In Extremis (eBook)

Dr. J. Kropp: Senior scientist at PIK; he studied chemistry and physics and in 1992 he took a diploma in theoretical chemistry at the University of Oldenburg. His doctoral thesis in theoretical physics was on Neural Networks and Qualitative Knowledge Bases in Environmental Systems Analysis. From 1993-1998 he was research fellow at PIK, from 1998-2001 project leader of a research project on costal zone management (Data integration and Qualitative Dynamics in the Wadden Sea) at the Institute for Chemistry and Biology of the Marine Environment (University of Oldenburg), and from 2001 research analyst and member of staff of the German Advisory Council on Global Change to the Federal Government (WBGU). He was a member of an expert council on New Concepts and Indicators in Fisheries and Aquaculture invited by the European Commission/DGXII and a contributor to the WBGU reports Transition to sustainable energy systems and special report Charging the global commons, and project leader of the international joint project Scaling Analysis of Hydrometeorological Time Series at the University of Giessen, Institute for Theoretical Physics. During 1999-2002 he was the PI for an integrated vulnerability assessment for the German state government of North-Rhine Westphalia. His research interests are the development of methods for integrated impact assessments, in particular, with respect to vulnerability, risk assessment, and adaptation to climate change and in the context of decision making and various institutional settings. Amongst the research project he leads are Uncertainty, Prediction and Risk Assessment of Extreme Events (UPRACE) and Development of Policies and Adaptation Strategies to Climate Change in the Baltics (ASTRA) which is of particular interest for the suggested project. For the latte he was awarded with the Amber Tree Award of the European INTERREG Office for the outstanding vision of the project bringing together various disciplines.He worked for the Council of Europe developing guideline for strengthening the adaptive capacity of European Societies with respect to climate change. For the German Society for Technical Cooperation he developed a climate proofing concept for the assessment of development programmes with regard to climate change. He leads several European joint projects (e.g. disaster and risk assessment) and has published numerous papers and is one editor of the books Science of Disasters: Climate Disruptions, Heart Attacks, and Market Crashes (Springer, 2002) and Advanced Methods for Decision Making and Risk Management in Sustainability Sciences (Nova Sci. Publ., 2007). Prof. Dr. H.J. Schellnhuber: Born in 1950 in Ortenburg (Germany). Training in physics and mathematics with a at the University of Regensburg. Doctorate in Theoretical Physics in 1980. Various periods of research abroad, in particular at several institutions of the University of California system (USA). Habilitation (German qualification for professorial status) in 1985, then Heisenberg Fellowship. 1989 Full Professor at the Interdisciplinary Centre for Marine and Environmental Sciences (ICBM) at the University of Oldenburg, later Director of the ICBM. 1991 Founding Director of the Potsdam Institute for Climate Impact Research (PIK); since 1993 Director of PIK and Professor for Theoretical Physics at the University of Potsdam. 2001-2005 additional engagement as Research Director of the Tyndall Centre for Climate Change Research and Professor at the Environmental Sciences School of the University of East Anglia in Norwich (UK). Distinguished Science Advisor for the Tyndall Centre since 2005. 2002 Royal Society Wolfson Research Merit Award; 2004 CBE (Commander of the Order of the British Empire) awarded by Queen Elizabeth II. Elected Member of the Max Planck Society, the US National Academy of Sciences, the Leibniz-Sozietät, the Geological Society of London, and the International Research Society Sigma Xi. Ambassador for the International Geosphere-Biosphere Programme (IGBP). Visiting Professor in Physics, Honorary Member of the Christ Church College High Table, and Senior James Martin Fellow at Oxford University. Active service on some dozen national and international panels for scientific strategies and policy advice on environment & development matters. Inter alia, Vice-Chair of the German Advisory Council on Global Change (WBGU), Chair of the Global Change Advisory Group for the 6th Framework Programme of the European Commission and Member of the corresponding panel for FP7, Member of the Scientific Board of the Dahlem Conferences, Member of the Committee on Scientific Planning and Review of the International Council for Science (ICSU), Member of the Board of the Stockholm Environment Institute (SEI). Chief Government Advisor on climate and related issues for the German G8-EU twin presidency in 2007.

