OTHER POSTS ON STATISTICAL FLAWS IN THE CARBON BUDGET

CLIMATE SCIENCE VS STATISTICS

CARBON BUDGETS AND THE TCRE

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THIS POST COMBINES & SUMMARIZES RELATED POSTS ON AGW CLIMATE CHANGE

1. The theory of AGW climate change since pre-industrial times; and the need for climate action against this trend (AGW-CC-CA) is based on a causation sequence as follows. First fossil fuel emissions of the industrial economy causes the atmospheric CO2 concentration to rise. Second the higher CO2 concentration of the atmosphere increases its GHG effect and causes warming. Third the warming is dangerous and possibly catastrophic in terms of sea level rise, extreme weather, mass extinctions, and effects on agriculture and health. Fourth the undesirable and dangerous changes being caused by AGW climate change can and must be attenuated by taking climate action in the form of a synchronized global emission reduction program. Climate action will work because emission reduction will reduce the rate of rise in atmospheric CO2 and at zero emissions, the rise will cease. Following that atmospheric CO2 can be reduced with carbon dioxide removal and sequestration technologies being developed [LINK] .
2. Fossil fuel emissions and atmospheric composition Part-1: The AGW-CC-CA causation sequence begins with the assumption that the observed changes in atmospheric concentration since pre-industrial times are explained exclusively in terms of fossil fuel emissions. Two arguments are presented by climate as proof of this relationship. The first argument is the flow account of the carbon cycle with and without fossil fuel emissions. The flow accounting presented shows that the rise in atmospheric CO2 is explained in terms of fossil fuel emissions. There are two problems with the methodology in this argument. First, nature’s carbon cycle flows are not directly measurable but are results of gross estimations with large uncertainties. To balance this flow account, uncertainties are ignored and the much larger natural flows of the carbon cycle are inferred with the implicit assumption that the increase in atmospheric CO2 derives from fossil fuel emissions. The flow accounting thus achieved of course shows that changes in atmospheric CO2 are driven by fossil fuel emissions. However, when uncertainties in natural flows are taken into account, it is shown that fossil fuel emissions cannot even be detected in the context of these uncertainties. The relevant analysis is presented in the post Carbon Cycle Measurement Problems Solved with Circular Reasoning 
3. Fossil fuel emissions and atmospheric composition Part-2: Yet another proof of the causal relationship between fossil fuel emissions and rising atmospheric CO2 concentration is the observation that atmospheric CO2 is rising during a time of continued fossil fuel emissions since the Industrial Revolution first noted in the Callendar 1938 paper and subsequently repeated in AGW studies that followed. And in fact, if we look at the correlation between the time series of source data we find a strong and apparently statistically significant positive correlation between rising atmospheric CO2 concentration and fossil fuel emissions. However, it is well known that correlations between the source data of time series often derive from shared trends and not necessarily from responsiveness of one to changes in the other at a finite time scale at which this causation should occur. This property of time series data has been extensively documented by Tyler Vigen [LINK] . To separate responsiveness at the time scale of interest from the spurious effect of shared trends it is necessary to remove the trends from the data in what is called detrended correlation analysis as explained by Alex Tolley in this lecture [LINK] .
4. When this procedure is used, the correlation in the source time series vanishes and no detrended correlation is found at scales from 1 to 5 years. This result supports and strengthens the conclusion drawn in the carbon flow accounting analysis with the common conclusion that no evidence is found in the observational data that atmospheric CO2 concentration is responsive to fossil fuel emissions in a measurable way. Details of this work is presented in a related post on this site [LINK] . It is noted in that post the analysis presented by climate science contains circular reasoning because it is carried out strictly in the context of assumed causes and in the absence of natural flows particularly the known large geological flows of carbon from plate tectonics and volcanism both above ground and in the ocean floor particularly so in the East Pacific Rise and in the Pacific Ring of Fire, a region of intense geological activity.
5. The 14C Dilution Argument: A further argument presented by climate science to support the attribution of the observed rise in atmospheric CO2 concentration to fossil fuel emissions is that of Carbon-14 dilution by fossil fuel emissions. Carbon-14 (14C) 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.
6. 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.
7. The primary evidence for such dilution is the Stuiver and Quay paper (SQ) based on tree ring analysis of Douglas Firs in the Pacific Northwest of the USA that grew during the period 1815 to 1975. Their data show a 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. These data are generally accepted as empirical evidence that the observed increase in atmospheric CO2 since pre-industrial times is derived from fossil fuel emissions because of the dilution of atmospheric 14C with pure 12C carbon of fossil fuels.
8. 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] .
9. Climate Action and the Carbon Budget. The essence of climate change activism is climate action, stated as reductions in fossil fuel emissions needed to limit AGW warming to an upper limit considered safe. The unspoken principle is reduction in the use of fossil fuels with eventual elimination of fossil fuels altogether from the global energy infrastructure but stated in terms of emissions. In that sense AGW theory and its claimed calamitous impacts serve as the rationale for the energy infrastructure changes sought.
