ALBERT

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: 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