Relationship between the Atmospheric CO2 and Climate Indices by Wavelet-Based Multifractal Analysis

Greenhouse gases are gases that can trap heat. Carbon dioxide, methane, and water vapour are the most important greenhouse gases. The atmospheric concentration of a greenhouse gas is a measure of the abundance of that gas in air, usually defined in terms of the proportion of the total volume that it accounts for. Nowadays, global average concentrations of various atmospheric greenhouse gases are continuing to increase, leading to a positive radiative forcing of climate and an expected warming of surface temperatures.  

Various objects in nature show the so-called self-similarity or fractal property. In general, fractal properties may be observed in the time series of the dynamics of complex systems. Climate change can also be interpreted from the view of fractals. A change of fractality may be observed when the climate changes.

Wavelet methods are useful for the analysis of complex non-stationary time series. The wavelet transform allows good multifractal analysis to be performed. In this paper, to study the relation between the atmospheric CO₂ concentration and the climate indices, the researchers investigated the change of fractal behavior of the CO₂, the carbon isotope ratio (δ¹³C) of atmospheric CO₂, the Southern Oscillation Index (SOI), the Pacific Decadal Oscillation (PDO), and the North Atlantic Oscillation (NAO) indices using the multifractal analysis.

The SOI, Niño3.4, PDO, NAO indices, and global mean surface air temperature anomalies provided by NOAA’s Climate Prediction Center, USA (CPC) were used. Atmospheric CO₂ concentrations (ppm) derived from in situ air measurements at Mauna Loa, Observatory, Hawaii was used. Monthly atmospheric 13C concentrations (per mil) in CO₂ derived from flask air samples at Mauna Loa Observatory was used. Annual mean growth rate of CO₂ for Mauna Loa obtained from NOAA was used.

The results showed that when the atmospheric CO₂ growth rate was large, the multifractality of CO₂, δ¹³C in CO₂, ENSO (SOI and Niño3.4), and NAO was large and the changes were large from the change of fractality. The changes of CO₂ and ENSO were closely related and the influence of the CO₂on the ENSO was strong from the change in fractality and wavelet coherence. When the El Niño occurred, the CO₂ growth rate was large. The CO₂ related to PDO, NAO, and global temperature from the change in fractality and wavelet coherence. Especially, the changes of CO₂ and global temperature were closely related. When the global warming hiatus occurred, the multifractality of the global temperature was weaker than that of CO₂ and the change of the global temperature was stable.

These findings will contribute to the research of the relation between the atmospheric CO₂and climate change.

Article by Fumio Maruyama, from Matsumoto University, Matsumoto, Japan.

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Image by francesco.pandolfi, from Flickr-cc.