Preface 5
Contents 9
Acronyms 16
Contributors 18
Part I Extremes, Uncertainty, and Reconstruction 20
1 The Statistics of Return Intervals, Maxima, and Centennial Events Under the Influence of Long-Term Correlations 22
Jan F. Eichner, Jan W. Kantelhardt, Armin Bunde, and Shlomo Havlin 22
1.1 Introduction 23
1.2 Statistics of Return Intervals 25
1.2.1 Mean Return Interval and Standard Deviation 25
1.2.2 Stretched Exponential and Finite-Size Effects for Large Return Intervals 27
1.2.3 Power-Law Regime and Discretization Effects for Small Return Intervals 30
1.2.4 Long-Term Correlations of the Return Intervals 33
1.2.5 Conditional Return Interval Distributions 35
1.2.6 Conditional Return Periods 36
1.3 Statistics of Maxima 41
1.3.1 Extreme Value Statistics for i.i.d. Data 43
1.3.2 Effect of Long-Term Persistence on the Distribution of the Maxima 44
1.3.3 Effect of Long-Term Persistence on the Correlations of the Maxima 46
1.3.4 Conditional Mean Maxima 48
1.3.5 Conditional Maxima Distributions 50
1.4 Centennial Events 53
1.5 Conclusion 58
References 60
2 The Bootstrap in Climate Risk Analysis 64
Manfred Mudelsee 64
2.1 Introduction 64
2.2 Method 66
2.2.1 Kernel Risk Estimation 68
2.2.2 Bootstrap Confidence Band Construction 69
2.3 Data 70
2.4 Results 72
2.5 Conclusion 74
References 76
3 Confidence Intervals for Flood Return Level Estimates Assuming Long-Range Dependence 79
Henning W. Rust, Malaak Kallache, Hans Joachim Schellnhuber, and Jürgen P. Kropp 79
3.1 Introduction 79
3.2 Basic Theory 81
3.2.1 The Generalized Extreme Value Distribution 81
3.2.2 GEV Parameter Estimation 82
3.3 Effects of Dependence on Confidence Intervals 83
3.4 Bootstrapping the Estimators Variance 85
3.4.1 Motivation of the Central Idea 85
3.4.2 Modelling the Distribution 87
3.4.3 Modelling the ACF 87
3.4.4 Combining Distribution and Autocorrelation 90
3.4.5 Generating Bootstrap Ensembles 90
3.5 Comparison of the Bootstrap Approaches 92
3.5.1 Monte Carlo Reference Ensemble 92
3.5.2 The Bootstrap Ensembles 92
3.5.3 Ensemble Variability and Dependence on Ensemble Size 94
3.6 Case Study 95
3.6.1 Extreme Value Analysis 96
3.6.2 Modelling the ACF of the Daily Series 96
3.6.3 Modelling the ACF of the Maxima Series 97
3.6.4 Combining Distribution and ACF 98
3.6.5 Calculating the Confidence Limit 98
3.7 Discussion 100
3.8 Conclusion 100
References 103
4 Regional Determination of Historical Heavy Rain for Reconstruction of Extreme Flood Events 108
Paul Dostal, Florian Imbery, Katrin Bürger, and Jochen Seidel 108
4.1 Introduction 108
4.2 Methodological Concept and Data Overview 109
4.2.1 Meteorological Data from October 1824 110
4.2.2 Methods 111
4.3 Results 114
4.3.1 The Extreme Weather Situation of October 1824 114
4.3.2 Calculation of the 1824 Precipitation 115
4.3.3 Modelling the Area Precipitation of 1824 116
4.3.4 Modelled Neckar Discharges for the Flood Eventof October 1824 117
4.4 Conclusion 117
References 118
5 Development of Regional Flood Frequency Relationships for Gauged and Ungauged Catchments Using L-Moments 121
Rakesh Kumar and Chandranath Chatterjee 121
5.1 Introduction 121
5.2 Regional Flood Frequency Analysis 123
5.2.1 At-Site Flood Frequency Analysis 123
5.2.2 At-Site and Regional Flood Frequency Analysis 123
5.2.3 Regional Flood Frequency Analysis 123
5.3 L-Moment Approach 126
5.3.1 Probability Weighted Moments and L-Moments 127
5.3.2 Screening of Data Using Discordancy Measure Test 128
5.3.3 Test of Regional Homogeneity 129
5.3.4 Identification of Robust Regional Frequency Distribution 131
5.4 Study Area and Data Availability 131
5.5 Analysis and Discussion of Results 132
5.5.1 Screening of Data Using Discordancy Measure Test 133
5.5.2 Test of Regional Homogeneity 133
5.5.3 Identification of Robust Regional Frequency Distribution 134
5.5.4 Regional Flood Frequency Relationship for Gauged Catchments 135
5.5.5 Regional Flood Frequency Relationship for Ungauged Catchments 137
5.6 Conclusion 139
References 142
Part II Extremes, Trends, and Changes 144
6 Intense Precipitation and High Floods -- Observations and Projections 146
Zbigniew W. Kundzewicz 146
6.1 Introduction 146
6.2 Observations of Intense Precipitation 147
6.3 Observations of River Flow 149
6.4 Projections of Intense Precipitation and High River Flow 152
6.5 Conclusion 154
References 156
7 About Trend Detection in River Floods 159
Maciej Radziejewski 159
