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Some Statistical Issues in AGW

Posted on: November 16, 2019

 

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. 

 

[LINK TO THE HOME PAGE OF THIS SITE]

 

  1. 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 attributed to atmospheric composition. Thus, a fundamental and necessary condition for AGW is that a causal relationship must exist between atmospheric composition and fossil fuel emissions such that the observed changes in atmospheric composition since pre-industrial times can be explained in terms of fossil fuel emissions of the industrial economy. An annual time scale is assumed in climate science. This relationship is tested in four different posts on this site and the results are summarized below.
  2. TEST#1[LINK] > Is atmospheric CO2 concentration responsive to 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 climate science assumes an annual time scale, time scales from one to five years are tested. The results are tabulated in Paragraph#3 below. There are two columns of results for each time scale, the correlation and the detrended 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 sufficient evidence that atmospheric CO2 concentration is responsive to fossil fuel emissions.
  3. COMPO-CHART
  4. TEST#2 > [LINK] > Can nature’s carbon cycle flows be measured with sufficient accuracy 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 change atmospheric CO2 concentration and cause anthropogenic global warming (AGW). Yet, 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 whether the much smaller emissions can be detected in the presence of much larger carbon cycle flows when their large uncertainties are considered. 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.
  5. 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 natural flows. The p-values for hypothesis tests for uncertainties in the natural flows from 1% of mean to 6.5% of mean are tabulated in Paragraph#6. 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. The lowest uncertainty found in the carbon cycle flows is 6.5% for photosynthesis. The other uncertainties are much larger and their flows are estimated to be higher than fossil fuel emissions by at least an order of magnitude. Therefore, given the uncertainty in our estimate of natural carbon cycle flows, it is not possible to determine the impact of fossil fuel emissions. 
  6. ISSUE #2 > 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.
  7. 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 here in {Paragraph#9 and Paragraph#10 below random numbers in the left frame and their cumulative values in the right frame}. The difference between the two charts is that in #9 the random numbers are truly random with no sign pattern imposed meaning that positive and negative values are equally likely; whereas in #10 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.
  8. UNCON-SOURCE-GIFUNCON-CUM-GIF
  9. CON-SOURCE-GIFCON-CUM-GIF
  10. 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. 
  11. 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 in Paragraph#13 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]
  12. SUMMARY-TABLE
  13. ISSUE#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.
  14. 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.
  15. TEST#2 > A further test of the validity of the carbon budget is seen in the Remaining Carbon Budget Puzzle (RCBPthat 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.
  16. 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.
  17. 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.
  18. 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 in Paragraph#20 . 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.
  19. SUMMARY
  20. ISSUE#5 > THE IMPACT OF AGW ON TROPICAL CYCLONES:   This issue is presented in a related post [LINK]
  21. ISSUE#6 > THE IMPACT OF AGW ON SEA ICE: This issue is presented in three related posts [LINK] [LINK] [LINK] 

 

 

 

 

 

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