THIS POST IS A CONTINUATION OF THE EXPLORATION OF THE CARBON BUDGET CONUNDRUM IN CLIMATE SCIENCE DESCRIBED IN THREE RELATED POSTS CARBON BUDGET POSTS: [LINK] [LINK] [LINK] . TOGETHER, THEY EXPOSE FUNDAMENTAL FLAWS AND INCONSISTENCIES IN THE THEORY OF CLIMATE ACTION

The Reference Document (RD) for this post is from the Cicero Center for Climate Research in Norway. The chief researcher is Glen Peters who is also the author of the RD which Dr. Peters has made available online [LINK] . The IPCC Synthesis Report used as a reference is also available online [LINK] . The Millar etal 2015 paper used in this post is discussed in more detail in a related post [LINK] and Richard Millar‘s commentary on his paper’s findings is available online courtesy of Carbon Brief [LINK] .

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1. In a related post we present the case that the essence of the climate change movement is that it is a reincarnation of the 1960s movement against fossil fuels [LINK] . In that context the fear of global warming, in terms of sea level rise, extreme weather, mass extinctions, mass migrations, agricultural and economic devastation, rampant epidemics, and the collapse of civilization, serves as motivation for climate action because climate action is guaranteed to control climate change and thereby to relieve humanity of these horrific climate impacts. In other words, the goal of climate change activism is climate action.
2. Thus, the essence of the climate change movement and the purpose of climate science is to push for climate action in the form of reducing and eventually eliminating the the use of fossil fuels as a way of reducing and eliminating the “external” and artificial carbon emissions of the industrial economy that act as a dangerous perturbation of nature’s balanced carbon cycle and climate system.
3. In practical terms, climate action is described as reducing fossil fuel emissions to meet maximum warming targets beyond which unacceptable levels of climate impacts are expected. The maximum warming target (MWT) was set in the Paris Agreement which sets the MWT at 2C but with bureaucratic language that also refers to a target of 1.5C. In practical terms for climate science, the 1.5C target is used to formulate the needed climate action procedures.
4. The usual procedure for a climate action plan is to compute what is known as a carbon budget. A carbon budget is the total amount of carbon that can be emitted from the present time to the target date (cumulative emissions) if the MWT is not to be exceeded. For example, suppose that the Paris Agreement MWT is 1.5C since pre-industrial times. Of that 1C has already been used up to the present and so the warming target from now to the target date is reduced to MWT=0.5C.
5. The total amount of carbon that can be emitted in for this MWT is computed using the Transient Climate Response to Cumulative Emissions (TCRE) described in the Matthews 2009 paper included in the bibliography below.  This reference paper shows that there is a near perfect proportionality between cumulative emissions and temperature. The linear regression coefficient derived from this proportionality is the TCRE parameter which describes degrees Celsius of warming per unit of cumulative emissions. When emissions are denominated in gigatons, the TCRE is the degC of warming per gigaton of cumulative emissions. The total gigatons of emission possible within the MWT constraint is then computed using the TCRE. This amount of cumulative emissions is the carbon budget.
6. For example, if our MWT is 0.5C and the TCRE is found to be 0.0025 degC/gigaton, the carbon budget is 0.5/0.0025 = 200 gigatons of carbon equivalent cumulative emissions. Sometimes the carbon budget is stated in carbon dioxide (molecular weight 44) instead of the carbon equivalent (molecular weight 12). In this case the equivalent carbon dioxide budget is 200*44/12 = 733 gigatons of carbon dioxide.
7. The IPCC published such a carbon budget in 2015 for a 0.5C MWT. That IPCC carbon budget is 250 gigatons of carbon dioxide. This carbon budget is the subject of Peter Glen’s analysis for the CICERO climate research center cited above and with full text available online [LINK] . There, Professor Peters points out that at an average rate of 40 gigatons of carbon dioxide emissions per year, the 250 gigaton CO2 budget would  be gone in 250/40 = 6.25 years and that therefore the carbon budget implies an unrealistically high rate of warming of 0.5/6.25 = 0.08C/year since the current rate of warming is closer to 0.025C/year. Clearly something is not right with the IPCC carbon budget for 1.5C.
