Complexity of Spatio-Temporal Correlations in Japanese Air Temperature Records

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

“…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.…”

“…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 ,…”

“…Its estimation by means of linear regression according to Equation (9) has been discussed in detail elsewhere [11,25].…”

“…Instead of using the classical fractal dimension concepts, in the last years it has therefore been suggested to consider alternative methods that allow quantifying the dimensionality of such records. Donner and Witt [11,23,24] utilized the multivariate version of the LVD dimension density (see Section 3.3) for studying long-term dynamical changes in the Antarctic offshore sediment decomposition associated with the establishment of significant oceanic currents across the Drake passage at the Oligocene-Miocene boundary. In a similar way, Donges et al used recurrence network analysis for sliding windows in time for identifying time intervals of subtle large-scale changes in the terrigenous dust flux dynamics off North Africa during the last 5 million years [10,79].…”

“…This pre-processing step is necessary since the annual cycle gives the main contribution to the intra-annual variability of surface air temperatures in the mid-latitudes and would thus lead to artificially strong correlations on short to intermediate time-scales (i.e. days to weeks) [11]. In addition, since some of the methods to be discussed can exhibit a considerable sensitivity to non-stationarity, linear trends for the residual mean temperatures are estimated by a classical ordinary least-squares approach and subtracted from the de-seasoned record.…”