ALBERT

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: Table of Contents 1 Introduction 1.1 Scripting versus Traditional Programming 1.1.1 Why Scripting is Useful in Computational Science 1.1.2 Classification of Programming Languages 1.1.3 Productive Pairs of Programming Languages 1.1.4 Gluing Existing Applications 1.1.5 Scripting Yields Shorter Code 1.1.6 Efficiency 1.1.7 Type-Specification (Declaration) of Variables 1.1.8 Flexible Function Interfaces 1.1.9 Interactive Computing 1.1.10 Creating Code at Run Time 1.1.11 Nested Heterogeneous Data Structures 1.1.12 GUI Programming 1.1.13 Mixed Language Programming 1.1.14 When to Choose a Dynamically Typed Language 1.1.15 Why Python? 1.1.16 Script or Program? 1.2 Preparations for Working with This Book 2 Getting Started with Python Scripting 2.1 A Scientific Hello World Script 2.1.1 Executing Python Scripts 2.1.2 Dissection of the Scientific Hello World Script 2.2 Working with Files and Data 2.2.1 Problem Specification 2.2.2 The Complete Code 2.2.3 Dissection 2.2.4 Working with Files in Memory 2.2.5 Array Computing 2.2.6 Interactive Computing and Debugging 2. 2.7 Efficiency Measurements 2.2.8 Exercises 2.3 Gluing Stand-Alone Applications 2.3.1 The Simulation Code 2.3.2 Using Gnuplot to Visualize Curves 2.3.3 Functionality of the Script 2.3.4 The Complete Code 2.3.5 Dissection 2.3.6 Exercises 2.4 Conducting Numerical Experiments 2.4.1 Wrapping a Loop Around Another Script 2.4.2 Generating an HTML Report 2.4.3 Making Animations 2.4.4 Varying Any Parameter 2.5 File Format Conversion 2.5.1 A Simple Read/Write Script 2.5.2 Storing Data in Dictionaries and Lists 2.5.3 Making a Module with Functions 2.5.4 Exercises 3 Basic Python 3.1 Introductory Topics 3.1.1 Recommended Python Documentation 3.1.2 Control Statements 3.1.3 Running Applications 3.1.4 File Reading and Writing 3.1.5 Output Formatting 3.2 Variables of Different Types 3.2.1 Boolean Types 3.2.2 The None Variable 3.2.3 Numbers and Numerical Expressions 3.2.4 Lists and Tuples 3.2.5 Dictionaries 3.2.6 Splitting and Joining Text 3.2.7 String Operations 3.2.8 Text Processing 3.2.9 The Basics of a Python Class 3.2.10 Copy and Assignment 3.2.11 Determining a Variable's Type 3.2.12 Exercises 3.3 Functions 3.3.1 Keyword Arguments 3.3.2 Doc Strings 3.3.3 Variable Number of Arguments 3.3.4 Call by Reference 3.3.5 Treatment of Input and Output Arguments 3.3.6 Function Objects 3.4 Working with Files and Directories 3.4.1 Listing Files in a Directory 3.4.2 Testing File Types 3.4.3 Removing Files and Directories 3.4.4 Copying and Renaming Files 3.4.5 Splitting Pathnames 3.4.6 Creating and Moving to Directories 3.4.7 Traversing Directory Trees 3.4.8 Exercises 4 Numerical Computing in Python 4.1 A Quick NumPy Primer 4.1.1 Creating Arrays 4.1.2 Array Indexing 4.1.3 Loops over Arrays 4.1.4 Array Computations 4.1.5 More Array Functionality 4.1.6 Type Testing 4.1.7 Matrix Objects 4.1.8 Exercises 4.2 Vectorized Algorithms 4.2.1 From Scalar to Array in Function Arguments 4.2.2 Slicing 4.2.3 Exercises 4.3 More Advanced Array Computing 4.3.1 Random Numbers 4.3.2 Linear Algebra 4.3.3 Plotting 4.3.4 Example: Curve Fitting 4.3.5 Arrays on Structured Grids 4.3.6 File I/O with NumPy Arrays 4.3.7 Functionality in the Numpyutils Module 4.3.8 Exercises 4.4 Other Tools for Numerical Computations 4.4.1 The ScientificPython Package 4.4.2 The SciPy Package 4.4.3 The Python- Matlab Interface 3 4.4.4 Symbolic Computing in Python 4.4.5 Some Useful Python Modules 5 Combining Python with Fortran, C, and C++ 5.1 About Mixed Language Programming 5.1.1 Applications of Mixed Language Programming 5.1.2 Calling C from Python 5.1.3 Automatic Generation of Wrapper Code 5.2 Scientific Hello World Examples 5.2.1 Combining Python and Fortran 5.2.2 Combining Python and C 5.2.3 Combining Python and C++ Functions 5.2.4 Combining Python and C++ Classes 5.2.5 Exercises 