - Literatur. - Sachverzeichnis.

Note: Contents Theme 1 History of Antarctic Research 1.1 The Road to Gondwana via the Early SCAR Symposia / A. B. Ford 1.2 Exploring the Unknown: History of the First German South Polar Expedition 1901–1903 / C. Lüdecke Theme 2 Antarctica – The Old Core 2.1 Characteristics of Metamorphosed Banded Iron Formation and Its Relation to the Magnetic Anomaly in the Mt. Riiser-Larsen Area, Amundsen Bay, Enderby Land, Antarctica / M. Funaki, P. Dolinsky, N. Ishikawa, A. Yamazaki 2.2 Experimental Constraints on the Decompressional P-T Paths of Rundvågshetta Granulites, Lützow-Holm Complex, East Antarctica / T. Kawasaki, Y. Motoyoshi 2.3 Sapphirine – Orthopyroxene – Garnet Granulite from Schirmacher Hills, Central Dronning Maud Land / S. Baba, M. Owada, E. S. Grew, K. Shiraishi 2.4 Genesis of Ferropotassic A-Type Granitoids of Mühlig-Hofmannfjella, Central Dronning Maud Land, East Antarctica / M. J. D’Souza, A. V. K. Prasad, R. Ravindra 2.5 Late Pan-African Fluid Infiltration in the Mühlig-Hofmann- and Filchnerfjella of Central Dronning Maud Land, East Antarctica / A. K. Engvik, S. Elvevold 2.6 Electron Microprobe (EMP) Dating on Monazite from Forefinger Point Granulites, East Antarctica: Implication for Pan-African Overprint / Y. Motoyoshi, T. Hokada, K. Shiraishi 2.7 Tectonic Subdivision of the Prince Charles Mountains: A Review of Geologic and Isotopic Data / E. V. Mikhalsky, A. A. Laiba, B. V. Beliatsky 2.8 Crustal Provinces of the Prince Charles Mountains Region and Surrounding Areas in the Light of Aeromagnetic Data / A. V. Golynsky, V. N. Masolov, V. S. Volnukhin, D. A. Golynsky 2.9 Magnetic Anomalies of the Grove Mountains Region and Their Geological Significance / A. V. Golynsky, D. A. Golynsky, V. N. Masolov, V. S. Volnukhin Theme 3 The Continent Beneath the Ice 3.1 ADMAP – A Digital Magnetic Anomaly Map of the Antarctic / A. V. Golynsky, M. Chiappini, D. Damaske, F. Ferraccioli, C. A. Finn, T. Ishihara, H. R. Kim, L. Kovacs, V. N. Masolov, P. Morris, R. von Frese 3.2 Identifying Major Sedimentary Basins Beneath the West Antarctic Ice Sheet from Aeromagnetic Data Analysis / R. E. Bell, M. Studinger, G. Karner, C. A. Finn, D. D. Blankenship 3.3 Bedrock Plateaus within the Ross Embayment and beneath the West Antarctic Ice Sheet, Formed by Marine Erosion in Late Tertiary Time / D. S. Wilson, B. P. Luyendyk 3.4 Inversion of Airborne Gravity Data Acquired over Subglacial Lakes in East Antarctica / I. Y. Filina, D. D. Blankenship, L. Roy, M. K. Sen, T. G. Richter, J. W. Holt 3.5 Russian Geophysical Studies of Lake Vostok, Central East Antarctica / V. N. Masolov, S. V. Popov, V. V. Lukin, A. N. Sheremetyev, A. M. Popkov 3.6 Morphology of the Subglacial Bed Relief of Lake Vostok Basin Area (Central East Antarctica) Based on RES and Seismic Data / S. V. Popov, A. N. Lastochkin, V. N. Masolov, A. M. Popkov 3.7 Deep Reflection Imaging beneath the Mizuho Plateau, East Antarctica, by SEAL-2002 Seismic Experiment / M. Yamashita, H. Miyamachi, M. Kanao, T. Matsushima, S. Toda, M. Takada, A. Watanabe 3.8 Seismic Anisotropy beneath Northern Victoria Land from SKS Splitting Analysis / S. Pondrelli, L. Margheriti, S. Danesi Theme 4 Gondwana Margins in Antarctica 4.1 Scouting Craton’s Edge in Paleo-Pacific Gondwana / C. A. Finn, J. W. Goodge, D. Damaske, C. M. Fanning 4.2 The Matusevich Fracture Zone in Oates Land, East Antarctica / G. Kleinschmidt, A. L. Läufer 4.3 Tectonic Model for Development of the Byrd Glacier Discontinuity and Surrounding Regions of the Transantarctic Mountains during the Neoproterozoic – Early Paleozoic / E. Stump, B. Gootee, F. Talarico 4.4 Depositional Environments of the Byrd Group, Byrd Glacier Area: A Cambrian Record of Sedimentation, Tectonism, and Magmatism / B. Gootee, E. Stump 4.5 Late-Ross Structures in the Wilson Terrane in the Rennick Glacier Area (Northern Victoria Land, Antarctica) / A. L. Läufer, G. Kleinschmidt, F. Rossetti 4.6 Style of Uplift of Paleozoic Terranes in Northern Victoria Land, Antarctica: Evidence from K-Ar Age Patterns / C. J. Adams Theme 5 Antarctic Peninsula Active Margin Tectonics 5.1 Patagonia – Antarctica Connections before Gondwana Break-Up / F. Hervé, H. Miller, C. Pimpirev 5.2 Moho Depth along the Antarctic Peninsula and Crustal Structure across the Landward Projection of the Hero Fracture Zone / T. Janik, P. Þroda, M. Grad, A. Guterch 5.3 Crustal Thinning and the Development of Deep Depressions at the Scotia- Antarctic Plate Boundary (Southern Margin of Discovery Bank, Antarctica) / J. Galindo-Zaldívar, J. C. Balanyá, F. Bohoyo, A. Jabaloy, A. Maldonado, J. M. Martínez-Martínez, J. Rodríguez-Fernández, E. Suriñach 5.4 Bransfield Basin Tectonic Evolution / J. Galindo-Zaldívar, L. Gamboa , A. Maldonado, S. Nakao, Y. Bochu 5.5 The Sedimentary Sequences of Hurd Peninsula, Livingston Island, South Shetland Islands: Part of the Late Jurassic–Cretaceous Depositional History of the Antarctic Peninsula / C. Pimpirev, K. Stoykova, M. Ivanov, D. Dimov 5.6 Regional Structures and Geodynamic Evolution of North Greenwich (Fort Williams Point) and Dee Islands, South Shetland Islands / J. F. Dumont, E. Santana, F. Hervé, C. Zapata 5.7 The Eocene Volcaniclastic Sejong Formation, Barton Peninsula, King George Island, Antarctica: Evolving Arc Volcanism from Precursory Fire Fountaining to Vulcanian Eruptions / S. B. Kim, Y. K. Sohn, M. Y. Choe 5.8 Elephant Island Recent Tectonics in the Framework of the Scotia-Antarctic-South Shetland Block Triple Junction (NE Antarctic Peninsula) / J. Galindo-Zaldívar, A. Maestro, J. López-Martínez, C. S. de Galdeano 5.9 Tectonics and Geomorphology of Elephant Island, South Shetland Islands / J. López-Martínez, R. A. J. Trouw, J. Galindo-Zaldívar, A. Maestro, L. S. A. Simões, F. F. Medeiros, C. C. Trouw 5.10 Geodynamical Studies on Deception Island: DECVOL and GEODEC Projects / M. Berrocoso, A. García-García, J. Martín-Dávila, M. Catalán-Morollón, M. Astiz, M. E. Ramírez, C. Torrecillas, J. M. E. de Salamanca Theme 6 Antarctic Rift Tectonics 6.1 Mawson Breccias Intrude Beacon Strata at Allan Hills, South Victoria Land: Regional Implications / D. H. Elliot, E. H. Fortner, C. B. Grimes 6.2 What Supports the Marie Byrd Land Dome? An Evaluation of Potential Uplift Mechanisms in a Continental Rift System / W. E. LeMasurier 6.3 A Multi-Phase Rifting Model for the Victoria Land Basin, Western Ross Sea / F. J. Davey, L. De Santis 6.4 Rift History of the Western Victoria Land Basin: A new Perspective Based on Integration of Cores with Seismic Reflection Data / C. R. Fielding, S. A. Henrys, T. J. Wilson 6.5 Constraints on the Timing of Extension in the Northern Basin, Ross Sea / S. C. Cande, J. M. Stock 6.6 The Structure of the Continental Margin off Wilkes Land and Terre Adélie Coast, East Antarctica / J. B. Colwell, H. M. J. Stagg, N. G. Direen, G. Bernardel, I. Borissova 6.7 Post-Rift Continental Slope and Rise Sediments from 38° E to 164° E, East Antarctica / P. E. O’Brien, S. Stanley, R. Parums Theme 7 Antarctic Neotectonics, Observatories and Data Bases 7.1 On Seismic Strain-Release within the Antarctic Plate / A. M. Reading 7.2 Vertical Crustal Deformation in Dronning Maud Land, Antarctica: Observation versus Model Prediction / M. Scheinert, E. Ivins, R. Dietrich, A. Rülke 7.3 Seismic Activity Associated with Surface Environmental Changes of the Earth System, around Syowa Station, East Antarctica / M. Kanao, K. Kaminuma 7.4 Geodynamic Features and Density Structure of the Earth’s Interior of the Antarctic and Surrounded Regions with the Gravimetric Tomography Method / R. Kh. Greku, V. P. Usenko, T. R. Greku 7.5 Some Recent Characteristics of Geomagnetic Secular Variations in Antarctica / A. Meloni, L. R. Gaya-Piqué, P. De Michelis, A. De Santis 7.6 Topographic and Geodetic Research by GPS, Echosounding and ERS Altimetric, and SAR Interferometric Surveys during Ukrainian Antarctic Expeditions in the West Antarctic / R. Greku, G. Milinevsky, Y. Ladanovsky, P. Bahmach, T. Greku 7.7 Geodetic Research o

Note: Introduction 1 Definitions 2 Historical Development of the Term Rockglacier 3 Rockglaciers: Description and Morphometry 3.1 General Description 3.2 Form Types 3.3 Morphometric Parameters 3.3.1 Rockglacier Sizes 3.3.2 Tongue-Shaped Rockg1aciers 3.3.3 Lobate Rockg1aciers 3.3.4 Rockglacier Thickness 3.3.5 Surface Relief 3.3.6 Rockglacier Surface and Source Area 4 Rockglacier Taxonomy 5 Rockglacier Distribution 5.1 General Information 5.2 Local Rockglacier Distribution 5.2.1 The Alps 5.2.2 The Mountains of Northern Europe 5.2.3 The Pyrenees 5.2.4 North American Mountains 5.2.5 The Andes of Central and South America 5.2.6 The Mountains of Asia 5.2.7 The Southern Alps 5.2.8 Antarctic Mountains 5.2.9 Conclusions 6 Rockglacier Material, Surficial Fabric and Internal Structure 6.1 Rock Type and Grain Size at and below the Surface 6.1.1 Rock Type 6.1.2 Grain Sizes at the Surface 6.1.3 Development of the Bouldery Mantle 6.1.4 Surface Fabric 6.1.5 Grain Sizes below the Bouldery Mantle 6.2 Internal Structure 6.2.1 Direct Information 6.2.1.1 Excavations, Outcrops, Tunnels 6.2.1.2 Smaller Boreholes 6.2.1.3 The Deep Borehole through the Rockglacier Murtel I 6.2.2 Indirect Information 6.2.2.1 Seismic Information 6.2.2.2 Geoelectric Soundings 6.2.2.3 Radio-Echo Soundings 6.2.2.4 Gravimetry 6.2.2.5 Borehole Geophysics and Related Measurements 6.2.2.6 BTS Measurements 6.2.2.7 Summary: The Inner Core of an Active Rockglacier 6.3 The Active Layer on Rockglaciers 7 Rockglacier Movement, Velocity, and Rheology 7.1 The Horizontal and Vertical Movement of Active Rockglaciers 7.1.1 Measurement Methods 7.1.2 Annual Horizontal Displacement 7.1.3 Long-Term Annual Averages 7.1.4 Long-Term Estimates 7.1.5 Longer Time Series 7.1.6 Monthly and Seasonal Measurements 7.1.7 Vertical Displacement 7.1.8 Conclusion 7.2 Geometry of Movement 7.2.1 The General Flow Patterns of Active Rockglaciers 7.2.1.1 Gruben Rockglacier 7.2.1.2 Macun Rockglacier 7.2.1.3 Arapaho Rockglacier 7.2.2 Horizontal Velocity on Longitudinal and Cross-Sectional Profiles 7.2.3 Surface and Subsurface Velocity 7.3 Rheologic Considerations 7.3.1 Shear Stress and Strain Rates in Active Rockglaciers 7.3.2 The Rheological Description of Active Rockglaciers 7.4 Rockglacier Movement and Climate 7.5 Discussion of Rockglacier Movement 8 Rockglacier Genesis and the Relation to Similar-Looking Landforms 8.1 Rockglacier Genesis 8.1.1 The Formation of Active Rockglaciers 8.1.1.1 Talus Rockglaciers 8.1.1.2 Debris Rockglaciers 8.1.1.3 Special Rockglaciers 8.1.1.4 Problematic Cases 8.1.2 Inactive Rockglaciers 8.1.3 Relict (Fossil) Rockglaciers 8.2 Published Hypotheses of Rockglacier Formation 8.2.1 Mass-Movement Hypotheses 8.2.1.1 The Bergsturz Hypothesis in General 8.2.1.2 Landslide Influences 8.2.2 The Glacial Hypothesis 8.2.2.1 Debris-Covered Glaciers and Thermokarst 8.2.2.2 Transition from True Glaciers to Rockglaciers? 8.2.2.3 The Moraine Hypothesis 8.2.3 The Periglacial (Blockstream) Hypothesis 8.3 True Rockglaciers under Wrong Labels 8.3.1 The Ostrem Ice-Cored Moraine Concept 8.3.2 The Protalus Rampart Concept 9 The Age of Rockglaciers 9.1 The Age of Active Rockglaciers 9.2 The Age of Climatic Inactive Rockglaciers 9.3 The Age of Relict (Fossil) Rockglaciers 10 Rockglaciers and the High Mountain Environment 10.1 Active Rockglaciers and Mountain Permafrost 10.2 Rockglaciers in the Coarse Debris Cycle 10.2.1 Rockglaciers and Talus Production 10.2.2 Rockglacier Size and Source Area 10.2.3 Rockglaciers as a Debris Transport System 10.3 Rockglaciers and Climate 10.3.1 Rockglaciers and Present Climate 10.3.2 Relict Rockglaciers and Paleoclimate Reconstruction 10.3.3 Reactivation of Inactive or Relict Rockglaciers 10.3.4 Rockglaciers and Climatic Change 10.4 Rockglaciers in the Alpine Hydrological Cycle 10.4.1 Rockglaciers as a Water Store 10.4.2 Discharge from Rockglacier Permafrost 10.4.3 Fluctuations in Rockglacier Permafrost Storage 10.5 Rockglaciers as Hazards in Alpine Environments 10.6 The Environment of Active Rockglaciers 11 Summary and Outstanding Problems 12 References Index of Place Names Subject Index

