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THE REMAINING CARBON BUDGET

Posted on: November 8, 2019

Millar, Richard J., and Pierre Friedlingstein. “The utility of the historical record for assessing the transient climate response to cumulative emissions.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376.2119 (2018): 20160449. ABSTRACT: The historical observational record offers a way to constrain the relationship between cumulative carbon dioxide emissions and global mean warming. We use a standard detection and attribution technique, along with observational uncertainties to estimate the all-forcing or ‘effective’ transient climate response to cumulative emissions (TCRE) from the observational record. Accounting for observational uncertainty and uncertainty in historical non-CO2 radiative forcing gives a best-estimate from the historical record of 1.84°C/TtC (1.43–2.37°C/TtC 5–95% uncertainty) for the effective TCRE and 1.31°C/TtC (0.88–2.60°C/TtC 5–95% uncertainty) for the CO2-only TCRE. While the best-estimate TCRE lies in the lower half of the IPCC likely range, the high upper bound is associated with the not-ruled-out possibility of a strongly negative aerosol forcing. Earth System Models have a higher effective TCRE range when compared like-for-like with the observations over the historical period, associated in part with a slight underestimate of diagnosed cumulative emissions relative to the observational best-estimate, a larger ensemble mean-simulated CO2-induced warming, and rapid post-2000 non-CO2 warming in some ensemble members. This article is part of the theme issue ‘The Paris Agreement: understanding the physical and social challenges for a warming world of 1.5°C above pre-industrial levels’.

 

THIS POST IS A CRITICAL REVIEW OF A RESEARCH PAPER ON THE CLIMATE SCIENCE IMPLICATIONS OF THE TCRE (Transient Climate Response to Cumulative Emissions) PUBLISHED IN THE PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY IN THEIR MATHEMATICAL, PHYSICAL, AND ENGINEERING SERIES IN 2018. THE CITATION AND ABSTRACT OF THE PAPER APPEARS ABOVE. 

 

 

[LINK TO THE HOME PAGE OF THIS SITE]

 

 

 

