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Anmerkung: Contents: List of Figures. - List of Tables. - 1. Introduction. - a. An Overview of Principal Component Analysis (PCA). - b. Outline of the Book. - c. A Brief History of PCA. - d. Acknowledgments. - 2. Algebraic Foundations of PCA. - a. Introductory Example: Bivariate Data Sets. - Monterey, California air temperatures. - Centering and rotating the data set. - Variances in the rotated frame. - Principal angles. - Principal variances. - Principal covariance. - Principal directions. - Principal components; principal directions as basis vectors. - Matrix representation. - The PCA property. - Invariance of the total variance under rotation. - Principal variances for standardized data sets. - PCA and estimates of the statistical parameters of normal populations. - PCA and the construction of Monte Carlo experiments. - Eigenvalues and eigenvectors of the covariance and scatter matrices. - b. Principal Component Analysis: Real-valued Scalar Fields. - t-centering the data set. - The scatter probe and the scatter matrix. - The eigenstructures of PCA. - The basic data set representations; analysis and synthesis formulas. - The PCA property. - Second-order properties of PCA; the total scatter . - The singular value decomposition (SVD) of a data set. - Second-order properties of PCA; correlations. - PCA characterized by the PCA property. - The asymptotic PCA property and dynamical systems. - PCA of spatial composites of data sets. - PCA of temporal composites of data sets. - c. Principal Component Analysis: Complex-valued Scalar Fields, and Beyond. - PCA of complex-valued data sets (C-PCA). - Complex algebra conventions. - The scatter probe and scatter matrix for C-PCA. - Derivation of the eigenstructures of C-PCA. - The fundamental formulas of C-PCA. - Generalization of PCA to quaternion-valued data sets (Q-PCA). - Matrix representations of complex and quaternion numbers. - PCA of matrix-valued data sets (M-PCA). - Reduction of M-PCA to C-PCA form. - d. Bibliographic Notes and Miscellaneous Topics. - Alternate interpretation of the scatter probe. - Numerical calculations of eigenstructures of a scatter matrix. - Some elementary properties of eigenstructures of a scatter matrix. - Sample space vs. state space: choosing the dual computation. - PCA for continuous domains. - PCA for continuous domains: the viewpoint of empirical orthogonal functions. - The sixteen possible domain pairs for PCA: abstract PCA. - 3. Dynamical Origins of PCA. - a. One-dimensional Hannonic Motion. - A spring-linked-mass model; general form. - A spring-linked-mass model; special form. - A numerical example of the asymptotic PCA property. - Further investigations of the asymptotic PCA property and of EOF's. - b. Two-dimensional Wave Motion. - Solution of a two-dimensional damped-wave model. - Demonstration of the asymptotic PCA property (forcing and friction absent). - Demonstration of the asymptotic PCA property (forcing and friction present). - Physical basis for eigenframe rotations. - c. Dynamical Origins of Linear Regression (LR). - From continuous to discrete solutions to the regression model. - The linear regression procedure. - Comparison of LRA and PCA. - d. Random Processes and Karhunen-Loeve Analysis. - Origins of random processes in linear settings. - Karhunen-Loeve representation of random data sets and comparison with PCA. - e. Stationary Processes and PCA. - Derivation of the PCA representation of a one-dimensional stationary process via a simple wave model. - Connections between PCA and stationary processes: the case of one dimension. - Connections between PGA and stationary processes: extension to two dimensions. - f. Bibliographic Notes. - 4. Extensions of PCA to Multivariate Fields. - a. Categories of Data and Modes of Analysis. - Examples. - Generalized notation: the concepts of "individual" and "variable" in PCA. - b. Local PCA of a General Vector Field. - The PCA