CO2 emissions: a piece of the pie.

In his Policy Forum “CO2 arithmetic” (9 Mar., p. [1371][1]), W. S. Broecker uses the idea of a permissible cumulative CO2 emissions “pie” to conceptualize the allocation of future emissions among the world's nations. The size of the pie is determined by the target for atmospheric CO2 concentration stabilization; the higher the target level, the larger the pie. To calculate the size of the pie for different stabilization levels, Broecker notes that, for every 4 Gt of carbon emitted today, atmospheric CO2 concentration increases by about 1 ppm. This corresponds to a current airborne fraction (i.e., the change in atmospheric loading per unit of total emissions) of about 0.5. He then assumes that this value for the airborne fraction can be applied to future concentration stabilization scenarios; i.e., he assumes that every 1 ppm of concentration increase relative to today increases the size of the pie by 4 Gt of carbon. This assumption is incorrect and leads to a serious underestimate of the size of the pie. ![Figure][2] ( Top ) WRE concentration stabilization profiles ([1][3]) stabilizing at 450 ppm (in 2100), 550 ppm (in 2150), and 650 ppm (in 2200). ( Middle ) Corresponding cumulative emissions from mid-2007. Emissions are the sum of fossil and land-use change emissions. The horizontal lines show the allowable cumulative emissions given by Broecker for the 450 and 550 ppm stabilization cases. Arrows show how much larger the corrected cumulative emissions are compared with the Broecker estimates. ( Bottom ) Airborne fractions (change in atmospheric loading per unit of total emissions) for the three stabilization cases. Broecker assumes that the airborne fraction will remain constant at the present value (around 0.5). A more credible estimate of permissible future emissions is shown in the accompanying figure, based on the standard WRE concentration stabilization profiles updated from ([1][3]). The figure shows the concentration profiles for stabilization at 450, 550, and 650 ppm, levels chosen here purely for illustrative purposes. Corresponding emissions (middle panel) are calculated with an inverse version of the MAGICC carbon cycle model ([2][4]), which accounts for both CO2 fertilization and climate feedbacks on the carbon cycle. Climate feedbacks are important because, for any given stabilization profile, they reduce the allowable emissions significantly below those that would be implied if climate feedbacks were ignored. It can be seen that Broecker's estimates of total cumulative emissions are much less than those calculated by the carbon cycle model. The model also shows that cumulative emissions continue to rise for centuries after concentration stabilization. This reflects a continuing and only slowly decreasing flux of CO2 into the oceans, in turn arising from the very long time that it takes for equilibrium between the atmosphere and ocean to be reestablished. The reason why Broecker's estimates are so low is because of his constant airborne fraction assumption. Although this is a useful approximation when CO2 emissions are increasing, it cannot be applied to stabilization cases where emissions must eventually decrease. That this assumption is incorrect in such cases is clear from the fact that, at stabilization, the airborne fraction must drop to zero. The decline in airborne fraction from the present value of around 0.5 to zero at stabilization is shown in the bottom panel of the figure. The primary objective of Article 2 of the United Nations Framework Convention on Climate Change is stabilization of atmospheric greenhouse gas concentrations. Describing a CO2 concentration stabilization target in terms of an allowable cumulative emissions “pie” that must be divided amongst nations in some equitable manner is an elegant way of visualizing this objective. Through this image, Broecker's Policy Forum provides a useful service, which, in principle, may help policy-makers construct policies that are more scientifically well founded than, for example, the Kyoto Protocol. It is unfortunate that Broecker has underestimated the size of the pie and ignored the fact that the size of the pie changes over time. Nevertheless, even with the much larger pie derived here, the message that the emissions requirements of the pie present a formidable technological challenge to society remains an important policy implication. 1. 1.[↵][5] 1. T.M.L. Wigley, 2. R. Richels, 3. J. A. Edmonds , Nature 379, 240 (1996). [OpenUrl][6][CrossRef][7][Web of Science][8] 2. 2.[↵][9] 1. T.M.L. Wigley, 2. S.C.B. Raper , Science 293, 451 (2001). [OpenUrl][10][Abstract/FREE Full Text][11] # CO2 Emissions: A Piece of the Pie {#article-title-2} Wigley is certainly correct in his assertion that on a time scale of several hundred years, the size of the carbon pie would be considerably greater than my estimate of 720 Gt of carbon. The reason is that, as the CO2 content of the atmosphere approaches stabilization, ocean uptake becomes ever more important. But during the transition period (now to 2075 A.D.) when the world is struggling to reduce its CO2 emissions, the permissible net CO2 emissions would be on the order of 720 Gt of carbon or, using the ocean model adopted by Wigley, 900 Gt of carbon (see figure below). ![Figure][2] On the basis of Wigley's model, the release of 720 Gt of carbon during the transition period from 2000 to 2075 A.D. would raise the atmosphere's CO2 content to 520 ppm. To bring it to 560 ppm during the same period would allow approximately 25% more CO2 to be released to the atmosphere. Then, as Wigley points out, over the following 200 years (2075 to 2275 A.D.), another 720 or so Gt could be added without any substantial increase in the atmosphere's CO2 content. I purposefully avoided the long term because my goal was to show, in a simple way, that, if an upper limit of 560 ppm were set and if the carbon pie was divided according to population, the rich countries would face a monumental emission-reduction task. With regard to the post-2075 world, I suspect that to quell the continuing rise in sea level driven by the melting of the polar ice caps, there would be a desire to bring the atmosphere's CO2 content back down at a rate far faster than offered by the ocean. If, as I deem necessary, CO2 capture from the atmosphere is to become a major player, then in the post-2075 A.D. world, it would be used to accomplish this drawdown. Hence, although useful during the 75-year or so period of transition from business-as-usual CO2 emissions to no net CO2 emissions, the carbon-pie concept will have little value in the posttransition period. Once it is stabilized, I suspect that CO2 capture from the atmosphere will be used not only to compensate ongoing CO2 emissions but also to draw down the atmosphere's CO2 content. [1]: /lookup/doi/10.1126/science.1139585 [2]: pending:yes [3]: #ref-1 [4]: #ref-2 [5]: #xref-ref-1-1 "View reference 1. in text" [6]: {openurl}?query=rft.jtitle%253DNature%26rft.volume%253D379%26rft.spage%253D240%26rft_id%253Dinfo%253Adoi%252F10.1038%252F379240a0%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [7]: /lookup/external-ref?access_num=10.1038/379240a0&link_type=DOI [8]: /lookup/external-ref?access_num=A1996TQ16900041&link_type=ISI [9]: #xref-ref-2-1 "View reference 2. in text" [10]: {openurl}?query=rft.jtitle%253DScience%26rft.stitle%253DScience%26rft.issn%253D0036-8075%26rft.aulast%253DWigley%26rft.auinit1%253DT.%2BM.%2BL.%26rft.volume%253D293%26rft.issue%253D5529%26rft.spage%253D451%26rft.epage%253D454%26rft.atitle%253DInterpretation%2Bof%2BHigh%2BProjections%2Bfor%2BGlobal-Mean%2BWarming%26rft_id%253Dinfo%253Adoi%252F10.1126%252Fscience.1061604%26rft_id%253Dinfo%253Apmid%252F11463906%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [11]: /lookup/ijlink/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6Mzoic2NpIjtzOjU6InJlc2lkIjtzOjEyOiIyOTMvNTUyOS80NTEiO3M6NDoiYXRvbSI7czoyNDoiL3NjaS8zMTYvNTgyNi84MjkuMy5hdG9tIjt9czo4OiJmcmFnbWVudCI7czowOiIiO30=