Thongchai Thailand

Carbon Cycle Measurement Problems Solved with Circular Reasoning

Posted on: May 31, 2018














  1. Paleo climate data tell us that prior to the Industrial era the mean annual CO2 concentration of the atmosphere stayed in range 180-290 ppm (IPCCAR5, 2013), a difference of 234 gigatons of carbon equivalent (GTC). The range is equivalent to total global fossil fuel emissions in the 33-year period 1985-2017 but since the Paleo changes occurred prior to the industrial age, these changes are ascribed to volcanic eruptions which inject both aerosols and CO2 into the atmosphere. Changes in solar activity are also considered as they can change the equilibrium partial pressure of CO2 over the oceans in accordance with the Henry’s Law relationship of the temperature dependence of the solubility of carbon dioxide in water (IPCCAR5, 2013).
  2. However, in the postindustrial era, these changes are shown to be much more rapid and are therefore explained in terms of anthropogenic fossil fuel emissions with the mathematics of the attribution computed in the context of the carbon cycle that describes the natural flows of carbon dioxide to and from the atmosphere. The IPCC describes the carbon cycle in terms of carbon dioxide flows among multiple sources and sinks. The atmosphere plays a role in nine of these flows. These mean flows, averaged over the decade 2000-2009 (Figure 7) and their standard deviations (SD) as reported by the IPCC are listed below in units of GTC/y (IPCCAR5, 2013). Non availability of data is indicated by N/A.
  3. Natural: Ocean surface to atmosphere:Mean=78.4,SD=N/A.
  4. Natural: Atmosphere to ocean:surface:Mean=80.0,SD=N/A
  5. Human: Fossil fuel emissions:surface to atmosphere:Mean=7.8,SD=0.6
  6. Human: Land use change:surface to atmosphere:Mean=1.1,SD=0.8
  7. Natural: Photosynthesis:atmosphere to surface:Mean=123.0,SD=8.0
  8. Natural: Respiration/fire:surface to atmosphere:Mean=118.7,SD=N/A
  9. Natural: Freshwater to atmosphere:Mean=1.0,SD=N/A
  10. Natural: Volcanic emissions surface to atmosphere:Mean=0.1,SS =N/A
  11. Natural: Rock weathering:surface to atmosphere:Mean=0.3,SD=N/A
  12. A simple flow accounting of the mean values without consideration of uncertainty shows a net CO2 flow from surface to atmosphere of 4.4 GTC/y. The details of this computation are as follows. In the emissions and atmospheric composition data we find that during the decade 2000-2009 total fossil fuel emissions were 78.1 GTC and that over the same period atmospheric CO2 rose from 369.2 to 387.9 ppm for an increase of 18.7 ppm equivalent to 39.6 GTC in atmospheric CO2 or 4.4 GTC/y. The ratio of the observed increase in atmospheric carbon to emitted carbon is thus =39.6/78.2=0.51. This computation is the source of the claim that the so called “Airborne Fractionis about 50%; that is to say that about half of the emitted carbon accumulates in the atmosphere on average and the other half is absorbed by the oceans, by photosynthesis, and by terrestrial soil absorption. The Airborne Fraction of AF=50% later had to be made flexible in light of a range of observed values (Figure 1).
  13. The left frame of Figure 1 above shows that a large range of values of the decadal mean Airborne Fraction of 0<DMAF<4 .5 for decades ending in 1860 to 2017. This sample period includes ice core CO2 data from the Law Dome for years prior to 1958. However, when the sample period is restricted to the more precise Mauna Loa data from 1958, a much smaller range of values are seen in the right frame of Figure 1 with 0.45<DMAF<0.65. These data appear to support the usual assumption in climate science that fossil fuel emissions have contributed about half of the decadal mean increase in atmospheric CO2 concentration since 1958; but as demonstrated in a related post [LINK] , without a correlation between emissions and changes in atmospheric CO2 concentration, airborne fractions can be computed but they have no interpretation in terms of cause and effect in the phenomenon being studied [LINK] .
  14. When uncertainties are not considered, the flow accounting appears to show an exact match of the predicted and computed carbon balance. It is noted, however, that this exact accounting balance is achieved, not with flow measurements, but with estimates of unmeasurable flows constrained by the circular reasoning that assigns flows according to an assumed flow balance.
  15. However, a very different picture emerges when uncertainties are included in the balance. Published uncertainties for three of the nine flows are available in the IPCC reports. Uncertainty for the other six flows are not known. However, we know that they are large because no known method exists for the direct measurement these flows. They can only be grossly inferred based in assumptions that exclude or minimize geological flows.
  16. We therefore set up a Monte Carlo simulation to estimate the highest value of the unknown standard deviations at which we can detect the presence of human emissions in the carbon cycle. For the purpose of this test we propose that an uncertain flow account is in balance as long as the Null Hypothesis that the sum of the flows is zero cannot be rejected. The alpha error rate for the test is set to a high value of alpha=0.10 to ensure that any reasonable ability to discriminate between the flow account WITH Anthropogenic Emissions from a the flow account WITHOUT Anthropogenic Emissions is taken into evidence that the relatively small fossil fuel emissions can be detected in the presence of much larger and uncertain natural flows. The spreadsheet used in this determination is available for download from an online data archive Data Archive Link .
