Analysis of Climate Variability
Applications of Statistical Techniques
Proceedings of an Autumn School
organized by the Commission
of the European Community
on Elba from October 30 to November 6,1993
With 89 Figures
Hans von Storch
Max-Planck-Institut für Meteorologie
Bundesstrasse 55
D-20146 Hantburg, Germany
Antonio Navarra
Istituto per 10 Studio delle Metodologie Geofisiche Ambientali
Via Emilia Est 770
1-41100 Modena, Italy
Springer
Contents
Foreword . 1
Preface ...
III
Contributors ...
Xlll
I Introduction 1
1 The Development of Climate Research 3
by ANTONIO NAVARRA
1.1 The Nature of Climate Studies . . . . . 3
1.1.1 The Big Storm Controversy . . . 4
1.1.2 The Great Planetary Oscillations 6
1.2 The Components of Climate Research 7
1.2.1 Dynamical Theory . . . . . 8
1.2.2 Numerical Experimentation 9
1.2.3 Statistical Analysis. . . . . 9
2 Misuses of Statistical Analysis in Climate Research 11
by HANS VON STORCH
2.1 Prologue.................... 11
2.2 Mandatory Testing and the Mexican Hat 13
2.3 Neglecting Serial Correlation . . . . . . . 15
2.4 Misleading Names: The Case of the Decorrelation Time 18
2.5 Use of Advanced Techniques . 24
2.6 Epilogue........................... 26
11 Analyzing The Observed Climate 27
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 "C02 Signal" 53
by PHIL JONES
4.1 Introduction................ 53
4.2 Homogeneity . . . . . . . . . . . . . . . 54
4.2.1 Changes in Instrumentation, Exposure
and Measuring Techniques. . . . . . . . 54
4.2.2 Changes in Station Locations . . . . . . 55
4.2.3 Changes in Observation Time and the Methods Used
to CaIculate Monthly A verages . . . . . . 55
4.2.4 Changes in the Station Environment .. 56
4.2.5 Precipitation and Pressure Homogeneity 56
4.2.6 Data Homogenization Techniques 57
4.3 Surface Climate Analysis 57
4.3.1 Temperature 57
4.3.2 Precipitation . . . 62
4.3.3 Pressure . . . . . . 62
4.4 The Greenhouse Detection Problem 66
4.4.1 Definition of Detection Vector and Data Used 67
4.4.2 Spatial Correlation Methods 69
4.5 ConcIusions........................ 71
5 Interpreting High-Resolution Proxy Climate Data - The Example
of Dendroclimatology 77
by KEITH R. B RIFFA
5.1 Introduction........ 77
5.2 Background........ 79
5.3 Site Selection and Dating 79
5.4 Chronology Confidence. . 80
5.4.1 Chronology Signal 80
5.4.2 Expressed Population Signal 81
5.4.3 Subsampie Signal Strength . 81
5.4.4 Wider Relevance of Chronology Signal. 83
5.5 "Standardization" and Its Implications for Judging Theoretical
Signal . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.5.1 Theoretical Chronology Signal ......... 84
5.5.2 Standardization of "Raw" Data Measurements 84
5.5.3 General Relevance of the "Standardization"
Problem. . . . . . . . 86
5.6 Quantifying Climate Signals
in Chronologies . . . . . . . . 86
5.6.1 Calibration of Theoretical Signal 87
5.6.2 Verification of Calibrated Relationships 90
5.7 Discussion. 93
5.8 Conclusions . . . . . . . . . . . . . . . . . . . . 94
6 Analysing the Boreal Summer Relationship Between Worldwide
Sea-Surface Temperature and Atmospheric Variability 95
by M. NEIL WARD
6.1 Introduction............................ 95
6.2 Physical Basis for Sea-Surface Temperature Forcing of the Atmosphere
...... 96
6.2.1 Tropics .......................... 96
6.2.2 Extratropics........................ 97
6.3 Characteristic Patterns of Global Sea Surface Temperature:
EOFs and Rotated EOFs 98
6.3.1 Introduction 98
6.3.2 SST Data . . 98
6.3.3 EOF method 98
6.3.4 EOFs p1_p3 99
6.3.5 Rotation of EOFs 101