8. At the more realistic rate of warming, the real carbon budget has to be 3.2 times larger or about 800 gigatons. And in fact that is exactly what we see in the Millar etal 2017 paper listed in the bibliography below. Glen Peters, a recognized authority on the issue of carbon budgets (alongside researchers like Joeri Rogelj cited below in the bibliography), then resolves this issue in his article cited above and in so doing presents several key issues in carbon budget mathematics that expose an underlying weakness in the science of climate science.
9. Carbon budgets are computed with the TCRE proportionality between cumulative emissions and temperature (temperature is cumulative warming). However, it is found that the procedure leads to mysterious inconsistencies when the time span is changed or when the remaining carbon budget is to be computed. In  climate science these inconsistencies are interpreted in terms of theory and their resolution is carried out with climate models in terms of Earth System Models and non-CO2 forcings.
10. These resolutions are by their very nature a form of circular reasoning because these variables are fine tuned until the carbon budget anomaly is resolved. However, they also yield very large uncertainties. For example, the Millar 2017 paper uses a “climate-carbon-cycle” model to find that that the carbon budget for 1.5C is 920 to 1,980 gigatons of carbon dioxide for the period 2016 to 2100. In any other science discipline an uncertainty this large would imply that “we don’t know” but the climate science conclusion is that a budget of 920 gigatons give us “a 66% likelihood of staying below the 1.5C target“.
11. However these mysterious complexities of the carbon budget including for example the mystery of the “remaining carbon budget” [LINK] have a much simpler and more rational explanation in terms of statistics. The underlying issue is that climate science is dealing with a spurious statistic and attempting to explain the random variations of the spurious statistic in terms of the science of climate change and with the help of climate models and earth system models of increasing complexity.
12. The essential carbon budget issue is that the proportionality between temperature and cumulative emissions is spurious and illusory and its use in carbon budget construction is not a science but an error in statistics. The statistical issues with the TCRE are explained in related posts [LINK] [LINK] . The issues that this statistics error creates in carbon budgets are discussed in these related posts [LINK] [LINK] [TCRE] .

CARBON BUDGET BIBLIOGRAPHY

1. Matthews, H. Damon, et al. “The proportionality of global warming to cumulative carbon emissions.” Nature 459.7248 (2009): 829.  The global temperature response to increasing atmospheric CO₂ is often quantified by metrics such as equilibrium climate sensitivity and transient climate response¹. These approaches, however, do not account for carbon cycle feedbacks and therefore do not fully represent the net response of the Earth system to anthropogenic CO₂ emissions. Climate–carbon modelling experiments have shown that: (1) the warming per unit CO₂ emitted does not depend on the background CO₂ concentration²; (2) the total allowable emissions for climate stabilization do not depend on the timing of those emissions^3,4,5; and (3) the temperature response to a pulse of CO₂ is approximately constant on timescales of decades to centuries^3,6,7,8. Here we generalize these results and show that the carbon–climate response (CCR), defined as the ratio of temperature change to cumulative carbon emissions, is approximately independent of both the atmospheric CO₂ concentration and its rate of change on these timescales. From observational constraints, we estimate CCR to be in the range 1.0–2.1 °C per trillion tonnes of carbon (Tt C) emitted (5th to 95th percentiles), consistent with twenty-first-century CCR values simulated by climate–carbon models. Uncertainty in land-use CO₂ emissions and aerosol forcing, however, means that higher observationally constrained values cannot be excluded. The CCR, when evaluated from climate–carbon models under idealized conditions, represents a simple yet robust metric for comparing models, which aggregates both climate feedbacks and carbon cycle feedbacks. CCR is also likely to be a useful concept for climate change mitigation and policy; by combining the uncertainties associated with climate sensitivity, carbon sinks and climate–carbon feedbacks into a single quantity, the CCR allows CO₂-induced global mean temperature change to be inferred directly from cumulative carbon emissions.