5.3 A Simple Computational Steering Example 5.3.1 Modified Time Loop for Repeated Simulations 5.3.2 Creating a P ython Interface 5.3.3 The Steering Python Script 5.3.4 Equipping the Steering Script with a GUI 5.4 Scripting Interfaces to Large Libraries 6 Introduction to GUI Programming 6.1 Scientific Hello World GUI 6.1.1 Introductory Topics 6.1.2 The First Python/Tkinter Encounter 6.1.3 Binding Events 6.1.4 Changing the Layout 6.1.5 The Final Scientific Hello World GUI 6.1.6 An Alternative to Tkinter Variables 6.1.7 About the Pack Command 6.1.8 An Introduction to the Grid Geometry Manager 6.1.9 Implementing a GUI as a Class 6.1.10 A Simple Graphical Function Evaluator 6.1.11 Exercises 6.2 Adding GUis to Scripts 6.2.1 A Simulation and Visualization Script with a GUI 6.2.2 Improving the Layout 6.2.3 Exercises 6.3 A List of Common Widget Operations 6.3.1 Frame 6.3.2 Label 6.3.3 Button 6.3.4 Text Entry 6.3.5 Balloon Help 6.3.6 Option Menu 6.3.7 Slider 6.3.8 Check Button 6.3.9 Making a Simple Megawidget 6.3.10 Menu Bar 6.3.11 List Data 6.3.12 Listbox 6.3.13 Radio Button 6.3.14 Combo Box 6.3.15 Message Box 6.3.16 User-Defined Dialogs 6.3.17 Color-Picker Dialogs 6.3.18 File Selection Dialogs 6.3.19 Toplevel 6.3.20 Some Other Types of Widgets 6.3.21 Adapting Widgets to the User's Resize Actions 6.3.22 Customizing Fonts and Colors 6.3.23 Widget Overview 6.3.24 Exercises 7 Web Interfaces and CGI Programming 7.1 Introductory CGI Scripts 7.1.1 Web Forms and CGI Scripts 7.1.2 Generating Forms in CGI Scripts 7.1.3 Debugging CGI Scripts 7.1.4 A General Shell Script Wrapper for CGI Scripts 7.1.5 Security Issues 7.2 Adding Web Interfaces to Scripts 7.2.1 A Class for Form Parameters 7.2.2 Calling Other Programs 7.2.3 Running Simulations 7.2.4 Getting a CGI Script to Work 7.2.5 Using Web Applications from Scripts 7.2.6 Exercises 8 Advanced Python 8.1 Miscellaneous Topics 8.1.1 Parsing Command-Line Arguments 8.1.2 Platform-Dependent Operations 8.1.3 Run-Time Generation of Code 8.1.4 Exercises 8.2 Regular Expressions and Text Processing 8.2.1 Motivation 8.2.2 Special Characters 8.2.3 Regular Expressions for Real Numbers 8.2.4 Using Groups to Extract Parts of a Text 8.2.5 Extracting Interval Limits 8.2.6 Extracting Multiple Matches 8.2.7 Splitting Text 8.2.8 Pattern-Matching Modifiers 8.2.9 Substitution and Backreferences 8.2.10 Example: Swapping Arguments in Function Calls 8.2.11 A General Substitution Script 8.2.12 Debugging Regular Expressions 8.2.13 Exercises 8.3 Tools for Handling Data in Files 8.3.1 Writing and Reading Python Data Structures 8.3.2 Pickling Objects 8.3.3 Shelving Objects 8.3.4 Writing and Reading Zip and Tar Archive Files 8.3.5 Downloading Internet Files 8.3.6 Binary Input/Output 8.3.7 Exercises 8.4 A Database for NumPy Arrays 8.4.1 The Structure of the Database 8.4.2 Pickling 8.4.3 Formatted ASCII Storage 8.4.4 Shelving 8.4.5 Comparing the Various Techniques 8.5 Scripts Involving Local and Remote Hosts 8.5.1 Secure Shell Commands 8.5.2 Distributed Simulation and Visualization 8.5.3 Client/Server Programming 8.5.4 Threads 8.6 Classes 8.6.1 Class Programming 8.6.2 Checking the Class Type 8.6.3 Private Data 8.6.4 Static Data 8.6.5 Special Attributes 8.6.6 Special Methods 8.6.7 Multiple Inheritance 8.6.8 Using a Class as a C-like Structure 8.6.9 Attribute Access via String Names 8.6.10 New-Style Classes 8.6.11 Implementing Get/Set Functions via Properties 8.6.12 Subclassing Built-in Types 8.6.13 Building Class Interfaces at Run Time 8.6.14 Building Flexible Class Interfaces 8.6.15 Exercises 8.7 Scope of Variables 8.7.1 Global, Local, and Class Variables 8.7.2 Nested Functions 8.7.3 Dictionaries of Variables in Namespaces 8.8 Exceptions 8.8.1 Handling Exceptions 8.8.2 Raising Exceptions 8.9 Iterators 8.9.1 Constructing an Iterator 8.9.2 A Pointwise Grid Iterator 8.9.3 A Vectorized Grid Iterator 8.9.4 Generators 8.

