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6. The China-US Climate Agreement: No Respite for the Atmosphere
John Austin

U.S. President Barack Obama and China’s President Xi Jinping agreed on future emissions limits. Image courtesy of the U.S. White House.

The recent signing by China and the USA to limit climate change was hailed by some in the world’s media as ground breaking. Here, I offer an alternative viewpoint.

China and the USA have signed an agreement which limits future growth in carbon dioxide so that by 2025 emissions will be 26-28% of 2005 values. China is committed to a reduction in greenhouse gases after 2030, and a reduction per unit economic output.

There lies the rub: With Chinese economic growth at 5% or more per annum, CO2 under this agreement could very well increase at several percent per year.That is fair enough up to a point, as developed nations have largely been responsible for the current globally polluted atmosphere, and it would be morally questionable if developing nations were not given at least some leeway in their race for development.

The agreement was preparation for world climate talks due in 2015. Assuming the “successful” outcome of next year’s talks, agreements are expected to be implemented from 2020 onwards.

Climate Change and Carbon Dioxide: Rate of Increase vs. Levels in Atmosphere

Atmospheric CO2 at Mauna Loa Observatory, Hawaii, credit NOAA/ESRL.

Note firstly that agreements relate to the rate of increase of CO2 not the amount of CO2 itself. If the emissions of this pollutant were suddenly reduced to zero (which would require literally an act of God) it would still take many decades for the actual CO2 levels in the atmosphere to reduce. Carbon Dioxide would need to go back into the biosphere – and also become locked up in rocks as calcium carbonate, the latter of which of course would take a geological timescale.

The implication is that various global agreements would be in place which would reduce the emissions by say 1 or 2% per annum. However, the CO2 would continue to accumulate in the atmosphere and oceans with damaging effects on the climate and sea levels around the globe.

That is why, in the end, the Intergovernmental Panel on Climate Change (a non-political organisation advised by the world’s scientists with no axe to grind) has advised that CO2 emissions need to be reduced to near ZERO by the end of this century to avoid major environmental damage.

Carbon dioxide becomes uniformly mixed in the atmosphere after a season or two, so it doesn’t matter where it is emitted — the consequences are the same. As a result we can do some fairly straightforward estimates of the impacts of the CO2 buildup.

Simplified Climate Estimates

To decide whether an effect is important, physicists often employ what we refer to as a “back of the envelope calculation.”It is, quite literally, a calculation that can be done on the back of an envelope if you happened to have one handy. This is what I will do here.

Greenhouse gas increases have essentially two effects – which complicate the problem. The first is the immediate response to the gases, and the second is the long term response.

The point is that the climate system has a lag time of many decades. For example if again I were to employ the hand of God and stop emissions tomorrow, the global climate would continue to warm until it reached its new “equilibrium” value. At present, the increase in global temperature since preindustrialisation has been close to 1.0 oC and the equilibrium response would add another perhaps 0.6 oC.

The other thing to recognise is that the global temperature response is approximately proportional to the logarithm of the CO2 amount (here is not the place to go into those details). Another issue is that the details will vary according to the other greenhouse gases present such as methane (CH4) and nitrous oxide (N2O), but I’ll ignore them for the purposes of illustration and assume that they increase in line with CO2.

To give some simple numbers, we are currently at 400 ppm (parts per million) CO2 amount compared with about 270 in the preindustrial atmosphere. A doubling of CO2 is well established in the top climate models as a fairly consistent response of about 3 oC for equilibrium. Applying the numbers for the actual atmosphere and assuming the logarithm response to concentration we would predict for a doubling of CO2, 1.6xlog2/log(400/270) = 2.8 oC, which is very close to the 3 oC value.

To summarise, then, based on atmospheric values, we estimate:
A global temperature response = log (c/270)/log(400/270), or simplifying, (in oC with the logarithm to base 10).
T1 = 5.8 log (c/270)
For the equilibrium temperature:
Teq = 9.3 log (c/270)
(c is the CO2 concentration in parts per million.)

How Will CO2 Change in the Future?

