Subject Index. Block maxima, 3 Bootstrap, 45, 67, 149, 176 Box-Cox transformation, 71, 85 Brownian noise, 219

Transcription

1 Subject Index Entries in this index are generally sorted with page number as they appear in the text. Page numbers that are marked in bold face indicate that the entry appears in a title or subheading. Page numbers that are marked in italics indicate that the entry appears in the caption of a table or figure. A Algorithm Dijkstra s, 254 regional L-moment, 108 Analysis canonical correlation, 108 detrended fluctuation (DFA), 4, 5, 6 extreme value, 78, 167, 179, 181 flood frequency, 106, 107, 116 frequency, 117 linear correlation, 288 multifractal, 274 principal component (PCA), 108 wavelet, 299 Approach scaling, 3 ARMA processes, 69 Assessment flood risk, 252 hydrological, 251 Autocorrelation, 203, 207, 209, 212, 217, 219, 228, 232, 234, 235, 253, 299 function, 28, 28, 29, 207, 217, 218, 222, 234, 242, 267 B B ack-shift operator, 70 Basin, 205, 205 area, 205, 205 Basin area, 221, 222, 230, 231, 240, 242 Bernier-test, 209 Bifractal, 220, 239, 240 fit, 240, 242 model, 217, 220, 237, 239, 239, 240, 241 Block maxima, 3 Bootstrap, 45, 67, 149, 176 Box-Cox transformation, 71, 85 Brownian noise, 219 C Capacity adaptation, 139 water holding, 137 Catchment gauged, 105, 119 ungauged, 105, 121, 124 CDF, 111 Centennial events, 3, 34, 35, 37, 38 Change point, , 206, 207, 208, 208, 209, 210, 210, 211, 211, 212 Climate, 220 change, 203 factor, 168, 218 model, regional, 138 zone, 220, 234, 240 Climate, changing, 218 Cluster/Clustering, 22, 29, 34, 38, 258 Coefficient Hurst, 154, 154 Concordance, 293 Conditional exceedance probability, 32, maxima, 30, 30 maxima distribution, 31, 33 mean maxima, 29, 30, 31, 32 residual waiting time, 19, 20, 21 return interval distribution, 18 return period, 17, 18, 19, 20 J.P. Kropp, H.-J. Schellnhuber (eds.), In Extremis, DOI / , C Springer-Verlag Berlin Heidelberg

2 316 Subject Index Confidence band, 50 percentile-t type, 50 percentile-based, 50 Correlation analysis, 220, 222 cross, 288 cross-, 212 exponent, 4, 6, 9, 15, 37, 38, 207, 208, 208, 217, 223, 230, 232 linear two-point, 267 long-range, 252 long-term, 3, 15, 15 of maxima, 27 of return intervals, 14 serial, 207, 209, 210 Spearman s rank, 156 time, 4, 25, 203, 218 two-point, 274 volatility, 282 Correlation exponent, 235 Cost function, 50, 254 Covariance function, 293 Cross-recurrence matrix, 295 Crossover, 217, 219, 232, 235, 236, 239, 242, 244, 245 D Damage flood, 132 Data artificial, 18, 37, 277 climatological, 18, 21, 22 correlated, 276 deseasonalised, 280 historical, 134 i.i.d., 24, 24 observed, 18 phase-randomized, 281 phase-substituted, 281 pseudo, 49 simulated, 50 surrogate, 306 Decomposition singular value, 254 Deseasonalising, 268 Design flood, 105, 106 Design storm, 106 Detrended Fluctuation Analysis (DFA), 203, 204, 224 Detrended Fluctuation Analysis (DFA), 207, 208, 208, 209, 211, 217, 218, 224, 224, 241 Detrending, 218, 219, 224, 225, 229, 235, 273 seasonal, 232, 234, 235, 238, 241 DFA, 4, 5 Diagram L-moment, 118 Dimension estimates, 287, 301 fractal, 154 KLD, 303 LVD, 304 Dimensionality reduction, 253, 255 Discharge, 176 Discretization effect, 11, 20 Distance Euclidean, 109, 254 geodesic, 254 Mahalanobis, 109 Distribution κ, 105, 114, 117 conditional return interval, 16, 17 density, 24 exponential, 9, 10, 11, 12, 14, 15, 17, 19, 20, 24, 25, 28, 29, 33 Fisher-Tippet-Gumbel, 24 Fréchet, 24 frequency, 105, 115, 116 Gaussian, 9, 10, 11, 11, 12, 14, 15, 17, 19, 24, 25, 28, 29, 33, 35 Gumbel, 24, 25, 26, 27, 36, 186, 191 log-normal, 9, 10, 11, 12, 15, 19, 20 of extreme events, 22 Pareto, 24 Poisson, 10 power-law, 9, 10, 11, 12, 15, 19, 20 probability, 268 return interval, 9, 10, 12, 14, 16 Wakeby, 116, 119 Weibull, 3, 25, 186, 191 Distribution function, 204 E E xtreme values magnitude, 178 Effect discretization, 13, 14 finite-size, 8, 10, 11, 11, 15, 16, 19, 22, 29, 29 El Niño, 288 Elevation, 220, 233, 234 Entropy Rényi, 294 Shannon, 294

