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64 N. H. A. Bowerman et al.<br />

4. Conclusions<br />

A number of recent studies have considered <strong>the</strong> concept of cumulative carbon<br />

emissions <strong>and</strong> <strong>the</strong>ir relation to peak warming. Here, we consider how <strong>the</strong> concept<br />

of cumulative emissions interacts with o<strong>the</strong>r aspects of <strong>global</strong> change, such as<br />

emissions floors <strong>and</strong> rates of warming.<br />

We consider o<strong>the</strong>r emission metrics, such as <strong>the</strong> emissions in year 2020 <strong>and</strong><br />

2050, <strong>and</strong> find that <strong>the</strong>se cause a much wider range of magnitudes of resultant<br />

peak warming than metrics based on cumulative carbon emissions to <strong>the</strong> time<br />

of peak warming. For small cumulative totals, however, 2050 emissions can<br />

be a good indicator of peak warming; however, as soon as we consider 2050<br />

emissions greater than around 5 GtC yr −1 , this relationship breaks down. We also<br />

find that, <strong>for</strong> large cumulative totals in particular, cumulative metrics based on<br />

integrations over smaller time periods, such as 2010–2050, do not correlate with<br />

peak warming as well as cumulative emissions to a given date near <strong>the</strong> time of<br />

peak warming.<br />

We extend <strong>the</strong> analysis of Allen et al. [11] of cumulative emissions to consider<br />

two types of emissions floors: ‘hard’ or constant floors, <strong>and</strong> exponentially decaying<br />

floors. In <strong>the</strong> situation that model temperatures peak be<strong>for</strong>e year 2500 <strong>and</strong> below<br />

4 ◦ C, we find that cumulative emissions between pre-industrial times <strong>and</strong> year<br />

2200 are highly correlated with that peak year, regardless of <strong>the</strong> type of emissions<br />

floor used. Floors do, however, provide a lower bound on cumulative totals at low<br />

values. We suggest that a natural geophysical time-frame <strong>for</strong> considering longterm<br />

climate policy is to <strong>the</strong> year 2200, instead of to <strong>the</strong> year 2100 as is often<br />

done today.<br />

Cumulative emissions, however, say little about rates of <strong>global</strong> warming, which<br />

affect <strong>the</strong> cost <strong>and</strong> feasibility of societal <strong>and</strong> ecosystem adaptation in <strong>the</strong> short<br />

term. We show that maximum rates of CO2-induced warming are much more<br />

closely correlated with peak emissions rates, <strong>and</strong> that, <strong>for</strong> each additional GtC<br />

per year on <strong>the</strong> peak emission rate, we will observe a best-guess increase of 0.016 ◦ C<br />

in <strong>the</strong> rate of warming per decade.<br />

We also consider <strong>the</strong> short-term policy implications of our findings. The<br />

relationship between cumulative emissions <strong>and</strong> peak warming allows us to show<br />

how delaying mitigation in <strong>the</strong> short term creates <strong>the</strong> need <strong>for</strong> more rapid emission<br />

reductions later, in order to stay below a given cumulative emissions limit.<br />

Our findings relating to <strong>the</strong> rates of warming also show that only two emission<br />

targets (peak emission rate <strong>and</strong> cumulative carbon emissions to 2200) are needed<br />

to constrain two key indicators of CO2-induced climate change: peak warming<br />

<strong>and</strong> maximum rate of warming. These targets could provide a simple <strong>and</strong> clear<br />

framework <strong>for</strong> specifying CO2 mitigation policy over <strong>the</strong> next two centuries, <strong>and</strong><br />

<strong>for</strong> comparing <strong>the</strong> effect of different policies.<br />

This work is supported by AVOID, a research programme funded by <strong>the</strong> UK Department of<br />

Energy <strong>and</strong> Climate Change (DECC) <strong>and</strong> <strong>the</strong> UK Department <strong>for</strong> Environment, Food <strong>and</strong> Rural<br />

Affairs. N.H.A.B. is supported by a Natural Environment Research Council (NERC) CASE<br />

studentship with <strong>the</strong> Met Office. M.R.A. received additional support from <strong>the</strong> US National Oceanic<br />

<strong>and</strong> Atmospheric Administration <strong>and</strong> <strong>the</strong> US Department of Energy through <strong>the</strong> International<br />

Detection <strong>and</strong> Attribution Group, IDAG.<br />

Some of this work was undertaken while D.J.F. was on secondment to DECC <strong>and</strong> NERC. The<br />

opinions expressed here are personal <strong>and</strong> in no way reflect those of his employers.<br />

Phil. Trans. R. Soc. A (2011)<br />

Downloaded from<br />

rsta.royalsocietypublishing.org on November 30, 2010

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