A New Ice Core Paleothermometer for Holocene and Transition Diffusion Processes Quantified by Spectral Methods
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FACULTY OF SCIENCE UNIVERSITY OF COPENHAGEN Master Thesis in Geophysics A New Ice Core Paleothermometer for Holocene and Transition Di®usion Processes Quanti¯ed by Spectral Methods Sebastian Bjerregaard Simonsen Centre for Ice and Climate, Niels Bohr Institute, University of Copenhagen Supervisor: Sigf¶usJ. Johnsen December 2008 II A New Ice Core Paleothermometer Master Thesis Title: A New Ice Core Paleothermometer for Holocene and Transition Subtitle: Di®usion Processes Quanti¯ed by Spectral Methods ECTS-points: 60 Supervisor: Sigfus J. Johnsen Name of department: Centre for Ice and Climate Neils Bohr Institute University of Copenhagen Author: Sebastian Bjerregaard Simonsen Date: December 31th 2008 Abstract Since the early 1950's stable water isotopes have been considered a temper- ature proxy with application in paleoclimatic reconstruction of permanently snow covered areas. In this thesis a new method of reconstructing the pale- oclimatic information preserved in the isotopic records from Arctic ice cores is tested. The method is based on the de¯nition of the di®erential di®usion 2 2 2 length ¢σ = σ18O ¡ σD. An investigation of the processes a®ecting the di®erential di®usion length is undertaken, covering the densi¯cation of ¯rn, ice flow modelling and isotopic di®usivity in the ¯rn and ice matrix. Three numerical power spectra density estimation methods have been used to retrieve the di®erential di®usion length in 22 sections of ice from two Greenlandic ice cores, GRIP and NGRIP. None of the methods are found superior, but both Burg's algorithm and the Autocorrelation methods show promising behaviors. The modelled and measured di®erential di®usion lengths form an estimate of the surface temperature at the origin of the ice core sections. The inves- tigation of the di®erential di®usion length in deep sections from the NGRIP ice core shows that the temperature reconstruction based on the di®erential di®usion length must be limited to ice younger than about 40 kyr for the two cores. This reduces the number of ice core sections available to 12. The low number of sections limits the interpretation of the tested temperature reconstruction. However, the estimated surface temperatures are within un- certainties of paleotemperatures records derived from combined bore hole temperature and isotope pro¯les from the GRIP and NGRIP ice cores. IV A New Ice Core Paleothermometer Preface The presented thesis accounts for the ¯nal exam of a Masters Degree in Geo- physics at the University of Copenhagen and covers 60-ECTS point. The study has been conducted in about a year of full time study. A basic knowledge of mathematics and physics is required to read this the- sis along with knowledge of Glaciology. If necessary terms are explained to clarify the de¯nitions used. The abbreviations used are all summarized in the Nomenclature at the end of the thesis. All plotted time scales start at present and end at a time before present. To ease the comparison between text and plots I write that the transition into the Last Glacial follows the Holocene, despite that it is reversed in real time. All programming has been conducted using Matlab. VI A New Ice Core Paleothermometer Acknowledgment I would like to thank my supervisor Sigfus J. Johnsen for the many hours of productive discussions of the problems at hand along with introducing me to the study subject. Trevor J. Popp is thanked for providing isotopic data from the NGRIP ice core and proof reading. I thank Ph.D student Hans Christian Steen-Larsen for showing interest and support for the work and proof reading, Ghita Hansen for proof reading and Lykke Pedersen for the love and support during the writing of this thesis and also for proof reading. I would also like to thank the Centre for Ice and Climate at the Niels Bohr Institute for supplying an ideal environment for working with this thesis, along with providing the opportunity to go to the NEEM drill site to expe- rience the ¯eld work involved in drilling ice cores. Finally, my o±ce mates deserve thanks for the productive discussions and the needed distractions. Sebastian B. Simonsen Copenhagen, December 2008 Preface for 2nd Edition After handing in this master thesis December 31th 2008 a couple of errors has come to my attention. They have not been corrected in the thesis. However a list will be given here: Page 51 : Equation (5.18) was ¯st described by [Johnsen et al., 2000]. Page 76 : Severinghaus et al. [1998] was not doing measurements on the GRIP ice core, but GISP2. Equation (5.21) : On the right hand side of the equation in the denomi- nator the subscript sam should be sec. If further errors are found in this work I would be glad to hear about it. Send me a mail on [email protected] Sebastian B. Simonsen Copenhagen, February 2009 VIII A New Ice Core Paleothermometer Contents Contents IX 1 Introduction 1 1.1 Dating Ice Cores . 