Characterisation of long-term climate change by dimension estimates of multivariate palaeoclimatic proxy data

The problem of extracting climatically relevant information from multivariate geological records is tackled by characterising the eigenvalues of the temporarily varying correlation matrix. From these eigenvalues, a quantitative measure, the linear variance decay (LVD) dimension density, is derived. The LVD dimension density is shown to serve as a suitable estimate of the fractal dimension density. Its performance is evaluated by testing it for (i) systems with independent components and for (ii) subsystems of spatially extended linearly correlated systems. The LVD dimension density is applied to characterise two geological records which contain information about climate variability during the Oligocene and Miocene. These records consist of (a) abundances of different chemical trace ele- ments and (b) grain-size distributions obtained from sedi- ment cores offshore the East Antarctic coast. The presented analysis provides evidence that the major climate change as- sociated with the Oligocene-Miocene transition is reflected in significant changes of the LVD dimension density. This is interpreted as a change of the interrelationships between dif- ferent trace elements in the sediment and to a change of the provenance area of the deposited sediment.

[1]  R. Preisendorfer,et al.  Principal Component Analysis in Meteorology and Oceanography , 1988 .

[2]  Sheila A. Farmer.  An Investigation into the Results of Principal Component Analysis of Data Derived from Random Numbers , 1971 .

[3]  Annette Witt,et al.  Temporary Dimensions of Multivariate Data from Paleoclimate Records - a Novel Measure for Dynamic Characterization of Long-Term Climate Change , 2007, Int. J. Bifurc. Chaos.

[4]  D. Harwood,et al.  Introduction to 'long-term changes in Southern high-latitude ice sheets and climate, the Cenozoic history' , 2005 .

[5]  Eckehard Olbrich,et al.  Analysing local observations of weakly coupled maps , 1998 .

[6]  C Raab,et al.  Estimation of large-scale dimension densities. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  M. Kramer.  Nonlinear principal component analysis using autoassociative neural networks , 1991 .

[8]  Henry S. Greenside,et al.  KARHUNEN-LOEVE DECOMPOSITION OF EXTENSIVE CHAOS , 1996, chao-dyn/9610007.

[9]  M. C. Jones,et al.  Tools for Constructing Chronologies; Crossing Disciplinary Boundaries , 2005 .

[10]  J. Lean,et al.  Reconstruction of solar irradiance since 1610: Implications for climate change , 1995 .

[11]  M. Mudelsee,et al.  Plio-/Pleistocene climate modeling based on oxygen isotope time series from deep-sea sediment cores: The Grassberger-Procaccia algorithm and chaotic climate systems , 1994 .

[12]  H. Fischer.  The climate in historical times : towards a synthesis of Holocene proxy data and climate models , 2004 .

[13]  Bose,et al.  Karhunen-Loeve local characterization of spatiotemporal chaos in a reaction-diffusion system , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[15]  Katharina Krischer,et al.  Transitions to electrochemical turbulence. , 2005, Physical review letters.

[16]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[17]  James W. Hurrell,et al.  The North Atlantic Oscillation: Climate Significance and Environmental Impact , 2003 .

[18]  Henry D. I. Abarbanel,et al.  Analysis of Observed Chaotic Data , 1995 .

[19]  J. M. Craddock,et al.  Eigenvectors for representing the 500 mb geopotential surface over the Northern Hemisphere , 1969 .

[20]  E. Sarachik,et al.  Understanding and predicting ENSO , 1995 .

[21]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[22]  M. B. Priestley,et al.  Non-linear and non-stationary time series analysis , 1990 .

[23]  Richard J. Telford,et al.  The secret assumption of transfer functions: problems with spatial autocorrelation in evaluating model performance , 2005 .

[24]  W. W. Hay.  Tectonics and climate , 1996 .

[25]  Martienssen,et al.  Characterization of spatiotemporal chaos from time series. , 1993, Physical review letters.

[26]  T. Williams,et al.  A high‐resolution record of early Miocene Antarctic glacial history from ODP Site 1165, Prydz Bay , 2005 .

[27]  John Aitchison,et al.  The Statistical Analysis of Compositional Data , 1986 .

[28]  C. Diks.  Nonlinear time series analysis , 1999 .

[29]  E. Oja,et al.  Independent Component Analysis , 2013 .

[30]  H. M. Sachs,et al.  Paleoecological Transfer Functions , 1977 .

[31]  Richard J. Telford,et al.  All age–depth models are wrong: but how badly? , 2004 .

[32]  R. Hegger,et al.  Estimation of Lyapunov spectra from space–time data , 1999, chao-dyn/9908004.

[33]  A. Roberts,et al.  Orbitally induced oscillations in the East Antarctic ice sheet at the Oligocene/Miocene boundary , 2001, Nature.

[34]  V. Holliday.  Paleoclimatology: Reconstructing climates of the quaternary, 2nd edition , 1999 .

[35]  Erkki Oja,et al.  Independent Component Analysis , 2001 .

[36]  P. Kyle,et al.  Geochemical indicators of weathering, Cenozoic palaeoclimates, and provenance from fine-grained sediments in CRP-2/2A, Victoria Land Basin, Antarctica , 2000 .

[37]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[38]  D. Paillard.  Glacial cycles: Toward a new paradigm , 2001 .

[39]  I. Jolliffe.  Principal Component Analysis , 2002 .

[40]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[41]  J. Lifland.  The North Atlantic Oscillation: Climatic Significance and Environmental Impact , 2003 .

[42]  秦 浩起,et al.  Characterization of Strange Attractor (カオスとその周辺(基研長期研究会報告)) , 1987 .

[43]  R. Vautard,et al.  Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series , 1989 .

[44]  R. Bradley.  Paleoclimatology: Reconstructing Climates of the Quaternary , 1999 .