7.1 Introduction 159
7.2 Methods 160
7.2.1 Testing of Significance 160
7.2.2 Resampling 162
7.2.3 Tests for Changes 164
7.3 Trends in Time Series of River Flows 166
7.4 Trends in Seasonal Maxima 170
7.5 Seasonal Peaks Over Threshold 173
7.6 Most Extreme Flows 176
7.7 Conclusion 178
References 178
8 Extreme Value Analysis Considering Trends: Application to Discharge Data of the Danube River Basin 181
Malaak Kallache, Henning W. Rust, Holger Lange, and Jürgen P. Kropp 181
8.1 Introduction 182
8.2 Method 183
8.2.1 Choice of the Extreme Values 183
8.2.2 Point Processes 184
8.2.3 Test for Trend 185
8.2.4 Return-Level Estimation 189
8.3 Results 190
8.4 Conclusion 194
References 195
9 Extreme Value and Trend Analysis Based on Statistical Modelling of Precipitation Time Series 199
Silke Trömel and Christian-D. Schönwiese 199
9.1 Introduction 199
9.2 Components 200
9.3 The Distance Function and the Model Selection Criterion 202
9.4 Application to a German Station Network 206
9.4.1 General Remarks 206
9.4.2 Example: Eisenbach--Bubenbach 207
9.4.3 Probability Assessment of Extreme Values 209
9.4.4 Changes in the Expected Value 211
9.5 Conclusions 213
References 214
10 A Review on the Pettitt Test 216
Diego Rybski and Jörg Neumann 216
10.1 Introduction 216
10.2 Data 217
10.3 Methods 217
10.4 Results 221
10.4.1 River Runoff Records 221
10.4.2 Simulations 222
10.4.3 Reasoning 222
10.5 Conclusion 224
References 225
Part III Long-Term Phenomena and Nonlinear Properties 227
11 Detrended Fluctuation Studies of Long-Term Persistence and Multifractality of Precipitation and River Runoff Records 229
Diego Rybski, Armin Bunde, Shlomo Havlin, Jan W. Kantelhardt, and Eva Koscielny-Bunde 229
11.1 Introduction 229
11.2 Data 232
11.3 Correlation Analysis 234
11.3.1 General 234
11.3.2 Standard Fluctuation Analysis (FA) 235
11.3.3 The Detrended Fluctuation Analysis (DFA) 236
11.3.4 Wavelet Transform (WT) 237
11.4 Multifractal Analysis 238
11.4.1 Multifractal DFA (MF-DFA) 238
11.4.2 Comparison with Related Multifractal Formalisms 239
11.5 Results of the Correlation Behaviour 240
11.5.1 River Runoff 240
11.5.2 Precipitation 244
11.6 Results of the Multifractal Behaviour 247
11.6.1 Fits by the Universal Multifractal Model 249
11.6.2 Fits by the Extended Multiplicative Cascade Model 251
11.6.3 Fits by the Bifractal Model 251
11.6.4 Results 252
11.7 Conclusion 253
References 257
12 Long-Term Structures in Southern German Runoff Data 262
Miguel D. Mahecha, Holger Lange, and Gunnar Lischeid 262
12.1 Introduction 263
12.2 Methods 264
12.2.1 Data Sets and Preparation 264
12.2.2 Dimensionality Reduction in Space 264
12.2.3 Dimensionality Reduction in Time 266
12.3 Results 269
12.3.1 Dimensionality Reduction 269
12.3.2 Dimensionality Reduction in the Time Domain 270
12.3.3 Regional Patterns and Hydrological Dependencies 272
12.4 Discussion 273
12.4.1 Methodological Outlook 274
12.5 Conclusion 274
References 275
13 Seasonality Effects on Nonlinear Properties of Hydrometeorological Records 278
Valerie N. Livina, Yosef Ashkenazy, Armin Bunde, and Shlomo Havlin 278
13.1 Introduction 278
13.2 Methodology 282
13.2.1 Detrended Fluctuation Analysis and Multifractal Detrended Fluctuation Analysis 282
13.2.2 Volatility Correlations and Surrogate Test for Nonlinearity 284
13.3 The Way Periodicities Affect the Estimation of Nonlinearities: Conventional Seasonal Detrending 284
13.4 A New Method for Filtering Out Periodicities 285
13.5 Results 287
13.5.1 Tests of Artificial Data 287
13.5.2 Results of Volatility Analysis of Observed River Data 288
13.5.3 Results of Multifractal Analysis of Observed River Data 291
13.6 Conclusion 293
References 294
14 Spatial Correlations of River Runoffs in a Catchment 297
Reik Donner 297
14.1 Introduction 297
14.2 Description of the Data 300
14.3 Correlation Functions and Related Quantities 302
14.3.1 Pearson's Linear Correlation 302
14.3.2 Non-parametric (Rank-Order) Correlations 302
14.3.3 (Cross-) Mutual Information 303
14.3.4 Recurrence Quantification Analysis (RQA) 304
14.4 Mutual Correlations Between Different Stations 306
14.5 Ensemble Correlations 311
14.5.1 KLD-Based Dimension Estimates 312
14.5.2 Case Study I: The Christmas 1967 Flood 314
14.5.3 Non-parametric Ensemble Correlations 316
14.5.4 Case Study II: The January 1995 Flood 318
14.6 Conclusion 320
References 321
Subject Index 324