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Posted on: July 28, 2019







Joeri Rogelj, Grantham Institute & Piers Forster University of Leeds

Schematic showing how the remaining carbon budget can be estimated from various independent quantities, including the historical human-induced warming, the zero emission commitment, the contribution of future non-CO2 warming, the transient climate response to cumulative emissions of carbon (TCRE), and further correcting for unrepresented Earth system feedbacks. Source: Rogelj et al. (2019)






  1. ROGELJ AND FORSTER: The concept of a carbon budget is simple but putting it into practice is complicated. The carbon budget theory is based on the proportionality between cumulative warming and cumulative emissions described in the Matthews 2009 paper on the TCRE. The proportionality is used to compute the cumulative emissions that are possible when cumulative warming reaches the target temperature and emissions cease. Stated another way, the carbon budget is the cumulative CO2 emitted (until emissions are taken down to zero) that will determines the maximum warming that the world will subsequently experience.
  2. COMMENTS: The carbon budget is determined by using the proportionality equation to compute cumulative emissions for a target cumulative warming to the target temperature. Suppose the target is 1.5C of warming and that currently we stand at 1C of warming. And suppose that the TCRE = 2 trillion tons of cumulative emissions per degC of cumulative warming. To restrict AGW to  0.5C of additional cumulative warming, we must hold cumulative emissions to 0.5*2 = 1 trillion tons of cumulative emissions.
  3. Now, suppose that after temperatures have risen to 1.3C, we wish to estimate the so called “remaining carbon budget (RCB)”. If the TCRE were a real proportionality, the RCB would be a simple ratio problem. Since we used up 0.3C of the 0.5C of warming or 60%, we must have used up 60% of the 1 trillion tonne carbon budget and the RCB is therefore 0.4 trillion tons. But in the TCRE carbon budget it does not work that way because the TCRE proportionality is illusory and not real.
  4. That the TCRE proportionality is a spurious correlation is shown in a related post on this site [LINK] and the relevant demonstration is shown in the video at the top of this post. When two time series have mostly the same sign (both mostly positive or both mostly negative), their cumulative values will tend to be correlated.
  5. However this correlation is illusory and has no interpretation because it is a product of a sign pattern and not a responsiveness of one variable to changes in the other. It is also noted that a time series of the cumulative values of another time series has neither time scale not degrees of freedom. It can be shown that when finite time scales are inserted with finite degrees of freedom, the TCRE correlation vanishes as shown in another related post at this site [LINK] .
  6. Various carbon budget issues with which climate science struggles, including the Remaining Carbon Budget (RCB) issue described below by Rogelj and Forster, are creations of a failed struggle to make sense of a spurious correlation and an illusory TCRE proportionality. For details please see the related post on the TCRE  [LINK] . This is at the root of the problem of what climate scientists call “the unresolved “remaining carbon budget” issue in the carbon budget theory.
  7. The three charts above in Figure 2 is an example of how the attempt to interpret the illusory correlation between cumulative values creates the RCB problem in climate science. In the same time series, the TCRE=2.8 in the full span, 0.84 in the first half, and 0.24 in the second half.  Yet, as can be seen from the values of the R-squared, all three charts show very high correlations.
  8. Therefore, carbon budgets become specific to the span for which it was computed and they do not apply to any other span. This is why there is a RCB problem in climate science. It is not a science problem. It is simply a failed attempt to interpret a spurious correlation that has no interpretation. Below, in the next paragraph, is the text from the Rogelj and Forster paper, where climate science misinterprets a spurious correlation issue in terms of the climate change theory.
  9. Here we see how climate science tries to solve problems by resorting the suite of variables with which they are familiar so that an attempt is made to solve a spurious correlation issue with things like non-CO2 drivers of temperature and Earth System feedbacks including thawing permafrost.
  10. The authors struggle with the logical implausibility of the carbon budget and Remaining Carbon Budget issues and credit to their intelligence and persistence they come up with solutions that must sound reasonable in the climate science context. However, they also underscore the thesis of this post which is that climate budgets based on a illusory correlation is fiction. The upside of such statistical fiction, as explained by Carl Wunsch [LINK] , is the unbounded potential for fantastic explanations. The less constrained one is by the data, the more fantastic the interpretation can be. In Carl’s own words, “… distinct advantage because they can construct interesting and exciting stories and rationalizations.  Colorful, sometimes charismatic, characters come to dominate the field, constructing their intriguing interpretations“.