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

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: One way to shape technology and its embedding in society in the 21st century is through the visions that guide their development, especially concerning the long-term societal perspective. A critical discussion and assessment of these visions is a prerequisite for influencing the course of development. Technology assessment, therefore, has to provide a methodological repertoire for assessing and constructing visions, taking into account the requirements for long-term orientation and the need for public legitimation. This volume draws upon insights from technology assessment (TA), political sciences, epistemology, sociology and ethics. It contributes to the recent literature on "shaping technology", taking into account the "co-evolution of technology and society". It is connected to the TA literature that emphasises TA's pro-active role and its contricution to political judgement. It uses those insights from policy planning and epistemology that may help to reconcile long-term planning and public legitimacy

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 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 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: Contents: 1 The Arctic Ocean: Boundary Conditions and Background Information. - 1.1 Physiography and Bathymetry of the Arctic Ocean. - 1.2 The Arctic Ocean: Modern Status and Recent Climate Change. - 1.3 The Tectonic Evolution of the Arctic Ocean: Overview and Perspectives. - 1.4 Geochemical Proxies Used for Organic Carbon Source Identification in Arctic Ocean Sediments. - 2 Modern Terrigenous Organic Carbon Input to the Arctic Ocean. - 2.1General Introduction. - 2.2 River Input. - 2.3 Organic Carbon Input to the Artic Seas Through Coastal Erosion. - 2.4 The Role of Arctic Sea Ice in Transporting and Cycling Terrestrial Organic Matter. - 2.5 Aeolian Input. - 2.6 Summary and Concluding Remarks. - 3 Primary and Secondary Production in the Arctic Seas. - 3.1 Introduction. - 3.2 Major Algal Groups and Their Distribution. - 3.3 Limitation and Control of Primary Production 3.4 Primary Production and Growth Rate. - 3.5 Seasonality. - 3.6 Distribution of Primary Production. - 3.7 Mesozooplankton . - 3.8 Primary Production - Impact of Climate Change. - 3.9 Summary and Concluding Remarks . - 4 The Role of Dissolved Organic Matter for the Organic Carbon Cycle in the Arctic Ocean. - 4.1 Introduction. - 4.2 Riverine DOM on Arctic Shelves and Beyond. - 4.3 Distribution, Chemical Composition, and Fluxes of Marine DOM in the Central Arctic Ocean. - 4.4 Summary and Concluding Remarks. - 5 Particulate Organic Carbon Flux to the Arctic Ocean Sea Floor. - 5.1 Introduction 5.2 What do we Know About Vertical Carbon Flux from the Arctic Ocean?. - 5.3 Case Studies. - 5.4 Regional Variability in POC Export Flux in the Arctic Ocean Determined Using 234Th as a Tracer. - 5.5 Particulate Organic Carbon Flux to the Sea floor of the Arctic Ocean: Quantity, Seasonality and Processes. - 5.6 Summary and Concluding Remarks. - 6 The Benthos of Arctic Seas and its Role for the Organic Carbon Cycle at the Seafloor. - 6.1 Introduction. - 6.2 Origin and Evolution of Arctic Habitats and Species. - 6.3 Food Supply of the Arctic Benthos: Sources and Pathways. - 6.4 Benthic Communities of the Arctic Seas. - 6.5 Organic Carbon Utilization by the Arctic Benthos. - 6.6 Summary and Concluding Remarks. - 7 Organic Carbon in Arctic Ocean Sediments: Sources, Variability, Burial, and Paleoenvironmental Significance. - 7.1 Organic Carbon in Arctic Ocean Sediments: A General Introduction. - 7.2 The Beaufort Sea: Distribution, Sources, Fluxes, and Burial Rates of Organic Carbon. - 7.3 The Continental Margin of the North Bering - Chukchi Sea: Distribution, Sources, Fluxes, and Burial Rates of Organic Carbon. - 7.4 The East Siberian Sea: Distribution, Sources, and Burial of Organic Carbon. - 7.5 The Laptev Sea: Distribution, Sources, Variability and Burial of Organic Carbon. - 7.6 The Kara Sea: Distribution, Sources, Variability and Burial of Organic Carbon. - 7.7 The Barents Sea: Distribution, Sources, Variability and Burial of Organic Carbon. - 7.8 Northern Fram Strait und Yermak Plateau: Distribution, Variability and Burial of Organic Carbon and Paleoenvironmental Implications. - 7.9 The Central Arctic Ocean: Distribution, Sources, Variability and Burial of Organic Carbon. - 8 Organic Carbon Budget: Arctic Ocean vs. Global Ocean. - 8.1 Introduction. - 8.2 Global Organic Carbon Fluxes: Sources and Sinks. - 8.3 Arctic Ocean Organic Carbon Fluxes: Sources and Sinks. - 8.4 Summary and Concluding Remarks. - 9 References.