Thongchai Thailand

Mathematical Impossibility of Stuiver and Quay

Posted on: February 10, 2019





















  1. The theory of Anthropogenic Global Warming (AGW) and climate change holds that the warming seen in this interglacial period since Pre-Industrial Times that got us out of the Little Ice Age (LIA) is caused by fossil fuel emissions from the Industrial Economy and that it is warming at such a dangerous rate that its effects may destroy human civilization and that this assessment implies that we must take urgent climate action in the form of sharp reductions in, or the complete elimination of, the use of fossil fuels. The relationship between fossil fuel emissions and global warming is presented as a two-step process. First, emissions cause atmospheric CO2 to rise and second, the higher level of CO2 concentration of the atmosphere causes surface temperature to rise in accordance with a proposed greenhouse gas (GHG) effect of CO2. A test of the first relationship, that between emissions and atmospheric composition is presented in a related post [LINK] where it is shown that no evidence for this relationship is found in the data for emissions and atmospheric CO2 concentration. However, an additional argument for this relationship is presented by climate science in terms of the observed dilution of the carbon-14 (hereafter 14C) isotope fraction of carbon in atmospheric CO2. It is claimed that this dilution proves that fossil fuel emissions accumulate in the atmosphere because fossil fuel carbon is known to contain low or no 14C having been dead and underground for millions of years. This post is a test of the 14C dilution hypothesis. The full text of the source document may be found here [LINK]
  2. Carbon-14 forms naturally in the atmosphere by the action of cosmic rays on nitrogen but it is radioactive and so, once formed, 14C decays exponentially with a half-life of about 5,700 years. Radioactive decay is balanced by new cosmogenic synthesis and at equilibrium roughly one part per trillion of atmospheric carbon dioxide is made with radiocarbon. All carbon life-forms contain the prevailing equilibrium ratio of atmospheric 14C as long as they are alive and their bodily carbon is being replenished. When they die, however, the radiocarbon fraction in their body begins an exponential decay. The relevance of these relationships in climate science derives from the idea that fossil fuels are dead remains of living things that has been dead for millions of years and that therefore all their 14C has decayed leaving them 14C-free. It is thus postulated that the release of fossil fuel emissions into the atmosphere reduces the radiocarbon portion of atmospheric carbon dioxide and that therefore the degree of such radiocarbon dilution serves as a measure of the contribution of fossil fuel emissions to the observed increase in atmospheric carbon dioxide (Stuiver, 1981) (Suess, 1953) (Revelle, 1957) (Tans, 1979).
  3. The Stuiver and Quay paper (Stuiver, 1981) presents carbon-14 measurements in tree rings of two Douglas Firs in the Pacific Northwest that grew from 1815 to 1975. The now famous graphic representation of these data taken from their paper is shown in Figure 1 above. The figure shows a fairly steady 14C ratio from 1820 to 1900 with perhaps a gradual decline of about 5% and then a steep decline of about 20% from 1900 to 1950 in sync with the generally agreed separation of pre-industrial times from the post industrial fossil fueled economy which is thought to have taken off sometime between 1850 and 1900. These data are therefore generally accepted as empirical evidence that the observed increase in atmospheric CO2 since pre-industrial times is derived from fossil fuel emissions (IPCC, 2007) (IPCC, 2014) by way of the dilution of atmospheric 14C with pure 12C carbon from fossil fuels. The value of these pre-bomb data is that almost immediately following the end of their sample period in 1950, atmospheric tests of nuclear weapons sharply increased the 14C ratio in atmospheric carbon dioxide and following the cessation of such tests after the nuclear test ban treaty the 14C ratio began a natural exponential decay thereby confounding the pure fossil fuel dilution effect.
