Why is Global Warming Projected to Accelerate?

Looks like it shouldn’t! So I asked a climate scientist.

While critically examining the case for human-caused global warming, I noticed something peculiar:

  1. Scientists agree that the greenhouse effect is logarithmic — meaning that as we add more CO2 to the atmosphere, its warming effect decreases.
  2. However, the IPCC projects that if we do not take steps to greatly reduce emissions, the rate of warming will speed up.
IPCC AR5 Synthesis Report, Page 11. RCP8.5 is business-as-usual, and RCP2.6 is totally sticking to the Paris agreement

Google didn’t offer an immediate explanation of this apparent contradiction, and I was a bit lazy to read through IPCC AR5 (Chapter 11?), so I turned to AskAClimateScientist:

If the climate responds logarithmically to CO2 emissions, why is global warming projected to accelerate in the future if we don’t transition off of fossil fuels?

My question was so awesome that it got this response:

Hi David, This is a really interesting question and one that I will definitely refer to 1 of my colleagues who teaches about this very thing. He is likely to be able to give you a far more clear and simple answer than I can.
I will send him a message and hopefully we will get a reply soon.
Cheers, AACS

Two days later…

Hi David, We have a response from Prof Steve Sherwood, a world leader in climate sensitivity research and also the lead co-ordinating author of the last IPCC Working Group 1 Chapter on Aerosols. He replies:
“It is a good question. The radiative effect of CO2 scales with the logarithm of concentration. But there were already 280 ppmv of CO2 in the atmosphere before the industrial era began. So the logarithmic effect doesn’t really kick in for a while.
For example the increase in CO2 from 1.3 to 1.6 x preindustrial would add about 80% of the radiative effect that the increase from 1.0 to 1.3 x preindustrial CO2 did.
Meanwhile, emissions are growing exponentially, and natural systems are expected to saturate so that their net uptake of carbon begins to weaken. This rapid acceleration of CO2 net emissions overwhelms the “diminishing of returns” associated with radiative saturation, at least for most of this century. Eventually if we hit 3–4 x preindustrial CO2 and start running out of fossil fuels so cannot keep increasing emissions, warming will markedly decelerate!” Even though it’s a bit technical, I hope this answer helps.
Cheers, AACS.

The phrase “doesn’t really kick in for a while” is quite confusing, since the “logarithmic effect” is always in effect. I think what he meant to say is that even though the logarithmic response looks something like this:

We don’t actually care about that curve below the red line because CO2 levels will not drop that low again (CO2 concentrations never dropped below about 275 ppm before human history), and we are probably not even able to go above 1100, because fossil fuels supplies will eventually run dry:

So this is the part we care about — especially the left side. It is not far from being a straight line, with a warming effect that gently levels off as emissions increase. Meanwhile, CO2 emissions have been, and are expected to continue, increasing along a curve with an exponential shape — a gentle upward slope:


If CO2 is increasing exponentially, it should look like a straight line when plotted on a logarithmic scale. But in fact, it still slopes upward when plotted logarithmically. This means CO2 is increasing slightly faster than exponentially. Below you can see CO2 plotted logarithmically as a magenta line (together with land and ocean temperatures):

The land (red) has warmed faster than the ocean surface (blue), because oceans are huge and take a long time to heat up. However, ocean temperatures have the most impact on the global average because oceans cover 71% of earth’s surface.

This super-exponential rise in CO2 more than compensates for the gentle downward bending of the logarithm to produce a mildly accelerating temperature increase. If the Paris agreement is not honored, CO2 emissions could keep rising approximately exponentially for decades, as prosperity spreads accross the world and billions of people use more and more fossil fuels.

Still, this is not enough to explain the amount of acceleration expected. Which brings us to the next part: “Natural systems are expected to saturate.” In other words, the world’s natural carbon sinks, such as the ocean and plants, will absorb CO2 more slowly as time goes on, leaving more of it in the atmosphere.

That is, the CO2 concentration graph will bend upward more steeply than an exponential increase alone would have caused. Therefore, scientists expect, warming will accelerate.

I was a little surprised he didn’t mention committed warming: the idea that even if we could stop all emissions instantly, the earth would continue warming because the climate takes time to fully respond. This is because of “positive feedback” which occurs over many years.

Major climate feedbacks (IPCC AR5 Synthesis Report)

If I understand correctly, there are three main positive feedbacks: first, CO2 causes a small amount of warming directly. Next, the surface of the ocean heats up, causing world humidity levels to rise slightly, which causes a larger amount of warming. Next, this extra warming is enough to melt ice in the arctic (and perhaps eventually the antarctic) — that’s the stage we’re in now. Since ice reflects sunlight into space, the melted ice absorbs more sunlight, causing even more warming, which melts more ice. Finally, over decades or even centuries, land permafrost melts, exposing dead plant life from long, long ago. It decomposes, releasing extra CO2 (and methane), starting additional feedback cycles which (if not counteracted) would take thousands of years to finish.

Perhaps he simply forgot to mention that stuff. He’s probably a busy guy. Or, perhaps this particular climatologist suspects that negative feedbacks, such as increased clouds and aerosols, will begin to counteract the positive feedbacks as we move forward. Or, perhaps the fact that polar ice has already been melting for many years means that we won’t see much “acceleration” — that it’s going to keep melting at roughly the same speed we see today.

This has been a companion to the main article:

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