Note: Contents Preface 1 Data Analysis in Earth Sciences 1.1 Introduction 1.2 Collecting Data 1.3 Types of Data 1.4 Methods of Data Analysis Recommended Reading 2 Introduction to MATLAB 2.1 MATLAB in Earth Sciences 2.2 Getting Started 2.3 The Syntax 2.4 Data Storage 2.5 Data Handling 2.6 Scripts and Functions 2.7 Basic Visualization Tools Recommended Reading 3 Univariate Statistics 3.1 Introduction 3.2 Empirical Distributions Measures of Central Tendency Measures of Dispersion 3.3 Example of Empirical Distributions 3.4 Theoretical Distributions Uniform Distribution Binomial or Bernoulli Distribution Poisson Distribution Normal or Gaussian Distribution Logarithmic Normal or Log-Normal Distribution Student's t Distribution Fisher's F Distribution Χ2 or Chi-Squared Distribution 3.5 Example ofTheoretical Distributions 3.6 Thet-Test 3.7 TheF-Test 3.8 The Χ2-Test Recommended Reading 4 Bivariate Statistics 4.1 Introduction 4.2 Pearson's Correlation Coefficient 4.3 Classical Linear Regression Analysis and Prediction 4.4 Analyzing the Residuals 4.5 Bootstrap Estimates of the Regression Coefficients 4.6 Jackknife Estimates of the Regression Coefficients 4.7 Cross Validation 4.8 Reduced Major Axis Regression 4.9 Curvilinear Regression Recommended Reading 5 Time-Series Analysis 5.1 Introduction 5.2 Generating Signals 5.3 Blackman-Tukey Autospectral Analysis 5.4 Blackman-Tukey Crossspectral Analysis 5.5 Interpolating and Analyzing Unevenly-Spaced Data 5.6 Evolutionary Blackman-Tukey Powerspectrum 5.7 Lomb-Scargle Powerspectrum 5.8 Wavelet Powerspectrum 5.9 Nonlinear Time-Series Analysis (by N. Marwarn) Phase Space Portrait Recurrence Plots Recommended Reading 6 Signal Processing 6.1 Introduction 6.2 Generating Signals 6.3 Linear Time-Invariant Systems 6.4 Convolution and Filtering 6.5 Comparing Functions for Filtering Data Series 6.6 Recursive and Nonrecursive Filters 6.7 Impulse Response 6.8 Frequency Response 6.9 Filter Design 6.10 Adaptive Filtering Recommended Reading 7 Spatial Data 7.1 Types of Spatial Data 7.2 The GSHHS Shoreline Data Set 7.3 The 2-Minute Gridded Global Elevation Data ETOPO2 7.4 The 30-Arc Seconds Elevation Model GTOPO30 7.5 The Shuttle Radar Topography Mission SRTM 7.6 Gridding and Contouring Background 7.7 Gridding Example 7.8 Comparison of Methods and Potential Artifacts 7.9 Statistics of Point Distributions Test for Uniform Distribution Test for Random Distribution Test for Clustering 7.10 Analysis of Digital Elevation Models (by R. Gebbers) 7.11 Geostatistics and Kriging (by R. Gebbers) Theorical Background Preceding Analysis Variography with the Classical Variogram Kriging Discussion of Kriging Recommended Reading 8 Image Processing 8.1 Introduction 8.2 Datastorage 8.3 Importing, Processing and Exporting Images 8.4 Importing, Processing and Exporting Satellite Images 8.5 Georeferencing Satellite Images 8.6 Digitizing from the Screen Recommended Reading 9 Multivariate Statistics 9.1 Introduction 9.2 Principal Component Analysis 9.3 Independent Component Analysis (by N. Marwan) 9.4 Cluster Analysis Recommended Reading 10 Statistics on Directional Data 10.1 Introduction 10.2 Graphical Representation 10.3 Empirical Distributions 10.4 Theoretical Distributions 10.5 Test for Randomness of Directional Data 10.6 Test for the Significance of a Mean Direction 10.7 Test for the Difference of Two Sets of Directions Recommended Reading General Index

Note: Contents I Review of Current Concepts 1 Introduction 1.1 Sequence Stratigraphy: A New Paradigm? 1.2 From Sloss to Vail 1.3 Problems and Research Trends: The Current Status 1.4 Stratigraphic Terminology 2 Methods for Studying Sequence Stratigraphy 2.1 Introduction 2.2 Erecting a Sequence Framework 2.2.1 The Importance of Unconformities 2.2.2 Facies Cycles 2.2.3 Stratigraphic Architecture: The Seismic Method 2.3 Methods for Assessing Regional and Global Changes in Sea Level, Other Than Seismic Stratigraphy 2.3.1 Areas and Volumes of Stratigraphic Units 2.3.2 Hypsometric Curves 2.3.3 Backstripping 2.3.4 Sea-Level Estimation from Paleoshorelines and Other Fixed Points 2.3.5 Documentation of Meter-Scale Cycles 2.4 Integrated Tectonic-Stratigraphic Analysis 3 The Four Basic Types of Stratigraphic Cycle 3.1 Introduction 3.2 The Supercontinent Cycle 3.3 Cycles with Episodicities of Tens of Millions of Years 3.4 Cycles with Million-Year Episodicities 3.5 Cycles with Episodicities of Less Than One Million Years 4 The Basic Sequence Model 4.1 Introduction 4.2 Terminology 4.3 Depositional Systems and Systems Tracts 4.4 Sequence Boundaries 4.5 Other Sequence Concepts 5 The Global Cycle Chart II The Stratigraphic Framework 6 Cycles with Episodicities of Tens to Hundreds of Millions of Years 6.1 Climate, Sedimentation, and Biogenesis 6.2 The Supercontinent Cycle 6.2.1 The Tectonic-Stratigraphic Model 6.2.2 The Phanerozoic Record 6.3 Cycles with Episodicities of Tens of Millions of Years 6.3.1 Intercontinental Correlations 6.3.2 Tectonostratigraphic Sequences 6.4 Main Conclusions 7 Cycles with Million-Year Episodicities 7.1 Extensional and Rifted Clastic Continental Margins 7.2 Foreland Basin of the North American Western Interior 7.3 Other Foreland Basins 7.4 Forearc Basins 7.5 Backarc Basins 7.6 Cyclothems and Mesothems 7;7 Carbonate Cycles of Platforms and Craton Margins 7.8 Evidence of Cyclicity in the Deep Oceans 7.9 Main Conclusions 8 Cycles with Episodicities of Less Than One Million Years 8.1 Introduction 8.2 Neogene Clastic Cycles of Continental Margins 8.3 Pre-Neogene Marine Carbonate and Clastic Cycles 8.4 Late Paleozoic Cyclothems 8.5 Lacustrine elastic and Chemical Rhythms 8.6 Clastic Cycles of Foreland Basins 8.7 Main Conclusions III Mechanisms 9 Long-Term Eustasy and Epeirogeny 9.1 Mantle Processes and Dynamic Topography 9.2 Supercontinent Cycles 9.3 Cycles with Episodicities of Tens of Millions of Years 9.3.1 Eustasy 9.3.2 Dynamic Topography and Epeirogeny 9.4 Main Conclusions 10 Milankovitch Processes 10.1 Introduction 10.2 The Nature of Milankovitch Processes 10.2.1 Components of Orbital Forcing 10.2.2 Basic Climatology 10.2.3 Variations with Time in Orbital Periodicities 10.2.4 Isostasy and Geoid Changes 10.2.5 The Nature of the Cyclostratigraphic Data Base 10.2.6 The Sensitivity of the Earth to Glaciation 10.2.7 Glacioeustasy in the Mesozoic? 