  1. It has long been recognized that the climate sensitivity of surface temperature to the logarithm of atmospheric CO2  (ECS), which lies at the heart of the anthropogenic global warming and climate change (AGW) proposition, was a difficult issue for climate science because of the large range of empirical values reported in the literature and the so called “uncertainty problem” it implies {Caldeira, et al “Climate sensitivity uncertainty and the need for energy without CO2 emission.” Science 299.5615 (2003): 2052-2054}. The ECS uncertainty issue was interpreted in two very different ways. Climate science took the position that ECS uncertainty implies that climate action has to be greater than that implied by the mean value of ECS in order to ensure that higher values of ECS that are possible will be accommodated while skeptics argued that the large range means that we don’t really know. At the same time skeptics also presented convincing arguments against the assumption that observed changes in atmospheric CO2 concentration can be attributed to fossil fuel emissions [[LINK] , [LINK] .
  2. A breakthrough came in 2009 when Damon Matthews, Myles Allen, and a few others almost simultaneously published almost identical papers reporting the discovery of a “near perfect” correlation (ρ≈1) between surface temperature and cumulative emissions {2009: Matthews, H. Damon, et al. “The proportionality of global warming to cumulative carbon emissions” Nature 459.7248 (2009): 829}. They had found that, irrespective of the timing of emissions or of atmospheric CO2 concentration, emitting a trillion tonnes of carbon will cause 1.0 – 2.1 C of global warming. This linear regression coefficient corresponding with the near perfect correlation between cumulative warming and cumulative emissions (note: temperature=cumulative warming), initially described as the Climate Carbon Response (CCR) was later termed the Transient Climate Response to Cumulative Emissions (TCRE). Initially a curiosity, it gained in importance when it was found that it was in fact predicting future temperatures consistent with model predictions. The consistency with climate models was taken as a validation of the new tool and the TCRE became integrated into the theory of climate change. However, as noted in a related post [LINK] [LINK] , the consistency likely derives from the assumption that emissions accumulate in the atmosphere.
  3. Thereafter the TCRE became incorporated into the foundation of climate change theory particularly so in terms of its utility in the construction of carbon budgets for climate action plans for any given target temperature rise, an application for which the TCRE appeared to be tailor made. Most importantly, it solved or perhaps bypassed the messy and inconclusive uncertainty issue in ECS climate sensitivity that remained unresolved. The importance of this aspect of the TCRE is found in the 2017 paper “Beyond Climate Sensitivity” by prominent climate scientist Reto Knutti where he declared that the TCRE metric should replace the ECS as the primary tool for relating warming to human caused emissions {2017: Knutti, Reto, Maria AA Rugenstein, and Gabriele C. Hegerl. “Beyond equilibrium climate sensitivity.” Nature Geoscience 10.10 (2017): 727}. The anti ECS Knutti paper was not only published but received with great fanfare by the journal and by the climate science community in general.
  4. The TCRE has continued to gain in importance and prominence as a tool for the practical application of climate change theory in terms of its utility in the construction and tracking of carbon budgets for limiting warming to a target such as the Paris Climate Accord target of +1.5C above pre-industrial.  {Matthews, H. Damon. “Quantifying historical carbon and climate debts among nations.” Nature climate change 6.1 (2016): 60}. A bibliography on the subject of TCRE carbon budgets is included below at the end of this post.
  5. However, a vexing issue has arisen in the practical matter of applying and tracking TCRE based carbon budgets. The unsolved matter in the TCRE carbon budget is the remaining carbon budget puzzle {Rogelj, Joeri, et al. “Estimating and tracking the remaining carbon budget for stringent climate targets.” Nature 571.7765 (2019): 335-342}. It turns out that midway in the implementation of a carbon budget, the remaining carbon budget computed by subtraction does not match the TCRE carbon budget for the latter period computed directly using the Damon Matthews proportionality of temperature with cumulative emissions for that period. As it turns out, the difference between the two estimates of the remaining carbon budget has a rational explanation in terms of the statistics of a time series of cumulative values of another time series described in a related post [LINK] .
  6. It is shown in the related  post that a time series of the cumulative  values of another time series has neither time scale nor degrees of freedom and that therefore statistical properties of this series can have no practical interpretation. It is demonstrated with random numbers that the only practical implication of the “near perfect proportionality” correlation reported by Damon Matthews is that the two time series being compared (annual warming and annual emissions) tend to have positive values. In the case of emissions we have all positive values, and during a time of global warming, the annual warming series contains mostly positive values. The correlation between temperature (cumulative warming) and cumulative emissions derives from this sign bias as demonstrated with random numbers with and without sign bias in a related post [LINK] .
  7.  The sign bias explains the correlation between cumulative values of time series data and also the remaining carbon budget puzzle. It is shown in the related post [LINK] that the TCRE regression coefficient between these time series of cumulative values derives from the positive value bias in the annual warming data. Thus, during a period of accelerated warming, the second half of the carbon budget period may contain a higher percentage of positive values for annual warming and it will therefore show a carbon budget that exceeds the proportional budget for the second half computed from the full span regression coefficient that is based on a lower bias for positive values.
  8. In short, the bias for positive annual warming is highest for the second half, lowest for the first half, and midway between these two values for the full span – and therein lies the simple statistics explanation of the remaining carbon budget issue that climate science is trying to solve in terms of climate theory and its extension to Earth System Models. The Millar and Friedlingstein 2018 paper is yet another in a long line of studies that ignore the statistical issues the TCRE correlation and instead try to explain its anomalous behavior in terms of climate theory whereas in fact their explanation lies in statistical issues that have been overlooked by these young scientists [LINK] .
  9. The fundamental problem with the construction of TCRE carbon budgets and their interpretation in terms of climate action is that the TCRE is a spurious correlation that has no interpretation in terms of a relationship between emissions and warming. Complexities in these carbon budgets such as the remaining carbon budget are best understood in these terms and not in terms of new and esoteric variables such as those in earth system models. 

 

 

 

