RELATED POST:  AN EXCLUSIVE RELIANCE ON FOSSIL FUEL EMISSIONS OVERLOOKS NATURAL CARBON FLOWS. [LINK]  

RELATED POST: THE CARBON BUDGET MYSTERIES OF CLIMATE SCIENCE  [LINK]

RELATED POST : WHEN DID AGW BEGIN? [LINK]  

RELATED POST: THE TCRE: TRANSIENT CLIMATE RESPONSE TO CUMULATIVE EMISSIONS  [LINK]

RELATED POST:  CORRELATION BETWEEN TEMPERATURE AND FORCINGS:  [LINK]

LIST OF POSTS AT THIS SITE:  [LINK]

ABSTRACT: 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]  

AN IMAGE FROM THE MEDIA

FIGURE 1A: RCP8.5 WITH TIME SCALE = 10 YEARS

FIGURE 1B: HADCRUT4 WITH TIME SCALE = 10 YEARS

FIGURE 2A: RCP8.5 WITH TIME SCALE = 15 YEARS

FIGURE 2B: HADCRUT4 WITH TIME SCALE = 15 YEARS

FIGURE 3A: RCP8.5 WITH TIME SCALE = 20 YEARS

FIGURE 3B: HACRUT4 WITH TIME SCALE = 20 YEARS

FIGURE 4A: RCP8.5 WITH TIME SCALE = 25 YEARS

FIGURE 4B: HADCRUT4 WITH TIME SCALE = 25 YEARS

FIGURE 5A: RCP8.5 WITH TIME SCALE = 30 YEARS

FIGURE 5B: HADCRUT4 WITH TIME SCALE = 30 YEARS

FIGURE 6: CORRELATION, DETRENDED CORRELATION, & SURVIVAL RATE

FIGURE 7: HYPOTHESIS TEST FOR DETRENDED CORRELATION

FIGURE 8: SUMMARY TABLE

[LIST OF POSTS ON THIS SITE]

