Statistical and spectral analysis of carbon dioxide variations in terrestrial environment
By Dr. Valentina Zharkova
May 25, 2026
Sponsored by ClimateCite and Tom Tamarkin
We analyse the annual mean and annual growth rate measurements of the global CO2 abundances taken from the NOAA General Monitoring Laboratory (GML). The annual CO2 variations are shown to have the best polynomial fit by a parabola with concavity up that is contrary to the straight line assigned to a growth of CO2 abundances produced by fossil fuel. The measured global CO2 abundance variations were shown to correlate closely with variations of the Global Mean Sea Level (GMSL)(r=0.60), Oceanic Nina Index/El Nino Southern Oscillations (ONI/ENSO) (r=0.24) and global13 terrestrial temperature (r=0.82). The de-trended CO2 abundance variations are found to have much stronger correlation with ONI/ENSO (r=0.79).
The spectral analysis with Morlet’s wavelet of the variations of CO2 abundances reveals the natural periods of 21.4, 9 and 3.7 years. The similar periods are derived for the variations of GMSL (21.4,17 and 8.5 years), ONI/ENSO index (21.4, 12 and 4.5 years ) and the GLB terrestrial temperature (21.4,18 8.36 and 3.75 years). The presence of a common period of 21.4 years indicates that all the datasets are affected by cyclic variations of the solar magnetic activity in a double solar cycle. The measured CO2 oscillations with a period of 9 years combined with the correlation of the de-trended CO2 abundances can be linked to the ONI/ENSO variations ranging within the periods of 4.5 and 12 years. The cross-correlation analysis of global CO2 abundance and terrestrial temperature variations reveals a time lag of about one year of the CO2 abundance variations from the GLB temperature variations. Furthermore, the coherence wavelet analysis of the global CO2 and GLB temperature datasets established a clear time lag of 1.2-1.8 years recorded for the CO2 abundances with respect to the GLB temperature variations during most observing intervals. This indicates that global CO2 variations follow the temperature variations and do not induce them.