Dmitry Vyushin PhD Thesis 2009

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<p>STATISTICAL APPROXIMATION OF NATURAL CLIMATE VARIABILITYbyDmitry I. VyushinA thesis submitted in conformity with the requirementsfor the degree of Doctor of PhilosophyGraduate Department of PhysicsUniversity of TorontoCopyright c 2009 by Dmitry I. VyushinAbstractStatistical Approximation of Natural Climate VariabilityDmitry I. VyushinDoctor of PhilosophyGraduate Department of PhysicsUniversity of Toronto2009One of the main problems in statistical climatology is to construct a parsimonious model ofnatural climate variability. Such a model serves for instance as a null hypothesis for detectionof human induced climate changes and of periodic climate signals. Fitting this model to variousclimatic time series also helps to infer the origins of underlying temporal variability and tocross validate it between different data sets. We consider the use of a spectral power-lawmodel in this role for the surface temperature, for the free atmospheric air temperature of thetroposphere and stratosphere, and for the total ozone. First, we lay down a methodologicalfoundation for our work. We compare two variants of ve different power-law tting methodsby means of Monte-Carlo simulations and their application to observed air temperature. Thenusing the best two methods we t the power-law model to several observational products andclimate model simulations. We make use of specialized atmospheric general circulation modelsimulations and of the simulations of the Coupled Model Intercomparison Project 3 (CMIP3).The specialized simulations allow us to explain the power-lawexponent spatial distribution andto account for discrepancies in scaling behaviour between different observational products. Wend that most of the pre-industrial control and 20th century model simulations capture manyaspects of the observed horizontal and vertical distribution of the power-law exponents. At thesurface, regions with robust power-law exponents the North Atlantic, the North Pacic, andthe Southern Ocean coincide with regions with strong inter-decadal variability. In the freeatmosphere, the large power-law exponents are detected on annual to decadal time scales iniithe tropical and subtropical troposphere and stratosphere. The spectral steepness in the formeris explained by its strong coupling to the surface and in the latter by its sensitivity to volcanicaerosols. However power-law behaviour in the tropics and in the free atmosphere saturateson multi-decadal timescales. We propose a novel diagnostic to evaluate the relative goodness-of-t of the autoregressive model of the rst order (AR1) and the power-law model. Thecollective behaviour of CMIP3 simulations appears to fall between the two statistical models.Our results suggest that the power-law model should serve as an upper bound and the AR1model should serve as a lower bound for climate persistence on monthly to decadal time scales.On the applied side we nd that the presence of power-law like natural variability increasesthe uncertainty on the long-term total ozone trend in the Northern Hemisphere high latitudesattributable to anthropogenic chlorine by about a factor of 1.5, and lengthens the expected timeto detect ozone recovery by a similar amount.iiiDedicationTo my wife, Oxana, and my parents, Igor and EugeniaivAcknowledgementsFirstly, I want to thank my supervisor, Paul J. Kushner. I am deeply indebted to Paul Kushnerfor his guidance and support during the years of my PhD study. Professor Kushner signi-cantly improved my ability to focus on important research questions and to identify the mostimportant features of a phenomenon under study. He was almost always available for scienticdiscussions and full of stimulating ideas, but also provided me a lot of freedom. I would alsolike to acknowledge Professor Kushners career advice.A part of my thesis work has been done in collaboration with Vitali Fioletov from Environ-ment Canada, Theodore G. Shepherd, and Josh Mayer. I have beneted from Vitali Fioletovsexpertise in ozone research and statistical modeling. I truly appreciate the fact that ProfessorShepherd introduced me to the Atmospheric Physics Group in the Department of Physics. Hissharp critical thinking and a strong common sense were very helpful in my scientic develop-ment. Josh Mayer spent two summers as a summer student in Prof. Kushners group and helpeda lot with the analysis of CMIP3 models and coauthoring an R-package containing functionsused in the thesis.I would like to thank my committee members, Dylan B. A. Jones and Francis W. Zwiers,for their support, encouragement, and fruitful advice. I acknowledge the insights of my ex-ternal reviewer, Professor Carl Wunsch, which lead to an improvement of the thesis. Specialthanks go to Michael Sigmond, Chris Fletcher, Slava Kharin, Steven Hardiman, Edwin Ger-ber, Henning Rust, Alexander Korobov, David Stephenson, Nickolas Watkins, and WladislavTchernov for useful feedback and helpful criticism. I am thankful to the Atmospheric Physicsformer and current graduate students and postdocs, Sorin Codoban, Tiffany Shaw, Lei Wang,Thomas Birner, Constantine Nenkov, Tobias Kerzenmacher, Ellie Farahani, Andreas Jonsson,Mark Parrington, Robert Field, Jane Liu, Annemarie Fraser, and Jeffrey Taylor, for their helpand suggestions as well as for creating a friendly and stimulating atmosphere in the group.vI am very much obliged to my wife, Oxana, for her support of my academic endeavours.I am grateful to my former supervisor, Professor Vadim Strygin, who brought me intoscience and shared with me the joy of doing it.I acknowledge the support of the Natural Sciences and Engineering Research Council,Canadian Meteorological and Oceanographic Society, Environment Canada, and the Centre forGlobal Change Science, which prevented my life during my PhD study from being miserable.viContents1 Introduction 11.1 Characteristics of natural climate variability . . . . . . . . . . . . . . . . . . . 