Abstract: “The hypothesis that the increase in atmospheric carbon dioxide is related to observable changes in the climate is tested using modern methods of time-series analysis. The results confirm that average global temperature is increasing, and that temperature and atmospheric carbon dioxide are significantly correlated over the past thirty years. Changes in carbon dioxide content lag those in temperature by five months.” (Note date: 22 February 1990)
Nature 343, 709 – 714 (22 February 1990); doi:10.1038/343709a0
Coherence established between atmospheric carbon dioxide and global temperature
Mathematical Sciences Research Center, AT&T Bell Labs, Murray Hill, New Jersey 07974, USA
The above work by Kuo et al is confirmed and strengthened in the following work using the availability of 20 years additional data. Full paper available at the link below.
A re-evaluation of the coherence between global-average atmospheric CO2 and temperatures at interannual time scales. by Jeffrey Park in GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L22704, doi:10.1029/2009GL040975, 2009 (full article linked below.)
Abstract: Frequency-dependent coherence between atmospheric CO2 and historical temperatures reveals climate feedbacks within Earth’s carbon cycle. Coherence between interannual fluctuations in global-average temperature and atmospheric CO2 has changed over time. Since 1979, at Mauna Loa and other observation sites, interannual coherence exhibits a 90 phase lag that suggests a direct correlation between temperatures and the time-derivative of CO2. …
Introduction: Statistical correlations between atmospheric carbon dioxide and global temperatures have been found on multiple time scales. Simple autoregressive prediction filters that utilize CO2, CO2-proxy and solar-variability time series show that a handful of free parameters can explain well the secular progression of 20th-century temperatures [Thomson, 1997; Kaufmann and Stern, 1997; Tol and de Vos, 1998; Stern and Kaufmann, 2000]. On interannual time scales, carbon-cycle feedbacks are evident in correlation analyses that show CO2 fluctuation to lag several months behind correlated fluctuations in global temperatures [Kuo et al., 1990; Martin et al., 1994; Dettinger and Ghil, 1998; Adams and Piovesan, 2005]. The earliest study [Kuo et al., 1990] used spectral coherence statistics to correlate CO2 and temperature, but most later studies use time-domain correlations, some statistical, some visual [see Keeling et al., 1995, Braswell et al., 1997; Langenfelds et al., 2002; Lintner, 2002; Buermann et al., 2007].
Kuo et al.  correlated global temperature with a 30-year record of monthly CO2 observations at Mauna Loa, Hawaii [Keeling, 2008]. 20 additional years of data is now available from Mauna Loa and the largely coeval South Pole CO2 time series. A global network of stations [GLOBALVIEW-CO2, 2008; Masarie and Tans, 1995], now provides time series as long as the Mauna Loa series originally analyzed by Kuo et al. . It seems timely to ask whether the spectral correlations reported in the 1990s have persisted. …
Results:  Our estimate of C(f) between Hadley-Centre global average temperature and CO2-concentration at Mauna Loa USA over 1958 – 1988 (Figure 1) agrees largely with Kuo et al. , but coherence over 1979 – 2008 differs significantly (Figure 2). For 1958 – 1988 jC( f )j 2 exceeds the 99% confidence level for nonrandomness over 0.2 < f < 0.6 cyc/yr, breaches the 90% confidence level for non-periodic variability near f = 1 cyc/yr, and breaches the 90% confidence level within 1.25 < f < 2.0 cyc/yr. For 1979– 2008 jC( f )j 2 exceeds 99% confidence over a narrower low-frequency bandpass and breaches 90% confidence modestly near f = 2.0 cyc/yr. A more telling comparison involves arg(C( f )). During 1958 –1988 a linear phase ramp mimics the effect of a 6-month delay in CO2 fluctuations relative to those in global DT. Kuo et al.  reported a 5-month delay; the discrepancy might relate to updates in the historical SST dataset [Brohan et al., 2006]. During 1979 – 2008 the interannual arg(C( f )) 90 where jC( f )j 2 is significant, i.e., a constant phase rather than a phase ramp.
Discussion:  Interannual arg(C( f )) > 0 suggests that CO2 fluctuations are caused by fluctuations DT in global temperature. The correlation coefficient is 2 –3 ppm/ C for interannual periods. If Earth climate warms by 3C for a doubling of preindustrial CO2, the predicted greenhouse feedback for a global-average DT = 1C ENSO fluctuation would be less than 0.05C, that is, <5% feedback.