  11. BACK TO ROGELJ AND FORSTER: The size of the Remaining Carbon Budget (RCB) can depend on many factors. It is not as easy as we thought it was. Our inability to compute the RCB makes it difficult to use the carbon budget concept. A new study was undertaken to untangle the carbon budget mess. The problem is that estimates from early carbon budget studies can’t be reconciled with estimates from new carbon budget studies. Also the conclusions of these studies are not consistent and they can’t be reconciled into a single coherent projection in the evaluation of the effectiveness of climate action proposals such as the Paris Agreement (PG).
  12. The essential issue is that the carbon budget mathematics developed by climate science, and used to impose climate action targets on the Parties in the conference of Parties (COP), is flawed. It does not work the way they  thought it did.
  13. In 2014 the IPCC had written in AR5 that there is a linear relationship between the cumulative emissions and cumulative warming in conformance with the Matthews 2009 paper described in a related post [LINK]. This is where the carbon budget theory comes from. It is based on the idea that the cumulative warming is determined by cumulative emissions.
  14. This is the idea used to propose and impose global emission reduction climate action programs such as the PG. The PG was designed to limit warming to either 2C or 1.5C. For reasons not known there is some confusion as to which of these targets is the real PG target. Even if we can agree on one of these targets, the harder question that still remains is this: how much of a carbon budget do we have left to meet the Paris Agreement? What is the RCB?
  15. Given the carbon budget theory that cumulative warming is proportional to cumulative emissions, it should be easy to figure out the RCB by subtraction and this is what has been done. But with the passage of time, as historical data became available, the RCB values that had been projected were found to be in error. In other words, it has been found in historical data that the RCB does not work. If this issue cannot be resolved, nothing remains of the carbon budget concept.
  16. Knowing how much remaining carbon budget is left is necessary to establish mitigation pathways towards achieving the PG and evaluate global climate action plans in terms of meeting PG targets.  Climate science and climate action cannot proceed without resolving this issue by providing the mathematics of the RCB.
  17. Many climate scientists have worked on thee project to develop the science and the mathematics of computing a reliable and robust estimate of the RCB and many solutions to the RCB problem have been proposed. However, these results created a greater confusion than that from which they started. Although the proposed procedures do provide an answer to the RCB question, the proposed procedures yield very different answers. The large and unexplained variations among the different estimates of these research works leaves the RCB issue in a greater state of confusion that which they had set out to resolve.
  18. It was in this context that the IPCC’s SR15 project set out to resolve this confusion by devising a method for projecting a reliable and reproducible RCB for a given warming target be it 1.5C or 2C without which no rational climate action initiative can be proposed.  It was decided that this procedure must involve an analysis of all factors , not just CO2, that could affect the size of the RCB.
  19. In the IPCC effort, the RCB issue was defined as a case of missing factors that had not been taken into account in the proportionality of cumulative warming with cumulative emissions. It was decided that five additional variables are needed to make an estimate of the RCB on the basis that they can explain the difference in the amount of warming for any given RCB.
  20. The proposed additional variables are non-CO2 forcings described as methane, black carbon soot, and the cooling effects of sulphate aerosols. The new model is to e verified against existing warming since pre-industrial times and then used to make the projections needed to compute the RCB. Five factors were proposed as the foundation of the new RCB procedure.
  21. The five factors are described as: (1) The estimate of global warming up to the present day, (2) The assumed future warming from non-CO2 forcings such as methane and black carbon and the reduction of cooling sulphate, (3) The amount of warming still in the pipeline due to lag, once emissions are brought back to zero (4) The ratio between cumulative CO2 emissions and global warming (TCRE); and (5) The extra emissions from Earth system processes or feedbacks that are typically not included in the models used to make these estimates, such as thawing permafrost.
  22. The revision of the RCB estimation procedure has been completed with positive and encouraging results. The result appears above in the chart marked Figure 1. In the chart, the x-axis is the cumulative CO2 emissions from today; along the y-axis is the temperature increase since pre-industrial times. The dashed lines show the different factors that can affect the total budget – such as the estimate of historical warming and the contribution of non-CO2 emissions. And then joining it all together is the estimate of TCRE – the diagonal bold black line, with the uncertainty range shaded grey.
  23. The chapter in the IPCC SR15 relevant to this effort, and authored by Rogelj and Forster, uses a version of framework shown in Figure 1 to assess the RCB (remaining carbon budget) to keep warming to 1.5C. Presented below is a demonstration of this procedure for the RCB.
  24. ASSUMPTIONS AND ESTIMATES: (1) First we assumed 0.97C of warming for the 2006-2015 (midpoint 2011) decadal mean temperature since pre-industrial times due to CO2 warming. (2) We estimated an additional non-CO2 warming of about 0.1C. The total warming as of 2006-2015 is thus 1.07C since pre-industrial. The value of the TCRE range from the AR5 of 0.8-2.5C per 1,000 gigatonnes of carbon (equivalent to 3,664Gt of CO2). The zero-emissions commitment was assessed to be around zero for warming of 1.5C by a different chapter of the report – and the estimated total remaining allowable warming was, thus, of the order of 0.4C. Finally, Earth system processes that are typically not included in models were assessed to be roughly of the effect of 100 GtCO2 additional emissions over this century, but would increase further over the following centuries.
  25. RCB ESTIMATE: Putting all these factors together and taking into account emissions since 2011 results in a remaining carbon budget from 2018 onwards of 580GtCO2 for a 50% chance of keeping warming below 1.5C. This is less than 15 years of global emissions at current rates.
  26. INTERPRETATION OF RCB ESTIMATE: This means that if we start reducing emissions steeply now and by the time we reach net-zero levels we have not emitted more than 580GtCO2, our best scientific understanding tells us have we expect a one-in-two (50%) chance that warming would be kept to 1.5C. 
  27. Moreover, if we want to be sure that this is also true until the end of the century, we’d have to aim to emit only 480GtCO2 until we reach net-zero instead. This is under 12 years of current emissionsOur best scientific understanding will, of course, improve with time and this number will, thus, be adjusted either up or down.
  28. If a current 50% chance of avoiding 1.5C is not enough, the budget you aim for should be smaller. And if you want to avoid the risk of a downward adjustment putting a particular climate target beyond reach, then you should start aiming for a smaller budget now. The variations around this number are now much better understood and quantified, and an overview of these can be found in chapter two of SR15.
  29. WHY WAS THERE RCB CONFUSION IN THE FIRST PLACE?  Now that we understand why estimates of remaining carbon budgets can differ, some of the confusing variations between earlier published carbon budget estimates can be explained. First of all, carbon budgets estimates starting from pre-industrial times are more likely to vary than those calculated from the present day. The main reason for this is that uncertainties and errors accumulate over the several centuries that are modelled in the lead-up to today. As a result, these studies are using starting points that are already less precise. When expressing remaining carbon budgets relative to a more recent reference period that is validated by observations, the variation between estimates is strongly reduced but not entirely eliminated.
  30. ADDITIONAL SOURCE OF UNCERTAINTY: An additional source of carbon-budget variations is the method that is used to estimate global warming. Different methods of calculating global temperatures are used by different scientific groups in the US, UK and Japan, for example. And each group uses slightly different approaches for how they treat issues such as changes in the way measurements have been taken over the decades and a lack of observed data over the Arctic. Also, analysis of climate change projections with climate models can also use yet another slightly different method. These differences are really nothing more than a labeling issue. However, when inappropriately mixed up, they result in arbitrary changes in reported remaining carbon budgets that, ultimately, can result in pursuing weaker climate targets than the well-below 2C and 1.5C limits set in the Paris Agreement.
  31. FUTURE WARMING DUE TO NON CO2 DRIVERS: Next, the contribution of future warming due to factors other than CO2 is difficult to assess if this information is not explicitly provided by the underlying studies. Hence, we call to make this information available when publishing new estimates of remaining carbon budgets. But it is worth noting that studies that provide estimates with and without particular additional Earth system feedbacks, such as permafrost thawing, do tend to show that the inclusion of such feedback consistently results in smaller remaining carbon budgets.
  32. COMPARISON OF UNRELATED VALUES: A final source of confusion is when numbers are compared that have little relationship to each other. This is the case when studies report cumulative CO2 emissions from scenarios – for example, from 2016 to 2100. Such numbers have little relationship with the physical definition of carbon budgets as discussed here, although at times they have been mistaken for carbon budgets. In our paper, we provide an overview of the various ways in which carbon budgets can be presented in scientific literature. And we have made available online an accompanying checklist of key information that future studies should provide so that their estimates can be adequately put into context.
  33. COMMUNICATING THE FUTURECarbon budgets have been proven to be a robust concept to characterize the climate change mitigation challenge. They also provide the scientific underpinning for net-zero targets and their implied adequacy of limiting warming to acceptable levels. However, communication around them can still vastly improve. Our new framework allows us to clearly understand and explain how scientific improvements result in updated estimates of the remaining carbon budget. Science communicators and analysts can then use this information both to track changes in estimates of the remaining carbon budget over time and to inform their expert judgment about how plausible or reliable updated estimates are.

