THIS POST IS A SUMMARY OF SOME METHODOLOGICAL AND STATISTICAL ISSUES IN ANTHROPOGENIC GLOBAL WARMING AND CLIMATE CHANGE (AGW) PRESENTED IN A NUMBER OF RELATED POSTS ON THIS SITE. 

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 ISSUE#1 > THE RESPONSIVENESS OF ATMOSPHERIC COMPOSITION TO FOSSIL FUEL EMISSIONS: The human cause of warming begins with the argument that our use of fossil fuels has caused atmospheric CO2 concentration to rise and conversely, that causal relationship implies that climate action in the form of reducing or eliminating fossil fuel emissions will reduce or halt the rise in atmospheric CO2 and thus attenuate the rate of warming. Therefore, a fundamental and necessary condition for AGW and its implied climate action imperative is that a causal relationship must exist between atmospheric composition and fossil fuel emissions such that (a) the observed changes in atmospheric composition since pre-industrial times can be explained in terms of fossil fuel emissions of the industrial economy, and (b) the effectiveness of climate action in attenuating and halting the rate of warming by reducing and eliminating fossil fuel emissions can be established . An annual time scale is assumed in climate science. This relationship is therefore tested at an annual time scale. Some longer time scales are also investigated.

TEST#1 > [LINK] > Is atmospheric CO2 concentration responsive to fossil fuel emissions at an annual time scale? Detrended correlation analysis is used to test this relationship. The detrending procedure removes the spurious effect of shared trends on correlation so that only the responsiveness at the specified time scale is measured in the correlation. Although strong correlations from ρ=0.742 for a 1-year time scale to ρ=0.931 for a 5-year time scale are seen in the source data time series, these correlations do not survive into the detrended series where no statistically significant correlation is found. We conclude that the data do not provide evidence that atmospheric CO2 concentration is responsive to fossil fuel emissions.

TEST#2 > [LINK] > Can nature’s carbon cycle flows be measured with sufficient precision to detect the presence of fossil fuel emissions? As seen in the IPCC carbon cycle flows presented in the linked document, the estimated mean values of the flows of the carbon cycle, with flow uncertainties not considered, provide an exact mass balance in the presence of fossil fuel emissions with the so called “Airborne Fraction” computed as 50%, meaning that the mass balance shows that 50% of the CO2 in fossil fuel emissions remain in the atmosphere where they accumulate, change atmospheric CO2 concentration, and cause anthropogenic global warming (AGW) by way of the GHG effect of rising atmospheric CO2. The issue here is that these flow estimates contain very large uncertainties because they cannot be directly measured but must be inferred. In the related post a statistical test is devised to determine the level of uncertainty in carbon cycle flows at which the much smaller CO2 flows in fossil fuel emissions can be detected in the presence of the much larger carbon cycle flows. In the related post [LINK] , a Monte Carlo simulation is devised to estimate the highest value of the unknown standard deviations in carbon cycle flows at which we can detect the presence of CO2 in fossil fuel emissions. In the test, an uncertain flow account is considered to be 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 as evidence that the relatively small fossil fuel emissions can be detected in the presence of much larger and uncertain natural flows. 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. 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 carbon cycle flows. The p-values for these hypothesis tests vary from 1% of mean to 6.5% of mean as shown in the tabulation below. The results show that when nature’s carbon cycle flows contain an uncertainty of 2% of the mean or less, the carbon cycle flow account can detect the presence of fossil fuel emissions. The presence of fossil fuel emissions cannot be detected at higher carbon cycle flow uncertainties. Climate science and the IPCC estimate that uncertainties in carbon cycle flows vary from 6.5% to more than 10%. The lowest value of 6.5% is for photosynthesis. We conclude from this Monte Carlo simulation that, given the uncertainty in our estimate of natural carbon cycle flows, it is not possible to detect the impact of fossil fuel emissions on atmospheric composition.