3 Subject Index 317 Estimation kernel, 49 least square, 188 maximum likelihood, 188 trend, 198 etst trend, 173 Exceedances threshold estimation, 169 Exceedances probability, 27, 28, 33, 35 Exponent Hurst, 252 Extended multiplicative cascade model, 217, 220, 230, 237, 239, 240, 243, 244, 244 Extreme event, 3, 13, 22 river flow, 145 value statistics, 22, 24 Extreme values auto-correlation, 170 frequency of occurrence, 178 trend, 171 F FARIMA parameter estimation, 70 Fisher information matrix, 85 Flood ice jam, 137 Flow quantile, 108 Fluctuation analysis, 210, 218 exponent, 207, 208, 209, 211, 218, 223, 229, 230, 233, 235, 241, 242 function, 208, 218, 224, 225, 226, 228, 229, 231, 231, 232, 233, 234, 235, 269 Fluctuation analysis, 271 detrended, 252 detrended (DFA), 271 multifractal detrendet (MF-DFA ), 271 Fluctuation Analysis (FA), 223, 223 Fluctuation exponent, 271 Fourier transform, 268, 275 amplitudes, 268 coefficient, 244 filtering technique, 244 frequency spectrum, 268 Fourier analysis, 255 Fourier filtering, 25 Fourier Filtering Method (FFM), 209 Fourier Transform, 244 Frequency, 218, 244 Function anticorrelation, 295 autocorrelation, 3, 4, 15, 15 G Gauge, , 205, 206, 208, 211, 211 number, 205, 205 Gaussian random vector, 306 Generalised Hurst exponents, 217, 226, 227, 237, 237, 238, 241 GEV, 63, 83 Gev, 109, 116 Global warming, 218 GPD, 169 Gumbel Hougaard copula, 110 H Hölder exponent, 228 Hannan-Quinn information criterion HIC, 71 HQ 100, 38 Hurst exponent, 207, 218, 225, 226, 244 phenomenon, 218 Hurst, H. E., 207, 217, 218, 225 Hydrology, 203, 204, , 219 Hypothesis null, 146 I IAAFT, 72 Illustration, 206, 209 Index trend, 156, 157, 158, 163 Indian monsoon, 288 Interval conditional return, 16, 16 return, 3 ISOMAP, 302 Isometric featuring mapping, 251, 254 Iterative, 205 J Joseph-Phenomenon, 229 K Kendall s Tau, 293 KLD, 302 Kurtosis, 110, 118 L L-moments, 105, 109, 110, 113, 117, 118 L-moments, 105 Landscape, 219

4 318 Subject Index LARSIM, 92 Legendre transform, 228, 272 Linearity, non-, 237, 239 Location parameter, 24 Long-range dependence (LRD), 65 Long-term correlation, 9, 10, 12, 18, 19, 20, 23, 29, 38 memory, 21, 38 persistence, 4, 25, 27, 31 Long-term memory, 299 Lovejoy-Schertzer, 219, 227, 228, 230, 237, 238, 242 M Mahanadi subzone, 106, 110, 115, , 123, 123 Map, 206 Matrix, 204, 205, 206, 211 Maxima annual, 23, 26, 35 centennial, 35, 36, 37 distribution, 25, Maximum, maxima, 22, 23, 24, 28 MDS, 302 Mean centennial maxima, 38 maximum, maxima, 24, 29, 30 Mean residual life plot (MRL), 169 Measure discordancy, 109, 112, 117, 117, 123 goodness of fit, 107, 115 heterogenity, 109, 113, 114, 117, 118, 124 Mechanism feedback, 287 Median, 18, 21 Memory effect, 19, 30, 31, 33, 39 Method k-nearest neighbour, 258 cross-validation, 49 delta, 85 fuzzy c-means, 108 kriging, 108 least squares, 110 maximum likelihoods, 110 Powells, 189 projection, 253 regression, 47 stepwise regression, 190 Ward s cluster, 108 Mode frequency, 251 Model coupled climate, 56 watershed, 106 Monofractal, 225, 226, 242 Mounder Minimum, 54 Moving average, 218 MSSA, 302 Multifractal, 217, 219, 221, , 235, 238, 239, analysis, 219, 220, 226, 228, 241 cascade model, 243, 244 fluctuation function, 235, 236, 239, 244, 244 formalisms, 220, 227 spectrum, 219, 239, 240, 242 spectrum, width, 240, 242, 282 Multifractal DFA (MF-DFA), 217, 219, 226, 226, 236, 241, 242, 244 Multifractal spectrum, 267 Multifractality, 210, 220, 222, 232, , 242, 244, 245 short-term, 236 strength, 228, 230, 240, 241, 241 Multiscaling, 40 Mutual Information, 293 N Neural network, 108 Nile historical water minima, 30, 32 Noah-Phenomenon, 229 Noise, 210, 211, 222, 289 Brownian, 219 red, 257 white, 218, 219 Noise, Gaussian, 211 Noise, white, 210 Nonlinear dimensionality reduction, 251 Nonlinearity artificial, 270 Nonstationarity, 154 North Atlantic thermohaline circulation, 287 Null hypothesis, 256 O Operational model, 217, 220, 237 P Parameter location, 120 scale, 120 shape, 120 PCA, 302 PDF, 46, 267 Peak flow, 106