11.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Methodological Basis 262.1 Introduction to long-range correlated processes . . . . . . . . . . . . . . . . . 262.2 Description and Tests of Power-law Estimators . . . . . . . . . . . . . . . . . 282.2.1 Spectral Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2.2 Time domain method: Detrended uctuation analysis (DFA) . . . . . . 312.3 Benchmark tests of the estimator methods . . . . . . . . . . . . . . . . . . . . 322.4 Trend variance and the number of years required to detect a trend . . . . . . . . 372.4.1 Estimation of trend variance through autocovariance . . . . . . . . . . 382.4.2 Approximation of autocovariance by exponential function . . . . . . . 392.4.3 Approximation of autocovariance by power law function . . . . . . . . 402.4.4 Estimation of trend variance through spectral density . . . . . . . . . . 412.4.5 Estimation of the number of years required to detect a trend . . . . . . 422.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 Total ozone trend detection 453.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45vii3.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.3 Analysis of long-range correlations in total ozone time series . . . . . . . . . . 493.3.1 Statistical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.3.2 Illustrations of long-range correlations . . . . . . . . . . . . . . . . . . 533.3.3 Quantication of long-range correlations in zonally averaged ozone . . 573.4 Signicance of long-term trends in zonal-mean total ozone . . . . . . . . . . . 623.4.1 Long-term ozone decline . . . . . . . . . . . . . . . . . . . . . . . . . 623.4.2 Recent and future ozone increase . . . . . . . . . . . . . . . . . . . . 653.5 Longitudinal structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.6 Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733.7 Appendix A: Comparison with ground based measurements for 1979-2008 . . . 763.8 Appendix B: Analysis of Kiss et al. results . . . . . . . . . . . . . . . . . . . . 784 Power-law characteristics of the atmospheric general circulation 884.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.2 Results for unltered data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 904.3 Effect of multitapering and frequency range . . . . . . . . . . . . . . . . . . . 924.4 Effects of ltering and choice of reanalysis product . . . . . . . . . . . . . . . 934.5 Hurst exponent estimates of zonal-mean temperature . . . . . . . . . . . . . . 984.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005 Reanalysis vs. specialized GCM simulations 1035.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1035.2 Specialized GCM simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.3 Inuence of tropical SSTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065.4 DFA3 vs GSPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.5 Effect of volcanic eruptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114viii6 Analysis of CMIP3 simulations 1166.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1166.2 Data and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1176.3 Results for the surface air temperature . . . . . . . . . . . . . . . . . . . . . . 1186.3.1 Time aggregation effect . . . . . . . . . . . . . . . . . . . . . . . . . 1186.3.2 Spatial patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226.3.3 Comparison to previously published results . . . . . . . . . . . . . . . 1306.3.4 Goodness of t tests of power-law and AR1 models . . . . . . . . . . . 1326.4 Results for the free atmosphere air temperature . . . . . . . . . . . . . . . . . 1356.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.6 Appendix A: A combination of multiscale AR1 models . . . . . . . . . . . . . 1437 Conclusions 1467.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1467.2 Potential Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151A A list of temporal power-law analysis studies related to climate 155B R-package PowerSpectrum documentation 161Bibliography 199ixThe list of acronyms20c3m CMIP3 simulations of the 20th centuryACF AutoCorrelation FunctionAR1 AutoRegressive model of the rst orderARFIMA AutoRegressive Fractionally Integrated Moving Average modelARMA AutoRegressive Moving Average modelCCMVal Chemistry-Climate Model Validation ActivityCET Central England TemperatureCMIP3 The third phase of the Coupled Model Intercomparison ProjectCRU Climatic Research UnitDFA3 Detrended Fluctuation Analysis of the third orderECMWF European Centre for Medium-Range Weather ForecastsEESC Equivalent Effective Stratospheric ChlorineENSO El Ni no-Southern OscillationERA40 ECMWF reanalysis (09.1957-08.2002)FAAT Free Atmosphere Air TemperatureFAR Fractional AutoRegressive modelGCM General Circulation ModelGFDL Geophysical Fluid Dynamics LaboratoryGFDL AM GFDL Atmospheric ModelGISS NASA Goddard Institute for Space StudiesGPHE Geweke-Porter-Hudak EstimatorGSPE Gaussian SemiParametric EstimatorHadCM Hadley Centre Climate ModelHDD Heating Degree DaysIPCC Intergovernmental Panel on Climate ChangexThe list of acronyms (continued)JRA-25 Japanese ReAnalysis (1979 till present)LRC Long-Range CorrelationsLTR linear trendMTM multitaper methodNAO North Atlantic OscillationNASA National Aeronautics and Space AdministrationNCAR National Center for Atmospheric ResearchNCEP National Centers for Environmental PredictionNP North Pacicpicntrl pre-industrial control CMIP3 simulationsPC Principal Component (from Principal Component Analysis)PCM Parallel Climate ModelPWLT PieceWise-Linear TrendQBO Quasi-Biennial OscillationSAGE Stratospheric Aerosol and Gas Experiment (satellite instrument)SAT Surface Air Te...</p>