TEST#3: Monte Carlo Simulation of fossil fuel emissions being inserted into carbon cycle flows. Carbon cycle flows for which no uncertainty data are found in the IPCC report are assigned the low photosynthesis value of 6.5% of the flow estimate provided. The results are displayed in the charts below. They demonstrate that it is not possible to detect an impact of fossil fuel emissions on atmospheric CO2 concentration when uncertainties in carbon cycle flows are taken into account. These results show that within the stated uncertainties of carbon cycle flows, no evidence is found in the data that fossil fuel emissions cause changes in atmospheric CO2 concentration. The uncertainty in carbon cycle flows is too large to detect the assumed effect as in the so called “retained fraction”. These results also imply that therefore there is no evidence in the observational data that climate action will have an effect on the observed dynamics of atmospheric composition.  [LINK TO MONTE CARLO SIMULATION]  

ISSUE#2: GEOLOGICAL CARBON FLOWS: In estimating the impact of fossil fuel emissions and climate action on changes to atmospheric composition, climate science looks at two sources of these flows – fossil fuel emissions and carbon cycle flows. Natural carbon flows from hydrocarbon seeps, submarine volcanism, mud volcanoes, mantle plumes, and hydrothermal vents to the atmosphere are not taken into account. A survey of geological flows of carbon to the atmosphere from these sources is presented in a related post.[LINK TO GEOLOGICAL FLOWS]  . We find in that analysis as follows:  {We conclude from the information presented in the bibliography and the analysis above, that there are significant natural flows of carbon from geological sources such as hydrocarbon seeps, methane hydrates, submarine volcanism, and submarine mud volcanoes and that these flows make it difficult to interpret changes in atmospheric CO2 exclusively in terms of the use of fossil fuels in the industrial economy.  In that context, it should also be noted that the bibliography below shows that oil and gas production lowers the pressure that forces out the natural hydrocarbon seeps. Without oil and gas production, the seepage rate will increase and undermine the apparent advantage to the climate of not producing oil and gas. It is noted that humans began using fossil fuels from seeps and natural outflows. It was only after its utility became obvious that seeps were no longer sufficient. It was then that humans began to look for the sources of those seeps.}. An extensive bibliography on this topic is provided.

ISSUE #3 > THE RESPONSIVENESS OF SURFACE TEMPERATURE TO FOSSIL FUEL EMISSIONS: Anthropogenic global warming (AGW) theory says that fossil fuel emissions cause warming and that their reduction and eventual elimination can be used to attenuate the rate of warming and this option is offered and demanded as the “climate action” plan needed to save the world from the destructive effects forecast for uncontrolled AGW. These relationships imply that a correlation must exist between the rate of emissions and the rate of warming and in fact, climate science has presented just such a correlation. It is called the Transient Climate Response to Cumulative Emissions (TCRE) described more fully in a related post [LINK] . And in fact, the TCRE provides the structure and mathematics of the proposed climate action in terms of the so called carbon budgets proposed to constrain warming to a given target level. The TCRE derives from the observation by Damon Matthews and others in 2009 that a near perfect proportionality exists between cumulative emissions and cumulative warming.

TEST#1 > Does the TCRE imply that the rate of warming is related to the rate of emissions such that climate action plans of reducing emissions can be used to attenuate the rate of warming? A test for this correlation is presented in a related post [LINK] where it is shown that a time series of the cumulative values of another time series has neither time scale nor degrees of freedom.

The details of the proof of this condition are provided in the post on carbon budgets where it is also shown that the observed correlation derives not from responsiveness of warming to emissions but from a fortuitous sign pattern in which emissions are always positive and in a time of rising temperatures, annual warming is mostly positive [LINK] where it is shown for example, that the TCRE correlation exists in random numbers if the same sign pattern is inserted into the random numbers and disappears when the sign pattern is also random.

The relevant GIF charts are reproduced below.  Random numbers in the left frame and their cumulative values in the right frame. The difference between the two charts is that in the first chart the random numbers are truly random with no sign pattern imposed meaning that positive and negative values are equally likely; whereas in the second chart the random number generator for both x and y favors positive values 55% to 45%. The analysis of the TCRE in these related posts implies that the observed correlation is illusory and spurious and has no implication for the real world phenomena the data apparently represent. Therefore, the TCRE has no interpretation in terms of a causal relationship between emissions and warming.

The only information content of the TCRE is the sign pattern. If the the two time series have a common sign bias, either both positive or both negative, the correlation will be positive. If the the two time series have different sign biases, one positive and the other negative, the correlation will be negative. If the the two time series have no sign bias, no correlation will be found. Therefore, the only information content of the TCRE is the sign pattern and no rational interpretation of such a proportionality exists in terms of a causal relationship that can be used in the construction of carbon budgets. The TCRE carbon budgets of climate science is a a meaningless exercise with an illusory statistic. 

