In reply to Horace Heffner's message of Wed, 15 Mar 2006 22:03:49 -0900: Hi, [snip] >Polar carbon dioxide increasing at surprising rate. See: > >http://www.guardian.co.uk/science/story/0,,1729255,00.html > >"In 1990 this key cause of global warming was rising at a rate of 1 >part per million (ppm). Recently, that rate reached 2 ppm per year. >Now, scientists at the Mount Zeppelin monitoring station have >discovered it is rising at between 2.5 and 3 ppm." > >Horace Heffner
This is actually catastrophic. An exponential model doesn't rise steeply enough to cover the change in the rate of increase (i.e. the acceleration). Or more accurately if one uses the formula:- N = N0 x exp(t/T) then the first derivative is (N0/T) x exp(t/T) and the second derivative is (N0/T^2) x exp(t/T). One can determine T either by dividing the base formula by the first derivative, or by dividing the first derivative by the second derivative. If the current level is 380 ppm, and the current growth rate (i.e. the first derivative) is 2.7 ppm/yr, and this was 1 ppm/yr in 1990, then the second derivative ~= (2.7-1)/(2006-1990) = 0.106 ppm/yr^2. (Since this is a linear calculation based on a 16 year time difference, the actual current value is likely to be higher). The first method of determining T yields T = 380 ppm /(2.7 ppm/yr) = 140 y. The second method yields T = (2.7 ppm/yr)/ (0.106 ppm/yr^2) = 25.5 yr. Basically this means that the curve has recently been getting steeper more rapidly than the first method would indicate (the first method would yield a second derivative of 380/140^2 = 0.02 ppm/yr^2). The second method yields an acceleration that is 5 times larger. The implication is that even the second method yields a T that is too large. Yet even if we assume this second T (25.5 yr) is correct, it means we would hit the 500 ppm "tipping point" in 7 years time. We should therefore expect to hit it sooner. Horace please correct any egregious errors. Regards, Robin van Spaandonk http://users.bigpond.net.au/rvanspaa/ Competition provides the motivation, Cooperation provides the means.