    TWEETS ON CARBON BUDGETS & EMISSION PATHWAYS  7/27/2019: The discussion reveals a general sense of confusion about the carbon budget in support of the thesis of this work that the carbon budget is a figment of a spurious correlation between cumulative values of time series data.

    1. And for those who’ve criticised this because it is based on an apparently unrealisticly high emission scenario, it is still possible to have 4C of warming even if we follow a lower emission pathway.
    2. To understand how big this is, 7 deg F (4 deg C) is about the same amount of warming as we experienced between the last glacial maximum and present day. That warming caused 300 ft of sea level rise, melting of huge glaciers, and enormous changes in what the world looked like.
    3. Trump admin assumes a (disastrous) 7 degree rise in temperature in this century based on its policies. And intends to do nothing about it (except make it worse). Can’t make this stuff up.
    4. RCP8.5 is a concentration pathway. Can we rule out carbon cycle feedbacks producing this pathway even for a lower emission pathway?
    5. How to turn as emission pathway into concrete actions so that the pathway is followed. This has to take in realities, can’t just be a simplified approach like a global carbon price.
    6. We also need to bear in mind that we could end up with an RCP8.5 concentration pathway even if we follow an emission pathway typically associated with a lower RCP (uncertainty in associating emissions with concentrations and carbon cycle feedbacks).
    7. every year’s delay before initiating emission reductions decreases by approximately two years the remaining time available to reach zero emissions on a pathway still remaining below 1.5°C.
    8. Carbon cycle feedbacks “could” lead to an addition 0.5°C if we follow a 2°C pathway. Could be bigger, could be smaller. Understanding these feedbacks is important yes, but the implication is not “hothouse earth imminent even with emission reductions” (as in some media)
    9. with 13 partner countries called today for an enhanced EU 2030 target, by 2020 ; and a 2050 EU strategy including a net zero emission pathway.
    10.  only 38% of emission cuts will come from technological change. […] the majority will need to come from societal and behavioral changes.” 
    11. 21st century civilization was founded on and is still based on fossil fuels. To wean ourselves, we must move beyond the easy wins of energy efficiency and a modest increase in renewable energy. We must completely transform our homes and businesses, our transport systems, and our food production.
      As a geologist, I recognize the specific challenge of creating an electrical society. Electrifying agriculture, transport, and heat will require more lithium, cobalt, copper, and more. We need to consider the balance of behavioral change, technology, and potential environmental tradeoffs elsewhere. We need to consider the impact of our own renewable revolution on the nations from which we will extract these resources. Tackling climate change creates opportunities in innovation and leadership—but it will not be easy, and the solutions will be contested. And that is why this is an emergency. It is not just because climate change is already causing harm. It is because addressing this challenge will be difficult, and arguably we have not even had the conversations necessary to identify an environmentally and socially just path forward. [LINK] .
    12. MEPs support 55% emission cuts for 2030, up from 40%. Follows Council conclusions on Tuesday, which urged the Commission to provide a 1.5°C-compliant scenario and “at least one pathway towards net-zero emissions in the EU by 2050”.
    13. Discussing the macro-criticality of climate change, fiscal policy tools and non-fiscal related instruments to incentivize a low carbon emission development pathway. There is an urgent need for action!
    14. A Nature paper presents a framework that allows researchers to track estimates of the remaining carbon budget and understand how estimates may improve. The framework may also help to reconcile differences between estimates (PRESENTED ABOVE)



[…] mysterious inconvenience discovered by climate scientists and described in a related post [LINK] . It turns out that partway into a carbon budgeted time span, the remaining budget cannot be […]

[…] consistent with that expected from the IPCC-AR5 likely range of TCRE”. In a related post [LINK] , it is shown that the complexity of the Remaining Carbon Budget issue in climate science derives […]

[…] consistent with that expected from the IPCC-AR5 likely range of TCRE”. In a related post [LINK] , it is shown that the complexity of the Remaining Carbon Budget issue in climate science derives […]

[…]  [LINK] [LINK] [LINK]  [LINK] […]


[…] of the progression of the carbon budget through the time span of its implementation [LINK] [LINK] . Yet carbon credit trading and carbon offset markets necessarily assume a linear relationship. […]

[…]  [LINK] [LINK] [LINK]  [LINK] […]

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