ALBERT

Note: Contents: 1 General introduction. - 1.1 Challenges of isotope-based temperature reconstructions. - 1.2 Thesis overview. - 1.3 Author contributions. - 2 Theoretical background. - 2.1 The isotopic composition of firn and ice. - 2.1.1 Fractionation of water isotopologues. - 2.1.2 Relationship with temperature. - 2.1.3 Measuring of the isotopic composition. - 2.2 Processes within the firn column. - 2.2.1 The firn column of polar ice sheets. - 2.2.2 The density of firn. - 2.2.3 The temperature profile of firn. - 2.2.4 Vapour diffusion in firn. - 2.3 Internal climate variability. - 3 Regional climate signal vs.local noise: a two-dimensional view of water isotopes. - 3.1 Introduction. - 3.2 Data and methods. - 3.3 Results. - 3.3.1 Trench isotope records. - 3.3.2 Single-profile representativity. - 3.3.3 Mean trench profiles. - 3.3.4 Spatial correlation structure. - 3.3.5 Statistical noise model. - 3.4 Discussion. - 3.4.1 Local noise vs. regional climate signal. - 3.4.2 Representativity of isotope signals. - 3.4.3 Implications. - 3.5 Conclusions. - 3.6 Appendix A: Derivation of noise model. - 3.6.1 Definitions. - 3.6.2 Derivation of model correlations. - 3.6.3 Estimation of parameters. - 3.7 Appendix B: Noise level after diffusion. - 4 Constraints on post-depositional isotope modifications in east antarctic firn. - 4.1 Introduction. - 4.2 Data and methods. - 4.2.1 Sampling and measurements. - 4.2.2 Trench depth scale. - 4.2.3 Spatial variability of trench profiles. - 4.2.4 Quantification of downward advection, densification and diffusion. - 4.2.5 Statistical tests. - 4.3 Results. - 4.3.1 Comparison of T15 and T13 isotope data. - 4.3.2 Expected isotope profile changes. - 4.3.3 Temporal vs. spatial variability. - 4.4 Discussion. - 4.4.1 Densification, diffusion and stratigraphic noise. - 4.4.2 Additional post-depositional modifications. - 4.5 Conclusions. - 5 On the similarity and apparent cycles of isotope variations. - 5.1 Introduction. - 5.2 Data and Methods. - 5.2.1 Data. - 5.2.2 Spectral analysis. - 5.2.3 Rice’s formula. - 5.2.4 Cycle length and amplitude estimation. - 5.2.5 Model for vertical isotope profiles. - 5.3 Results. - 5.3.1 Spectral analysis of isotope profiles. - 5.3.2 Theoretical and observed cycle length. - 5.3.3 Illustrative examples. - 5.3.4 Depth dependency of cycle length. - 5.3.5 Simulated vs. observed isotope variations. - 5.4 Discussion and summary. - 5.5 Conclusions. - 5.6 Appendix A: Input sensitivity. - 5.7 Appendix B: Additional results. - 5.8 Appendix C: Spectral significance testing. - 6 Timescale-dependency of antarctic isotope variations. - 6.1 Introduction. - 6.2 Data and methods. - 6.2.1 DML and WAIS isotope records. - 6.2.2 Spectral model. - 6.2.3 Timescale-dependent signal-to-noise ratio. - 6.2.4 Effects of diffusion and time uncertainty. - 6.2.5 Present-day temperature decorrelation. - 6.3 Results. - 6.3.1 Illustration of model approach. - 6.3.2 DML and WAIS isotope variability. - 6.4 Discussion. - 6.4.1 Interpretation of noise spectra. - 6.4.2 Interpretation of signal spectra. - 6.4.3 Signal-to-noise ratios. - 6.4.4 Differences between DML and WAIS. - 6.5 Conclusions. - 7 Declining temperature variability from LGM to holocene. - 8 General discussion and conclusions. - 8.1 Short-scale spatial and temporal isotope variability. - 8.1.1 Local spatial variability. - 8.1.2 Seasonal to interannual variability. - 8.1.3 Spatial vs. temporal variability. - 8.2 Extension to longer scales. - 8.2.1 Spatial vs. temporal variability on interannual timescales. - 8.2.2 Holocene and longer timescales. - 8.3 Concluding remarks and outlook. - Bibliography. - A Methods to: declining temperature variability from lgm to holocene. - A.1 Temperature proxy data. - A.2 Model-based temperature and variability change. - A.3 Temperature recalibration of proxy records. - A.3.1 Recalibration of ice-core records. - A.3.2 Recalibration of marine records. - A.4 Variance and variance ratio estimation. - A.5 Noise correction. - A.5.1 Testing effect of noise correction. - A.6 Effect of ecological adaption and bioturbation. - A.7 Effect of proxy sampling locations. - B Layering of surface snow and firn: noise or seasonal signal?. - B.1 Introduction. - B.2 Materials and methods. - B.2.1 Firn-core density profiles. - B.2.2 Trench density profiles. - B.2.3 Dielectric profiling and density estimates. - B.2.4 Comparison of DEP and CT density. - B.2.5 Ion measurements. - B.3 Results. - B.3.1 2-D trench density data. - B.3.2 Spatial correlation structure. - B.3.3 Comparison of mean density, isotope and impurity profiles. - B.3.4 Spectral analysis of vertical density data. - B.4 Discussion. - B.4.1 Spatial variability. - B.4.2 Representativeness of single profiles. - B.4.3 Seasonal cycle in snow density. - B.4.4 Density layering in firn and impurities. - B.5 Conclusions. - Acknowledgements - Danksagung.