AN IMAGE FROM THE MEDIA

1. The essential feature of climate science, and its activism for climate action in the form of reductions in fossil fuel emissions, is a causal relationship between emissions and the rate of warming with the implication that emission reduction will reduce the rate of warming. This relationship is found in the Transient Climate Response to Cumulative Emissions or TCRE based on a near perfect proportionality between cumulative emissions and surface temperature. Accordingly, the TCRE not only serves as the rationale for climate action but also as the tool for the construction of so called “carbon budgets” that define the maximum amount of emissions for a given target rate of global warming.
2. However, it has been shown in two related posts  [LINK]  [LINK] that there is a fatal statistical flaw in the TCRE methodology. Correlations between cumulative values of time series data are spurious because the effective sample size of the cumulative value series is EFFN=2 leaving it with neither time scale nor degrees of freedom.  This weakness of the TCRE is demonstrated with correlations between random numbers in the two related posts described above [LINK]  [LINK]
3. This work addresses these shortcomings of the TCRE by defining finite time scales shorter than the full span of the time series so that the effective sample size will be greater than two (EFFN>2) and thus yield positive degrees of freedom so that a hypothesis test can be constructed to determine the statistical significance of the correlation. The effective sample size procedure is described in a related SSRN paper [LINK] . Data for fossil fuel emissions in millions of tons of carbon equivalent are provided by the Carbon Dioxide Information Analysis Center of the Oak Ridge National Laboratories (CDIAC, 2017). Two surface temperature datasets for the study peruid 1861 to 2016 are used for the analysis. They are the RCP8.5 theoretical temperature forecasts from climate models with CMIP5 forcings (hereafter referred to as RCP), and the HadCRUT4 global mean temperature reconstruction (hereafter referred to as HAD) provided by the Hadley Centre of the Climate Research Unit of the UK Met Office. The comparison between these temperature datasets are made in the context that the RCP8.5 represents the theory of Anthropogenic Global Warming by way of fossil fuel emissions (AGW) because it was created by climate models that contain the causal relationship between the rate of emissions and the rate of warming. The HadCRUT4 reconstruction represents observational data although they are not direct observations but reconstructions from observations.
4. To insert a time scale and finite degrees of freedom into the TCRE model, we use five different time scales for this analysis from 10 years to 30 years at 5 year increments. For each time scale we compute the cumulative emissions in the duration of the time scale and the rate of warming within the time scale. The time scale window then moves across the full span of the data one year at a time. For example, in the 10-year time scale, cumulative emissions is computed as the total emissions in a moving 10-year window that moves one year at a time through the full span of the data. Likewise, the rate of warming is computed within a moving 10-year window that moves through the full span of the data one year at a time. We then compute the detrended correlation between warming and emissions net of the contribution to source data correlation by shared long term trends. The rationale for detrended analysis is described in a related post [LINK]
5. Figure 1A to Figure 5B above show the data for both RCP and HAD against the cumulative emissions in moving windows of 10, 15, 20, 25, and 30 years along with a graphical display of the correlations and detrended correlations. The results are summarized in Figure 6 and Figure 7. Both temperature datasets show that source data correlation (CORR) rises as the time scale is increased from 10-years to 30-years but more rapidly at the lower time scales than at higher time scales. The theoretical model predictions (RCP) show much stronger source data correlations (CORR=0.5 to 0.8) than the observational data (HAD) with source data correlations of (CORR=0.27 to 0.65). When the spurious effect of long term trends is removed from the source data correlation, lower correlations are seen in the detrended data (DETCOR) with values of (DETCOR=0.3 to 0.56) in the RCP climate model prediction and much lower values of (DETCOR=0.1 to 0.2) in the HAD observational data. We also note that a much larger portion of the model prediction RCP source correlation CORR survives into the detrended series DETCOR (56% to 68%) than in the observational data HAD (29% to 35%) indicating a much stronger relationship between emissions and warming in climate models than in observational data. It is also noted that the behavior of the detrended correlation curve and the percent survival curve are different in the HAD data series than in the RCP climate model series.
6. The rising value of correlations with increasing values of the time scale from 10-years to 30-years comes at a price because higher time scales reduce the effective value of the sample size (EFFN) and therefore of the degrees of freedom (DF). (see reference paper at SSRN [LINK] . In Figure 8 we see that as the time scale is increased from 10-years to 30-years, the effective sample size drops from 16.6 to 6.4 and takes down the degrees of freedom with it computed as DF=EFFN-2. There is a price to be paid for the higher correlations in longer time scales. The standard deviation of the correlation coefficient is estimated using Bowley’s procedure (Bowley, 1928). To test for positive values of the correlation coefficient, the null hypothesis is set to H0: ρ≤0 with the alternate HA: ρ>0. Hypothesis tests for correlation are carried out at a maximum false positive error rate of α=0.001 per comparison in keeping with “Revised Standards for Statistical Evidence” published by the NAS (Johnson, 2013) as a way of addressing an unacceptably high rate of irreproducible results in published research (Siegfried, 2010).
7. In these tests 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. These results show that though the causal relationship between emissions and warming, assumed in the motivation for costly climate action, is found in the RCP8.5 generated by climate models, it is not found in the data. This result is consistent with the finding in the TCRE post [LINK]  that the correlation seen between temperature and cumulative emissions is spurious and that in fact there is no evidence that the correlation between emissions and warming found in climate models exists in the data.
8. The Transient Climate Response to Cumulative Emissions (TCRE) does show that the rate of warming is responsive to emissions in the observational data but that metric contains a fatal statistical flaw. It is based on a spurious correlation and contains neither time scale nor degrees of freedom as shown in a related post at this site [LINK] .
9. We conclude from these results that no empirical evidence exists to support the rationale for costly climate action that assumes a causal relationship between the rate of emissions and the rate of warming. The evidence does not show that reducing emissions will lower the rate of warming. 
10. The comparative analysis methodology used in this work is validated by a positive result for the theoretical temperature series in RCP8.5 compared with a negative result for observational data.

SUMMARY AND CONCLUSIONS:  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. 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.