2. Allen, Myles R., et al. “Warming caused by cumulative carbon emissions towards the trillionth tonne.” Nature 458.7242 (2009): 1163.  Global efforts to mitigate climate change are guided by projections of future temperatures¹. But the eventual equilibrium global mean temperature associated with a given stabilization level of atmospheric greenhouse gas concentrations remains uncertain^1,2,3, complicating the setting of stabilization targets to avoid potentially dangerous levels of global warming^4,5,6,7,8. Similar problems apply to the carbon cycle: observations currently provide only a weak constraint on the response to future emissions^9,10,11. Here we use ensemble simulations of simple climate-carbon-cycle models constrained by observations and projections from more comprehensive models to simulate the temperature response to a broad range of carbon dioxide emission pathways. We find that the peak warming caused by a given cumulative carbon dioxide emission is better constrained than the warming response to a stabilization scenario. Furthermore, the relationship between cumulative emissions and peak warming is remarkably insensitive to the emission pathway (timing of emissions or peak emission rate). Hence policy targets based on limiting cumulative emissions of carbon dioxide are likely to be more robust to scientific uncertainty than emission-rate or concentration targets. Total anthropogenic emissions of one trillion tonnes of carbon (3.67 trillion tonnes of CO₂), about half of which has already been emitted since industrialization began, results in a most likely peak carbon-dioxide-induced warming of 2 °C above pre-industrial temperatures, with a 5–95% confidence interval of 1.3–3.9 °C.
3. Mackey, Brendan, et al. “Untangling the confusion around land carbon science and climate change mitigation policy.” Nature climate change 3.6 (2013): 552.  Depletion of ecosystem carbon stocks is a significant source of atmospheric CO₂ and reducing land-based emissions and maintaining land carbon stocks contributes to climate change mitigation. We summarize current understanding about human perturbation of the global carbon cycle, examine three scientific issues and consider implications for the interpretation of international climate change policy decisions, concluding that considering carbon storage on land as a means to ‘offset’ CO₂ emissions from burning fossil fuels (an idea with wide currency) is scientifically flawed. The capacity of terrestrial ecosystems to store carbon is finite and the current sequestration potential primarily reflects depletion due to past land use. Avoiding emissions from land carbon stocks and refilling depleted stocks reduces atmospheric CO₂concentration, but the maximum amount of this reduction is equivalent to only a small fraction of potential fossil fuel emissions.
4. Gignac, Renaud, and H. Damon Matthews. “Allocating a 2 C cumulative carbon budget to countries.” Environmental Research Letters 10.7 (2015): 075004.  Recent estimates of the global carbon budget, or allowable cumulative CO₂ emissions consistent with a given level of climate warming, have the potential to inform climate mitigation policy discussions aimed at maintaining global temperatures below 2 °C. This raises difficult questions, however, about how best to share this carbon budget amongst nations in a way that both respects the need for a finite cap on total allowable emissions, and also addresses the fundamental disparities amongst nations with respect to their historical and potential future emissions. Here we show how the contraction and convergence (C&C) framework can be applied to the division of a global carbon budget among nations, in a manner that both maintains total emissions below a level consistent with 2 °C, and also adheres to the principle of attaining equal per capita CO₂emissions within the coming decades. We show further that historical differences in responsibility for climate warming can be quantified via a cumulative carbon debt (or credit), which represents the amount by which a given country’s historical emissions have exceeded (or fallen short of) the emissions that would have been consistent with their share of world population over time. This carbon debt/credit calculation enhances the potential utility of C&C, therefore providing a simple method to frame national climate mitigation targets in a way that both accounts for historical responsibility, and also respects the principle of international equity in determining future emissions allowances.
