Kaya Identity part II – and a ‘diamond law’?

Are some apparent CO2 emission reductions ‘too good to be true’? In this post, I discuss how the Kaya Identity leads to what might be called the ‘diamond law’ of CO2 emissions. This ‘law’ (in fact just chemistry) allows us to check the plausibility of apparently dramatic CO2 reductions.

The Kaya Identity relates a country’s CO2 emissions to four factors:

CO2 emissions = Population x Standard of living x Energy intensity of the economy x CO2 intensity of energy
Factor 1 Factor 2 Factor 3 Factor 4
Calculated as: Population GDP per capita Energy per unit of GDP CO2 emissions per unit of Energy

In my previous post I considered the first two factors of the Kaya Identity (population and wealth). In this post I consider the third and fourth factors (Energy Intensity of the Economy and CO2 Intensity of Energy). It is the fourth factor that leads to the ‘diamond law’.

Factors 3 and 4 can be calculated from data in the World Bank Indicators database for 131 countries in 2010. Energy intensity of the Economy (Factor 3) is Total Energy Use divided by GDP (millions of dollars). CO2 Intensity of Energy (Factor 4) is CO2 Emissions (ktonnes of CO2) divided by Total Energy Use. ‘Total Energy Use’ is shown in the database as ‘ktonnes of oil equivalent’ even though it includes energy from all sources, not just fossil fuels.

Figure 1 shows Energy intensity of the economy (Factor 3) against per capita wealth.

Figure 1. Energy intensity of the Economy versus per capita GDP (data from World Bank Indicators).

Figure 1. Energy intensity of the Economy versus per capita GDP (2010 data from World Bank Indicators).

There was surprisingly little variation in Factor 3. The vast majority of the 131 countries used between 0.05 and 0.2 ktonnes of oil equivalent (i.e. the energy that would be produced by burning 50 to 200 tonnes of oil) to generate a million-dollars-worth of GDP. Rich and poor countries all clustered around this ratio – the world average in 2010 was 0.14. A few countries had higher energy intensities, mainly countries with vanishingly small GDP (and indeed tiny energy use in absolute terms) – this may reflect the largely non-monetary economies of such countries. Almost every other country had an energy intensity within a narrow range, although as the graph shows, a few countries with moderate or high per capita GDP also had high energy intensity (Iceland, perhaps, because it has abundant geothermal energy).

CO2 Intensity of Energy (Factor 4) showed more variation with wealth (shown in Figure 2). Countries with low per capita wealth had low CO2 intensity of energy, and that intensity rose very rapidly with increasing wealth. That surprised me – I had expected that the poorest countries would have high CO2 per energy use (being unable to afford wind, solar or nuclear power), but the reverse was the case, perhaps because those countries burn more wood and other ‘traditional biofuels’. Slightly wealthier countries buy more fossil fuels, and CO2 intensity goes up.

Figure 2. CO2 intensity vs GDP per capita.

Figure 2. CO2 intensity vs GDP per capita.

But as the graph shows, CO2 intensity of energy does not go up indefinitely as wealth increases. Very few countries had CO2 intensity above about 3.5. Even Qatar (which has the highest per capita income and per capita CO2 emissions in the world) had a relatively modest CO2 intensity of energy. Which is where chemistry comes in. If you burn a tonne of pure carbon (diamonds, for instance) you will get 3.7 tonnes of CO2 (the extra weight comes from the oxygen atoms). Actual fossil fuels have less carbon per tonne than diamonds, with methane (CH4) being the least ‘carbon-rich’ and producing about 2 tonnes CO2 per tonne of fuel (converted to ‘tonnes of oil equivalent’). Coal and oil produce about 3 tonnes on the same scale. So the amount of CO2 emitted must be in the range 2 to 3.7 tonnes CO2 per tonne of fossil fuel burned. This is what I term the ‘diamond law’. It’s named, of course, in homage to Roger Pielke Jr’s ‘Iron Law‘.

Of course that does not mean that the CO2 intensity of energy cannot be below 2. Countries can produce energy without large net CO2 emissions (e.g. by using nuclear, hydroelectric or renewable power sources). So, to investigate that, we can plot the CO2 intensity of energy against the fraction of fossil fuel used to produce energy (another World Bank indicator) as in Figure 3.

Figure 3. CO2 intensity of energy versus fossil fuel fraction of energy

Figure 3. CO2 intensity of energy versus fossil fuel fraction of energy

As expected, there’s a very close relationship between CO2 intensity of energy and fraction of fossil fuels used. Of course, the relationship should be close, as they both contain essentially the same indicator. CO2 emissions are not measured directly, but by adding up the sources of CO2 – and that is mainly the amount of fossil fuel burned in each country. The graph is exactly as expected, almost all countries whose energy comes mainly from fossil fuels had CO2 intensities close to 3 tonnes per tonne of fuel burned, while those with very low fossil fuel fractions had very low CO2 intensity of energy. So far, so good (for chemistry) – but what about the countries that were well above or below the line?

