Another round on greenhouse

Ken Parish responds to my piece on the rate of global warming with a range of issues. I’ll start with the easy ones. Ken notes what appear to be two offsetting errors, saying

[John] says the current warming record shows a trend of 0.2 degrees C per decade. In fact, it’s about 0.4 degrees over the last 26 years (which is somewhat lower than John says). John also observes that IPCC says about half of this increase is attributable to human emissions of greenhouse gases. In fact IPCC says just under 3/4 is attributable to human emissions. As you can see, this amounts to approximately 0.1 degrees C per decade from human greenhouse emissions. Hence, as I’ve observed before, a straight line extrapolation of current warming trends results in an approximate temperature increase of about 1 degree C by 2100. John reaches that figure (because his two errors cancel each other out), and agrees that a warming of that magnitude and speed isn’t too much to worry about.

I’ve been a bit rushed during the move, and have been making a few minor errors, but this time I’m pretty much in the clear. I ran a regression estimate for the trend which came out at 0.196 degrees per decade and I knew that the IPCC had attributed 0.1 degrees to emissions so I worked backward to get 1/2.

Ken also makes some good points about population growth, saying that UN estimates have been revised downwards. However, the most contentious IPCC estimates (the A scenarios) have population stabilising around 9 billion, which is the estimate cited by Ken.
The big issue relates to the question of whether if economic growth continues at , say, 3.6 per cent per year, and no specific mitigation action is taken, emissions will keep growing or remain stable. I assert that, under Business As Usual emissions are likely to double. Ken suggests that this requires that the rate of economic growth should also double to 7.2 per cent. I say that as long as GDP grows steadily at a constant rate, so will emissions and therefore the rate of growth of atmospheric concentration and the rate of increase of equilibrium temperature.

Ken’s argument reflects a confusion between stocks, flows and acceleration. HTML is not well-suited to resolving this kind of thing, but I’ll try my best. Under the standard model in which equilbrium temperature depends on the concentration of greenhouse gases, the following types of variables should move together (not necessarily proportionally, since there are lags, sinks, feedbacks etc)

Concentration of CO2
Equilibrium Temperature
Cumulative Emissions
Cumulative world output of goods &services

Addition to concentrations of CO2
Rate of change in equilibrium temperature
Annual emissions
Annual output (GDP)

Acceleration in growth of CO2 concentration
Acceleration in temperature change
Rate of growth of annual emissions
Rate of growth of GDP

So with a constant growth rate of GDP (and BAU) , output, emissions and the rate of temperature change all rise steadily. Because the energy-intensity of GDP declines with rising income, you need something like a quadrupling of GDP tp get a doubling of emissions, but this doesn’t affect the main point.

It’s not easy to see this by eyeballing the data for a decade or two – in fact, it’s quite difficult statistically to distinguish between a linear trend and an exponential if the growth rate is modest. But the basic logic set out above is clear-cut. I’ll try soon to make available a PDF file in which this is proved algebraically – words are really cumbersome for this kind of problem.