5. Rogelj, Joeri, et al. “Mitigation choices impact carbon budget size compatible with low temperature goals.” Environmental Research Letters 10.7 (2015): 075003.  Global-mean temperature increase is roughly proportional to cumulative emissions of carbon-dioxide (CO₂). Limiting global warming to any level thus implies a finite CO₂ budget. Due to geophysical uncertainties, the size of such budgets can only be expressed in probabilistic terms and is further influenced by non-CO₂ emissions. We here explore how societal choices related to energy demand and specific mitigation options influence the size of carbon budgets for meeting a given temperature objective. We find that choices that exclude specific CO₂mitigation technologies (like Carbon Capture and Storage) result in greater costs, smaller compatible CO₂ budgets until 2050, but larger CO₂ budgets until 2100. Vice versa, choices that lead to a larger CO₂ mitigation potential result in CO₂ budgets until 2100 that are smaller but can be met at lower costs. In most cases, these budget variations can be explained by the amount of non-CO₂ mitigation that is carried out in conjunction with CO_2, and associated global carbon prices that also drive mitigation of non-CO₂ gases. Budget variations are of the order of 10% around their central value. In all cases, limiting warming to below 2 °C thus still implies that CO₂ emissions need to be reduced rapidly in the coming decades.
6. Riahi, Keywan, et al. “Locked into Copenhagen pledges—implications of short-term emission targets for the cost and feasibility of long-term climate goals.” Technological Forecasting and Social Change 90 (2015): 8-23.  This paper provides an overview of the AMPERE modeling comparison project with focus on the implications of near-term policies for the costs and attainability of long-term climate objectives. Nine modeling teams participated in the project to explore the consequences of global emissions following the proposed policy stringency of the national pledges from the Copenhagen Accord and Cancún Agreements to 2030. Specific features compared to earlier assessments are the explicit consideration of near-term 2030 emission targets as well as the systematic sensitivity analysis for the availability and potential of mitigation technologies. Our estimates show that a 2030 mitigation effort comparable to the pledges would result in a further “lock-in” of the energy system into fossil fuels and thus impede the required energy transformation to reach low greenhouse-gas stabilization levels (450 ppm CO₂e). Major implications include significant increases in mitigation costs, increased risk that low stabilization targets become unattainable, and reduced chances of staying below the proposed temperature change target of 2 °C in case of overshoot. With respect to technologies, we find that following the pledge pathways to 2030 would narrow policy choices, and increases the risks that some currently optional technologies, such as carbon capture and storage (CCS) or the large-scale deployment of bioenergy, will become “a must” by 2030.
7. Rogelj, Joeri, et al. “Differences between carbon budget estimates unravelled.” Nature Climate Change 6.3 (2016): 245.  Several methods exist to estimate the cumulative carbon emissions that would keep global warming to below a given temperature limit. Here we review estimates reported by the IPCC and the recent literature, and discuss the reasons underlying their differences. The most scientifically robust number — the carbon budget for CO₂-induced warming only — is also the least relevant for real-world policy. Including all greenhouse gases and using methods based on scenarios that avoid instead of exceed a given temperature limit results in lower carbon budgets. For a >66% chance of limiting warming below the internationally agreed temperature limit of 2 °C relative to pre-industrial levels, the most appropriate carbon budget estimate is 590–1,240 GtCO₂ from 2015 onwards. Variations within this range depend on the probability of staying below 2 °C and on end-of-century non-CO₂ warming. Current CO₂ emissions are about 40 GtCO₂ yr⁻¹, and global CO₂ emissions thus have to be reduced urgently to keep within a 2 °C-compatible budget.
8. 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.
9. Anderson, Kevin, and Glen Peters. “The trouble with negative emissions.” Science 354.6309 (2016): 182-183.  In December 2015, member states of the United Nations Framework Convention on Climate Change (UNFCCC) adopted the Paris Agreement, which aims to hold the increase in the global average temperature to below 2°C and to pursue efforts to limit the temperature increase to 1.5°C. The Paris Agreement requires that anthropogenic greenhouse gas emission sources and sinks are balanced by the second half of this century. Because some nonzero sources are unavoidable, this leads to the abstract concept of “negative emissions,” the removal of carbon dioxide (CO₂) from the atmosphere through technical means. The Integrated Assessment Models (IAMs) informing policy-makers assume the large-scale use of negative-emission technologies. If we rely on these and they are not deployed or are unsuccessful at removing CO₂from the atmosphere at the levels assumed, society will be locked into a high-temperature pathway.