10.2.8 Nonglacial Milankovitch Cyclicity 10.3 The Cenozoic Record 10.4 Late Paleozoic Cyclothems 10.5 The End-Ordovician Glaciation 10.6 Main Conclusions 11 Tectonic Mechanisms 11.1 Introduction 11.2 Rifting and Thermal Evolution of Divergent Plate Margins 11.2.1 Basic Geophysical Models and Their Implications for Sea-Level Change 11.2.2 Some Results from the Analysis of Modern Data Sets 11.3 Tectonism on Convergent Plate Margins and in Collision Zones 11.3.1 Magmatic Arcs and Subduction 11.3.2 Tectonism Versus Eustasy in Foreland Basins 11.3.2.1 The North American Western Interior Basin 11.3.2.2 The Appalachian Foreland Basin 11.3.2.3 Pyrenean and Himalayan Basins 11.3.3 Rates of Uplift and Subsidence 11.3.4 Discussion 11.4 Intraplate Stress 11.4.1 The Pattern of Global Stress 11.4.2 In-Plane Stress as a Control of Sequence Architecture 11.4.3 In-Plane Stress and Regional Histories of Sea-Level Change 11.5 Basement Control 11.6 Other Speculative Tectonic Hypotheses 11.7 Sediment Supply and the Importance of Big Rivers 11.8 Environmental Change 11.9 Main Conclusions IV Chronostratigraphy and Correlation: Why the Global Cycle Chart Should Be Abandoned 12 Time in Sequence Stratigraphy 12.1 Introduction 12.2 Hierarchies of Time and the Completeness of the Stratigraphic Record 12.3 Main Conclusions 13 Correlation, and the Potential for Error 13.1 Introduction 13.2 The New Paradigm of Geological Time? 13.3 The Dating and Correlation of Stratigraphic Events: Potential Sources of Uncertainty 13.3.1 Identification of Sequence Boundaries 13.3.2 Chronostratigraphic Meaning of Unconformities 13.3.3 Determination of the Biostratigraphic Framework 13.3.3.1 The Problem of Incomplete Biostratigraphic Recovery 13.3.3.2 Diachroneity of the Biostratigraphic Record 13.3.4 The Value of Quantitative Biostratigraphic Methods 13.3.5 Assessment of Relative Biostratigraphic Precision 13.3.6 Correlation of Biozones with the Global Stage Framework 13.3.7 Assignment of Absolute Ages 13.3.8 Implications for the Exxon Global Cycle Chart 13.4 Correlating Regional Sequence Frameworks with the Global Cycle Chart 13.4.1 Circular Reasoning from Regional Data 13.4.2 A Rigorous Test of the Global Cycle Chart 13.4.3 A Correlation Experiment 13.4.4 Discussion 13.5 Main Conclusions 14 Sea-Level Curves Compared 14.1 Introduction 14.2 The Exxon Curves: Revisions, Errors, and Uncertainties 14.3 Other Sea-Level Curves 14.3.1 Cretaceous Sea-Level Curves 14.3.2 Jurassic Sea-Level Curves 14.3.3 Why Does the Exxon Global Cycle Chart Contain So Many More Events Than Other Sea-Level Curves? 14.4 Main Conclusions V Approaches to a Modern Sequence-Stratigraphic Framework 15 Elaboration of the Basic Sequence Model 15.1 Introduction 15.2 Definitions 15.2.1 The Hierarchy of Units and Bounding Surfaces 15.2.2 Systems Tracts and Sequence Boundaries 15.3 The Sequence Stratigraphy of Clastic Depositional Systems 15.3.1 Pluvial Deposits and Their Relationship to Sea-Level Change 15.3.2 The Concept of the Bayline 15.3.3 Deltas, Beach-Barrier Systems, and Estuaries 15.3.4 Shelf Systems: Sand Shoals and Condensed Sections 15.3.5 Slope and Rise Systems 15.4 The Sequence Stratigraphy of Carbonate Depositional Systems 15.4.1 Platform Carbonates: Catch-Up Versus Keep-Up 15.4.2 Carbonate Slopes 15.4.3 Pelagic Carbonate Environments 15.5 Main Conclusions 16 Numerical and Graphical Modeling of Sequences 16.1 Introduction 16.2 Model Design 16.3 Selected Examples of Model Results 16.4 Main Conclusions VI Discussion and Conclusions 17 Implications for Petroleum Geology 17.1 Introduction 17.2 Integrated Tectonic-Stratigraphic Analysis 17.2.1 The Basis of the Methodology 17.2.2 The Development of an Allostratigraphic Framework 17.2.3 Choice of Sequence-Stratigraphic Models 17.2.4 The Search for Mechanisms 17.2.5 Reservoir Characterization 17.3 Controversies in Practical Sequence Analysis 17.3.1 The Case of the Tocito Sandstone, New Mexico 17.3.2 The Case of Gippsland Basin, Australia 17.3.3 Conclusions: A Modified Approach to Sequence Analysis for Practicing Petroleum Geologists and Geophysicists 17.4 Main Conclusions 18 Conclusions and Recommendations 18.1 Sequences in the Stratigraphic Record 18.1.1 Long-Term Stratigraphic Cycles 18.1.2 Cycles with Million-Year Episodicities 18.1.3 Cycles with Episodicities of Less Than One Million Years 18.2 Mechanisms 18.2.1 Long-Term Eustasy and Epeirogeny 18.2.2 Milankovitch Processes 18.2.3 Tectonic Mechanisms 18.3 Chronostratigraphy and Correlation 18.3.1 Concepts of Time 18.3.2 Correlation Problems, and the Basis of the Global Cycle Chart 18.3.3 Comparison of Sea-Level Curves 18.4 Modern Sequence Analysis 18.4.1 Elaboration of the Basic Sequence Model 18.4.2 Numerical and Graphical Modeling of Stratigraphic Sequences 18.5 Implications for Petroleum Geology 18.6 The Global-Eustasy Paradigm: Working Backwards from the Answer? 18.6.1 The Exxon Factor 18.6.2 Conclusions . 18.7 Recommendations References Author Index Subject Index