TCRE CARBON BUDGET BIBLIOGRAPHY

  1. MacDougall, Andrew H., et al. “Sensitivity of carbon budgets to permafrost carbon feedbacks and non-CO2 forcings.” Environmental Research Letters 10.12 (2015): 125003.  The near proportionality between cumulative CO2 emissions and change in near surface temperature can be used to define a carbon budget: a finite quantity of carbon that can be burned associated with a chosen ‘safe’ temperature change threshold. Here we evaluate the sensitivity of this carbon budget to permafrost carbon dynamics and changes in non-CO2 forcings. The carbon budget for 2.0 C ◦ of warming is reduced from 1320 Pg C when considering only forcing from CO2 to 810 Pg C when considering permafrost carbon feedbacks as well as other anthropogenic contributions to climate change. We also examined net carbon budgets following an overshoot of and return to a warming target. That is, the net cumulative CO2 emissions at the point in time a warming target is restored following artificial removal of CO2 from the atmosphere to cool the climate back to a chosen temperature target. These overshoot net carbon budgets are consistently smaller than the conventional carbon budgets. Overall carbon budgets persist as a robust and simple conceptual framework to relate the principle cause of climate change to the impacts of climate change. [FULL TEXT PDF]
  2. Millar, Richard, et al. “The cumulative carbon budget and its implications.” Oxford Review of Economic Policy 32.2 (2016): 323-342.  The cumulative impact of carbon dioxide (CO 2 ) emissions on climate has potentially profound economic and policy implications. It implies that the long-term climate change mitigation challenge should be reframed as a stock problem, while the overwhelming majority of climate policies continue to focus on the flow of CO 2 into the atmosphere in 2030 or 2050. An obstacle, however, to the use of a cumulative carbon budget in policy is uncertainty in the size of this budget consistent with any specific temperature-based goal such as limiting warming to 2°C. This arises from uncertainty in the climate response to CO 2 emissions, which is relatively tractable, and uncertainty in future warming due to non-CO 2 drivers, which is less so. We argue these uncertainties are best addressed through policies that recognize the need to reduce net global CO 2 emissions to zero to stabilize global temperatures but adapt automatically to evolving climate change. Adaptive policies would fit well within the Paris Agreement under the UN Framework Convention on Climate Change.
  3. Rogelj, Joeri, et al. Differences between carbon budget estimates unravelled,  Nature Climate Change 6.3 (2016): 245-252.  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.
  4. MacDougall, Andrew H., et al. “Corrigendum: Sensitivity of carbon budgets to permafrost carbon feedbacks and non-CO2 forcings (2015Environ. Res. Lett. 10.” (2016). The near proportionality between cumulative CO2 emissions and change in near surface temperature can be used to define a carbon budget: a finite quantity of carbon that can be burned associated with a chosen ‘safe’ temperature change threshold. Here we evaluate the sensitivity of this carbon budget to permafrost carbon dynamics and changes in non-CO2 forcings. The carbon budget for 2.0 C ◦ of warming is reduced from 1320 Pg C when considering only forcing from CO2 to 810 Pg C when considering permafrost carbon feedbacks as well as other anthropogenic contributions to climate change. We also examined net carbon budgets following an overshoot of and return to a warming target. That is, the net cumulative CO2 emissions at the point in time a warming target is restored
    following artificial removal of CO2 from the atmosphere to cool the climate back to a chosen temperature target. These overshoot net carbon budgets are consistently smaller than the conventional carbon budgets. Overall carbon budgets persist as a robust and simple conceptual framework to relate the principle cause of climate change to the impacts of climate change.
  5. Friedlingstein, P. “Differences between carbon budget estimates unravelled. (2016).  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 [FULL TEXT] .
  6. Matthews, H. Damon, et al. “Estimating carbon budgets for ambitious climate targets.” Current Climate Change Reports 3.1 (2017): 69-77.  Carbon budgets, which define the total allowable CO2 emissions associated with a given global climate target, are a useful way of framing the climate mitigation challenge. In this paper, we review the geophysical basis for the idea of a carbon budget, showing how this concept emerges from a linear climate response to cumulative CO2 emissions. We then discuss the difference between a “CO2-only carbon budget” associated with a given level of CO2-induced warming and an “effective carbon budget” associated with a given level of warming caused by all human emissions. We present estimates for the CO2-only and effective carbon budgets for 1.5 and 2 °C, based on both model simulations and updated observational data. Finally, we discuss the key contributors to uncertainty in carbon budget estimates and suggest some implications of this uncertainty for decision-making. Based on the analysis presented here, we argue that while the CO2-only carbon budget is a robust upper bound on allowable emissions for a given climate target, the size of the effective carbon budget is dependent on the how quickly we are able to mitigate non-CO2 greenhouse gas and aerosol emissions. This suggests that climate mitigation efforts could benefit from being responsive to a changing effective carbon budget over time, as well as to potential new information that could narrow uncertainty associated with the climate response to CO2 emissions.
