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  • 1
    Monograph available for loan
    Monograph available for loan
    Climate time series analysis : classical statistical and bootstrap methods (2014)
    Cham [u.a.] : Springer
    Associated volumes
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    Call number: AWI S2-14-0040
    In: Atmospheric and oceanographic sciences library
    Description / Table of Contents: Contents: PART 1 FUNDAMENTAL CONCEPTS. - 1 Introduction. - 1.1 Climate archives, variables and dating. - 1.2 Noise and statistical distribution. - 1.3 Persistence. - 1.4 Spacing. - 1.5 Aim and structure of this book. - 1.6 Background material. - 2 Persistence models. - 2.1 First-Order Autoregressive Model. - 2.1.1 Even spacing. - 2.1.2 Uneven Spacing. - 2.2 Second-Order Autoregressive Model. - 2.3 Mixed Autoregressive Moving Average Model. - 2.4 Other models. - 2.4.1 Long-memory process. - 2.4.2 Nonlinear and non-gaussian models. - 2.5 Climate theory. - 2.5.1 Stochastic climate models. - 2.5.2 Long memory of temperature fluctuations?. - 2.5.3 Long memory of river runoff. - 2.6 Background material. - 2.7 Technical issues. - 3 Bootstrap confidence intervals. - 3.1 Error bars and confidence intervals. - 3.1.1 Theoretical example: Mean estimation of Gaussian White Noise. - 3.1.2 Theoretical example: Standard deviation estimation of Gaussian White Noise. - 3.1.3 Real world. - 3.2 Bootstrap principle. - 3.3 Bootstrap resampling. - 3.3.1 Nonparametric: Moving block bootstrap. - 3.3.2 Parametric: Autoregressive Bootstrap. - 3.3.3 Parametric: Surrogate Data. - 3.4 Bootstrap Confidence Intervals. - 3.4.1 Normal confidence interval. - 3.4.2 Student's t confidence interval. - 3.4.3 Percentile confidence interval. - 3.4.4 BCa Confidence Interval. - 3.5 Examples. - 3.6 Bootstrap hypothesis tests. - 3.7 Notation. - 3.8 Background material. - 3.9 Technical issues. - PART 2 UNIVARIATE TIME SERIES. - 4 Regression I. - 4.1 Linear regression. - 4.1.1 Weighted least-squares and ordinary least-squares estimation. - 4.1.2 Generalized least-squares estimation. - 4.1.3 Other estimation types. - 4.1.4 Classical confidence intervals. - 4.1.5 Bootstrap confidence intervals. - 4.1.6 Monte Carlo Experiments: Ordinary least-squares estimation. - 4.1.7 Timescale errors. - 4.2 Nonlinear regression. - 4.2.1 Climate Transition Model: Ramp. - 4.2.2 Trend-Change Model: Break. - 4.3 Nonparametric regression or smoothing. - 4.3.1 Kernel estimation. - 4.3.2 Bootstrap confidence intervals and bands. - 4.3.3 Extremes or outlier detection. - 4.4 Background material. - 4.5 Technical issues. - 5 Spectral analysis. - 5.1 Spectrum. - 5.1.1 Example: AR(1) process, discrete time. - 5.1.2 Example: AR(2) process, discrete time. - 5.1.3 Physical meaning. - 5.2 Spectral estimation. - 5.2.1 Periodogram. - 5.2.2 Welch's overlapped segment averaging. - 5.2.3 Multitaper estimation. - 5.2.4 Lomb-Scargle estimation. - 5.2.5 Peak detection: red-noise hypthesis. - 5.2.6 Example: Peaks in monsoon spectrum. - 5.2.7 Aliasing. - 5.2.8 Timescale errors. - 5.2.9 Example: Peaks in monsoon spectrum (continued). - 5.3 Background material. - 5.4 Technical Issues. - 6 Extreme value time series. - 6.1 Data types. - 6.1.1 Event times. - 6.1.2 Peaks over threshold. - 6.1.3 Block extremes. - 6.1.4 Remarks on data selection. - 6.2 Stationary models. - 6.2.1 Generalized extreme value distribution. - 6.2.2 Generalized pareto distribution. - 6.2.3 Bootstrap confidence intervals. - 6.2.4 Example: Elbe summer floods, 1852-2002. - 6.2.5 Persisitence. - 6.2.6 Remark: Tail estimation. - 6.2.7 Remark: Optimal estimation. - 6.3 Nonstationary models. - 6.3.1 Time-dependent generalized extreme value distribution. - 6.3.2 Inhomogenous poisson process. - 6.3.3 Hybrid: Poisson-Extreme value distribution. - 6.4 Sampling and time spacing. - 6.5 Background material. - 6.6 Technical issues. - PART 3 BIVARIATE TIME SERIES. - 7. Correlation. - 7.1 Pearson's Correlation Coefficient. - 7.1.1 Remark: Alternative correlation measures. - 7.1.2 Classical confidence intervals, nonpersistent processes. - 7.1.3 Bivariate time series models. - 7 .1.4 Classical Confidence Intervals, Persistent Processes. - 7.1.5 Bootstrap Confidence Intervals. - 7.2 Spearman's Rank Correlation Coefficient. - 7.2.1 Classical Confidence Intervals, Nonpersistent Processes. - 7.2.2 Classical Confidence Intervals, Persistent Processes. - 7.2.3 Bootstrap Confidence Intervals. - 7.3 Monte Carlo Experiments. - 7.4 Example: Elbe Runoff Variations. - 7.5 Unequal Timescales. - 7.5.1 Binned Correlation. - 7.5.2 Synchrony Correlation. - 7.5.3 Monte Carlo Experiments. - 7.5.4 Example: Vostok Ice Core Records. - 7.6 Background Material. - 7. 