Note: Contents Foreword Preface Contributors I Introduction 1 The Development of Climate Research / by ANTONIO NAVARRA 1.1 The Nature of Climate Studies 1.1.1 The Big Storm Controversy 1.1.2 The Great Planetary Oscillations 1.2 The Components of Climate Research 1.2.1 Dynamical Theory 1.2.2 Numerical Experimentation 1.2.3 Statistical Analysis 2 Misuses of Statistical Analysis in Climate Research / by HANS VON STORCH 2.1 Prologue 2.2 Mandatory Testing and the Mexican Hat 2.3 Neglecting Serial Correlation 2.4 Misleading Names: The Case of the Decorrelation Time 2.5 Use of Advanced Techniques 2.6 Epilogue II Analyzing The Observed Climate 3 Climate Spectra and Stochastic Climate Models / by CLAUDE FRANKIGNOUL 3.1 Introduction 3.2 Spectral Characteristics of Atmospheric Variables 3.3 Stochastic Climate Model 3.4 Sea Surface Temperature Anomalies 3.5 Variability of Other Surface Variables 3.6 Variability in the Ocean Interior 3.7 Long Term Climate Changes 4 The Instrumental Data Record: Its Accuracy and Use in Attempts to Identify the "CO2 Signal" / by PHIL JONES 4.1 Introduction 4.2 Homogeneity 4.2.1 Changes in Instrumentation, Exposure and Measuring Techniques 4.2.2 Changes in Station Locations 4.2.3 Changes in Observation Time and the Methods Used to Calculate Monthly Averages 4.2.4 Changes in the Station Environment 4.2.5 Precipitation and Pressure Homogeneity 4.2.6 Data Homogenization Techniques 4.3 Surface Climate Analysis 4.3.1 Temperature 4.3.2 Precipitation 4.3.3 Pressure 4.4 The Greenhouse Detection Problem 4.4.1 Definition of Detection Vector and Data Used 4.4.2 Spatial Correlation Methods 4.5 Conclusions 5 Interpreting High-Resolution Proxy Climate Data - The Example of Dendr о climatology / by KEITH R. BRIFFA 5.1 Introduction 5.2 Background 5.3 Site Selection and Dating 5.4 Chronology Confidence 5.4.1 Chronology Signal 5.4.2 Expressed Population Signal 5.4.3 Subsample Signal Strength 5.4.4 Wider Relevance of Chronology Signal 5.5 "Standardization" and Its Implications for Judging Theoretical Signal 5.5.1 Theoretical Chronology Signal 5.5.2 Standardization of "Raw" Data Measurements 5.5.3 General Relevance of the "Standardization" Problem 5.6 Quantifying Climate Signals in Chronologies 5.6.1 Calibration of Theoretical Signal 5.6.2 Verification of Calibrated Relationships 5.7 Discussion 5.8 Conclusions 6 Analysing the Boreal Summer Relationship Between World wide Sea-Surface Temperature and Atmospheric Variability / by M. NEIL WARD 6.1 Introduction 6.2 Physical Basis for Sea-Surface Temperature Forcing of the Atmosphere 6.2.1 Tropics 6.2.2 Extratropics 6.3 Characteristic Patterns of Global Sea Surface Temperature: EOFs and Rotated EOFs 6.3.1 Introduction 6.3.2 SST Data 6.3.3 EOF method 6.3.4 EOFs p^→1 - p^→3 6.3.5 Rotation of EOFs 6.4 Characteristic Features in the Marine Atmosphere Associated with the SST Patterns p^→2, p ^→3 and p^→2R in JAS 6.4.1 Data and Methods 6.4.2 Patterns in the Marine Atmosphere Associated with EOF p^→2 6.4.3 Patterns in the Marine Atmosphere Associated with EOF p^→3 6.4.4 Patterns in the Marine Atmosphere Associated with Rotated EOF p^→2R 6.5 JAS Sahel Rainfall Links with Sea-Surface Temperature and Marine Atmosphere 6.5.1 Introduction 6.5.2 Rainfall in the Sahel of Africa 6.5.3 High Frequency Sahel Rainfall Variations 6.5.4 Low Frequency Sahel Rainfall Variations 6.6 Conclusions III Simulating and Predicting Climate 7 The Simulation of Weather Types in GCMs : A Regional Approach to Control-Run Validation / by KEITH R. BRIFFA 7.1 Introduction 7.2 The Lamb Catalogue 7.3 An "Objective" Lamb Classification 7.4 Details of the Selected GCM Experiments 7.5 Comparing Observed and GCM Climates 7.5.1 Lamb Types 7.5.2 Temperature and Precipitation 7.5.3 Relationships Between Circulation Frequencies and Temperature and Precipitation 7.5.4 Weather-Type Spell Lengths and Storm Frequencies 7.6 Conclusions 7.6.1 Specific Conclusions 7.6.2 General Conclusions 8 Statistical Analysis of GCM Output / by CLAUDE FRANKIGNOUL 8.1 Introduction 8.2 Univariate Analysis 8.2.1 The i-Test on the Mean of a Normal Variable 8.2.2 Tests for Autocorrelated Variables 8.2.3 Field Significance 8.2.4 Example: GCM Response to a Sea Surface Temperature Anomaly 8.3 Multivariate Analysis 8.3.1 Test on Means of Multidimensional Normal Variables 8.3.2 Application to Response Studies 8.3.3 Application to Model Testing and Intercomparison 9 Field Intercomparison / by ROBERT E . LIVEZEY 9.1 Introduction 9.2 Motivation for Permutation and Monte Carlo Testing 9.2.1 Local vs. Field Significance 9.2.2 Test Example 9.3 Permutation Procedures 9.3.1 Test Environment 9.3.2 Permutation (PP) and Bootstrap (BP) Procedures 9.3.3 Properties 9.3.4 Interdependence Among Field Variables 9.4 Serial Correlation 9.4.1 Local Probability Matching 9.4.2 Times Series and Monte Carlo Methods 9.4.3 Independent Samples 9.4.4 Conservatism 9.5 Concluding Remarks 10 The Evaluation of Forecasts / by ROBERT E. LIVEZEY 10.1 Introduction 10.2 Considerations for Objective Verification 10.2.1 Quantification 10.2.2 Authentication 10.2.3 Description of Probability Distributions 10.2.4 Comparison of Forecasts 10.3 Measures and Relationships: Categorical Forecasts 10.3.1 Contingency and Definitions 10.3.2 Some Scores Based on the Contingency Table 10.4 Measures and Relationships: Continuous Forecasts 10.4.1 Mean Squared Error and Correlation 10.4.2 Pattern Verification (the Murphy-Epstein Decomposition) 10.5 Hindcasts and Cross-Validation 10.5.1 Cross-Validation Procedure 10.5.2 Key Constraints in Cross-Validation 11 Stochastic Modeling of Precipitation with Applications to Climate Model Downscaling / by DENNIS LETTENMAIER 11.1 Introduction 11.2 Probabilistic Characteristics of Precipitation 11.3 Stochastic Models of Precipitation 11.3.1 Background 11.3.2 Applications to Global Change 11.4 Stochastic Precipitation Models with External Forcing 11.4.1 Weather Classification Schemes 11.4.2 Conditional Stochastic Precipitation Models 11.5 Applications to Alternative Climate Simulation 11.6 Conclusions IV Pattern Analysis 12 Teleconnections Patterns / by ANTONIO NAVARRA 12.1 Objective