13Carbon / 12Carbon Ratio of Atmospheric CO2

By Jamal Munshi, April 28, 2019
















  1. Fossil fuel reservoirs deep under the ground contain a large inventory of carbon that has been sequestered for millions of years from the delicately balanced surface-atmosphere carbon cycle that sustains a stable climate system and life on earth as we know it. The theory of anthropogenic global warming and climate change (AGW) addresses this issue in terms of the response of the surface-atmosphere system to the perturbation caused by fossil fuel emissions that inject extraneous carbon into it.
  2. In view of a concurrent and corresponding rise in fossil fuel emissions and atmospheric CO2 since the Industrial Revolution, it is taken as axiomatic that these changes are causally related and empirical evidence is provided in terms of correlations between cumulative values and also in terms of observed changes in isotopic ratios of carbon in atmospheric CO2 (Callendar, 1938) (IPCC, 2007) (IPCC, 2014) (Kheshgi, 2005) (Levin, 2000) (Matthews, 2009) (Raupach, 2007) (Revelle, 1956) (Hansen, Impact of Increasing Atmospheric Carbon Dioxide, 1981) (Stuiver M. , 1987) (Stuiver M. , 1981) (Suess, 1953).
  3. In a related post, we examine this relationship in terms of detrended fluctuation analysis [LINK]  and also in terms of the 14C/12C ratio in atmospheric CO2 [LINK] . In this post we extend this line of inquiry by examining changes in the 13C/12C ratio in atmospheric CO2 to determine whether these changes can serve as empirical evidence of a relationship between fossil fuel emissions and changes in atmospheric CO2 as claimed by these climate scientists (Stuiver M. , 1987) (Stuiver, 1984) (TANS, 1980) (Robertson, 1887) (RealClimate, 2004) (Severinghaus, 2014).
  4. Data for the 13C/12C ratio in atmospheric CO2 are available form a large number of stations around the world maintained by the Scripps Institute of Oceanography (SIO) and these data are made available online (Keeling, 2005) (Graven, 2016) (ScrippsCO2, 2016). Six SIO measuring stations are selected for this study based on the somewhat arbitrary condition that at least twenty years of data should be available up to and including the year 2014. Typically there are about a thousand observations made during this period. If there are fewer than five hundred observations the data are considered sparse and that station is eliminated from consideration. The stations that meet our conditions are listed in Figure 1.
  5. The relevance of this measure to the idea that the observed increase in atmospheric CO2 derives from fossil fuel emissions is that plant photosynthesis has an isotope bias and prefers 12C. For this reason, plants, and therefore fossil fuels, contain a lower ratio of 13C/12C than the atmosphere. In this context, the combustion of large quantities of fossil fuels is like a sudden injection of low 13C/12C CO2 into the atmosphere that should cause a measurable reduction of the 13C/12C ratio in atmospheric CO2. In fact, what we find in the data is that indeed there has been a gradual reduction of the 13C/12C ratio in atmospheric CO2 during a period of rising fossil fuel emissions as shown in Figure 2. The data are from the Christmas Island dataset. AGW theory attributes increases in atmospheric CO2 to fossil fuel emissions and this attribution implies a negative correlation between 13C in atmospheric CO2 and fossil fuel emissions. In fact, if we look at the numbers we find that the 13C/12C ratio is strongly negatively correlated with cumulative emissions. The Pearson correlation coefficient of R = -0.987. It is this correlation that has led climate science to claim that the 13C/12C data support the attribution that the observed rise in atmospheric CO2 to fossil fuel emissions.
  6. However, this correlation is unreliable because it is a correlation between cumulative values. It has been shown in a related post that such correlations are spurious and that no conclusions can be drawn from correlations between cumulative values  [LINK] . To support causation, it must be shown that a correlation exists at the theoretical time scale at which the causation is supposed to work. In the case of fossil fuel emissions, it is generally held that the time scale for its effect on the atmosphere is one year (IPCC, 2014) (IPCC, 2007) (Falkowski, 2000) (Rodhe, 1990) (Keeling C. , 1995). For a time scale of one year, it is necessary to show that annual changes in atmospheric 13C can be related to annual emissions. To test that hypothesis we compute the correlation between annual fossil fuel emissions and the change in atmospheric 13C from the previous year to the current year. Data for fossil fuel emissions from 1977-2010 are available from the CDIAC4 and the ORNL5 (Marland-Andres, 2016). It is found that most measurement stations show a seasonal cycle in the 13C/12C ratio for atmospheric CO2. The data are therefore deseasonalized as a first step. Further analysis refers only to the deseasonalized series. All hypothesis tests for statistical significance are carried out at a maximum false positive error rate of α=0.001 as recommended in “Revised standards for statistical evidence” in a PNAS publication to address the unacceptably high rate of irreproducible results in research publications (Johnson, 2013). Where necessary an appropriate adjustment is made for multiple comparisons (Holm, 1979). The data and their correlations are presented in Figure 2 to Figure 7. No statistically significant correlation is found to support the hypothesis that observed year to year increases in atmospheric CO2 are attributable to fossil fuel emissions. In Figures 2-7, the term “C13” refers to the 13C/12C ratio in atmospheric CO2.
  7. SUMMARY: In all six stations studied we find that the 13C/12C ratio in atmospheric CO2 has declined in the study period from about -7.5 to about -8.5 At the same time fossil fuel emissions have risen from 5 GTY (gigatons per year) to more than 9.7 GTY. These charts present the correlation of changes at an annual time scale. Here, we find no correlation between annual changes in the 13C/12C ratio and annual fossil fuel emissions. The highest value of R-squared is found  for Cape Kumukahi as R-squared = 0.0104. For N=25 observations, the corresponding t-statistic is t=1.94 and the corresponding p-value is p=0.0318. At our maximum error rate of α=0.001, we fail to reject H0: R=0 and find no evidence that changes in the 13C/12C ratio are related to fossil fuel emissions.

CONCLUSION: We conclude that the 13C data do not provide empirical evidence that observed changes in atmospheric CO2 concentration can be attributed to fossil fuel emissions. We further note that the high correlation between cumulative changes in the 13C/12C ratio in atmospheric CO2 and cumulative emissions is unreliable and unacceptable as empirical evidence because of the spuriousness of correlations between cumulative values discussed in a related post [LINK] .









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