10. Pfeiffer, Alexander, et al. “The ‘2 C capital stock’for electricity generation: Committed cumulative carbon emissions from the electricity generation sector and the transition to a green economy.” Applied Energy 179 (2016): 1395-1408.  This paper defines the ‘2°C capital stock’ as the global stock of infrastructure which, if operated to the end of its normal economic life, implies global mean temperature increases of 2°C or more (with 50% probability). Using IPCC carbon budgets and the IPCC’s AR5 scenario database, and assuming future emissions from other sectors are compatible with a 2°C pathway, we calculate that the 2°C capital stock for electricity will be reached by 2017 based on current trends. In other words, even under the very optimistic assumption that other sectors reduce emissions in line with a 2°C target, no new emitting electricity infrastructure can be built after 2017 for this target to be met, unless other electricity infrastructure is retired early or retrofitted with carbon capture technologies. Policymakers and investors should question the economics of new long-lived energy infrastructure involving positive net emissions.
11. Peters, Glen P., et al. “Key indicators to track current progress and future ambition of the Paris Agreement.” Nature Climate Change 7.2 (2017): 118.  Current emission pledges to the Paris Agreement appear insufficient to hold the global average temperature increase to well below 2 °C above pre-industrial levels¹. Yet, details are missing on how to track progress towards the ‘Paris goal’, inform the five-yearly ‘global stocktake’, and increase the ambition of Nationally Determined Contributions (NDCs). We develop a nested structure of key indicators to track progress through time. Global emissions^2,3 track aggregated progress¹, country-level decompositions track emerging trends^4,5,6 that link directly to NDCs⁷, and technology diffusion^8,9,10 indicates future reductions. We find the recent slowdown in global emissions growth¹¹ is due to reduced growth in coal use since 2011, primarily in China and secondarily in the United States¹². The slowdown is projected to continue in 2016, with global CO₂ emissions from fossil fuels and industry similar to the 2015 level of 36 GtCO₂. Explosive and policy-driven growth in wind and solar has contributed to the global emissions slowdown, but has been less important than economic factors and energy efficiency. We show that many key indicators are currently broadly consistent with emission scenarios that keep temperatures below 2 °C, but the continued lack of large-scale carbon capture and storage¹³ threatens 2030 targets and the longer-term Paris ambition of net-zero emissions.
12. Millar, Richard J., et al. “Emission budgets and pathways consistent with limiting warming to 1.5 C.” Nature Geoscience10.10 (2017): 741.  The Paris Agreement has opened debate on whether limiting warming to 1.5 °C is compatible with current emission pledges and warming of about 0.9 °C from the mid-nineteenth century to the present decade. We show that limiting cumulative post-2015 CO₂ emissions to about 200 GtC would limit post-2015 warming to less than 0.6 °C in 66% of Earth system model members of the CMIP5 ensemble with no mitigation of other climate drivers. We combine a simple climate–carbon-cycle model with estimated ranges for key climate system properties from the IPCC Fifth Assessment Report. Assuming emissions peak and decline to below current levels by 2030, and continue thereafter on a much steeper decline, which would be historically unprecedented but consistent with a standard ambitious mitigation scenario (RCP2.6), results in a likely range of peak warming of 1.2–2.0 °C above the mid-nineteenth century. If CO₂emissions are continuously adjusted over time to limit 2100 warming to 1.5 °C, with ambitious non-CO₂ mitigation, net future cumulative CO₂emissions are unlikely to prove less than 250 GtC and unlikely greater than 540 GtC. Hence, limiting warming to 1.5 °C is not yet a geophysical impossibility, but is likely to require delivery on strengthened pledges for 2030 followed by challengingly deep and rapid mitigation. Strengthening near-term emissions reductions would hedge against a high climate response or subsequent reduction rates proving economically, technically or politically unfeasible.

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