Teleconnections 12.2 Singular Value Decomposition 12.3 Teleconnections in the Ocean-Atmosphere System 12.4 Concluding Remarks 13 Spatial Patterns: EOFs and CCA / by HANS VON STORCH 13.1 Introduction 13.2 Expansion into a Few Guess Patterns 13.2.1 Guess Patterns, Expansion Coefficients and Explained Variance 13.2.2 Example: Temperature Distribution in the Mediterranean Sea 13.2.3 Specification of Guess Patterns 13.2.4 Rotation of Guess Patterns 13.3 Empirical Orthogonal Functions 13.3.1 Definition of EOFs 13.3.2 What EOFs Are Not Designed for 13.3.3 Estimating EOFs 13.3.4 Example: Central European Temperature 13.4 Canonical Correlation Analysis 13.4.1 Definition of Canonical Correlation Patterns 13.4.2 CCA in EOF Coordinates 13.4.3 Estimation: CCA of Finite Samples 13.4.4 Example: Central European Temperature 14 Patterns in Time : SSA and MSSA / by ROBERT VAUTARD 14.1 Introduction 14.2 Reconstruction and Approximation of Attractors 14.2.1 The Embedding Problem 14.2.2 Dimension and Noise 14.2.3 The Macroscopic Approximation 14.3 Singular Spectrum Analysis 14.3.1 Time EOFs 14.3.2 Space-Time EOFs 14.3.3 Oscillatory Pairs 14.3.4 Spectral Properties 14.3.5 Choice of the Embedding Dimension 14.3.6 Estimating Time and Space-Time Patterns 14.4 Climatic Applications of SSA 14.4.1 The Analysis of Intraseasonal Oscillations 14.4.2 Empirical Long-Range Forecasts Using MSSA Predictors 14.5 Conclusions 15 Multivariate Statistical Modeling : POP-Model as a First Order Approximation / by JIN-SONG VON STORCH 15.1 Introduction 15.2 The Cross-Covariance Matrix and the Cross-Spectrum Matrix 15.3 Multivariate AR(1) Process and its Cross-Covariance and Cross-Spectrum Matrices 15.3.1 The System Matrix A and its POPs 15.3.2 Cross-Spectrum Matrix in POP-Basis: Its Matrix Formulation 15.3.3 Cross-Spectrum Matrix in POP-Basis: Its Diagonal Components 15.3.4

Note: Inhalt Geleitwort Danksagung Bildnachweis 1 Einleitung 2 Vom Wetter zum Klima 3 Das Klima der Vergangenheit Die Kleine Eiszeit Die quartären Vereisungen Die Geschichte des Klimas seit der Entstehung der Erde 4 Die Luft und das Wasser - die treibenden Elemente des Planeten Die atmosphärische Zirkulation Die ozeanische Zirkulation 5 Die Funktionsweise der Klimamaschine Luft und Wasser treten in Aktion Eis und Klima Das Leben und das Klima 6 Der Mensch und das Klima Die Treibhausgase Folgen der Verstärkung des Treibhauseffektes Das Ozon 7 Vorbereitung auf die Zukunft Literaturverzeichnis

Note: Contents 1. Introduction 1.1 Historical Background 1.2 Some Examples of Spectral Methods 1.2.1 A Fourier Galerkin Method for the Wave Equation 1.2.2 A Chebyshev Collocation Method for the Heat Equation 1.2.3 A Legendre Galerkin with Numerical Integration (G-NI) Method for the Advection-Diffusion-Reaction Equation 1.2.4 A Legendre Tau Method for the Poisson Equation 1.2.5 Basic Aspects of Galerkin, Collocation, G-NI and Tau Methods 1.3 Three-Dimensional Applications in Fluids: A Look Ahead 2. Polynomial Approximation 2.1 The Fourier System 2.1.1 The Continuous Fourier Expansion 2.1.2 The Discrete Fourier Expansion 2.1.3 Differentiation 2.1.4 The Gibbs Phenomenon 2.2 Orthogonal Polynomials in (−1, 1) 2.2.1 Sturm-Liouville Problems 2.2.2 Orthogonal Systems of Polynomials 2.2.3 Gauss-Type Quadratures and Discrete Polynomial Transforms 2.3 Legendre Polynomials 2.3.1 Basic Formulas 2.3.2 Differentiation 2.3.3 Orthogonality, Diagonalization and Localization 2.4 Chebyshev Polynomials 2.4.1 Basic Formulas 2.4.2 Differentiation 2.5 Jacobi Polynomials 2.6 Approximation in Unbounded Domains 2.6.1 Laguerre Polynomials and Laguerre Functions 2.6.2 Hermite Polynomials and Hermite Functions 2.7 Mappings for Unbounded Domains 2.7.1 Semi-Infinite Intervals 2.7.2 The Real Line 2.8 Tensor-Product Expansions 2.8.1 Multidimensional Mapping 2.9 Expansions on Triangles and Related Domains 2.9.1 Collapsed Coordinates and Warped Tensor-Product Expansions 2.9.2 Non-Tensor-Product Expansions 2.9.3 Mappings 3. Basic Approaches to Constructing Spectral Methods 3.1 Burgers Equation 3.2 Strong and Weak Formulations of Differential Equations 3.3 Spectral Approximation of the Burgers Equation 3.3.1 Fourier Galerkin 3.3.2 Fourier Collocation 3.3.3 Chebyshev Tau 3.3.4 Chebyshev Collocation 3.3.5 Legendre G-NI 3.4 Convolution Sums 3.4.1 Transform Methods and Pseudospectral Methods 3.4.2 Aliasing Removal by Padding or Truncation 3.4.3 Aliasing Removal by Phase Shifts 3.4.4 Aliasing Removal for Orthogonal Polynomials 3.5 Relation Between Collocation, G-NI and Pseudospectral Methods 3.6 Conservation Forms 3.7 Scalar Hyperbolic Problems 3.7.1 Enforcement of Boundary Conditions 3.7.2 Numerical Examples 3.8 Matrix Construction for Galerkin and G-NI Methods 3.8.1 Matrix Elements 3.8.2 An Example of Algebraic Equivalence between G-NI and Collocation Methods 3.9 Polar Coordinates 3.10 Aliasing Effects 4. Algebraic Systems and Solution Techniques 4.1 Ad-hoc Direct Methods 4.1.1 Fourier Approximations 4.1.2 Chebyshev Tau Approximations 4.1.3 Galerkin Approximations 4.1.4 Schur Decomposition and Matrix Diagonalization 4.2 Direct Methods 4.2.1 Tensor Products of Matrices 4.2.2 Multidimensional Stiffness and Mass Matrices 4.2.3 Gaussian Elimination Techniques 4.3 Eigen-Analysis of Spectral Derivative Matrices 4.3.1 Second-Derivative Matrices 4.3.2 First-Derivative Matrices 4.3.3 Advection-Diffusion Matrices 4.4 Preconditioning 4.4.1 Fundamentals of Iterative Methods for Spectral Discretizations 4.4.2 Low-Order Preconditioning of Model Spectral Operators in One Dimension 4.4.3 Low-Order Preconditioning in Several Dimensions 4.4.4 Spectral Preconditioning 4.5 Descent and Krylov Iterative Methods for Spectral Equations 4.5.1 Multidimensional Matrix-Vector Multiplication 4.5.2 Iterative Methods 4.6 Spectral Multigrid Methods 4.6.1 One-Dimensional Fourier Multigrid Model Problem 4.6.2 General Spectral Multigrid Methods 4.7 Numerical Examples