Note: Dissertation, Universität Potsdam, 2020 , Table of contents Abstract Kurzfassung Table of contents Chapter 1: Introduction 1.1 The challenge of proxy uncertainties 1.2 Aims and approaches 1.3 Thesis outline and author's contributions Chapter 2: Comparing methods for analysing time scale dependent correlations in irregularly sampled time series data 2.1 Abstract 2.2 Introduction 2.3 Methods 2.3.1 Time scale dependency 2.3.2 Irregularity 2.3.3 Surrogate data 2.3.3.1 Construction of surrogate signals 2.3.3.2 Construction of irregular sampling 2.3.4 Evaluation of the estimation methods 2.4 Results 2.4.1 Correlation of red signal - white noise time series 2.4.2 Correlation of white signal - white noise time series 2.5 Discussion 2.5.1 Effect of irregularity and non-simultaneousness in sampling 2.5.2 Choosing the best method 2.5.2.1 Handling irregularity 2.5.2.2 Accounting for time scale dependency 2.5.3 Example application to observed proxy records 2.6 Conclusion 2.7 Computer code availability 2.8 Acknowledgements 2.9 Appendix 2-A. Significance test for time scale dependent correlation estimates Chapter 3: Empirical estimate of the signal content of Holocene temperature proxy records 3.1 Abstract 3.2 Introduction 3.3 Data 3.3,1 Proxy records 3.3.2 Climate model simulations 3.4 Method 3.4.1 Approach and assumptions 3.4.2 Spatial correlation structure of model vs. reanalysis data 3.4.3 Processing steps 3.4.3.1 Estimation of the spatial correlation structure 3.4.3.2 Estimation of the SNRs 3.5 Results 3.5.1 Spatial correlation structure and correlation decay length 3.5.2 SNR estimates 3.6 Discussion 3.6.1 Spatial correlation structure of model simulations 3.6.2 Finite number of proxy records 3.6.3 Proxy-specific recording of climate variables 3.6.4 Time uncertainty and non-climatic components of the proxy signal 3.6.5 Implications and future steps forward 3.7 Conclusion 3.8 Code availability 3.9 Data availability 3.10 Acknowledgements Chapter 4: Testing the consistency of Holocene and Last Glacial Maximum spatial correlations in temperature proxy records 4.1 Abstract 4.2 Introduction 4.3 Data 4.4 Method 4.4.1 Approach and assumptions 4.4.2 Holocene and LGM spatial correlation structure from climate model simulation 4.4.3 Effect of changes in climate variability on the predicted correlations 4.4.4 Effect of changes in time uncertainty on the predicted correlations 4.4.S Estimating the surrogate-based LGM spatial correlation and accounting for parameter uncertainty 4.5 Results 4.6 Discussion 4.6.1 Proxy-specific recording and finite number of records 4.6.2 Time uncertainty of proxy records 4.6.3 Contrary behaviour of U K'37 records 4.6.4 Spatial correlation structure and orbital trends 4.7 Conclusion 4.8 Acknowledgements 4.9 Appendix 4-A. Deriving the effect of a different signal variance on the correlation Chapter 5: Synthesis 5.1 Irregular sampling and time scale dependent correlations 5.2 Spatial correlation structure of proxy records 5.3 Consistency of spatial correlations for different climate states 5.4 Signal content of proxy records 5.5 Concluding remarks and Outlook Chapter A: Supplement of Chapter 3 - Empirical estimate of the signal content of Holocene temperature proxy records A.1 Supplementary Figures A.2 Supplementary Tables Chapter B: Supplement of Chapter 4 - Testing the consistency of Holocene and Last Glacial Maximum spatial correlations of temperature proxy records 8.1 Supplementary Figures 8.2 Supplementary Tables References Danksagung Eidesstattliche Erklärung