TEST#2 > The problem with the TCRE correlation is that it has no time scale and no degrees of freedom. Both issues can be resolved by inserting a fixed time scale X into the TCRE computation such that the correlation is rendered statistically valid as TCREX. The second research question is therefore, {Does the TCREX show that the rate of warming is responsive to the rate of emissions} such that climate action plans of reducing emissions can be used to attenuate the rate of warming? This test is carried out in a related post [LINK] with time scales of ten to thirty years. The test is carried out with both climate model estimations of global mean temperature (RCP) and reconstructions of global mean temperature from the instrumental record  (HADCRUT4). The results of detrended correlation analysis are summarized below. They show strong statistically significant detrended correlations in the theoretical temperatures from climate models but no statistically significant result is found in the observational data. The agreement with the theoretical temperature series validates the procedure and therefore the absence of evidence to relate observational data to emissions provides convincing evidence that when the TCRE measure is corrected to insert time scale and degrees of freedom, the “near perfect proportionality” of the TCRE disappears. We conclude from these results that no evidence is found in the observational data that the rate of warming is responsive to the rate of emissions. [DETAILS] 

TEST#3: CARBON BUDGETS: The claimed catastrophic impacts of AGW Climate Change serve as the needed motivation for Climate Action. Climate action involves the reduction and eventual elimination of the use of fossil fuels – and thereby of fossil fuel emissions. The theoretical linkage between climate change and climate action is the Carbon Budget. A climate action plan specifies the maximum warming target over a specified time span. The corresponding carbon budget is the maximum amount of carbon in fossil fuel emissions that can be emitted over that time period to comply with the climate action plan. The statistical issue in this case arises because the carbon budget is based on the flawed TCRE – Transient Climate Response to Cumulative Emissions discussed  above in Issue#2.TEST#1 > The use of the illusory TCRE correlation in the construction of carbon budgets renders the carbon budget equally spurious and illusory as described in this related post [LINK] . It shows that the carbon budget computed from the TCRE has no interpretation in the real world because it is based on an illusory correlation that is the creation of sign patterns and not based on the responsiveness of temperature to emissions. The further consideration is that the absence of time scale and degrees of freedom in the carbon budget renders it a spurious statistic that has no interpretation in terms of the emissions and warming dynamics it apparently represents.TEST#2 > A further test of the validity of the carbon budget is seen in the Remaining Carbon Budget Puzzle (RCBP) that has created a state of confusion in climate science as described in a related post [LINK] . In brief, the RCBP issue is that the carbon budget for the full span of the budget period does not equal the sum of the carbon budgets computed for its sub-spans. There is a simple statistics explanation of this apparent oddity in terms of the spuriousness of the correlation and the TCRE regression coefficient. The positive TCRE correlation is a creation of a fortuitous sign pattern such that emissions are always positive and during a time of warming, annual warming values are mostly positive, as shown in a related post [LINK] . Thus, the TCRE regression coefficient is determined by the fraction of annual warming values that are positive; and this fraction is not likely to be the same in different sub-spans and not the same in any given sub-span as in the full span. It is this statistical oddity and not the absence of Earth System climate model variables that explains the RCBP. And yet, as seen in the literature, climate science reaches out to Earth System Models to explain and then to apparently solve the RCBP, as shown in a related post [LINK] . In summary, the Remaining Carbon Budget issue is a simple statistical issue that has been interpreted in climate science in terms of AGW climate forcing portfolio needed to implement carbon budgets.

ISSUE#4: > WILL CLIMATE ACTION MODERATE THE RATE OF SEA LEVEL RISE? A principal argument for climate action has been the fear of sea level rise that threatens hundreds of millions of people in vulnerable small island states, low lying deltas such as Bangladesh, and coastal communities such as Florida [LINK] [LINK] [LINK] [LINK] and it is therefore proposed that climate action in the form of reducing or eliminating fossil fuel emissions must be taken to attenuate the rate of sea level rise [LINK] . The only empirical evidence presented to relate sea level rise to emissions is the paper by Professor Peter Clark of Oregon State University [LINK] [Reducing carbon emissions will limit sea level rise] . The Clark paper shows a strong and statistically significant correlation between cumulative emissions and cumulative sea level rise in the TCRE format and thus suffers from the same limitations as the TCRE in that there is no time scale and no degrees of freedom, and that the correlation derives from a sign pattern in that emissions are always positive and annual sea level rise values are mostly positive.