  7. MacDougall, Andrew H. “The oceanic origin of path-independent carbon budgets.” Scientific reports 7.1 (2017): 10373.  Virtually all Earth system models (ESM) show a near proportional relationship between cumulative emissions of CO2 and change in global mean temperature, a relationship which is independent of the emissions pathway taken to reach a cumulative emissions total. The relationship, which has been named the Transient Climate Response to Cumulative CO2 Emissions (TCRE), gives rise to the concept of a ‘carbon budget’. That is, a finite amount of carbon that can be burnt whilst remaining below some chosen global temperature change threshold, such as the 2.0 °C target set by the Paris Agreement. Here we show that the path-independence of TCRE arises from the partitioning ratio of anthropogenic carbon between the ocean and the atmosphere being almost the same as the partitioning ratio of enhanced radiative forcing between the ocean and space. That these ratios are so close in value is a coincidence unique to CO2. The simple model used here is underlain by many assumptions and simplifications but does reproduce key aspects of the climate system relevant to the path-independence of carbon budgets. Our results place TCRE and carbon budgets on firm physical foundations and therefore help validate the use of these metrics for climate policy.
  8. van der Ploeg, Frederick. “The safe carbon budget.” Climatic change 147.1-2 (2018): 47-59.  Cumulative emissions drive peak global warming and determine the carbon budget needed to keep temperature below 2 or 1.5 °C. This safe carbon budget is low if uncertainty about the transient climate response is high and risk tolerance (willingness to accept risk of overshooting the temperature target) is low. Together with energy costs, this budget determines the optimal carbon price and how quickly fossil fuel is abated and replaced by renewable energy. This price is the sum of the present discounted value of all future losses in aggregate production due to emitting one ton of carbon today plus the cost of peak warming that rises over time to reflect the increasing scarcity of carbon as temperature approaches its upper limit. If policy makers ignore production losses, the carbon price rises more rapidly. If they ignore the peak temperature constraint, the carbon price rises less rapidly. The alternative of adjusting damages upwards to factor in the peak warming constraint leads initially to a higher carbon price which rises less rapidly.
  9. Matthews, H. Damon, et al. “Focus on cumulative emissions, global carbon budgets and the implications for climate mitigation targets.” Environmental Research Letters 13.1 (2018): 010201.  The Environmental Research Letters focus issue on ‘Cumulative Emissions, Global Carbon Budgets and the Implications for Climate Mitigation Targets’ was launched in 2015 to highlight the emerging science of the climate response to cumulative emissions, and how this can inform efforts to decrease emissions fast enough to avoid dangerous climate impacts. The 22 research articles published represent a fantastic snapshot of the state-or-the-art in this field, covering both the science and policy aspects of cumulative emissions and carbon budget research. In this Review and Synthesis, we summarize the findings published in this focus issue, outline some suggestions for ongoing research needs, and present our assessment of the implications of this research for ongoing efforts to meet the goals of the Paris climate agreement.
  10. Millar, Richard J., and Pierre Friedlingstein. “The utility of the historical record for assessing the transient climate response to cumulative emissions.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376.2119 (2018): 20160449. The historical observational record offers a way to constrain the relationship between cumulative carbon dioxide emissions and global mean warming. We use a standard detection and attribution technique, along with observational uncertainties to estimate the all-forcing or ‘effective’ transient climate response to cumulative emissions (TCRE) from the observational record. Accounting for observational uncertainty and uncertainty in historical non-CO2 radiative forcing gives a best-estimate from the historical record of 1.84°C/TtC (1.43–2.37°C/TtC 5–95% uncertainty) for the effective TCRE and 1.31°C/TtC (0.88–2.60°C/TtC 5–95% uncertainty) for the CO2-only TCRE. While the best-estimate TCRE lies in the lower half of the IPCC likely range, the high upper bound is associated with the not-ruled-out possibility of a strongly negative aerosol forcing. Earth System Models have a higher effective TCRE range when compared like-for-like with the observations over the historical period, associated in part with a slight underestimate of diagnosed cumulative emissions relative to the observational best-estimate, a larger ensemble mean-simulated CO2-induced warming, and rapid post-2000 non-CO2 warming in some ensemble members. This article is part of the theme issue ‘The Paris Agreement: understanding the physical and social challenges for a warming world of 1.5°C above pre-industrial levels’.
  11. Rogelj, Joeri, et al. “Estimating and tracking the remaining carbon budget for stringent climate targets.” Nature 571.7765 (2019): 335-342.  Research reported during the past decade has shown that global warming is roughly proportional to the total amount of carbon dioxide released into the atmosphere. This makes it possible to estimate the remaining carbon budget: the total amount of anthropogenic carbon dioxide that can still be emitted into the atmosphere while holding the global average temperature increase to the limit set by the Paris Agreement. However, a wide range of estimates for the remaining carbon budget has been reported, reducing the effectiveness of the remaining carbon budget as a means of setting emission reduction targets that are consistent with the Paris Agreement. Here we present a framework that enables us to track estimates of the remaining carbon budget and to understand how these estimates can improve over time as scientific knowledge advances. We propose that application of this framework may help to reconcile differences between estimates of the remaining carbon budget and may provide a basis for reducing uncertainty in the range of future estimates.

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