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Naked Copenhagen

The numbers behind the OpEd

Richard A Muller

The "Naked Copenhagen" op ed that appeared in the Wall Street Journal contains a chart that shows the expected increase of CO2 emissions from burning fuel; cement production and cutting of forests is not included. The chart is a redraft of the one that appears below:

CO2 emissions after Copenhagen

You can download the numbers used to create the chart in Excel format: NakedCopenhagen.xls

The model used to produce this chart was very simple, and that was done on purpose, to illustrate an extremely simple point: that even in an ideal Copenhagen treaty, CO2 emission would not stop, but would continue to grow. Prior charts, such as those that appear in the IPCC reports, are based on such complex models that it is often difficult for the reader to understand what is causing the observed effects. For example, when readers of the IPCC reports see large increases in temperatures projected under "business as usual" scenarios, they often don't appreciate the fact that most of the increase is coming from CO2 emitted by the developing world. (The term "business as usual" doesn't bring up an image of surging economies in China and India.)


For years 1990 to 2007, the numbers came from the International Energy Agency. In October 2009 they published a report titled:
IEA Statistics, CO2 Emissions from Fuel Combustion, 2009 Edition

This report is for sale (expensive). The IEA also provides two free documents that contain the key details. Their Highlights report can be downloaded at:

This report gives the background information for the numbers and describes their context. It also purports to give the yearly numbers for the emissions, but it actually only gives a sample (skipping years between 1990 and 1995, for example). The complete set of numbers can be downloaded in Excel format at:

The Netherlands Environmental Assessment Agency shows that CO2 emissions from China have been growing at 10% per year over the past 10 years, rather than at the 6% rate we have assumed. The difference may be due, in part, to the fact that this report includes CO2 from cement manufacture. Their numbers are available at:


The data ends at 2007, but the Copenhagen treaty begins (presumably) in 2012. Rather than do anything complicated for these intervening years, I assumed that the U.S. and Kyoto Annex-I countries CO2 emissions would continue to grow at 1% per year up to 2010, and then would begin to implement a 40 year linear decline in emissions. I assumed the the Non-Annex-I countries would continue to grow at 6% per year until 2040, and then begin a linear decline down reaching 20% of their 2040 values in 2080 (not shown on the chart).

The 6% annual increase in the Non-Annex-I CO2 emissions was based on the observed growth in India and other developing nations of about 6% per year in GDP averaged over the last 10 years. China's GDP has averaged 10% growth per year over this same period; but if we assume that they will reduce their carbon per GDP by 4% per year, then their net CO2 growth will also be 6% per year. Again, these assumptions were chosen in part because they are as good as any other assumptions, and their simplicity makes the calculations transparent.

Climate Change

It is a great deal of effort to run a complete set of climate models for any new scenario. So to get estimates of the effect of the Naked Copenhagen scenario, I made the following simplifying assumptions.
  • Changes in fuel use will be a rough guide to the total effect of all greenhouse gases. Thus the CO2 from fuel use (that's what is plotted in the figure) can be used as a proxy for all greenhouse emissions.
  • Assume linearity. Over small changes, even nonlinear processes are linear. Many people think that there are "tipping points" at which non-linear effects become dominant; most of these tipping points will cause greater temperature rises than do the linear ones. Thus, the temperature rises that I calculate based on linearity, large as they are, would be underestimates if any of the tipping points prove to be important.
  • During the period of 1957 to 2007, the rise in the earth's temperature (according to the 2007 IPCC report) was about 1 degree F, and "most" of this is accounted for by human greenhouse emissions. This rate of rise was about 0.2 degrees F per decade. Assume this was the average rate of rise for the period 1990 to 1999.
  • According to the spreadsheet, the amount of CO2 from fuels for the decade 1990 to 1999 was 209 million tons.
Based on the assumptions, we now expect that the emission of 209 billion tons of CO2 will give rise to about a 0.2 F temperature rise. The coefficient is roughly 1 degree F for every trillion tons of CO2 from fuel (assuming other greenhouse gases follow proportionally).

In our model, the accumulated sum by 2050 is 3 trillion tons (see the spreadsheet). At 1 F per trillion tons, that should increase the average temperature by about 3 F. At that point we assume that the CO2 emissions continue to decline, as the developing economies begin to follow the U.S. lead and cut their emissions by 80% over the following 30 years. Since they are primarily due to the developing world, we can simply take a linear approximation. The spreadsheet shows that the accumulated emissions will grow to 4.8 trillion tons, giving rise to a temperature increase of about 5 F, 6 F above the baseline of 1957 (roughly the time when human-caused temperature rise began to kick in). The temperature will be higher at the poles (primarily due to the known stratification of the atmosphere in those regions); typically the temperature is expected to be twice the average at the poles, i.e. about 10 F. If non-linear effects kick in then the temperature could rise much higher. Of course, it is possible that cloud cover will increase, and give a negative feedback.


1. Slower growth for China? Some "optimists" may think that the continued 10% growth of China is unrealistic. That may be true. Many projections for future climate do, in fact, assume that the Chinese economy slows drastically. That is a viable alternative model. However, I think it is important that anybody who presents such a model explicitly state what the assumptions are. In fact, it may well be that continued growth of the economically expanding will make the Kyoto approach to climate control completely inadequate.

In fact, as stated in the Op Ed, if a slower growth for China delays its transition to being a "developed" country, then that might delay the year when it begins substantial cuts in CO2, and the net effect would be a higher ultimate temperature. So, in fact, if you are worried about CO2, then you want China to develop as rapidly as possible.

2. Faster growth of CO2? As mentioned in the Data section above, recent report by the Netherlands Environmental Assessment Agency shows that CO2 emissions from China have been growing at 10% per year over the past 10 years, rather than at the 6% rate we have assumed. The difference may be due, in part, to the fact that this report includes CO2 from cement manufacture. Their numbers are available at:

If the Chinese continue at a 10% growth in CO2 emissions, then the emissions will grow at a faster rate. Unfortunately, this does not imply a more rapid growth in the Chinese economy, and so it implies that the emissions will go much higher before China reaches a sufficient standard of living that it begins to follow the example of the developed nations and cuts back by 80% over 40 years. In this scenario (see spreadsheet, columns to the far right) 9.4 trillion tons of CO2 will be released by 2080, and the temperature rise will be over 11 F above the current temperature, higher at the poles.


These scenarios suggest that even if the IPCC climate models are accurate, the Kyoto/Copenhagen approach (developed countries cut now; developing countries follow eventually) will not work.

What would work? The only clear hope would be a massive effort into making the energy use of the developing economies cleaner (more solar, wind, and nuclear) and more efficient. How can one achieve this? I suspect it would require much more intrusive cooperation between the developed world and the emerging one.
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