So I calculated the ‘CO2 intensity of fossil fuel’ (CO2 intensity of energy divided by the fossil fuel fraction of energy), the amount of CO2 produced from every tonne of fossil fuel burned. Just as the ‘diamond law’ predicted, almost every country produced at least 2 tonnes of CO2 per tonne of fossil fuel burned, whether fossil fuels contributed a low or high proportion of its total energy (Figure 4).

Figure 4. CO2 intensity of fossil fuel versus Fossil Fuel fraction of energy

Figure 4. CO2 intensity of fossil fuel versus Fossil Fuel fraction of energy

Several countries produced ‘too much’ CO2 per tonne of fossil fuel, that is, they produced more molecules of CO2 than there were carbon atoms in the fossil fuel burned – a chemical impossibility if that were the only source of CO2. But there are possible reasons for higher ratios. CO2 could be emitted from non-fuel sources (land-use changes, agriculture etc) or the country could export a lot of electricity. Of course there could also be errors in CO2, fuel or energy accounting.

But what should we make of the two countries that produce less than 2 tonnes CO2 per tonne fossil fuel (Moldova and Singapore)? Have these countries implemented large-scale Carbon Capture and Storage (CCS) without telling anyone? I don’t think so.

Singapore is the most extreme outlier, apparently producing only 0.4 tonnes of CO2 per tonne of fossil fuel burned, a fifth of the minimum that the ‘diamond law’ predicts. It is (chemically) impossible that this result can be right. The World Bank data for Singapore since 1990 shows a rapid fall in CO2 emissions and an increase in energy use, despite little change in the fossil fuel fraction of energy (above 97%). These figures cannot all be true – while minor emissions reductions can be achieved by changing fuel types, CO2 emissions cannot fall that much if more fossil fuel is burned – again, it’s ‘just chemistry’. So I looked more closely at the sources of the World Bank’s data.

The World Bank uses data from the US Carbon Dioxide Information Analysis Center (CDIAC) for CO2 emissions and from the International Energy Authority (IEA) for total energy use and fossil fuel fraction. IEA also reports CO2 emissions in its Key World Energy Statistics, but the IEA’s numbers for Singapore were much higher than those of the World Bank/CDIAC for 2008 to 2011. Figure 5 shows Singapore’s CO2 intensity of fossil fuel calculated from both sets of figures.

Figure 5. CO2 intensity of fossil fuels over time (World Bank (WB) and International Energy Authority (IEA) data compared)

Figure 5. Singapore’s CO2 intensity of fossil fuels over time (World Bank (WB) and International Energy Authority (IEA) data compared)

I have no idea what caused the discrepancy in the CO2 emissions for Singapore from the two sources. But I am sure that the World Banks’s numbers since 2003 are ‘chemically impossible’ while the IEA’s numbers give Singapore a CO2 intensity of fossil fuel of just over 2, consistent with the ‘diamond law’. This ‘law’ – derived entirely from the chemistry of carbon – therefore provides a useful check on the plausibility of reported CO2 emissions data.


3 thoughts on “Kaya Identity part II – and a ‘diamond law’?

  1. Pingback: A Graphical Look at the Kaya Identity | My Garden Pond

  2. 1. Are you including natural gas as a fossil fuel? Given that Coal is allegedly produces twice the emissions. 2. Surely the efficiency with which the fuel is converted into energy is important. 3. The fact that Singapore has a low number of private cars per population (49 per 1000 people) and that the total distance traveled by all land transportation is tiny compared with anywhere else in the world plus the economies of scale built into its minuscule footprint on the planet should be taken into account. Interestingly, Iceland has the 5th most cars in the world (745), ahead of Australia at 7th with 717!

    • HI Scott, many thanks for commenting. I read your post on WUWT.

      1. Yes, natural gas gives the low end of the range of CO2 intensity (~2 tonnes/ tonne fuel) while coal and oil give at least 3 tonnes of CO2. That’s why there is a range in Figs 4 and 5.

      I should note that the range is a slight approximation as the datasets show all fuels converted to ‘tonnes of oil equivalent’, and I can’t calculate the exact ratio for each fuel without knowing the precise assumptions used in that conversion (I used conversion factors reported by DECC). Even then, it would still be an approximation, as not all coal has the same carbon content per tonne, and the same goes for oil and gas of different chemical compositions.

      2. The CO2 intensity of fossil fuel is just the CO2 emissions from burning the fuel and is not affected by what is done with the energy (the fuel could be burned with zero useful energy production, it would not affect the analysis). The issue of efficient energy production is of course important, but does not appear in that factor, which is just the total CO2 emissions divided by all the fossil fuel used in the year. The total amount of energy produced is removed from the equation (that is, the variables on both axes in Figure 3 are each divided by total energy). It’s an interesting question, I plan to do some more calculations to see whether the efficiency of energy production is related to any of the other variables, but it doesn’t affect the analysis above.

      3. Countries use energy in vastly different ways, as you say. And that does indeed depend on land area among many other things. But my analysis strips all that out and simply asks, ‘how much CO2 was produced from each tonne of fossil fuel actually used?’ Even if Singapore only contained a single car, that car could not produce less CO2 than the carbon in the fuel it burned. I’m still trying to understand the discrepancies between the two datasets for Singapore, and if I find out more I’ll add it to the post.

      Thanks again for your thought-provoking questions.

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