10. AGW theory holds that warming occurs in a two-step process without a well defined time scale. First, emissions cause atmospheric CO2 to rise and second the higher atmospheric CO2 level increases surface temperature so that relative to the lower CO2 concentration prior to the increase, a warming trend is created such that emissions cause warming. This relationship can be used in climate models to create pathways for different emission reduction plans and these pathways can then be used to design an emission reduction plan for a target rate of warming. The target rate is usually stated as the total amount of warming since pre-industrial times by the target date as for example 1.5C of warming since pre-industrial times by the year 2100. The sum of all the emissions that can be made from the present to the target date to stay within the warming limit is called the carbon budget. The carbon budget has thus become the focal point of climate action design and evaluation.
11. However because of inconvenient non-linearity and large uncertainties in climate model pathways, carbon budget mathematics are instead based on the TCRE (Transient Climate Response to Emissions) described in a related post [LINK] . The TCRE arises from the near perfect proportionality between cumulative warming and cumulative emissions first noticed by climate scientists in 2009. The corresponding regression coefficient in units of degC of cumulative warming per trillion tons of cumulative emissions is the TCRE. This relationship is supported byn a linear relationship with correlation > 90%.  The TCRE is simpler to compute and appears to be mathematically more precise and robust than emission pathway computations of climate models.
12. The important contribution of the TCRE in climate science has been in the area of climate action. In its AGW theory, climate science forecasts what it thinks are the undesirable effects of AGW such as sea level rise and extreme weather, attributed to fossil fuel emissions of the industrial economy. In its climate action plan, climate science shows humanity the path to avoid these undesirable impacts of climate. Climate action refers to a globally coordinated effort to reduce fossil fuel emissions as a way of attenuating the rate of AGW and thus moderating its undesirable impacts.
13. Globally coordinated climate action plans such as the Paris Agreement are designed according to a carbon budget. The carbon budget refers to the total amount of cumulative emissions that can be made to stay at or below a given target temperature. The carbon budget is derived from the TCRE. For example, after 1C of warming from pre-industrial times, the carbon budget for a target of 1.5C would be the cumulative emissions that correspond to cumulative warming of 0.5C. Thus cumulative emissions from now to the 1.5C target would be the 0.5C/TCRE where TCRE is denominated in degC/trillion tons of cumulative emissions. A typical v alue of the TCRE coefficient is TCRE=2 degC/trillion tons. Thus in this case, the carbon budget would be 0.5/2 or 2.5 trillion tons of cumulative emissions allowable to stay at or below 1.5C warming since pre-industrial.
14. THE IMPOSSIBILITY OF A CARBON BUDGET: The carbon budget can be computed as shown in the previous two paragraphs, but in light of the absence of attribution of changes atmospheric CO2 concentration to fossil fuel emissions, the carbon budget is an anomaly. Although a carbon budget can be computed, and well developed procedures exist for its computation, the budget thus computed may not have a real interpretation. This intuition becomes evident when we examine the remaining carbon budget problem in the next section of this presentation.
15. THE REMAINING CARBON BUDGET PROBLEM: The convenience in constructing carbon budgets offered by the TCRE comes with an apparently mysterious inconvenience discovered by climate scientists and described in a related post [LINK] . It turns out that partway into a carbon budgeted time span, the remaining budget cannot be estimated by subtraction. Instead the TCRE carbon budget computation must be done anew for the remaining portion of the time span. The reason for this, described in the same document linked above, is that the TCRE proportionality, though showing a strong near perfect correlation, does not survive the so called “split-half test” in which the time span of a time series is split into two halves and the correlation is tested in both halves. In the case of the TCRE proportionality, the value of the regression coefficient fails the split half test [LINK] in the sense that its value can change significantly when its time span is changed. The split-half instability implies that the remaining carbon budget must be computed according to the different regression coefficient in the remaining time span.
16. FAILURE OF THE TCRE: Although the RCB computations can be carried out and the remaining carbon budget can be computed, the underlying weakness of the TCRE implied by this anomaly cannot be ignored. As shown in the TCRE post [LINK] , the real problem with the TCRE is that time series of cumulative values have neither time scale nor degrees of freedom. The effective N (sample size) of the cumulative values of a time series is EFFN=2 and therefore the degrees of freedom is DF=2-2=0. Therefore, although a TCRE coefficient can be computed it has no interpretation in the real world because both correlation and regression coefficient are spurious and illusory.
17. FINITE TIME SCALES: Finite time scales can be created in this kind of computation if a finite time scale is used instead of using the full span. For example in a full span of 100 years, if a moving window of 20 years is used the time scale is now 20 years and the effective degrees of freedom is approximately 100/20 or 5. If the TCRE implies a real correlation between the rate of emissions and the rate of warming, we should be able to find it at finite time scales. This test is presented in a related post [LINK] where time scales of 10 to 30 years are tried. No statistically significant correlation is found. We can therefore conclude that the high correlations seen in the cumulative value time series is illusory and is not a real property of the data. AND THAT THEREFORE CARBON BUDGETS BASED ON THE TCRE ARE ILLUSORY. They can be computed but they have no interpretation in the real world.

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