7 Technical Issues. - 8 Regression II. - 8.1 Linear Regression. - 8.1.1 Ordinary Least-Squares Estimation. - 8.1.2 Weighted Least-Squares for Both Variables Estimation. - 8.1.3 Wald-Bartlett Procedure. - 8.2 Bootstrap Confidence lntervals. - 8.2.1 Simulating Incomplete Prior Knowledge. - 8.3 Monte Carlo Experiments. - 8.3.1 Easy Setting. - 8.3.2 Realistic Setting: Incomplete Prior Knowledge. - 8.3.3 Dependence on Accuracy of Prior Knowledge. - 8.3.4 Mis-Specified Prior Knowledge. - 8.4 Example: Climate Sensitivity. - 8.5 Prediction. - 8.5.1 Example: Calibration of a Proxy Variable. - 8.6 Lagged Regression. - 8.6.1 Example: CO2 and Temperature Variations in the Pleistocene. - 8.7 Background Material. - 8.8 Technical Issues. - PART 4 OUTLOOK. - 9 Future Directions. - 9 .1 Timescale Modeling. - 9.2 Novel Estimation Problems. - 9.3 Higher Dimensions. - 9.4 Climate Models. - 9.4.1 Fitting Climate Models to Observations. - 9.4.2 Forecasting with Climate Models. - 9.4.3 Design of the Cost Function. - 9.4.4 Climate Model Bias. -9.5 Optimal Estimation. - 9.6 Background Material. - References. - Author Index. - Subject Index.
    Description / Table of Contents: Climate is a paradigm of a complex system. Analysing climate data is an exciting challenge, which is increased by non-normal distributional shape, serial dependence, uneven spacing and timescale uncertainties. This book presents bootstrap resampling as a computing-intensive method able to meet the challenge. It shows the bootstrap to perform reliably in the most important statistical estimation techniques: regression, spectral analysis, extreme values and correlation. This book is written for climatologists and applied statisticians. It explains step by step the bootstrap algorithms (including novel adaptions) and methods for confidence interval construction. It tests the accuracy of the algorithms by means of Monte Carlo experiments. It analyses a large array of climate time series, giving a detailed account on the data and the associated climatological questions.
    Type of Medium: Monograph available for loan
    Pages: xxxii, 454 S. : Ill., graph. Darst.
    Edition: 2nd ed.
    ISBN: 9783319044491
    Series Statement: Atmospheric and oceanographic sciences library 51
    Branch Library: AWI Library
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  • 2
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    Optimal heavy tail estimation – Part 1: Order selection (2017)
    Copernicus
    Details
    Publication Date: 2017-12-06
    Description: The tail probability, P, of the distribution of a variable is important for risk analysis of extremes. Many variables in complex geophysical systems show heavy tails, where P decreases with the value, x, of a variable as a power law with a characteristic exponent, α. Accurate estimation of α on the basis of data is currently hindered by the problem of the selection of the order, that is, the number of largest x values to utilize for the estimation. This paper presents a new, widely applicable, data-adaptive order selector, which is based on computer simulations and brute force search. It is the first in a set of papers on optimal heavy tail estimation. The new selector outperforms competitors in a Monte Carlo experiment, where simulated data are generated from stable distributions and AR(1) serial dependence. We calculate error bars for the estimated α by means of simulations. We illustrate the method on an artificial time series. We apply it to an observed, hydrological time series from the River Elbe and find an estimated characteristic exponent of 1.48 ± 0.13. This result indicates finite mean but infinite variance of the statistical distribution of river runoff.
    Print ISSN: 1023-5809
    Electronic ISSN: 1607-7946
    Topics: Geosciences , Physics
    Published by Copernicus on behalf of European Geosciences Union.