6.4 Characteristic Features in the Marine Atmosphere Associated
with the SST Patterns p2, p3 and pA in JAS. . . . . . . .. 101
6.4.1 Data and Methods . . . . . . . . . . . . . . . . . . .. 101
6.4.2 Patterns in the Marine Atmosphere Associated with
EOF p2 .......................... 106
6.4.3 Patterns in the Marine Atmosphere Associated with
EOF p3 .......................... 107
6.4.4 Patterns in the Marine Atmosphere Associated with
Rotated EOF PA . . . . . . . . . . . . . . . . . . . .. 108
6.5 JAS Sahel Rainfall Links with Sea-Surface Temperature and
Marine Atmosphere .......... 109
6.5.1 Introduction ................ 109
6.5.2 Rainfall in the Sahel of Africa. . . . . . . 109
6.5.3 High Frequency Sahel Rainfall Variations 110
6.5.4 Low Frequency Sahel Rainfall Variations. 116
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . 116
III Simulating and Predicting Climate 119
7 The Simulation of Weather Types in GCMs: A Regional
Approach to Control-Run Validation 121
by KEITH R. BRIFFA
7.1 Introduction................ 121
7.2 The Lamb Catalogue . . . . . . . . . . . 122
7.3 An "Objective" Lamb Classification .. 123
7.4 Details of the Seleded GCM Experiments 126
7.5 Comparing Observed and GCM Climates 128
7.5.1 Lamb Types ............ 128
7.5.2 Temperature and Precipitation . . 131
7.5.3 Relationships Between Circulation Frequencies and
Temperature and Precipitation 133
7.5.4 Weather-Type Spell Lengths
and Storm Frequencies . 133
7.6 Conclusions......... 136
7.6.1 Specific Conclusions . . 136
7.6.2 General Conclusions . . 138
8 Statistical Analysis of GCM Output 139
by CLAUDE FRANKIGNOUL
8.1 Introduction.......................... 139
8.2 Univariate Analysis. . . . . . . . . . . . . . . . . . . . . . 140
8.2.1 The t-Test on the Mean of a Normal Variable. . . 140
8.2.2 Tests for Autocorrelated Variables 141
8.2.3 Field Significance . . . . . . . . . . . . . 143
8.2.4 Example: GCM Response
to a Sea Surface Temperature Anomaly 143
8.3 Multivariate Analysis. . . . . . . . . . . . . . 145
8.3.1 Test on Means
of Multidimensional Normal Variables 145
8.3.2 Application to Response Studies 146
8.3.3 Application to Model Testing
and Intercomparison . . . . . . . 152
9 Field Intercomparison 159
by ROBERT E. LIVEZEY
9.1 Introduction................ 159
9.2 Motivation for
Permutation and Monte Carlo Testing 160
9.2.1 Local vs. Field Significance 161
9.2.2 Test Example . . . 164
9.3 Permutation Procedures . 166
9.3.1 Test Environment 166
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 SampIes .
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 Prob ability 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
XIII
11 Stochastic Modeling of Precipitation with Applications to
Climate Model Downscaling 197
by DENNIS LETTEN MAlER
11.1 Introduction . . . . . . . . . 197
11.2 Probabilistic Characteristics
of Precipitation . . . . . . . . 198
11.3 Stochastic Models of Precipitation 201
11.3.1 Background . . . . . . . . . 201
11.3.2 Applications to Global Change 201
11.4 Stochastic Precipitation Models with External Forcing 203
11.4.1 Weather Classification Schemes . . . . . . . . 204
11.4.2 Conditional Stochastic Precipitation Models. 206
11.5 Applications to Alternative Climate Simulation . 210
11.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . 212
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 Coeflicients 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 Sampies .. .
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 .
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