AN IMAGE FROM THE MEDIA

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CLIMATE ACTION PARIS AGREEMENT BIBLIOGRAPHY

1. 2016: Rogelj, Joeri, et al. “Paris Agreement climate proposals need a boost to keep warming well below 2 C.” Nature 534.7609 (2016): 631. The Paris climate agreement aims at holding global warming to well below 2 degrees Celsius and to “pursue efforts” to limit it to 1.5 degrees Celsius. To accomplish this, countries have submitted Intended Nationally Determined Contributions (INDCs) outlining their post-2020 climate action. Here we assess the effect of current INDCs on reducing aggregate greenhouse gas emissions, its implications for achieving the temperature objective of the Paris climate agreement, and potential options for overachievement. The INDCs collectively lower greenhouse gas emissions compared to where current policies stand, but still imply a median warming of 2.6–3.1 degrees Celsius by 2100. More can be achieved, because the agreement stipulates that targets for reducing greenhouse gas emissions are strengthened over time, both in ambition and scope. Substantial enhancement or over-delivery on current INDCs by additional national, sub-national and non-state actions is required to maintain a reasonable chance of meeting the target of keeping warming well below 2 degrees Celsius.
2. 2016: Hale, Thomas. ““All hands on deck”: The Paris agreement and nonstate climate action.” Global Environmental Politics 16.3 (2016): 12-22. The 2015 Paris Climate summit consolidated the transition of the climate regime from a “regulatory” to a “catalytic and facilitative” model. A key component of this shift was the intergovernmental regime’s embrace of climate action by sub- and nonstate actors. Although a groundswell of transnational climate action has been growing over time, the Paris Agreement seeks to bring this phenomenon into the heart of the new climate regime. This forum article describes that transition and considers its implications.
3. 2016: Falkner, Robert. “The Paris Agreement and the new logic of international climate politics.” International Affairs 92.5 (2016): 1107-1125. This article reviews and assesses the outcome of the 21st Conference of the Parties (COP-21) to the United Nations Framework Convention on Climate Change (UNFCCC), held in Paris in December 2015. It argues that the Paris Agreement breaks new ground in international climate policy, by acknowledging the primacy of domestic politics in climate change and allowing countries to set their own level of ambition for climate change mitigation. It creates a framework for making voluntary pledges that can be compared and reviewed internationally, in the hope that global ambition can be increased through a process of ‘naming and shaming’. By sidestepping distributional conflicts, the Paris Agreement manages to remove one of the biggest barriers to international climate cooperation. It recognizes that none of the major powers can be forced into drastic emissions cuts. However, instead of leaving mitigation efforts to an entirely bottom-up logic, it embeds country pledges in an international system of climate accountability and a ‘ratchet mechanism’, thus offering the chance of more durable international cooperation. At the same time, it is far from clear whether the treaty can actually deliver on the urgent need to de-carbonize the global economy. The past record of climate policies suggests that governments have a tendency to express lofty aspirations but avoid tough decisions. For the Paris Agreement to make a difference, the new logic of ‘pledge and review’ will need to mobilize international and domestic pressure and generate political momentum behind more substantial climate policies worldwide. It matters, therefore, whether the Paris Agreement’s new approach can be made to work.
4. 2016: Bodansky, Daniel. “The Paris climate change agreement: a new hope?.” American Journal of International Law 110.2 (2016): 288-319.  Know your limits. This familiar adage is not an inspirational rallying cry or a recipe for bold action. It serves better as the motto for the tortoise than the hare. But, after many false starts over the past twenty years, states were well advised to heed it when negotiating the Paris Agreement. While it is still far too early to say whether the Agreement will be a success, its comparatively modest approach provides a firmer foundation on which to build than its more ambitious predecessor, the Kyoto Protocol.
5. 2016: Schleussner, Carl-Friedrich, et al. “Science and policy characteristics of the Paris Agreement temperature goal.” Nature Climate Change 6.9 (2016): 827.  The Paris Agreement sets a long-term temperature goal of holding the global average temperature increase to well below 2 °C, and pursuing efforts to limit this to 1.5 °C above pre-industrial levels. Here, we present an overview of science and policy aspects related to this goal and analyse the implications for mitigation pathways. We show examples of discernible differences in impacts between 1.5 °C and 2 °C warming. At the same time, most available low emission scenarios at least temporarily exceed the 1.5 °C limit before 2100. The legacy of temperature overshoots and the feasibility of limiting warming to 1.5 °C, or below, thus become central elements of a post-Paris science agenda. The near-term mitigation targets set by countries for the 2020–2030 period are insufficient to secure the achievement of the temperature goal. An increase in mitigation ambition for this period will determine the Agreement’s effectiveness in achieving its temperature goal.
