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

Abstract

Abstract. 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 elements and (b) grain-size distributions obtained from sediment cores offshore the East Antarctic coast. The presented analysis provides evidence that the major climate change associated 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 different trace elements in the sediment and to a change of the provenance area of the deposited sediment.

Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution

“…It has several advantages above other frequently used techniques for detecting (incipient) bifurcations in time series: (i) RN analysis is not explicitly based on temporal correlations but on geometric considerations (47). Hence it is more robust with respect to noisy and nonuniformly sampled paleoclimate time series with uncertain timing than methods relying on temporal correlations (42)(43)(44)48) like degenerate fingerprinting (42) and detrended fluctuation analysis (43). (ii) As a nonlinear technique, RN analysis is not restricted to detecting only changes in linear statistical properties (i.e., the autocovariance structure) of a time series (42,(44)(45)(46).…”

Complexity Concepts and Non-Integer Dimensions in Climate and Paleoclimate Research

“…It should be mentioned that * does not yet give a properly normalized dimension density with values in the range between 0 and 1, which can already be observed for simple stochastic model systems [23,25]. However, using the limiting cases of identical (lowest …”

“…As an alternative, Donner and Witt [11,23,24,25] suggested studying the characteristic functional behavior of KLD in dependence on the explained variance fraction f. Specifically, if the residual variances decayed exponentially, i.e. 22 11 () 1 e x p ,…”

“…Corresponding approaches utilizing basic methods from multivariate statistics have been referred to as multivariate dimension estimates [11,23,24,25] and provide meaningful characteristics that can be reliably estimated even from rather short time series, which still constitute a fundamental limit for classical fractal dimension analysis.…”

“…Let i 2 , i=1,…,N, again be the non-negative eigenvalues of the associated correlation matrix S given in descending order. The aforementioned number of degrees of freedom, which is referred to as the KLD dimension, can then be defined as follows [23]:…”