of Direct and Iterative Methods 4.7.1 Fourier Collocation Discretizations 4.7.2 Chebyshev Collocation Discretizations 4.7.3 Legendre G-NI Discretizations 4.7.4 Preconditioners for Legendre G-NI Matrices 4.8 Interlude 5. Polynomial Approximation Theory 5.1 Fourier Approximation 5.1.1 Inverse Inequalities for Trigonometric Polynomials 5.1.2 Estimates for the Truncation and Best Approximation Errors 5.1.3 Estimates for the Interpolation Error 5.2 Sturm-Liouville Expansions 5.2.1 Regular Sturm-Liouville Problems 5.2.2 Singular Sturm-Liouville Problems 5.3 Discrete Norms 5.4 Legendre Approximations 5.4.1 Inverse Inequalities for Algebraic Polynomials 5.4.2 Estimates for the Truncation and Best Approximation Errors 5.4.3 Estimates for the Interpolation Error 5.4.4 Scaled Estimates 5.5 Chebyshev Approximations 5.5.1 Inverse Inequalities for Polynomials 5.5.2 Estimates for the Truncation and Best Approximation Errors 5.5.3 Estimates for the Interpolation Error 5.6 Proofs of Some Approximation Results 5.7 Other Polynomial Approximations 5.7.1 Jacobi Polynomials 5.7.2 Laguerre and Hermite Polynomials 5.8 Approximation in Cartesian-Product Domains 5.8.1 Fourier Approximations 5.8.2 Legendre Approximations 5.8.3 Mapped Operators and Scaled Estimates 5.8.4 Chebyshev and Other Jacobi Approximations 5.8.5 Blended Trigonometric and Algebraic Approximations 5.9 Approximation in Triangles and Related Domains 6. Theory of Stability and Convergence 6.1 Three Elementary Examples Revisited 6.1.1 A Fourier Galerkin Method for the Wave Equation 6.1.2 A Chebyshev Collocation Method for the Heat Equation 6.1.3 A Legendre Tau Method for the Poisson Equation 6.2 Towards a General Theory 6.3 General Formulation of Spectral Approximations to Linear Steady Problems 6.4 Galerkin, Collocation, G-NI and Tau Methods 6.4.1 Galerkin Methods 6.4.2 Collocation Methods 6.4.3 G-NI Methods 6.4.4 Tau Methods 6.5 General Formulation of Spectral Approximations to Linear Evolution Problems 6.5.1 Conditions for Stability and Convergence: The Parabolic Case 6.5.2 Conditions for Stability and Convergence: The Hyperbolic Case 6.6 The Error Equation 7. Analysis of Model Boundary-Value Problems 7.1 The Poisson Equation 7.1.1 Legendre Methods 7.1.2 Chebyshev Methods 7.1.3 Other Boundary-Value Problems 7.2 Singularly Perturbed Elliptic Equations 7.2.1 Stabilization of Spectral Methods 7.3 The Eigenvalues of Some Spectral Operators 7.3.1 The Discrete Eigenvalues for Lu = −uxx 7.3.2 The Discrete Eigenvalues for Lu = −νuxx + βux 7.3.3 The Discrete Eigenvalues for Lu = ux 7.4 The Preconditioning of Spectral Operators 7.5 The Heat Equation 7.6 Linear Hyperbolic Equations 7.6.1 Periodic Boundary Conditions 7.6.2 Nonperiodic Boundary Conditions 7.6.3 The Resolution of the Gibbs Phenomenon 7.6.4 Spectral Accuracy for Non-Smooth Solutions 7.7 Scalar Conservation Laws 7.8 The Steady Burgers Equation Appendix A. Basic Mathematical Concepts A.1 Hilbert and Banach Spaces A.2 The Cauchy-Schwarz Inequality A.3 Linear Operators Between Banach Spaces A.4 The Fr´echet Derivative of an Operator A.5 The Lax-Milgram Theorem A.6 Dense Subspace of a Normed Space A.7 The Spaces Cm(Ω), m ≥ 0 A.8 Functions of Bounded Variation and the Riemann(-Stieltjes) Integral A.9 The Lebesgue Integral and Lp-Spaces A.10 Infinitely Differentiable Functions and Distributions A.11 Sobolev Spaces and Sobolev Norms A.12 The Sobolev Inequality A.13 The Poincar´e Inequality A.14 The Hardy Inequality A.15 The Gronwall Lemma Appendix B. Fast Fourier Transforms Appendix C. Iterative Methods for Linear Systems C.1 A Gentle Approach to Iterative Methods C.2 Descent Methods for Symmetric Problems C.3 Krylov Methods for Nonsymmetric Problems Appendix D. Time Discretizations D.1 Notation and Stability Definitions D.2 Standard ODE Methods D.2.1 Leap Frog Method D.2.2 Adams-Bashforth Methods D.2.3 Adams-Moulton Methods D.2.4 Backwards-Difference Formulas D.2.5 Runge-Kutta Methods D.3 Integrating Factors D.4 Low-Storage Schemes References Index

Note: Inhaltsverzeichnis 1 Einführung 1.1 Übersicht 1.2 Modernes naturwissenschaftliches Klimaverständnis 1.3 Modelle in der Klimaforschung 2 Klimarelevante Prozesse 2.1 Energie und Strahlung 2.1.1 Strahlung 2.1.2 Wärmetrausporte 15 2.1.3 Transport von Energie im Wasserkreislauf 2.2 Dynamik der Atmosphäre 2.2.1 Erzeugung von Bewegung 2.2.2 Vertikalstruktur der Atmosphäre 2.2.3 Allgemeine Zirkulation 2.2.4 Regionale Strukturen 2.2.5 Turbulenz 2.2.6 Aerosolpartikel 2.2.7 Wolken und Niederschlag 2.3 Zirkulation des Ozeans 2.3.1 Meeresoberflächenströmungen 2.3.2 Tiefenzirkulation 2.3.3 Wellen und Wirbel 2.4 Spurenstoffkreisläufe 2.4.1 Wasserdampf 2.4.2 Kohlendioxid 2.4.3 Methan 2.4.4 Stickstoffverbindungen 2.5 Kryosphäre 3 Natürliche Klimavariabilität 3.1 Jahres- und Tagesgang 3.2 Wetter 3.3 Interannuale Klimaschwankungen 3.3..1 ENSO-Phänomen 3.3.2 Nordatlantische Oszillation 3.3.3 Temperaturentwicklung seit 1900 3.3.4 Die Frage der Sonnenflecken 3.1 Homogenitätsproblematik 3.5 Historische Klimavariationen 3.6 Paläoklimatologie 3.6.1 Vereisungen 3.6.2 Klimarekonstruktion der Kalt- und Warmzeiten 3.6.3 Milanković-Theorie 4 Konzeptionelle Modelle 4.1 Klimazonen 4.2 Ein exemplarisches Energiebilanzmodell 4.2.1 Vereinfachte Bilanzgleichung für Energie 4.2.2 Diskretisierung 4.2.3 Schließung der Gleichung 4.2.4 Berechnungen: Integration 4.3 Physikalisch orientierte Modelle 4.4 Nichtlinearität und Chaos 4.5 Fluktuationen als stochastische Vorgänge 4.6 Wechselwirkungen verschiedener Prozesse 4.6.1 Gedämpftes System mit Störungen 4.6.2 Wirkung von positiven Rückkopplungen 5 Grundlagen von Strömungsmodellen 5.1 Grundgleichungen der Strömungs- und Thermodynamik 5.1.1 Zustandsvariablen 5.1.2 Gesetz der Massenerhaltung 5.1.3 Prinzip der Energieerhaltung 5.1.4 Impulserhaltung 5.1.5 Massenbilanzen für Beimengungen 5.1.6 Zustandsgleichungen 5.1.7 Zusammenfassung 5.2 Diskretisierung 5.2.1 Räumliche