6. 2016: Dimitrov, Radoslav S. “The Paris agreement on climate change: Behind closed doors.” Global Environmental Politics16.3 (2016): 1-11. The Paris Agreement constitutes a political success in climate negotiations and traditional state diplomacy, and offers important implications for academic research. Based on participatory research, the article examines the political dynamics in Paris and highlights feature2016s of the process that help us understand the outcome. It describes battles on key contentious issues behind closed doors, provides a summary and evaluation of the new agreement, identifies political winners and losers, and offers theoretical explanations of the outcome. The analysis emphasizes process variables and underscores the role of persuasion, argumentation, and organizational strategy. Climate diplomacy succeeded because the international conversation during negotiations induced cognitive change. Persuasive arguments about the economic benefits of climate action altered preferences in favor of policy commitments at both national and international levels.
7. 2016: Van Asselt, Harro. “The role of non-state actors in reviewing ambition, implementation, and compliance under the Paris agreement.” Climate Law 6.1-2 (2016): 91-108. Non-state actors will play a unique and crucial role in the implementation of the Paris Agreement. Although much of the focus in the lead-up to Paris was on the mitigation commitments and actions of non-state actors, this essay focuses on another valuable contribution they can make: to hold the parties to their obligations under the Paris Agreement. I argue that, while the formal avenues for non-state-actor participation in review processes—encompassing the review of implementation, compliance, and effectiveness—remain limited, there are several other ways in which non-state actors can be, and already have been, influential
8. 2017: Höhne, Niklas, et al. “The Paris Agreement: resolving the inconsistency between global goals and national contributions.” Climate Policy 17.1 (2017): 16-32. he adoption of the Paris Agreement in December 2015 moved the world a step closer to avoiding dangerous climate change. The aggregated individual intended nationally determined contributions (INDCs) are not yet sufficient to be consistent with the long-term goals of the agreement of ‘holding the increase in global average temperature to well below 2°C’ and ‘pursuing efforts’ towards 1.5°C. However, the Paris Agreement gives hope that this inconsistency can be resolved. We find that many of the contributions are conservative and in some cases may be overachieved. We also find that the preparation of the INDCs has advanced national climate policy-making, notably in developing countries. Moreover, provisions in the Paris Agreement require countries to regularly review, update and strengthen these actions. In addition, the significant number of non-state actions launched in recent years is not yet adequately captured in the INDCs. Finally, we discuss decarbonization, which has happened faster in some sectors than expected, giving hope that such a transition can also be accomplished in other sectors. Taken together, there is reason to be optimistic that eventually national action to reduce emissions will be more consistent with the agreed global temperature limits.
9. 2017: Rogelj, Joeri, et al. “Understanding the origin of Paris Agreement emission uncertainties.” Nature Communications 8 (2017): 15748. The UN Paris Agreement puts in place a legally binding mechanism to increase mitigation action over time. Countries put forward pledges called nationally determined contributions (NDC) whose impact is assessed in global stocktaking exercises. Subsequently, actions can then be strengthened in light of the Paris climate objective: limiting global mean temperature increase to well below 2 °C and pursuing efforts to limit it further to 1.5 °C. However, pledged actions are currently described ambiguously and this complicates the global stocktaking exercise. Here, we systematically explore possible interpretations of NDC assumptions, and show that this results in estimated emissions for 2030 ranging from 47 to 63 GtCO₂e yr⁻¹. We show that this uncertainty has critical implications for the feasibility and cost to limit warming well below 2 °C and further to 1.5 °C. Countries are currently working towards clarifying the modalities of future NDCs. We identify salient avenues to reduce the overall uncertainty by about 10 percentage points through simple, technical clarifications regarding energy accounting rules. Remaining uncertainties depend to a large extent on politically valid choices about how NDCs are expressed, and therefore raise the importance of a thorough and robust process that keeps track of where emissions are heading over time.