5 Subject Index 319 Pearson correlation, 292 Persistence, 288 Pettitt, A. N., 204 Pettitt-test, 203, 203, 204, 206, 208, 208, , 211, 212 Phase coherence, 288 substitution, 270, 275 synchronisation, 288 Plot recurrence, 294 POT, 48, 134, 152, 159, 160 Power spectral analysis, 207, 219, 225, 235 spectrum, 218, 244, 256 spectrum exponent, 207, 209, 223 Power spectrum, 268 Power-law, 4 regime, 11, 12, 13 Prague annual temperature, 18, 19 Precipitation records, 220 Principal component analysis, 253 nonlinear, 263 Process AR[1], 257 linear, 268 monofractal long-term correlated, 277 multifractal long-term correlated, 277 nonlinear, 268 Processes Poisson, 170 FARIMA, 70 point, 170, 176 Profile, 210, 219, 223, 224, 224, 225, 227 Pseudo-periodicity, 55 PWM, 112 Q Q 100, 36, 37, 37 Quantile, 7, 14, 15, 18, 35, 36, 37 R Random walk, 210, 218 Randomizing, 268 Rank-order correlations, 292 Rate occurence, 49 Ratio signal noise, 294 Reconstructed data Jones northern hemisphere temperature, 18, 19 Moberg northern hemisphere temperature, 30, 32 Recurrence function, 295 Recurrence matrix, 294 Recurrence rate, 299 Regression, 218 Renyi exponents, 227, 228, 239 Rescaled Range Analysis, 207, 218, 225, 226, 235 Return interval, 3, 6, 6, 7, 7, 10, 12, 13, 15 level, 64, 175, 181 estimation, 175 uncertainty (delta method), 175 period, 7, 8, 13, 48, 108, 122, 123, 124 Risk flood, 131 River flow, 135 annual maximum, 131 Robustness, 306 RQA, 294 Runoff records, 203, 208, 209, 211, 220 S Scaling, 13, 15, 25, 29 exponent, 269 multidimensional, 251, 253 parameter, 24 Seasonal adjustment, 274 Seasonal cycle, 71, 204, 218 Sensitivity, 287 Separability, 257 Short-range dependence, 70 Sign-function, 204, 206 Simulations Monte Carlo, 110, 114, 198 Singularity spectrum, 228, 239, 242 width, 239, 242 strength, 228 Skewness, 110, 118 Smoothing kernel, 49 running mean, 49 Solar activity, 54 Spearman s Rho, 293 Spectrum monofractal, 270 multifractal, 270 power, 4 singularity, 272 SSA, 302 Standard deviation, 6, 7, 8 Stationarity, 134, 207, 209 non-, , 222, 225, 235 Stationary, 209, 210, 210, 218, 219

6 320 Subject Index Statistic deviance, 173 discordancy, 113, 117 Statistical significance, 305 Statistics extreme value, 3 Sustainable management, 105 Synchronization, 252 System analysis dynamical, 255 singular, 251 T Temperature, 218, 230 Test F, 190 goodness of fit, 172, 176 Kolmogorov-Smirnov, 170 likelihood-ratio, 172, 191 Mann-Kendall, 136, 156 resampling, 149 trend, 135, 171 Test for nonlinearity Schreibers, 269 surrogate, 273 Test of significance, 256 Theorem Fisher-Tippett, 63, 169, 172 Wiener-Khintchin, 4 Time series, 133 Trace moment technique, 219 Transformation z, 253 Transition, 287 Trend, 203, 207, , 224, 225, 234, 243 seasonal, 222, 229, 235, 241 Turbulence, 219, 227 Type I, 24 Type II, 24 Type III, 25 U Uncorrelated, 207, 209, 211, 218, 222, 223, 232, 233, 236, 237 Universal multifractal model, 217, 220, 237 V Value missing, 135 threshold, 6 Variability natural, 146 Volatility, 4 series, 270 Vulnerability, 140 W Wavelet, 225 analysis, 231, 231 method, 225 technique, 218 Wavelet Transform (WT), 225 Wavelet Transform Modulus Maxima (WTMM), 226 discrete, 225 Gaussian, 225 Haar, 225 White noise, 8, 15