  4. The Stuiver and Quay tree ring data imply that from 1900 to 1950, fossil fuel emissions, being free of radiocarbon, caused the radiocarbon portion of atmospheric CO2 to decline by 20%. Fossil fuel emissions during this period are shown in Figure 2. A total of 50 gigatons of carbon (GTC) or about 180 gigatons of CO2 were released into the atmosphere during this period. At the same time atmospheric CO2 concentration rose 15.6 ppm or 5.38% from 296 ppm to 311 ppm. The increase of 15.6 ppm is equivalent to 33 GTC or 120 gigatons of CO2. Even if all of the emissions had gone into increasing atmospheric CO2 concentration, the dilution of 14C could not have been more than 8%. The dilution of 20% claimed by Stuiver and Quay is an impossibility in this context.
  5. These results imply that the Stuiver and Quay data do not have a simple interpretation in terms of dilution of atmospheric CO2 with fossil fuel emissions and therefore do not provide evidence that rising atmospheric CO2 concentration can be explained in terms of fossil fuel emissions.
  6. The sudden rise in atmospheric 14C due to nuclear bomb testing (the so called “bomb spike”) and its eventual decay after the nuclear test ban treaty are shown in  Figure 3. These data from 1955 to 1993 are available from the Wellington, New Zealand measuring station and they  show a rapid increase in the 14C fraction of atmospheric CO2 during nuclear testing and exponential decay after the nuclear test ban treaty . The bomb intervention confounds the fossil fuel effect in the decay data in the post bomb period. However, there is an important difference in the behavior of the decay and dilution effects because the decay of bomb 14C is exponential while the dilution by fossil fuel 12C is linear. The rate of exponential decay of bomb 14C slows with time and rate of the linear fossil fuel intervention increases with time as the rate of fossil fuel emissions rises. We therefore postulate that the linear effect of fossil fuel emissions will change the computed exponential decay equation in later periods when compared with earlier periods as fossil fuel emissions rise.
  7. Accordingly we set up a an empirical test by comparing the equation of exponential decay in the Wellington data with later measurements from various stations around the world shown in Figure 4. The post bomb spike portion of the Wellington data (Figure 3) runs from 1965 to 1993. The data show a close agreement with the exponential decay model. We can now test whether the later data for brief periods up to and including the year 2007 (Figure 4) can be explained as an extension of the same exponential decay curve. We do that by appending the data for each of the seven stations to the Wellington curve. The exponential decay curve parameters are displayed in Figure 5 and summarized in Figure 6. No significant change is found in the model parameters (Figure 6) upon appending the later brief datasets (Figure 5). CONCLUSION: The data do not provide convincing evidence that the recent datasets are not simply extensions of the Wellington curve and therefore we find no evidence that the decline in radiocarbon in atmospheric CO2 contain properties inserted by fossil fuel dilution and not explained by the natural exponential decay of bomb 14C. Yet another consideration is that it is not possible for carbon isotopic ratios to identify fossil fuel emissions as the source of the rise in atmospheric CO2 because isotopic ratios are unable to distinguish between fossil carbon and geological carbon. 


