FIGURE 1: CO2 AIRBORNE FRACTION

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 Fraction” is 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 of these flows. They can only be grossly inferred based in assumptions that exclude or minimize geological flows.
16. Here, we 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.