formalism. - Squared correlations. - Variational origin of the scatter matrix. - Examples. - c. Global PCA of a General Vector Field: Time-Modulation Form. - The PGA formalism. - Squared correlations. - Degeneracy of global PGA to local PGA. - Variational origin of the scatter matrix. - d. Global PCA of a General Vector Field: Space-Modulation Form. - The PCA formalism. - Squared correlations. - Variational origin of the scatter matrix. - e. PCA of Spectral Components of a General Vector Field. - Fourier analysis of the vector field components. - The scatter matrix in the spectral setting. - Example of spectral PCA of a windfield. - f. Bibliographic Notes and Miscellaneous Topics. - The eight modes of analysis and Cattell's classifications. - Time-modulation PGA as a special case of matrix-valued PGA. - Applications to the PGA of wind fields. - Distinction between time-modulation PGA and complex PGA. - Applications to the PGA of storm tracks. - 5. Selection Rules for PCA. - a. Random Reference Data Sets. - b. Dynamical Origins of the Dominant-Variance Selection Rules. - A dynamical model. - Rationale for selection rules. - c. Rule A4. - Statistical basis and discussion. - Choice of λ0. - d. Rule N . - Statistical basis and discussion. - Adjustments for correlated data: effective sample size. - Asymptotic eigenvalues for large data sets. - e. Rule M. - f. Comments on Dominant-Variance Rules . - g. Dynamical Origins of the Time-History Selection Rules. - h. Rule KS2. - The white spectrum and the cumulative periodogram. - Statement of Rule KS2. - i. Rules AMPλ. - Fisher's test. - Siegel's test. - Statement of Rules AMPλ. - j. Rule Q. - k. Selection Rules for Vector-Valued Fields. - Local PCA rules. - Global PCA (time-modulated) rules. - Global PCA (space-modulated) rules. - I. A Space-map Selection Rule. - Canonic direction angles. - Differential relations between unit vectors and canonic direction angles. - An r-tile metric for comparing canonic direction angles. - Statistical aspects: critical values for class errors. - Statement of the selection rule. - m. Bibliographic Notes and Miscellaneous Topics. - Puzzles and problems underlying Rule N; the logarithmic eigenvalue curve. - Numerical intractability of the classical formulas for the eigenvalues of a random matrix. - Monte Carlo approaches to the eigenvalue distribution problem. - Comparison of Monte Carlo methods and asymptotic formulas for eigenvalue distributions. - The problem of closely spaced eigenvalues; tests for equal eigenvalues. - The generalized basis for dominant variance selection rules. - Parallel work in atomic physics. - 6. Factor Analysis (FA) and PCA. - a. Comparison of PCA, LRA, and FA. - Similarities between PCA, LRA, and FA. - Dissimilarities between PCA, LRA, and FA. - The usual algebraic form of FA; its PC and LR interpretations. - b. The Central Problems of FA. - The matrix formulation of FA. - The detailed sub-problems of FA. - c. Bibliographic Notes. - The selection rule problem in FA. - The parameter estimation problem in FA. - 7. Diagnostic Procedures via PCA and FA. - a. Dual Interpretations of a Data Set: State Space and Sample Space. - b. Interpreting E-frames in PCA State Space. - Example: graphical display of eigenvectors. - Rationales for interpreting eigenmaps and time series. - PCA as a means, rather than an end. - c. Informative and Uninformative E-frames in PCA State Space. - d. Rotating E-frames in PCA State Space (varimax). - A two-dimensional example of the varimax procedure. - The general varimax procedure. - The loss of the PCA property for rotated E-frames. - e. Projections onto E-frames in PCA State Space (procrustes). - Derivation of the procrustes technique. - Some observations on the generality of the procrustes technique. - f. Interpreting A-frames in PCA Sample Space. - g. Rotating A-frames in PCA Sample Space (varimax). - h. Projections onto A-frames in PCA Sample Space (procrustes). - i. Detecting Clusters of Points in PCA State or Sample Spaces. - Minimal spanning trees. - Defining cluster pairs, and te