  17. In the simulation we assign different levels of uncertainty to the flows for which no uncertainty data are available and test the null hypothesis that the flows balance with anthropogenic emissions (AE) included and again with AE excluded. If the flows balance when AE are included and they don’t balance when AE are excluded then we conclude that the presence of the AE can be detected at that level of uncertainty. However, if the flows balance with and without AE then we conclude that the stochastic flow account is not sensitive to AE at that level of uncertainty because it is unable to detect their presence. If the presence of AE cannot be detected no role for their effect on climate can be deduced from the data at that level of uncertainty in natural flows.
  18. The balance is computed from the atmospheric perspective as Balance=Input-Output where Input is flow to the atmosphere and Output is flow from the atmosphere. The p-values for hypothesis tests for uncertainties in the natural flows from 1% of mean to 6.5% of mean are presented below both as a tabulation and as a line chart.
  1. In the tabulation the PCT column shows the assumed percent standard deviation in the natural flows for which no uncertainty information is available. In the”base case”, the blanket statement by the IPCC that the uncertainty is 20% is interpreted to mean that the width of the 95% confidence interval is 20% of the mean and the corresponding standard deviation computed as (20/2)/1.96 is almost identical to that in the 5% (5PC) row. The data in each row shows the p-values of two hypothesis tests labeled as WITH and WITHOUT. The WITH column shows p-values when the AE are included in the balance computation. The WITHOUT column shows the p-values when the AE are left out of the balance computation.
  2. We use a critical p-value of alpha=0.1 for the test of the null hypothesis that Balance=0. Balance=0 means that the stochastic flow account is in balance. If the p-value is less than apha we reject the null hypothesis and conclude that the stochastic flow account is not in balance. If we fail to reject the null then we conclude the stochastic flow account is in balance.
  3. The p-values for WITH and WITHOUT in each row taken together tell us whether the stochastic flow system is sensitive to AE, that is whether the relatively small AE flow can be detected in the context of uncertainty in much larger natural flows. If we fail to reject the null hypothesis that Balance=0 in both WITH and WITHOUT columns, the stochastic flow account balances with and without the AE flows. In these cases the stochastic flow account is not sensitive to AE, that is it is unable to detect the presence of the AE flows. This is true for the five rows in which the uncertainty in natural flows is 3% of mean or higher.
  4. For the two lower uncertainty levels of 2% and 1% we find that the null hypothesis Balance=0 is not rejected when AE are included (the stochastic flow account is in balance) but rejected when AE are not included (the stochastic flow account is not in balance). Under these uncertainty conditions, the stochastic flow account is sensitive to the presence of AE, that is the flow account can detect the presence of the relatively small AE flows. The chart shows that the crossover uncertainty lies somewhere between 2% and 3% and in fact it is found by trial and error that the crossover occurs at 2.3%.
  5. These results imply that the IPCC carbon cycle stochastic flow balance is not sensitive to the presence of the relatively low flows from human activity involving fossil fuel emissions and land use change. The large natural flows of the carbon cycle cannot be directly measured and they can only be indirectly inferred. These inferred values contain uncertainties much larger than 2.3% of the mean. It is not possible to carry out a balance of the carbon cycle under these conditions.
  6. In the case of the conclusion by climate scientists that the observed increase in atmospheric CO2 concentration is caused by fossil fuel emissions, natural flows in the carbon cycle that are an order of magnitude larger than fossil fuel emissions and that cannot be directly measured are inferred with the implicit assumption that the increase in atmospheric CO2 comes from fossil fuel emissions. The flow balance can then be carried out and it does of course show that the increase in atmospheric CO2 derives from fossil fuel emissions The balance presented by the IPCC with inferred flows thus forces an exact balance by way of circular reasoning. Therefore, the IPCC carbon cycle balance does not contain useful information that may be used to ascertain the impact of fossil fuel emissions on the carbon cycle or on the climate system.
  7. A rationale for the inability to relate changes in atmospheric CO2 to fossil fuel emissions is described by Geologist James Edward Kamis in terms of natural geological emissions due to plate tectonics [LINK] . The essential argument is that, in the context of significant geological flows of carbon dioxide and other carbon based compounds, it is a form of circular reasoning to describe changes in atmospheric CO2 only in terms of human activity. It is shown in a related post, that in the context of large uncertainties in natural flows, changes in atmospheric CO2 is not responsive to the rate of emissions [LINK] .
  8. Circular reasoning in this case can be described in terms of the “Assume a spherical cow” fallacy [LINK]  which refers to the use of simplifying assumptions needed to solve a problem that change the context of the problem so that the solution no longer answers the original research question.