With China currently contributing 29% of the global emissions, it will have a major effect on global values.

Let us assume that it reigns back CO2 production as a function of economic growth, but that because its growth is accelerating, it continues to increase at say 2% per annum, at least until 2020. The USA might cut back by 1% per annum. Europe might also reduce by 1% per annum. The effect is that global emissions from these regions will likely remain constant at best until 2020. Other countries will presumably do similarly. Thus by 2020 I would estimate that global CO2 emissions will be very similar to what they are now. Or, to put it another way, we will have squandered another 5 years of potential greenhouse gas reductions, waiting for politicians to implement what they’ve agreed.

Thereafter, CO2 might reduce at perhaps 1% per year. To make this change would require a concerted global effort to adopt renewable sources which are sustainable. In other words, it might be easy making a 10% reduction from the current emissions rates, but achieving the final few % reductions will be extremely challenging. For example switching from coal to natural gas as a fuel is a one-off change that only buys a few years, since the infrastructure cannot switch from natural gas to something more efficient. Nonetheless, assuming a 1% reduction per annum on a compound basis from the year 2020 would reduce emissions by a factor 1.0180 = 2.2. In other words, we would still be emitting 45% of current rates by the end of the century.

In this context, the move to fracking by the US and UK as well as other countries to recover more hydrocarbons to burn is distinctly counterproductive. So the 1% per annum reduction rate may appear pessimistic to those with rose-tinted spectacles.

The Effect of Future Scenarios

As a simple calculation, the following is just one of a host of different possibilities. Let us take the figure of 45% in the last paragraph for the end of the century. Don’t forget this is still way short of the IPCC warning of a need to reduce emissions to near zero.

There is a very helpful website which can be used for this purpose – Trillionthtonne.org. This shows for example that we have already released almost 0.6 trillion tonnes of carbon and “only” 1 trillion are needed to reach an estimated 2 oC warming. At current rates, this will take about 25 years according to these calculations.

Hence, from 2020, assuming an average of 70% of current emissions will add 0.4×80/25×70% =0.9 trillion tons + 5 years of emissions at current rates (=0.08) = very nearly 1 trillion tonnes of carbon. On that basis, we can expect the change in atmospheric concentration to increase by a factor of 1.6/0.6 = 2.7. This would give a year 2100 concentration of about 270 + 130×2.7 = 620 ppm (approximately).

We now finally arrive at an estimate for global temperature increase, based in part on these latest climate agreements. My figures are
5.8xlog(620/270) (immediate) or 9.3xlog(620/270) (equilibrium).

Calculating the logarithms, we obtain T1 = 2.1 oC and Teq = 3.3 oC.

This is of course just the global averaged figure. It includes places such as the poles where very large changes have occurred and other locations where small changes have occurred. Globally we have already seen how just a small increase in global temperatures has disrupted previous weather patterns, so a 2-3 degrees warming is extremely serious and warrants activity.

Climate Change vs. Politicians: Politics Wins

President Obama is of course not the only politician to pretend that he is working to solve the world’s climate change problems. In the last few years, the UK and parts of Europe have seen increased storms and flooding. The UK prime minister, David Cameron is quoted by the BBC as publicly agreeing with a Met Office report indicating a link with climate change. Cameron, however, is simultaneously supporting further exploitation of fossil fuels through fracking, rather than investing further in renewables.


  • McGrath, Matt. Will Obama's climate surprise deliver a global deal?. (2014). BBC News. Accessed on November 16, 2014
  • University of Oxford: Trillionth Tonne. Explaining the need to limit cumulative emissions of carbon dioxide. (2014). Accessed on November 16, 2014
  • BBC. Met Office: Evidence 'suggests climate change link to storms'. (2014). Accessed on November 16, 2014
  • Met Office. A global perspective on the recent storms and floods in the UK. (2014). Accessed on November 16, 2014

Article initially prepared 16 November 2014 for decodedscience.com and transferred to enigmascientific.com on 28 January 2015.

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Website revised by John Austin, 28/1/2015. © Enigma Scientific Publishing, 2015.