Anmerkung: Contents: Contributors. - Preface. - Acknowledgements. - PART I SETTING THE SCENE. - 1. Introduction: Why Sub-seasonal to Seasonal Prediction (S2S)? / Frédéric Vitart, Andrew W. Robertson. - 1 History of Numerical Weather and Climate Forecasting. - 2 Sub-seasonal to Seasonal Forecasting. - 3 Recent National and International Efforts on Sub-seasonal to Seasonal Prediction. - 4 Structure of This Book. - 2. Weather Forecasting: What Sets the Forecast Skill Horizon? / Zoltan Toth, Roberto Buizza. - 1 Introduction. - 2 The Basics of Numerical Weather Prediction. - 3 The Evolution of NWP Technique. - 4 Enhancement of Predictable signals. - 5 Ensemble Techniques: Brief Introduction. - 6 Expanding the forecast skill Horizon. - 7 Concludmg Remarks: Lessons for S2S Forecasting. - Acknowledgements. - 3. Weather Within Climate: Sub-seasonal Predictability of Tropical Daily Rainfall Characteristics / Vincent Moron, Andrew W. Robertson, Lei Wang. - 1 Introduction. - 2 Data and Methods. - 3 Results. - 4 Discussion and Concluding Remarks. - 4. Identifying Wave Processes Associated With Predictability Across Time Scales: An Empirical Normal Mode Approach / Gilbert Brunet, John Methven. - 1 Introduction. - 2 Partitioning Atmospheric Behavior Using Its Conservation Properties. - 3 The ENM Approach to Observed Data and Models and Its Relevance to S2S Dynamics and Predictability. - 4 Conclusion. - Acknowledgments. - PART II SOURCES OF S2S PREDICTABILITY. - 5. The Madden-Julian Oscillation / Steven J. Woolnough. - 1 Introduction. - 2 The Real-Time Multivariate MJO Index. - 3 Observed MJO Structure. - 4 The Relationship Between the MJO and Tropical and Extratropical Weather. - 5 Theories and Mechanisms for MJO Initiation, Maintenance, and Propagation. - 6 The Representation of the MJO in Weather and Climate Models. - 7 MJO Prediction. - 8 Future Priorities for MJO Research for S2S Prediction. - Acknowledgments. - 6. Extratropical Sub-seasonal to Seasonal Oscillations and Multiple Regimes: The Dynamical Systems View / Michael Ghil, Andreas Groth, Dmitri Kondrashov, Andrew W. Robertson. - 1 Introduction and Motivation. - 2 Multiple Midlatitude Regimes and Low-Frequency Oscillations. - 3 Extratropical Oscillations in the S2S Band. - 4 Low-Order, Data-Driven Modeling, Dynamical Analysis, and Prediction. - 5 Concluding Remarks. - Acknowledgments. - 7. Tropical-Extratropical Interactions and Teleconnections / Hai Lin, Jorgen Frederiksen, David Straus, Christiana Stan. - 1 Introduction. - 2 Tropical Influence on the Extratropical Atmosphere. - 3 Extratropical Influence on the Tropics. - 4 Tropical-Extratropical, Two-Way Interactions. - 5 Summary and Discussion. - Appendix. Technical Matters Relating to Section 4.2. - 8. Land Surface Processes Relevant to Sub-seasonal to Seasonal (S2S) Prediction / Paul A. Dirmeyer, Pierre Gentine, Michael B. Ek, Gianpaolo Balsamo. - 1 Introduction. - 2 Process of Land-Atmosphere Interaction. - 3 A Brief History of Land-Surface Models. - 4 Predictability and Prediction. - 5 Improving Land-Driven Prediction. - 9. Midlatitude Mesoscale Ocean-Atmosphere Interaction and Its Relevance to S2S Prediction / R. Saravanan, P. Chang. - 1 Introduction. - 2 Data and Models. - 3 Mesoscale Ocean-Atmosphere Interaction in the Atmospheric Boundary Layer. - 4 Local Tropospheric Response. - 5 Remote Tropospheric Response. - 6 Impact on Ocean Circulation. - 7 Implications for S2S Prediction. - 8 Summary and Conclusions. - Acknowledgments. - 10. The Role of Sea Ice in Sub-seasonal Predictability / Matthieu Chevallier, François Massonnet, Helge Goessling, Virginie Guémas, Thomas Jung. - 1 Introduction. - 2 Sea Ice in the Coupled Atmosphere-Ocean System. - 3 Sea Ice Distribution, Seasonality, and Variability. - 4 Sources of Sea Ice Predictability at the Sub-seasonal to Seasonal Timescale. - 5 Sea Ice Sub-seasonal to Seasonal - Predictability and Prediction Skill in Models. - 6 Impact of Sea Ice on Sub-seasonal Predictability. - 7 Concluding Remarks. - Acknowledgments. - 11. Sub-seasonal Predictability and the Stratosphere / Amy Butler, Andrew Charlton-Perez, Daniela I. V. Domeisen, Chaim Garfinkel, Edwin P. Gerber, Peter Hitchcock, Alexey Yu. Karpechko, Amanda C. Maycock, Michael Sigmond, Isla Simpson, Seok-Woo Son. - 1 Introduction. - 2 Stratosphere-Troposphere Coup ling in the Tropics. - 3 Stratosphere-Troposphere Coupling in the Extratropics. - 4 Predictability Related to Extratropical Stratosphere-Troposphere Coupling. - 5 Summary and Outlook. - PART Ill S2S MODELING AND FORECASTING. - 12. Forecast System Design, Configuration, and Complexity / Yuhei Takaya. - 1 Introduction. - 2 Requirements and Constraints of the Operational Sub-seasonal Forecast. - 3 Effect of Ensemble Size and Lagged Ensemble. - 4 Real-Time Forecast Configuration. - 5 Reforecast Configuration. - 6 Summary and Concluding Remarks. - Acknowledgments. - 13. Ensemble Generation: The TIGGE and S2S Ensembles / Roberto Buizza. - 1 Global Sub-seasonal and Seasonal Prediction Is an Initial Value Problem. - 2 Ensembles Provide More Complete and Valuable Information Than Single States. - 3 A Brief Introduction to Data Assimilation. - 4 A Brief Introduction to Model Uncertainty Simulation. - 5 An Overview of Operational, Global, Sub-seasonal, and Seasonal Ensembles, and Their Initialization and Generation Methods. - 6 Ensembles: Considerations About Their Future. - 7 Summary and Key Lessons. - 14. GCMs With Full Representation of Cloud Microphysics and Their MJO Simulations / In-Sik Kang, Min-Seop Ahn, Hiroaki Miura, Aneesh Subramanian. - 1 Introduction. - 2 Global CRM. - 3 Superparameterized GCM. - 4 GCM With Full Representation of Cloud Microphysics and Scale-Adaptive Convection. - 5 Summary and Conclusion. - Acknowledgments. - 15. Forecast Recalibration and Multimodel Combination / Stefan Siegert, David B. Stephenson. - 1 Introduction. - 2 Statistical Methods for Forecast Recalibration. - 3 Regression Methods. - 4 Forecast Combination. - 5 Concluding Remarks. - Acknowledgments. - 16. Forecast Verification for S2S Timescales / Caio A. S. Coelho, Barbara Brown, Laurie Wilson, Marion Mittermaier, Barbara Casati. - 1 Introduction. - 2 Factors Affecting the Design of Verification Studies. - 3 Observational References. - 4 Review of the Most Common Verification Measures. - 5 Types of S2S Forecasts and Current Verification Practices. - 6 Summary, Challenges, and Recommendations in S2S Verification. - PART IV S2S APPLICATIONS. - 17. Sub-seasonal to Seasonal Prediction of Weather Extremes / Frédérik Vitart, Christopher Cunningham, Michael Deflorio, Emanuel Dutra, Laura Ferranti, Brian Golding, Debra Hudson, Charles Jones, Christophe Lavaysse, Joanne Robbins, Michael K. Tippett. - 1 Introduction. - 2 Prediction of Large-Scale, Long-Lasting Extreme Events. - 3 Prediction of Mesoscale Events. - 4 Display and Verification of Sub-seasonal Forecasts of Extreme Events. - 5 Conclusions. - 18. Pilot Experiences in Using Seamless Forecasts for Early Action: The "Ready-Set-Go!" Approach in the Red Cross / Juan Bazo, Roop Singh, Mathieu Destrooper, Erin Coughlan de Perez. - 1 Introduction. - 2 Why Sub-seasonal?. - 3 Case Study: Peru El Niño. - 4 Reflections on the Use of S2S Forecasts. - 5 Conclusions. - 19. Communication and Dissemination of Forecasts and Engaging User Communities / Joanne Robbins, Christopher Cunningham, Rutger Dankers, Matthew Degennaro, Giovanni Dolif, Robyn Duell, Victor Marchezini, Brian Mills, Juan Pablo Sarmiento, Amber Silver, Rachel Trajber, Andrew Watkins. - 1 Introduction. - 2 Sector-Specific Methods and Practices in S2S Forecast Communication, Dissemination, and Engagement. - 3 Guiding principles for improved communication Practices. - 4 Summary and Recommendations for Future Research. - 20. Seamless Prediction of Monsoon Onset and Active/Break Phases / A.