TEST#1 > The correlation presented by the Peter Clark paper is evaluated in a related post and found to be spurious and illusory because it has neither time scale nor degrees of freedom [LINK] . This spurious correlation contains no information in terms of a causal relationship between emissions and sea level rise. It is necessary to test the correlation with time scale and degrees of freedom restored.

TEST#2 > The Peter Clark correlation is tested in a related post [LINK] with finite time scales inserted. Time scales of 30, 35, 40, 45, and 50 years are used in the test. The correlation and detrended correlation between emissions and sea level rise are shown in the summary of results table below. A statistically significant positive correlation is required to support the causation hypothesis being tested. Although such correlations are seen in the source data, none of them survives into the detrended series where the correlations are negative. Note that source data correlations between time series data is influenced by shared trends and therefore have no interpretation in terms of responsiveness at a finite time scale. We conclude from these results that, although a significant correlation is seen between the cumulative values, no evidence of correlation between emissions and sea level rise is found in the data at finite time scales and with degrees of freedom restored. Thus there is no evidence that climate action in the form of reducing fossil fuel emissions will attenuate sea level rise.

ISSUE#5 > THE IMPACT OF AGW ON TROPICAL CYCLONES:   This issue is presented in a related post [LINK]ISSUE#6 > THE IMPACT OF AGW ON SEA ICE: This issue is presented in three related posts [LINK] [LINK] [LINK] 

ISSUE#6: WILL EMISSION REDUCTION CHANGE THE RATE OF WARMING? [LINK].

Climate science has presented a causal relationship between emissions and warming in terms of the TCRE where we find a near perfect proportionality between cumulative emissions and surface temperature. The TCRE is used in climate science to construct “CARBON BUDGETS” Tto relate the climate action needed for any given warming target.

However, as shown in related posts [LINK]  [LINK] , the TCRE has no interpretation in terms of the data because of a fatal statistical error. This work addresses these shortcomings of the TCRE by defining finite time scales shorter than the full span. Here we use data for fossil fuel emissions from the CDIAC and the theoretical temperatures from these emissions in the CMIP5 forcings found in the RCP8.5 as well as the HadCRUT4 temperature reconstructions. We then compute the corresponding correlations between emissions and warming as in the TCRE but with the changes needed to retain degrees of freedom.

The results are summarized in Figure 6 and Figure 7 below where we find that the source data correlation rises as the time scale is increased. The theoretical model predictions (RCP) show stronger detrended correlations (0.3 to 0.56) than the HAD observational data (0.1 to 0.2) because a larger portion of the model prediction RCP source correlation survives into the detrended series, indicating a stronger relationship between emissions and warming in climate models than in observational data. We find that the four time scales greater than ten years (15, 20, 25, and 30 years) show statistically significant detrended correlations for the climate model series RCP8.5. No statistically significant detrended correlation is found in the observational data HadCRUT4. 

We conclude from these results that though the causal relationship between emissions and warming is found in the RCP8.5 generated by climate models, it is not found in the data and that thereforee no empirical evidence is found to support the rationale for costly climate action that assumes a causal relationship between the rate of emissions and the rate of warming. 

THE ESSENTIAL FINDING HERE IS THAT CLIMATE ACTION WORKS IN CLIMATE MODELS BUT NOT IN THE REAL WORLD. THE ANOMALIES IN CARBON BUDGETS THAT CLIMATE SCIENTISTS ARE STRUGGLING WITH MAY BE UNDERSTOOD IN THIS CONTEXT.  [LINK]  

CONCLUSION: The analyses presented above imply that the assumption in climate science that relates changes in atmospheric composition to fossil fuel emissions such as to explain the rate of warming and the effectiveness of the proposed climate action has no empirical support. The further proposition by climate science that relates warming directly to cumulative emissions is statistically flawed and also inconsistent with their original theory that warming is explained by accumulation in the atmosphere of CO2 from fossil fuel emissions and its GHG warming effect thereof. This means that the theory of global warming as proposed by climate science contains fatal statistical flaws. When these statistical errors are corrected no evidence of human caused global warming by way of fossil fuel emissions remains and no evidence is found that the proposed climate action of reducing fossil fuel emissions will change the rate of warming.