REFERENCES: Climate Change

  1. Anderson, K. (2011). Beyond ‘dangerous’ climate change: emission scenarios for a new world. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 369.1934 (2011): 20-44.
  2. Arora, V. (2011). Carbon emission limits required to satisfy future representative concentration pathways of greenhouse gases. Geophysical Research Letters, 38.5.
  3. Botzen, W. (2008). Cumulative CO2 emissions: shifting international responsibilities for climate debt. Climate Policy, 8.6, 569-576.
  4. Box, G. (1994). Time series analysis: forecasting and control. Englewood Cliffs, NJ: Prentice Hall.
  5. Brovkin, V. (2004). Role of land cover changes for atmospheric CO2 increase and climate change during the last 150 years. Global Change Biology, 10.8 (2004): 1253-1266.
  6. Callendar, G. (1938). The Artificial Production of Carbon Dioxide and Its Influence on Climate. Quarterly Journal of the Royal Meteorological Society, 64: 223-40.
  7. Canadell, J. (2007). Contributions to accelerating atmospheric CO2 growth from economic activity, carbon intensity, and efficiency of natural sinks. Proceedings of the national academy of sciences, 18866-18870.
  8. Draper&Smith. (1998). Applied Regression Analysis. Wiley.
  9. Gleisner, H. (2011). Latitudinal Binning and Area-Weighted Averaging. GRAS SAF Report 10: Danish Meteorological Institute.
  10. Graven, H. (2016). Scripps CO2 Program. La Jolla, CA: Scripps Institution of Oceanography, University of California.
  11. Guilderson, T. (2016). Accelerator Mass Spectrometry . Livermore, CA: Lawrence Livermore National Laboratories.
  12. Hansen, J. (1981). Impact of Increasing Atmospheric Carbon Dioxide. Science, 213: 957-66.
  13. Hansen, J. (2016). Ice melt, sea level rise and superstorms:. Atmos. Chem. Phys., 16, 3761–3812, 2016.
  14. Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6:2:65-70.
  15. IPCC. (2007). AR4 WG1 Chapter 7: Couplings between changes in the climate system and biogeochemistry. Geneva: IPCC.
  16. IPCC. (2014). Climate Change 2013 The Physical Science Basis. Geneva: IPCC/UNEP.
  17. Joos, F. (1998). Long‐term variability of the terrestrial and oceanic carbon sinks and the budgets of the carbon isotopes 13C and 14C. Global Biogeochemical Cycles, 277-295.
  18. Keeling, C. (2005). Atmospheric CO2 and 13CO2 exchange with the terrestrial biosphere and oceans from 1978 to 2000: observations and carbon cycle implications. In J. Ehleringer, History of atmospheric CO2 and its effects on plants, animals, and ecosystems (pp. 83-113). NY: Springer Verlag.
  19. Kheshgi, H. (2005). Emissions and atmospheric CO2 stabilization: Long-term limits and paths. In Mitigation and Adaptation Strategies for Global Change (pp. 10.2 213-220).
  20. Lacis, A. (2010). Principal Control Knob Governing Earth’s Temperature. Science, 330.
  21. Levin, I. (2000). Radiocarbon – a unique tracer of global carbon cycle dynamics. Radiocarbon, v42, #1, pp69-80.
  22. Levin-Hesshaimer. (2000). Radiocarbon – a unique tracer of global carbon cycle dynamics. Radiocarbon, V43 #1, 69-80.
  23. Marland-Andres. (2016). Regional and National Fossil-Fuel CO2 Emissions. Oak Ridge, TN: Oak Ridge National Laboratory.
  24. Matthews, H. (2009). The proportionality of global warming to cumulative carbon emissions. Nature, 459.7248 (2009): 829-832.
  25. Mearns, E. (2014). What’s up with the bomb model. Retrieved 2016, from
  26. Meinshausen, M. (2009). Greenhouse-gas emission targets for limiting global warming to 2 C. Nature, 458.7242 (2009): 1158-1162.
  27. Munshi, J. (2015). Responsiveness of Atmospheric CO2 to Anthropogenic Emissions. Retrieved 2016, from
  28. Munshi, J. (2015). Uncertainty in Radiocarbon Dating. Retrieved 2016, from
  29. Munshi, J. (2016). C14paperArchve. Retrieved 2016, from Google Drive:
  30. Munshi, J. (2016). The Spuriousness of Correlations between Cumulative Values. Retrieved 2016, from
  31. NASA-GISS. (2016). Global Mean CO2 Mixing Ratios. Retrieved 2016, from GISS.NASA.GOV:
  32. NOAA/CMDL. (2008). NWR. Retrieved 2016, from
  33. NOAA/ESRL. (2010). The Data: What 14C Tells Us. Retrieved 2016, from Stable and Radiocarbon Isotopes of Carbon Dioxide:
  34. Reimer, P. (2013). IntCal13 and Marine13 radiocarbon calibration curves. Radiocarbon, 1869-1887.
  35. Renfrew, C. (1974). Problems of the radiocarbon calendar and its calibration. Archaeometry, 16: 5-18.
  36. Revelle, R. (1957). Carbon dioxide exchange between atmosphere and ocean and the question of an increase of atmospheric CO2 during the past decades. Tellus, 9: 18.
  37. ScrippsCO2. (2016). Atmospheric CO2 data. Retrieved 2016, from scrippsco2:
  38. Shumway, R. (2011). Time series analysis. Springer. . Springer.
  39. Solomon, S. e.-0. (2009). Irreversible climate change due to carbon dioxide emissions. Proceedings of the national academy of sciences, 0812721106.
  40. Stuiver, M. (1981). Atmospheric 14C changes resulting from fossil fuel CO2 release and cosmic ray flux variability. Earth and Planetary Science Letters, 53: 349-362.
  41. Suess, H. (1953). Natural Radiocarbon and the rate of exchange of carbon dioxide between the atmosphere and the sea. Washington, DC: National Academy of Sciences.
  42. Szidat, S. (2006). Contributions of fossil fuel, biomass‐burning, and biogenic emissions to carbonaceous aerosols in Zurich as traced by 14C. Journal of Geophysical Research: Atmospheres, 111.D7.
  43. Tans, P. (1979). Natural atmospheric 14C variation and the Suess effect. Nature, 280: 826-827.
  44. Turnbull, J. (2006). Comparison of 14CO2, CO, and SF6 as tracers for recently added fossil fuel CO2 in the atmosphere and implications for biological CO2 exchange. Geophysical research letters, 33.1 (2006).
  45. UNEP. (2016). Paris Agreement. Retrieved 2016, from COP121:




These works appear to have a creationist bias in that the research question is loaded with a purpose of finding supporting evidence for the creationist view.