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  • 3
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    Planktic and Benthic 14C Reservoir Ages for Three Ocean Basins, Calibrated by a Suite of 14C Plateaus in the Glacial-to-Deglacial Suigetsu Atmospheric 14C Record (2015)
    Cambridge University Press
    Details
    Publication Date: 2015-01-01
    Description: This article presents a compilation of planktic and benthic 14C reservoir ages for the Last Glacial Maximum (LGM) and early deglacial from 11 key sites of global ocean circulation in the Atlantic and Indo-Pacific Ocean. The ages were obtained by 14C plateau tuning, a robust technique to derive both an absolute chronology for marine sediment records and a high-resolution record of changing reservoir/ventilation ages (Δ14C values) for surface and deep waters by comparing the suite of planktic 14C plateaus of a sediment record with that of the atmospheric 14C record. Results published thus far have used as atmospheric 14C reference U/Th-dated corals, the Cariaco planktic record, and speleothems. We have now used the varve-counted atmospheric 14C record of Lake Suigetsu terrestrial macrofossils to recalibrate the boundary ages and reservoir ages of the seven published records directly to an atmospheric 14C record. In addition, the results for four new cores and further planktic results for four published records are given. Main conclusions from the new compilation are the following: (1) The Suigetsu atmospheric 14C record on its varve-counted timescale reflects all 14C plateaus, their internal structures, and relative length previously identified, but implies a rise in the average 14C plateau age by 200–700 14C yr during the LGM and early deglacial times. (2) Based on different 14C ages of coeval atmospheric and planktic 14C plateaus, marine surface water Δ14C may have temporarily dropped to an equivalent of ∼0 yr in low-latitude lagoon waters, but reached 〉2500 14C yr both in stratified subpolar waters and in upwelled waters such as in the South China Sea. These values differ significantly from a widely assumed constant global planktic Δ14C value of 400 yr. (3) Suites of deglacial planktic Δ14C values are closely reproducible in 14C records measured at neighboring core sites. (4) Apparent deep-water 14C ventilation ages (equivalents of benthic Δ14C), deduced from the sum of planktic Δ14C and coeval benthic-planktic 14C differences, vary from 500 up to 〉5000 yr in LGM and deglacial ocean basins.
    Print ISSN: 0033-8222
    Electronic ISSN: 1945-5755
    Topics: Archaeology , Energy, Environment Protection, Nuclear Power Engineering , Geosciences
    Published by Cambridge University Press
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  • 4
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    Optimal heavy tail estimation, Part I: Order selection (2017)
    Copernicus
    Details
    Publication Date: 2017-06-20
    Description: The tail probability, P, of the distribution of a variable is important for risk analysis of extremes. Many variables in complex geophysical systems show heavy tails, where P decreases with the value, x, of a variable as a power law with characteristic exponent, α. Accurate estimation of α on the basis of data is currently hindered by the problem of the selection of the order, that is, the number of largest x-values to utilize for the estimation. This paper presents a new, widely applicable, data-adaptive order selector, which is based on computer simulations and brute force search. It is the first in a set of papers on optimal heavy tail estimation. The new selector outperforms competitors in a Monte Carlo experiment, where simulated data are generated from stable distributions and AR(1) serial dependence. We calculate error bars for the estimated α by means of simulations. We illustrate the method on an artificial time series. We apply it to an observed, hydrological time series from the river Elbe and find an estimated characteristic exponent of 1.48 ± 0.13. This result indicates finite mean but infinite variance of the statistical distribution of river runoff.
    Electronic ISSN: 2198-5634
    Topics: Geosciences , Physics
    Published by Copernicus on behalf of European Geosciences Union.
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  • 5
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    On the low frequency component of the ENSO–Indian Monsoon relationship; a paired proxy perspective (2013)
    Copernicus
    In:  EPIC3Climate of the Past Discussions, Copernicus, 9, pp. 3103-3123, ISSN: 1814-9324
    Details
    Publication Date: 2019-07-17
    Description: There are a number of clear examples in the instrumental period where positive El Niño events were coincident with a severely weakened summer monsoon over India (ISM). ENSO's influence on the Indian Monsoon has therefore remained the centerpiece of various predictive schemes of ISM rainfall for over a century. The teleconnection between the monsoon and ENSO has undergone a protracted weakening since the late 1980's suggesting the strength of ENSO's influence on the monsoon may vary considerably on multidecadal timescales. The recent weakening has specifically prompted questions as to whether this shift represents a natural mode of climate variability or a fundamental change in ENSO and/or ISM dynamics due to anthropogenic warming. The brevity of empirical observations and large systematic errors in the representation of these two systems in state-of-the-art general circulation models hamper efforts to reliably assess the low frequency nature of this dynamical coupling under varying climate forcings. Here we place the 20th century ENSO-Monsoon relationship in a millennial context by assessing the phase angle between the two systems across the time spectrum using a continuous tree-ring ENSO reconstruction from North America and a speleothem oxygen isotope (δ18O) based reconstruction of the ISM. The results suggest that in the high-frequency domain (≤ 15 yr), El Niño (La Niña) events persistently lead to a weakened (strengthened) monsoon consistent with the observed relationship between the two systems during the instrumental period. However, in the low frequency domain (≥ 60 yr), periods of strong monsoon are, in general, coincident with periods of enhanced ENSO variance. This relationship is opposite to which would be predicted dynamically and leads us to conclude that ENSO is not pacing the prominent multidecadal variability that has characterized the ISM over the last millennium.
    Repository Name: EPIC Alfred Wegener Institut
    Type: Article , notRev
    Format: application/pdf
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