Anmerkung: Contents Preface Acknowledgements List of Abbreviations Part 1: Introduction and Background Chapter 1. Introduction to the Arctic: Significance and History 1.1 The Arctic Ocean and Its Significance for the Earth's Climate System 1.2 History of Arctic Ocean Research 1.3 Plate Tectonic Evolution and Palaeogeography 1.4 Glaciations in Earth's History Chapter 2. Modern Physiography, Hydrology, Climate, and Sediment Input 2.1 Bathymetry and Physiography 2.2 Oceanic Circulation Pattern and Water-Mass Characteristics 2.3 Sea-Ice Cover: Extent, Thickness, and Variability 2.4 Primary Production and Vertical Carbon Fluxes in the Arctic Ocean 2.5 River Discharge 2.6 Permafrost 2.7 Coastal Erosion 2.8 Aeolian Input 2.9 Modern Sediment Input: A Summary Part 2: Processes and Proxies Chapter 3. Glacio-Marine Sedimentary Processes 3.1 Sea-Ice Processes: Sediment Entrainment and Transport 3.2 Ice Sheet- and Iceberg-Related Processes 3.3 Sediment Mass-Wasting Processes 3.4 Turbidite Sedimentation in the Central Arctic Ocean Chapter 4. Proxies Used for Palaeoenvironmental Reconstructions in the Arctic Ocean 4.1 Lithofacies Concept 4.2 Grain-Size Distribution 4.3 Proxies for Sources and Transport Processes of Terrigenous Sediments 4.4 Trace Elements Used for Palaeoenvironmental Reconstruction 4.5 Micropalaeontological Proxies and Their (Palaeo-) Environmental and Stratigraphical Significance 4.6 Stable Isotopes of Foraminifers 4.7 Organic-Geochemical Proxies for Organic-Carbon Source and Palaeoenvironment Part 3: The Marine-Geological Record 5 Modern Environment and its record in surface sediments 5.1 Terrigenous (non-biogenic) components in Arctic Ocean surface sediments: Implications for provenance and modern transport processes 5.2 Organic-Carbon Content: Terrigenous Supply versus Primary Production Chapter 6. Quaternary Variability of Palaeoenvironment and Its Sedimentary Record 6.1 The Stratigraphic Framework of Arctic Ocean Sediment Cores: Background, Problems, and Perspectives 6.2 Variability of Quaternary Ice Sheets and Palaeoceanographic Characteristics: Terrestrial, Model, and Eurasian Continental Margin Records 6.3 Circum-Arctic Glacial History, Sea-Ice Cover, and Surface-Water Characteristics: Quaternary Records from the Central Arctic Ocean 6.4 Accumulation of Particulate Organic Carbon at the Arctic Continental Margin and Deep-Sea Areas During Late Quaternary Times Chapter 7. Mesozoic to Cenozoic Palaeoenvironmental Records of High Northern Latitudes 7.1 Mesozoic High-Latitude Palaeoclimate and Arctic Ocean Palaeoenvironment 7.2 Cenozoic High-Latitude Palaeoclimate and Arctic Ocean Palaeoenvironment Chapter 8. Open Questions and Future Geoscientific Arctic Ocean Research 8.1 Quaternary and Neogene Climate Variability on Sub-Millennial to Milankovich Time Scales 8.2 The Mesozoic-Cenozoic History of the Arctic Ocean References Index