In praise of... basic numeracy, oh, and solar power

We will surely never solve the problem of global warming until basic numeracy is required for in the recruits to the organisations that claim to represent our views. How can you have a view without a feel for the numbers?

The Guardian's recent article "Desert cities are living on borrowed time, UN warns" recently committed the cardinal sin of saying "square miles" (that is, x square miles) rather than "miles square" (that is, x2 [squared] square miles). Doh! My old maths teacher would have given them a 5 minute lecture about what the consequences would have been had he made such a mistake during the war... and then belted them round the head. At least the Graunida has now added the correction to the original article on its website.

Obviously the good old Beeb did not want to be outdone. In a direct quote(!!) [though one that is never terminated] in their report on the start of work on a solar power array being built in Portugal they claimed: "It will save 30 tonnes of CO2 emissions...". Over an area of 60 hectares this would be less than 0.5 tonnes/hectare, far less than planting trees. Double doh! This is where basic numeracy comes in. How can you report on this sort of stuff without some kind of a feel for the figures?

Thanks to the Google brothers we can find the same story reported by dozens of news organisations from Business Week to the local press in Nova Scotia to China and India (which unfortunately gives a larger site). If I were a (modern, online) news organisation I'd have thought the low switching cost of the broadband user would put a high premium on preserving a reputation for accuracy, but seemingly not.

Incidentally, the figure of emissions saved is 30,000 tonnes (or maybe tons of a British Imperial or American variety, media "opinion" is divided - what does a 10% difference matter?) of CO2 PER YEAR, which NONE of my sample of media outlets managed to copy from the Press Release. A report from GE did manage to clarify this point. And what's more it added the crucial proviso "compared with equivalent fossil fuel generation", because if the coal, oil or gas doesn't stay in the groundyou haven't saved anything, a point, dear reader, that we may return to at a later date.

When we start to think about renewable energy, a crucial point is the amount of land required. This often seems to be forgotten. I mean, it's only a resource we have been fighting over for millennia. At 30,000/60 = 500 ton[ne]s CO2 emissions saved p.a., solar power seems pretty effective. Compare that to a range from negative values to 7 tonnes absolute tops for biofuels. Hmm...


Warning: the following is in note form. I may or may not get round to tidying it up.

A quick check:
Back to that Guardian article. 800 km * 800 km is 640 000km2 which is 64 million hectares. At 0.2 MW/hect (11 MW over 60 hectares) as implied by the Portugal plant, the Sahara box gives a total generating capacity of approx. 13 million MW, that is 13 tera (10 exp 12) Watts.

Over a year this is 13 * 365 * 24 = approx. 110 * 10 exp 15 [peta] Watt hours. But the Sun doesn't shine all the time, so let's give it 20% efficiency, so we have approx. 20 * 10 exp 15 Watt hours.

This compares with current world energy consumption of approx. 400 "quadrillion" [that is, peta] BTUs. i.e approx. 400 * 0.3 (1 BTU = approx 0.3 Watt hours) * 10 exp 15 = 130 * 10 exp 15 [aka peta] Wh.

Another check: Philip's World Atlas (p.38) gives a figure of 9,124.8 million tonnes oil equivalent for 2001 world energy consumption. According to no less an authority than BP 1 tonne of oil equivalent is 40 million BTU, so 2001 world energy consumption was (rounding) approx. 9 * 10 exp 9 * 40 * 10 exp 6 BTU, i.e. 9 * 40 = 360 * 10 exp 15 ["quadrillion" or peta] BTU, not too far off the figure above.

So it seems that when the Gruniaad claims this area could generate "enough electricity for the whole world", perhaps they mean all the electricity we're generating now, NOT all the power we require. This would require an area 6.5 times bigger by my rough calculation, that is 6.5 * 640,000 km2 = getting on for 4 million square kilometres. Still less than half the area of the Sahara. Unless of course the 11MW ouput is the average and not the peak. Be nice if someone told us.

This is just under 1% of the area of the world (land and sea), which seems a bit high compared to Wikipedia's quote: "Solar cells can convert around 15% of the energy of incident sunlight to electrical energy. If built out as solar collectors, 1% of the land today used for crops and pasture could supply the world's total energy consumption."

Odd. Solar influx at top of atmosphere is (on average) 240 Watts/m2 = 2.4 MW/hectare day and night. At 0.2 MW/hectare this plant is reasonably efficient, though nowhere near 15% (assuming Portugal gets an average amount of sunlight).