The following posts on this site are relevant to this discussion:

  1. Fossil Fuel Emissions and Atmospheric Composition
  2. Will Emission Reduction Change the Rate of Warming?
  3. Ocean Acidification by Fossil Fuel Emissions
  4. Spurious Correlations in Climate Science






bandicam 2018-06-26 09-38-07-779

  1. The Global Carbon Project, with a goal to “fully understand the carbon cycle” has instead evolved into the world’s foremost and most trusted accountants of fossil fuel emissions. The Project keeps records of fossil fuel emissions the world over on a country by country and year by year basis and these data are made publicly available and also analyzed for trends as well as implications for future climate change scenarios. According to Wikipedia, “The Global Carbon Project (GCP) was established in 2001. The organisation seeks to quantify global carbon emissions and their sources.”
  2. Their pretension to the study of the carbon cycle is not as useful as their emissions data because it is presented completely in the context of circular reasoning. Observed changes of CO2 concentration in natural systems are assumed to derive wholly from fossil fuel and land use change. The carbon cycle accounting is carried out on that basis. Uncertainties are noted but ignored in the accounting calculations. The procedure is described below for the decade 2008-2017.
  3. The average annual carbon cycle for the decade 2008-2017 is presented here as an example of the reliance of the Global Carbon Project on circular reasoning. The flows used in the flow accounting are provided by the Global Carbon Project as GTY of carbon dioxide. They have been converted to GTY of carbon (GTCY) for ease of comparison with the IPCC figures above.
  4. The use of net flows (net flow to land sink and net flow to ocean sink) insert assumptions and circular reasoning into the carbon cycle flow account. These are differences between very large flows in the order of 100 GTY with large uncertainties in their measurement. These differences therefore contain even larger uncertainties.
  5. In cases where a net flow is a direct measurement, it’s interpretation subsumes that which the flow account is carried out to determine. For example, if the net flow to ocean sink is measured as a change in the average inorganic carbon concentration of the oceans, then the flow account assumes that the change was caused by surface phenomena such as fossil fuel emissions ignoring emissions from plate tectonics, submarine volcanoes, hydrothermal vents, and hydrocarbon seeps.
  6. Carbon cycle flow accounts of this nature are not pure data that can be used to test theory but rather the theory itself expressed in terms of flow account values.

Fossil fuel emissions: mean=9.3545, stdev=0.5454 [IPCC 2000-2009: 7.8]

Land use change emissions: mean=1.485, stdev=0.818 [IPCC 2000-2009: 1.1]

Net flow to land sink: mean=3.054, stdev=0.818 [IPCC 2000-2009: 4.3]

Net flow to ocean sink: mean=2.37, stdev=0.545 [IPCC 2000-2009: 1.6]

Growth in atmospheric CO2: mean=4.718. stdev=0.0545 [IPCC 2000-2009: 4.4]



18 Responses to "Carbon Cycle Measurement Problems Solved with Circular Reasoning"

If you invite me to buy, for the same investment, one of two businesses – A with an annual profit of one million dollars or B with a profit of two million – I might plump for B. But if due diligence shows me that A’s profit was based on revenues of two million and expenses of one million, while B had revenues of one billion and expenses of nine hundred and ninety-eight million…

I would have some searching questions for B’s accountant.

