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THIS POST IS A CRITICAL REVIEW OF A RESEARCH PAPER THAT SHOWS THAT THE EARTH’S SURFACE TEMPERATURE IS CORRELATED WITH LAGGED CO2 CONCENTRATION OF THE ATMOSPHERE. THE CITATION AND ABSTRACT OF THE PAPER APPEARS BELOW:  

Humlum, Ole, Kjell Stordahl, and Jan-Erik Solheim. “The phase relation between atmospheric carbon dioxide and global temperature.” Global and Planetary Change 100 (2013): 51-69. 

Abstract: Using data series on atmospheric carbon dioxide and global temperatures we investigate the phase relation (leads/lags) between these for the period January 1980 to December 2011. Ice cores show atmospheric CO2 variations to lag behind atmospheric temperature changes on a century to millennium scale, but modern temperature is expected to lag changes in atmospheric CO2, as the atmospheric temperature increase since about 1975 generally is assumed to be caused by the modern increase in CO2. In our analysis we use eight well-known datasets: 1) globally averaged well-mixed marine boundary layer CO2 data, 2) HadCRUT3 surface air temperature data, 3) GISS surface air temperature data, 4) NCDC surface air temperature data, 5) HadSST2 sea surface data, 6) UAH lower troposphere temperature data series, 7) CDIAC data on release of anthropogene CO2, and 8) GWP data on volcanic eruptions. Annual cycles are present in all datasets except 7) and 8), and to remove the influence of these we analyze 12-month averaged data. We find a high degree of co-variation between all data series except 7) and 8), but with changes in CO2 always lagging changes in temperature. The maximum positive correlation between CO2 and temperature is found for CO2 lagging 11–12 months in relation to global sea surface temperature, 9.5–10 months to global surface air temperature, and about 9 months to global lower troposphere temperature. The correlation between changes in ocean temperatures and atmospheric CO2 is high, but do not explain all observed changes. ► Changes in global atmospheric CO2 are lagging 11–12 months behind changes in global sea surface temperature. ► Changes in global atmospheric CO2 are lagging 9.5–10 months behind changes in global air surface temperature. ► Changes in global atmospheric CO2 are lagging about 9 months behind changes in global lower troposphere temperature. ► Changes in ocean temperatures explain a substantial part of the observed changes in atmospheric CO2 since January 1980. ► Changes in atmospheric CO2 are not tracking changes in human emissions.

FIGURE 1: 12-MONTH LAG SOURCE DATA CORRELATIONS

FIGURE 2: 12-MONTH LAG DETRENDED CORRELATIONS

FIGURE 3: 9-MONTH LAG SOURCE DATA CORRELATIONS

FIGURE 4: 9-MONTH LAG DETRENDED CORRELATIONS

1. The correlations claimed by the authors of the paper are tested with UAH satellite data for monthly mean lower troposphere temperatures 1979 to 2018 against Mauna Loa monthly mean CO2 data 1977 to 2018. Twenty four regional temperatures are tested. They are labeled numerically in the charts above as 1 to 24. They are, in sequence from 1 to 24, Global, G land, G ocean, Northern Hemisphere, NH land, NH ocean, Southern Hemisphere, SH land, SH ocean, Tropics, T land, T ocean, Northern Extent, NE land, NE ocean, Southern Extent, SE land, SE ocean, North Polar, NP land, NP ocean, South Polar, SP land, SP ocean. Both 12-month and 9-month lags are tested.
2. Correlation and detrended correlation between temperature and lagged CO2 are computed and the results are summarized in the charts above. Figure 1 and Figure 3 show correlations between the source data at 12-month and 9-month lags. At both lags we find a large range of correlations from negative values to very high correlations of max-ρ=[0.787,0.811] with medians of median-ρ=[0.695,0.658] for 12-month and 9-month lag respectively. These correlations are statistically significant and appear to support the authors claim of a lagged correlation between atmospheric CO2 and surface temperature indicating that temperature rises first and CO2 follows 9-12 months later and that therefore it is not possible for atmospheric CO2 to be the causal agent of the observed warming.
3. However, as described in related posts, correlations between two time series where both series have long term trends, can be driven by the trends and not by responsiveness at any finite time scale less than the full span of the data [LINK] . Detrended correlation is used to remove the spurious shared trend effect so that responsiveness of atmospheric CO2 to temperature can be tested. These detrended correlations are shown in Figure 2 and Figure 4. The charts show near zero detrended correlations of median-ρ=[0.011,0.009] for 12-month and 9-month lag respectively. Virtually none of the source data correlation survives into the detrended series. This result implies that the correlations seen in the source data are spurious and that the relationship they imply is illusory. Their only information content is that both series have a rising trend. No responsiveness at an annual time scale is found.
4. CONCLUSION: The lagged correlation between surface temperature and atmospheric carbon dioxide concentration reported by these authors is spurious. Therefore the apparent responsiveness of atmospheric CO2 to surface temperature is illusory. In the absence of such responsiveness it cannot be claimed that the data presented show a reverse relationship between temperature and atmospheric carbon dioxide such that temperature drives carbon dioxide and not the other way around.