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# Arithmetic for sceptics

The link between global warming and CO2 production from industrial use of coal and oil, as well as wood-burning during massive deforestation, is certainly clear, precisely because the CO2 exists in the atmosphere. Whilst transparent for visible light, it is a very strong absorber of long wavelength light (i.e. heat radiated from the surface temperature of the earth). Because we cannot see in the long wavelength, infrared region, we lack an intuitive idea of how absorbing the gas is likely to be, so I will offer a very simplistic analogy for light that we can see.

If we start with a piece of pure aluminium oxide crystal a few millimetres thick, it will look like a clear piece of glass. Indeed, because it is a very hard material, it is often used as a very tough ‘glass’ for watch faces, so it is something we have seen many times. If we now add some contaminants at, say, 200 parts per million, then it can absorb light and become coloured. The colour depends on the particular material we add to it. If we choose chromium, it will transform into a very nice red ruby; titanium will give a blue sapphire; and nickel a yellow sapphire. So in terms of light absorption, the level of parts per million can be quite effective.

The more difficult question is whether our industry has added enough to make a significant change. Climate change and the role of CO2 is such a hot political and scientific topic that there are many conferences, opinions, and experts using data that most of us have never seen, and computer modelling that may not be infallible. I am not a sceptic, but I have seen many overexcited claims when reputations are at stake. Therefore, I want to consider if I could attribute the increase in CO2 gas in the atmosphere directly to our industrial output. My mathematics is trivial. We know both the surface area of the earth and the air pressure on the surface; therefore by multiplying the two together we can estimate the total weight of the atmosphere. The number is quite large at 5,600 million million tons (in alternative notation this is written as 56 X 1014 tons). If we burn one ton of carbon into CO2 gas, we would produce 2.8 tons of it because we added oxygen during the conversion. For one ton of coal, there will be a little less because of ash residues. Currently we are now consuming 9 billion tons of coal per year.

We need to consider how much CO2 could arise from the use of oil. Current consumption is around 34 billion barrels per year, which is roughly 5 billion tons. The amount turned into gas, rather than other products, will be somewhat less. Deforestation is hard to assess, in part because it also reduces the take-up of CO2 from the atmosphere. Nevertheless, the arithmetic says each year we are now adding a mass of CO2 of at least 2 parts per million. Indeed, it will easily explain why, since the start of the Industrial Revolution, we have gone from 180 to around 360 parts per million. The rate of rise and use of fuels offers a similar pattern over time.

I am therefore convinced that we are responsible for introducing the additional CO2 into the atmosphere. The only surprise from my simple arithmetic is that the rise has not been greater. Therefore, so far we have been lucky that natural processes are removing some of the gas from the atmosphere. This is not totally good news, as it makes the oceans acidic, and hence will perturb, or destroy, corals and other ocean life. The arithmetic confirms that our industrial input of CO2 into the atmosphere is more than enough to have driven the rising values since the start of the Industrial Revolution.

The estimates of actual temperature increases that will result are a totally different and a far more complicated problem. The only reliable fact is that we have good records (especially in the UK) that say there is an upward drift in temperature. The changes certainly have a pattern that matches the CO2 increases, and therefore the inevitable conclusion is that, since we are still adding more pollutants, then the rise in temperature will continue.

A pragmatic comment is that in the early history of the world, there have been periods when the CO2 concentrations were very much higher, as was the global temperature. These were times when our present crops and creatures (including us) could not have survived. So viewed in terms of survival of the planet, the greenhouse effect is just a passing phase. Viewed in terms of humanity and the world as we know it, there is potential disaster and possible annihilation. Maybe the next intelligent species will do better.

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