Atmospheric concentrations of greenhouse gases are rising, leading to a positive radiative forcing of climate and an expected warming of surface temperatures. In general, fractal properties may be observed in the time series of the dynamics of complex systems. To study the relation between the atmospheric CO2 concentration and the climate indices, we investigated the change of fractal behavior of the CO2, the carbon isotope ratio (δ13C) of atmospheric CO2, the El Ni?o-Southern Oscillation (ENSO), the Pacific Decadal Oscillation (PDO), and the North Atlantic Oscillation (NAO) indices using the multifractal analysis. When the atmospheric CO2 growth rate was large, the multifractality of CO2, δ13C in CO2, ENSO, 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 CO2 on the ENSO was strong from the change in fractality and wavelet coherence. When the El Ni?o 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 CO2 and climate change.
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