Present concentration of carbon dioxide gas in the atmosphere is 31 per cent above the pre-industrial level, and we also know from the Vostock ice core that it is now higher than it has been any time in the last 420,000 years; furthermore, using information from sediments, we know it is likely to be higher than at any time during the last 20 million years.

The 9 Gt/yr of carbon dioxide (or its equivalent, expressed as carbon: 9 / 3.664 = 2.5 Gt carbon) is important, because if every human being were to be allowed the modest emission of 4.5 tCO2/yr, then, by simple arithmetic, human population would need to be 2 billion. In order to gauge the modesty of that 4.5 tCO2/cap/yr, we may note that the average citizen of the USA emits about 20 t/yr, the average European 10 t/yr, the average Canadian and average Australian 16 t/yr.

The idea that renewable energy can substantially replace fossil fuels - although widely canvassed and to be a central tenet of UK energy policy - has yet to be translated into reality; therefore the 9 GtCO2/year figure is an emissions limit which needs to be applied while fossil fuels last, and this deserves an in-depth study.

Engelman (1994), in Stabilizing the Atmosphere, was the first to indicate the 9 GtCO2/yr figure [8.9 Gt, p27]. He filled in the background [p40]as follows: 'This was also the year [1990] used by the scientists advising the Intergovernmental Panel on Climate Change for their estimate that a 60% to 80% reduction in CO2 emissions [from the 1990 level of 22.3 billion tonnes a year] would result in stabilisation of atmospheric concentrations of that gas at 353 parts per million.' Note, incidentally, that Engelman uses 353 parts per million ("ppm") as the 1990 carbon dioxide figure, whereas in Vital Signs (2002), p. 53, a figure of 354 is listed (a minor difference). Using carbon emission data from the same edition of Vital Signs, a 60% reduction implies an emission limit of 5.931 x 0.40 = 2.4 GtC/yr, and an 80% reduction implies an emission limit of 5.931 x 0.20 = 1.2 GtC/yr. Note that we have now switched to using carbon weights (following the recent tendency). The switch is easy, since 1 tC = 3.664 tCO2. Note also that the IPCC range of 1.2 to 2.4 GtC/yr, estimated as being required to achieve stabilisation at the 1990 level of 353 ppm, lies below the 2.5 GtC/yr that is being considered here as a benchmark.

Profiles in Carbon [Engelman, 1998, p15] sets out the background somewhat similarly as follows:

The Intergovernmental Panel on Climate Change (the IPCC, a panel of hundreds of scientists working under UN auspices) suggested that a reduction of at least 60% in CO2 emissions from their 1990 level [of 22.3 billion tonnes] would be needed to stabilize carbon dioxide concentrations at the 1990 level of 353 parts per million by volume. Current (2003) CO2 concentrations are above 370ppm.

There is a possible ambiguity as to whether that means a 60% reduction in emissions from burning fossil fuels, or a 60% reduction in all the emissions humans are responsible for. However, common sense makes the requirement clear. It would be unwise to anticipate decreases in the amount of carbon released from deforestation and change of land use, so it comes down to how much we must reduce our emissions from burning fossil fuels. That is what we will consider.

Our purpose here is not to just to accept an IPCC figure, but to look at the underlying reasons, so let us start by taking a datum from page 10 of Stabilizing the Atmosphere, namely that there are 2,750 billion tCO2 in the atmosphere, or 2,750 billion tonnes/ 3.664 = 750 GtC. This is confirmed by a note to a diagram on page 23 of Houghton (1997), which gives 750 GtC as the weight of carbon in the air, as carbon dioxide, in 1990.

Combining this 750 GtC with the concentration of 353 ppm, we can deduce that each ppm is equivalent to 750 / 353 = 2.125 GtC.

Over the past decade, the concentration of carbon dioxide has increased by 15.4 parts per million by volume (the 1990-2000 rate). Perhaps more striking is the fact that there has been an increase in the carbon held in the atmosphere, as carbon dioxide, amounting to 15.4 x 2.125 = 33 billion tonnes, equal to 15 cubic km of solid graphite. Note that it is necessary to include the words, "as carbon dioxide", since carbon is also held in the air in the form of methane (CH4), and other gases, which are also increasing.

At the concentration of CO2 in 2000, 369 ppm, the amount of additional carbon that is now in the atmosphere as CO2, compared to the pre-industrial level of 280 ppm, is (369 - 280) x 2.125 = 189 GtC, more easily envisaged as a volume of solid graphite of 85 cubic kilometres. Taking this investigation further, as a matter of simple logic, in order to stabilize carbon dioxide at any particular concentration, the following relationships must hold true:

1. Excess emissions = yearly increment in atmospheric carbon.
2. Allowable emissions = annual emissions - excess emissions.

Accurate measurement of carbon dioxide concentrations only started in 1958. Working in decade-long periods (i.e. using increments based on an annual average over each past decade), we can work out allowable emissions as follows:

* Note: Allowable emissions are emissions which are allowable if the then current level of CO2 is to be kept stable. Both actual emissions and allowable emissions are seen here to be rising. This is because as carbon emissions rise, more carbon is absorbed by land and sea.