  1. Snelling, A. A. “Geological conflict: young radiocarbon date for ancient fossil wood challenges fossil dating.” Creation Ex Nihilo 22.2 (2000): 44-47.  No abstract or source document available online.
  2. Giem, Paul. “Carbon-14 content of fossil carbon.” Origins 51 (2001): 6-30.  No abstract available online. Full text download:
  3. Baumgardner, John R., et al. “Measurable 14C in fossilized organic materials: confirming the young earth creation-flood model.” Proceedings of the fifth international conference on creationism. Vol. 2. Creation Science Fellowship, Pittsburgh, PA, 2003. Given the short 14C half-life of 5730 years, organic materials purportedly older than 250,000 years, corresponding to 43.6 half-lives, should contain absolutely no detectable 14C. (One gram of modern carbon contains about 6 × 1010 14C atoms, and 43.6 half-lives should reduce that number by a factor
    of 7.3 × 10-14.) An astonishing discovery made over the past 20 years is that, almost without exception, when tested by highly sensitive accelerator mass spectrometer (AMS) methods, organic samples from every portion of the Phanerozoic record show detectable amounts of 14C! 14C/C ratios from all but the youngest Phanerozoic samples appear to be clustered in the range 0.1–0.5 pmc (percent modern carbon), regardless of geological “age.” A straightforward conclusion that can be drawn
    from these observations is that all but the very youngest Phanerozoic organic material was buried contemporaneously much less than 250,000 years ago. This is consistent with the biblical account of a global Flood that destroyed most of the air-breathing life on the planet in a single brief cataclysm only a few thousand years ago. Full Text download:



10 Responses to "Mathematical Impossibility of Stuiver and Quay"

[…] Mathematical Impossibility of Stuiver and Quay […]

The more tests you make the more clear it becomes that human emissions of CO2 are not causing global warming. I applaud your ingenuity and dedication to finding and exposing this analysis. It has been very helpful to me coming to a clear understanding of this controversy. I am now faced with the dilemma of how to communicate it to those around me and use it to move towards realism in our political discourse. I have been disallowed to point it out in our local paper, accused of listening to crackpots instead of real scientists, and written off as impossible to teach. Interestingly though most of the folks I know have some innate distrust of the global warming message without searching for the proof. My concern is this headlong rush I see coming from the newly empowered democrats to push their agendas to the detriment of so many without any concern for efficacy of their actions to “fight climate change”.

Really great comment. It identifies the heart of the issue and that is that the alarmists have won the propaganda war.

[…] emissions and atmospheric CO2 concentration is studied in four related posts [LINK] [LINK] [LINK] [LINK] . No evidence is found to relate changes in atmospheric CO2 concentration to fossil fuel […]

[…] 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 […]

[…] However the attribution of these changes to fossil fuels contains a fatal flaw. During the period of the SQ study, 1900-1950, total fossil fuel emissions were 50 gigatons of carbon equivalent or 180 gigatons of carbon dioxide. These flows could not have caused a 14C dilution of more than 8%. The dilution of 20% reported by SQ is therefore not evidence of the effect of fossil fuel emissions. It should be mentioned in this context that geological carbon emissions are also pure 12C free of 14C carbon isotopes. If anything, the SQ data point to the more plausible geological flow explanation of changes to atmospheric composition. The Stuiver and Quay post on this site may be found here [LINK] . […]

If the decay rate for C14 hasn’t changed post bomb spike, does this mean the extra C in the atmosphere 70 years later has come from the biosphere? Is it possible to identify that source?

And by the way, wouldn’t the same argument of dilution with time if fossil fuel sources, apply if the added C was from geological sources?

Yes sir. Geological carbon would also dilute the 14/12 ratio.

Leave a Reply to DMA Cancel reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

  • Paul H: Completely agree, but at what cost to us all when the system' does implode, what goods and services will be left available? The preppers have a very g
  • chaamjamal: "The system will fall under its own contradictions". Thank you for that insight.
  • skeptic16: Nobody ever voted for their freedom. We are not voting our way out. Unfortunately, the system will have to fall under its own staggering logical contr
%d bloggers like this: