Cumulative Emissions and Climate Models

As my summer research continues, I’m learning a lot about previous experiments that used the UVic ESCM (Earth System Climate Model), as well as beginning to run my own. Over the past few years, the UVic model has played an integral role in a fascinating little niche of climate research: the importance of cumulative carbon emissions.

So far, global warming mitigation policies have focused on choosing an emissions pathway: making a graph of desired CO2 emissions vs. time, where emissions slowly reduce to safer levels. However, it turns out that the exact pathway we take doesn’t actually matter. All that matters is the area under the curve: the total amount of CO2 we emit, or “cumulative emissions” (Zickfeld et al, 2009). So if society decides to limit global warming to 2°C (a common target), there is a certain amount of total CO2 that the entire world is allowed to emit. We can use it all up in the first ten years and then emit nothing, or we can spread it out – either way, it will lead to the same amount of warming.

If you delve a little deeper into the science, it turns out that temperature change is directly proportional to cumulative emissions (Matthews et al, 2009). In other words, if you draw a graph of the total amount of warming vs. total CO2 emitted, it will be a straight line.

This is counter-intuitive, because the intermediate processes are definitely not straight lines. Firstly, the graph of warming vs. CO2 concentrations is logarithmic: as carbon dioxide builds up in the atmosphere, each extra molecule added has less and less effect on the climate.

However, as carbon dioxide builds up and the climate warms, carbon sinks (which suck up some of our emissions) become less effective. For example, warmer ocean water can’t hold as much CO2, and trees subjected to heat stress often die and stop photosynthesizing. Processes that absorb CO2 become less effective, so more of our emissions actually stay in the air. Consequently, the graph of CO2 concentrations vs. CO2 emissions is exponential.

These two relationships, warming vs. concentrations and concentrations vs. emissions, more or less cancel each other out, making total warming vs. total emissions linear. It doesn’t matter how much CO2 was in the air to begin with, or how fast the allowable emissions get used up. Once society decides how much warming is acceptable, all we need to do is nail down the proportionality constant (the slope of the straight line) in order to find out how much carbon we have to work with. Then, that number can be handed to economists, who will figure out the best way to spread out those emissions while causing minimal financial disruption.

Finding that slope is a little tricky, though. Best estimates, using models as well as observations, generally fall between 1.5°C and 2°C for every trillion tonnes of carbon emitted (Matthews et al, 2009; Allen et al, 2009; Zickfeld et al, 2009). Keep in mind that we’ve already emitted about 0.6 trillion tonnes of carbon (University of Oxford). Following a theme commonly seen in climate research, the uncertainty is larger on the high end of these slope estimates than on the low end. So if the real slope is actually lower than our best estimate, it’s probably only a little bit lower; if it’s actually higher than our best estimate, it could be much higher, and the problem could be much worse than we thought.

Also, this approach ignores other human-caused influences on global temperature, most prominently sulfate aerosols (which cause cooling) and greenhouse gases other than carbon dioxide (which cause warming). Right now, these two influences basically cancel, which is convenient for scientists because it means we can ignore both of them. Typically, we assume that they will continue to cancel far into the future, which might not be the case – there’s a good chance that developing countries like China and India will reduce their emissions of sulfate aerosols, allowing the non-CO2 greenhouse gases to dominate and cause warming. If this happened, we couldn’t even lump the extra greenhouse gases into the allowable CO2 emissions, because the warming they cause does depend on the exact pathway. For example, methane has such a short atmospheric lifetime that “cumulative methane emissions” is a useless measurement, and certainly isn’t directly proportional to temperature change.

This summer, one of my main projects at UVic is to compare what different models measure the slope of temperature change vs. cumulative CO2 emissions to be. As part of the international EMIC intercomparison project that the lab is coordinating, different modelling groups have sent us their measurements of allowable cumulative emissions for 1.5°C, 2°C, 3°C, and 4°C global warming. Right now (quite literally, as I write this) I’m running the same experiments on the UVic model. It’s very exciting to watch the results trickle in. Perhaps my excitement towards the most menial part of climate modelling, watching as the simulation chugs along, is a sign that I’m on the right career path.


6 thoughts on “Cumulative Emissions and Climate Models

  1. That’s an interesting point about diminishing carbon sinks. It will be interesting to see what values you get for the slope.

  2. At the risk of seeming like an insufferably smug bar steward, here is what I said on this subject (referring to the work of Dr Myles Allen [2009]) almost 9 months ago:
    “The fact that AGW may suffer from issue fatigue, and the fact that I sometimes feel like an old-style street preacher being completely ignored by passers-by, does not change the fact that, on well above the balance of probability, we face an environmental catastrophe if we fail to take significant action within the next 5 years. Furthermore, every year we fail to act, makes taking effective action much, much harder. This is because it is the total (i.e. cumulative) amount of fossilised carbon that we (have and will) put into the atmosphere that will determine the temperature change we will see over the next 50 years or so.”

    See also Wikipedia‘s exhaustively-referenced summary of the 4 Degrees and Beyond International Climate Conference in Oxford in 2009 (at which the work of Allen and many others was first presented).

  3. Thanks for an interesting post, Kate. I recently came across this methodology when looking at the climate effect of the exploitation of the Alberta tar sands at Skeptical Science. I’ll insert a link to your post in my article, since your explanation explains the methodology nicely.

    It is fortuitous (computationally, at least) that the effects of the diminishing carbon sinks and the infra-red band saturation roughly cancel out to make the climate response to cumulative emissions linear. (We would be better off in terms of climate effect, though, if the effectiveness of the carbon sinks did not decrease with increasing emissions.) Thinking about cumulative emissions as the key parameter does simplify the metrics for the mitigation response we need to make. It’s a pity that the slopes can’t be better constrained, but I look forward to hearing from you if you make some progress on this.

    For those of us without subscriptions, free pdfs of the Matthews et al and the Allen et al papers are available here:

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