Fractal Analysis of Long-Range Paleoclimatic Data: Oxygen Isotope Record of Pacific Core V28-239

Abstract

R/S analysis of the oxygen isotope curve of Pacific core V28–239 yields a fractal dimension of 1.22. This value is considered to characterize global climatic change over the last 2 million years as expressed by changing δO¹⁸ ratios and confirms that climatic variations are characterized by long-term persistence. The fractal dimension of 1.22 compares favorably with the approximate fractal dimension of 1.26 for annual precipitation records for nine major cities in the United States. Although the precipitation and oxygen isotope data are measured in different physical units and recorded at different time scales, fractal analysis allows for a mathematical comparison of the two phenomena. Additionally, since the fractal dimensions of the oxygen isotope and precipitation records are similar, it is implied that such fractal dimensions are characteristic of climate change over the spectral range of 10 to 10⁶ years. Given this, temperature curves based on fractal parameters of long-term δO¹⁸ data could be constructed which would allow examination of characteristics of temperature variation over tens and hundreds of years. Such studies may allow the establishment of limits on natural temperature variation and document the persistence of temperature trends through time. If these trends and limits can be resolved, long-range climatic prediction is feasible.