Along the same lines, there is the old joke about the wealthy but uneducated businessman who explains his success thus:

“I buy things for a dollar and sell them for two dollars. You would be amazed at how that one percent profit builds up!”

To that list of uncertain natural flows, I would add the net transfer of organic carbon from the surface of the ocean to lower parts. That used to be estimated at two billion tons a year. Now the biologists guess it is between six and twelve billion tons – but the climatologists do not even seem to have noticed this discussion!

Talk about settled, joined-up, science!

thank you for your interesting observations

Good one! I tracked down the numbers but baulked at the full statistical analysis. My take away conclusion was that our total industrial addition was about 1% of the mobile CO2. No natural system is critically sensitive to that small degree of change.

You may find interesting the table I put together in:


Thank you I will take a look

Thank you. The link did not work on my phone but i will try again on the computer after dinner.

very interesting work indeed. thank you. if i use any of it i will cite you. my work is not as comprehensive. it says simply that an uncertain flow account can’t be balanced without taking the uncertainty into account.

Very nice.

The evidence that the rise in atmospheric CO2 is not due to anthropogenic forcing is compelling. The evidence it is due to anthropogenic forcing is a bunch of hand waving rationalization, downplaying of uncertainty (as you note), and misunderstanding of how feedback dynamics evolve.

A lot of people are going to have egg on their faces when the truth finally wins out.

[…] relationship between 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 […]

[…] The “build-up” of energy on the earth is described in climate science in terms of a build up of atmospheric CO2. The higher the CO2 concentration the greater the greenhouse forcing of CO2 through the sensitivity equation that temperature is proportional to ln(CO2). The human cause in this equation is that the industrial economy of humans burning fossil fuels is injecting external CO2 that does not belong in the current account of the carbon cycle. It is claimed that the external and previously sequestered CO2 from fossil fuels dug up from under the ground is causing atmospheric CO2 to rise. This relationship between fossil fuel emissions and atmospheric CO2 concentration is a critical element of AGW. Yet, there is no empirical evidence in the observational data outside of climate models to support this crucial and necessary relationship between emissions and changes in atmospheric composition [LINK] [LINK] . […]

[…] Atmospheric Scientist Murry Salby had claimed in public presentations that the uncertainty in the carbon cycle of much larger flows of CO2 is such that the much smaller flows from fossil fuel emissions can’t be detected. He was criticized for not providing statistical evidence of the claimed irrelevance of fossil fuel emissions. That evidence is now available online at this link [LINK] . […]

[…] It has long been recognized that the climate sensitivity of surface temperature to the logarithm of atmospheric CO2  (ECS), which lies at the heart of the anthropogenic global warming and climate change (AGW) proposition, was a difficult issue for climate science because of the large range of empirical values reported in the literature and the so called “uncertainty problem” it implies {Caldeira, et al “Climate sensitivity uncertainty and the need for energy without CO2 emission.” Science 299.5615 (2003): 2052-2054}. The ECS uncertainty issue was interpreted in two very different ways. Climate science took the position that ECS uncertainty implies that climate action has to be than that implied by the mean value of ECS in order to ensure that higher values of ECS will be accommodated while skeptics argued that the large range means that we don’t really know. At the same time skeptics had also presented convincing arguments against the assumption that observed changes in atmospheric CO2 concentration can b e attributed to fossil fuel emissions [[LINK] , [LINK] . […]

[…] in the context of the very high uncertainties in carbon cycle flows described in a related post [LINK] and the interpretation of this change must be made in the context of the AGW theoretical framework […]

Still reading through your posts… I’ve been wary of this ‘increase through natural sources’ argument, because of the matching Mauna Loa CO2 and anthropogenic emissions time series. So thank you for explaining the C budget uncertainties. I also see where you pulled this apart using DCA with up to 5 year periods; interesting, and the first I’ve seen that done. Have you addressed the C14 C12 isotope ratios arguments elsewhere?

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