, Germaine Cornelissen2 and Franz Halberg2
(1)
Department of Chronomics & Gerontology, Tokyo Women’s Medical University Medical Center East, Arakawa-ku, Tokyo, Japan
(2)
Halberg Chronobiology Center, University of Minnesota, Minneapolis, MN, USA
Abstract
Variations in the average annual tree rings of 11 sequoia for 2189 years are studied. The power spectrum of tree ring variations, calculated by the Maximum Entropy Method, is power-law in character with the coefficient β (beta) close to −1.00, suggesting the fractal character of the considered time series. The calculation of the coefficient β in the 200-year sliding window showed that this coefficient rapidly drops to zero or very minor positive values, including a break in the fractal structure. We identified seven such episodes, two (the latest) of which correspond to Spörer and Maunder solar minima. The other five episodes, which occurred around 100 BC and 500, 820, and 880 AD, i.e., before regular sunspot observations, may correspond to climate change. By combining methods aimed at identifying the specific spectral components, such as the Schwabe cycle and behavior of the 1/f dependence as a chaos characteristic, the chronobiologic (chronomics) approach can be used to study the global climate processes – such as cycles of about 500 years – bearing on global warming.
Keywords
Chronomics of tree ringsChronobiologic serial sectionFractal scalingSolar activity7.1 From Chronobiology to Transdisciplinary Chronomics
We consider how chronobiology and chronomics can serve in dealing with civilization and culture. Chronobiology started with circadian rhythms and led to the mapping of chronomes with a spectral element consisting of photic and nonphotic, visible and largely invisible (except for the aurorae) cycles. Photic cycles involve electromagnetic radiation in the visible domain; nonphotic cycles involve corpuscular emissions from the sun and beyond, including helio-, seleno-, and geomagnetics, ultraviolet flux and gravitation, and other stimuli such as anthropogenic ones. Cycles include, at one extreme, those in the action potentials of the major generators of electric and magnetic fields, the heart and the brain, recorded in ECGs and EEGs and in encephalo- and cardiomagnetograms. When such records become long, they reveal decadal cycles found not only in demographic and other data bases but also in much needed longitudinal heart rate data [1].
Statistical studies have also revealed new non-daily, non-yearly, i.e., nonphotic cycles in both magnetism and corresponding physiological cycles in humans and other organisms [2–5]. Thus it has become increasingly clear that invisible nonphotic (involving largely magnetic) influences from the sun affect the cycles of life on earth today and apparently have even left genetic footprints in partly endogenous physiological chronomes (time structures) that are open to the environment [6].
7.2 Why Tree Rings
Whenever a solar origin is postulated in physics, economics, agriculture, or psychophysiology, the postulate of quasi-reciprocal cycles in and around us can be helpful, and indeed some solar rhythms exhibit cycle lengths found in biology and vice versa [1]. But the physicists’ records of aurorae and sunspots are not long enough to look for cycles half a millennium in length. It seemed interesting therefore to look again for a proxy marker of solar activity in tree ring widths that cover the past 2,000 years or more, as others had done before us.
7.3 Background on Tree Maps
The journal “Tree-Ring Research” has a multi-decadal history, and for about a century, tree rings have been recognized as indicators of climatic and other environmental, notably solar changes. Douglass’s three volumes of “Climatic Cycles and Tree-Growth” [7, 8] were reproduced in 1971 in the series “Historiae naturalis classica” [9]. We had analyzed 11 sequoias that grew on the lower western slopes of the Sierra Nevada and had found cycles with periods of about 6.51, 13.2, 38.3, 58.1, 98.6, 186, and 534 years [10]. In data taken from a published graph, an about 500-year cycle was also found to characterize the coloring of stalagmites, possibly reflecting changes in earth’s subsurface temperature [11].
7.4 Fractal Scaling Calculated by the Maximum Entropy Method
Fractal scaling is one of the characteristics of chaos (or complexity). The concept of a fractal is most often associated with irregular geometric objects that display self-similarity. Fractal forms are composed of subunits (and sub-subunits, and so on) that resemble the structure of the overall object [12]. In an ideal model, this property holds on all scales. The real world, however, necessarily imposes upper and lower bounds over which such scale-invariant behavior applies. Many non-Euclidean structures in nature, such as branching trees, wrinkly coastlines, and the rough surfaces of mountains, are fractal. A number of complex anatomic structures also display fractal-like geometry. Application of fractal analysis in biology and medicine may provide a new approach to risk assessment and to forecast sudden death in animals (including humans). Elucidating the fractal nature involved in physiology and in complex signaling networks is emerging as a major challenge in the post-genomic era.
For the analysis presented herein, the average measurements of studies on 11 sequoia trees were taken from reference [9], pp. 119–23, covering 2,189 years. A time plot (chronogram) is presented in Fig. 7.1 (top). The fractal nature of the time series of tree ring width was assessed by computing the power spectrum of the 2,175-year time series by the Maximum Entropy Method (MEM). A robust line fitting algorithm of log (power) on log (frequency) was then applied to the power spectrum between 10−4 and 0.50 Hz (where the relationship between these variables was linear), and the slope (β) of this line was calculated.
Fig. 7.1
Time series of tree ring widths (top) and its power spectrum (bottom). Top: Average measurements of 11 sequoia trees were taken from Douglass (1971), pp. 119–23, covering 2,189 years. Bottom: Power spectrum of the 2,175-year time series by the Maximum Entropy Method (MEM). The slope (β) is −1.0017, indicative of the fractal nature of tree rings
As a result, the slope (β) of the log(power) vs. log(frequency) spectrum of the 2,189 years of tree ring widths was −1.0017 (Fig. 7.1, bottom). A slope (β) around −1.00 means fractal nature, indicating that the system is under control. The time series of sunspot numbers between 1700 and 2000 was also analyzed by MEM, and the slope of the power-law behavior was −1.0543, indicative of a fractal nature, Fig. 7.2.
Fig. 7.2
Time series of sunspot numbers between 1700 and 2000 (top) and its MEM spectrum (bottom). The slope of the power-law behavior is −1.0543, indicating that sunspots show a fractal nature
7.5 Chronomics of Tree Rings Can Approach the Global Climate Processes
Changes in the fractal nature of tree ring width were assessed by repeating the MEM analysis over a 200-year interval progressively displaced by 5 years throughout the time series. Figure 7.3 (left) shows three examples of 200-year intervals, and Fig. 7.3 (right) shows the corresponding MEM spectra. Changes as a function of time in the slope (β) of the power-law behavior are shown in Fig. 7.4 (bottom), revealing episodic disruptions of the fractal nature. Seven episodes (arrows) are identified in Fig. 7.4. The last two episodes coincide with the Spörer and Maunder minima. Global climate changes may also have happened at times corresponding to the other 5 episodes of disturbed fractal nature.