3 2 Ice Cores as a Paleothermometer 5 2.1 Stable Water Isotopes . 5 2.1.1 Temperature Proxy from Water Isotopes . 8 2.2 Other Methods . 11 2.2.1 Borehole Inversion . 11 2.2.2 Melt Layer Analysis . 11 2.2.3 Accumulation Change . 11 2.2.4 Gas Isotopes . 12 2.3 Outline of a New Palaeothermometer . 12 3 Densi¯cation of Firn 13 3.1 Densi¯cation by the Arnaud-model . 14 3.2 Densi¯cation by the Herron-Langway-model . 15 3.3 Comparison of the Two Models . 16 4 Models of Ice Flow 19 4.1 Flow in Firn . 19 4.2 Flow in Ice . 20 4.2.1 Coordinate System . 20 4.2.2 Derivation of Normal Strain Rates . 21 4.3 The Dansgaard-Johnsen Flow Model . 22 4.3.1 De¯nition of the Shape Function . 24 4.4 Modelling the Ice Flow . 24 X A New Ice Core Paleothermometer 4.5 Parametrization of the Flow Equation . 25 4.6 Forward Modelling of Particle Paths . 29 4.7 Formulation of the Inverse Problem . 32 4.7.1 A Priori Information . 32 4.7.2 Occam's Inversion . 33 4.7.3 Probability Density of Data and Likelihood Function . 34 4.7.4 Metropolis Algorithm for Monte Carlo Simulations . 34 4.7.5 Burn-in and Model Sampling . 35 4.7.6 Model Parameter Estimation After Sampling . 36 4.8 NGRIP A Priori Information . 37 4.8.1 Estimation of Lagrange Multipliers . 38 4.9 Results of the Monte Carlo Simulations . 39 4.10 Comparison with the ss09sea . 41 5 Isotopic Di®usion in Firn and Ice 45 5.1 Di®usion in Firn . 46 5.1.1 Analytical Solution of the Di®usion Length . 47 5.1.2 Numerical Solution of the Di®usion Length . 47 5.1.3 Temperature Dependency of the Di®usion length . 48 5.2 Di®usion in Ice . 50 5.3 Di®erential Di®usion Length . 51 5.4 Modelled Di®usion Length . 52 6 Spectral Analysis of Isotopic Data 55 6.1 Depositional Spectra of Snow . 55 6.2 Power Spectral Properties of Di®usion . 56 6.2.1 The Fourier Transformed Isotopic Di®usion . 56 6.2.2 Sampling E®ects . 57 6.2.3 Measuring Noise and Cut-O® . 59 6.2.4 Climate Variability Correction . 59 6.3 Data Processing . 60 6.3.1 Fast Fourier Transform . 60 6.3.2 Autocorrelation Method . 63 6.3.3 Burg's Algorithm . 65 7 Results and Discussion 69 7.1 Spectral Estimates of Di®erential Di®usion . 69 7.2 Ice Di®usivity in the NGRIP Core . 72 7.3 Paleoclimatic Record from Di®erential Di®usion . 73 7.3.1 GRIP Record . 73 7.3.2 NGRIP Record . 76 7.4 Processing Long Records . 76 7.5 Bias in the Presented Paleothermometer . 78 7.5.1 Firn Depth . 78 CONTENTS XI 7.5.2 Flow Model Induced Uncertainties . 79 7.5.3 Ice Sheet Evolution . 79 7.5.4 Sample Size of the Measured Water Isotopes . 80 7.5.5 Cut-o® . 80 8 Conclusion 83 9 Outlook 85 10 Danish Summery - Dansk Resume 87 Appendices 91 A Analysis and Data for the Flow model 91 A.1 Testing the Forward Algorithm . 91 A.2 Inverse modelling with out Occam . 93 A.3 NGRIP and NEEM Depth vs. Age Data . 94 B Di®usion lengths 95 Bibliography 97 List of Figures 105 List of Tables 107 Nomenclature 109 XII A New Ice Core Paleothermometer 1 Introduction In the past couple of years the climate has caught a lot of attention in the broad media picture. The global warming is on everybody's lips. Suddenly, the present warming has become a global issue. Big organizations such as the UN have turned there focus on it through the Intergovernmental Panel on Climate Change (IPCC, [IPCC, 2007]). The reason that we are talking about a global warming is due to our ability to determine the past climate, past the time scale of manmade temperature measurements. A whole sci- ence has developed around this called paleoclimatology, covering a broad range of study disciplines, e.g. tree rings, sedimentary, corals, speleotherms and ice cores. All are able to determine past climate on di®erent time scales and time resolution. One of the most successful methods to determine the past climate for the last couple of hundred thousand years has proven to be ice cores. Depending on the site, ice cores have a climate record of di®erent lengths; Greenland about 115 to 250 kyr1 back in time [Dansgaard et al., 1993], and Antarctica at least 800 kyr back in time [EPICA Members, 2004].