Diskretisierung 5.2.2 Zeitliche Diskretisierung 5.3 Parametrisierung und subskalige Prozesse 5.3.1 Schließungsproblem 5.3.2 Beispiel 1: Turbulenz 5.3.3 Beispiel 2: Konvektion und Wolkenbildung 5.3.4 Kritische Übersicht 5.4 Numerische Integration 6 Realitätsnahe Modelle des Klimasystems 6.1 Wettervorhersagemodelle 6.2 Modelle zur Klimasimulation 6.2.1 Methodik von Simulationen 6.2.2 Wechselwirkung von Atmosphäre und Ozean 6.2.3 Klimadrift und Flußkorrektur 6.2.4 Technische Details 6.2.5 Modellierung von Stoffkreisläufen und Biosphäre 6.3 Simulationen von Klimazuständen 6.3.1 Kontrollsimulationen des derzeitigen Klimas 6.3.2 Rekonstruktion von Paläoklimaten 6.3.3 Klimate anderer Planeten 6.3.1 Regionale und lokale Strukturen 6.4 Numerische Experimente mit Modellen 6.1.1 Zielsetzung 6.4.2 Wirksamkeit von Prozessen 6.4.3 Einschwingzeit der Atmosphäre 6.4.4 Sensitivität gegenüber Randbedingungen 6.5 Anwendung zur Klimavorhersage 6.5.1 Prognosen des ENSO-Phänomens 6.5.2 Großskalige Ölbrände in Kuwait 6.6 Beurteilung der Klimamodelle 7 Anthropogene Klimänderung 7.1 Übersicht 7.2 Emissions- und Konzentrations-Szenarien 7.2.1 Szenarien zukünftiger Emissionen 7.2.2 Erwartete Konzentrationen der Treibhausgase 7.3 Klimaszenarien realitätsnaher Modelle 7.3.1 Transiente Szenarienrechnungen 7.3.2 Ergebnisse eines exemplarischen Klima-Szenarios 7.3.3 Problem Kaltstart 7.3.4 2 x CO2-Simulationen 7.3.5 Informationswert von Szenarienrechnungen 7.3.6 Kritische Bewertung der Szenarien 7.4 Nachweis anthropogener Klimabeeinflussung 7.4.1 Zielsetzung 7.4.2 Natürliche Variabilität 7.4.3 Gewichtungsmuster und Nachweisvariable 7.4.4 Nachweis 7.4.5 Beurteilung 7.5 Lokale und regionale Szenarien 7.5.1 Hochaufgelöste Zeitscheibenexperimente 7.5.2 Regionalmodelle 7.5.3 Empirische Modelle 7.5.4 Implikationen 8 Klima und Gesellschaft 8.1 Übersicht 8.2 Historischer Überblick : gesellschaftliche Vorstellungen zum Einfluß von Klima 8.3 Klimafolgenforschung 8.3.1 Grundproblematik 8.3.2 Direkt beeinflußte Systeme 8.3.3 Indirekt beeinflußte Systeme 8.4 Ökonomische Aspekte des Klimawandels 8.4.1 Klimaänderung als Kostenfaktor 8.4.2 Ein zeitabhängiges Sechs-Komponenten-Modell 8.4.3 Beurteilung 8.4.4 Übersicht Klimapolitik 8.5 Vorstellungen von Klimawandel 8.5.1 Problemstellung 8.5.2 Natürliche Variabilität versus Kausalitätsdenken 8.5.3 Die Kempton-Studie 8.5.4 Soziale Interpretationsmechanismen 9 Résumé 10 Anhang 11 Literatur Stichwortverzeichnis

Note: Inhalt: 1 Einleitung. - 1.1 Alltägliche Probleme. - 1.2 Uni- und multivariate Daten. - 1.3 Wege ins Statistiklabyrinth. - 2 Statistische Grundlagen. - 2.1 Einführung in die Terminologie. - 2.2 Datentypen -Skalenniveaus. - 2.3 Korrelation. - 2.4 Regression. - 2.5 Lineare Regression. - 2.6 Multiplelineare Regression. - 2.7 Unimodale Modelle - die Gauß'sche Regression. - 2.8 Logistische und Gauß'sche logistische Regression. - 2.9 Interaktionen. - 2.10 Gewichtetes Mittel. - 2.11 Partielle Analysen. - 3 Datenmanipulationen. - 3.1 Normalverteilung und Transformationen. - 3.2 Standardisierungen. - 3.3 Transponieren, Umkodieren und Maskieren. - 4 Ähnlichkeits- und Distanzmaße. - 4.1 Qualitative Ähnlichkeitsmaße. - 4.2 Quantitative Ähnlichkeitsmaße. - 4.3 Distanzmaße. - 4.4 Vergleich der geschilderten Koeffizienten. - 5 Ordinationen - das Prinzip. - 5.1 Dimensionsreduktion als Analysestrategie. - 5.2 Polare Ordination. - 6 Korrespondenzanalyse (CA). - 6.1 Das Prinzip. - 6.2 Mathematische Artefakte - Probleme der CA. - 6.3 DCA {Detrended Correspondence Analysis). - 6.4 Zusammenfassendes zu Problemen der CA und DCA. - 7 Interpretation von CA und DCA. - 7.1 Zur Skalierung und Interpretation der Ordinationsdiagramme. - 7.2 Umweltvariablen-Interaktionen von Effekten. - 7.3 Ordination und Umweltdaten. - 8 Kanonische Ordination (constrained ordination). - 8.1 Prinzip der Kanonischen Korrespondenzanalyse (CCA). - 8.2 Interpretation eines CCA-Diagramms. - 8.3 Forward selection bei kanonischen Ordinationen. - 8.4 Überprüfung einer CCA. - 9 Hauptkomponentenanalyse (PCA). - 9.1 Das Prinzip - geometrische Herleitung. - 9.2 Das Prinzip - der mathematische Ansatz. - 9.3 Optionen bei einer PCA. - 9.4 Stärken und Schwächen der PCA. - 9.5 Faktorenanalyse. - 10 Lineare Methoden und Umweltdaten: PCA und RDA. - 10.1 Indirekte Ordination. - 10.2 Kanonische Ordination - Prinzip der Redundanzanalyse. - 10.3 Interpretation einer RDA. - 11 Partielle Ordination und variance partitioning. - 11.1 Kovariablen. - 11.2 Partielle PCA, CA, DCA. - 11.3 Partielle kanonische Ordination. - 11.4 Variance partitioning. - 12 Multidimensionale Skalierung. - 12.1 Der andere Weg zum Ziel. - 12.2 Metrische Multidimensionale Skalierung - Hauptkoordinatenanalyse. - 12.3 Nichtmetrische Multidimensionale Skalierung. - 12.3.1 Das Prinzip. - 12.3.2 NMDS - Optionen und Probleme. - 12.3.3 Ablauf einer NMDS. - 13 Klassifikation - das Prinzip. - 13.1 Das Wesen von Klassifikationen. - 13.2 Die wichtigsten Klassifikationsstrategien. - 14 Agglomerative Klassifikationsverfahren. - 14.1Clusteranalyse - Grundlagen. - 14.2 Auswertung von Dendrogrammen. - 15 Divisive Klassifikationsverfahren. - 15.1 Ordination Space Partitioning. - 15.2 TWINSPAN. - 15.3 Ablauf einer TWINSPAN-Analyse. - 15.4 Kritik an der TWINSPAN-Analyse. - 16 Sonstige Verfahren zur Beschreibung von Gruppenstrukturen. - 16.1 Nichthierarchische agglomerative Verfahren. - 16.2 Nichthierarchische divisive Verfahren. - 16.3 Numerische "treue"-basierte Verfahren. - 16.4 Diskriminanzanalyse. - 16.4.1 Das Prinzip. - 16.4.2 Voraussetzungen. - 16.4.3 Gütekriterien/Prüfung der Ergebnisse. - 17 Permutationsbasierte Tests. - 17.1 Das Prinzip von Permutationstests. - 17.2 Test auf Signifikanz von Ordinationsachsen. - 17.3 Mantel-Test. - 17.4 Gruppenvergleiche - Mantel-Tests und MRPP. - 17.5 Procrustes-Analysen. - 17.6 Indicator Species Analysis. - 17.7 Ausblick Randomisierungsverfahren. - Literatur. - Sachverzeichnis.