BOE: Quantifying Catastrophe
This is a rather complex chart, but we can break it down pretty quickly.
The subchart (b) is the probability distribution function for a normal fit to the airborne fraction of CO2 emissions from the ultimate resource recovery (URR) of aggregated fossil fuels plus the preindustrial baseline of 280 PPM CO2 and the non-fossil fuel component of landuse and cement manufacturing at 35 PPM CO2. The currently proven reserves are set at -2 sigma. The ‘most optimistic’ scenario (with an unconfirmed reference to the Oil & Gas Journal) is set at +1 sigma. The fit has a maximum likely emission of 6100 gigatonnes of CO2, with a 1700 Gt standard deviation. After retaining only the airborne fraction and adding in the preindustrial and non-fossil fuel components, we calculate a probable future CO2 concentration of 769 PPM with a s.d. of 109 PPM. The figure below shows only the fossil fuel component – add an additional 315 to account for the preindustrial baseline and non-fossil component.
The subcharts (a) show the probability distribution function for the equilibrium climate sensitivity. The PDF was visually fitted to the Meinshausen 2009 PDF with a gamma distribution. The gamma distribution parameters are α = 12, β = α/3.25. This provides an 85% probability of the ECS lying between 2C and 4.5C with a max at 3C.
Previously, we examined a set of temperature responses to a discrete range of climate sensitivities and CO2 scenarios. The ECS range was set at the [2, 3, 4.5]. The CO2 concentrations with the range [551, 660, 769, 878, 987] PPM. It was noted that with a CO2 concentration in the upper 50% of the range and the ECS with the highest value, that there exists a possibility of warming of 6C, one of my two suggested limits for ‘catastrophe.’ The other limit – 1000 PPM CO2 – also lies within the range of possibilities, but outside the 2-sigma limit.
Instead of relying on discrete scenarios for fossil fuel production and climate sensitivities, we can build a near-continuous range of both the temperature responses and their probabilities by creating a matrix of temperature results as a function of ECS and CO2 and a corresponding product matrix of their probabilities. Chart (c) above is the probability distribution for the product of the PDFs for ECS and CO2 (fossil-fuel + non-fossil-fuel). The solid line is the contour for 50% probability. The dashed line is the contour for 84% probability. And the dotted line is the contour for 95% probability.
The temperature response is Chart (d). The green contours on this chart are the temperature responses (degC, leftmost contour = 1C) for various climate sensitivities (x-axis, degC) CO2 (y-axis) and CO2 emissions. I have retained the probability contours from the left hand side for the 2-variable PDF. Visual inspection indicates that there is a 50% likelihood that burning all the fossil fuels we can produce will have a net warming effect of about 2.5-5.5C.
We can use the two charts, the temperature responses and their probability distribution, along with the information calculated earlier for the CO2 distribution, and calculate the likelihood that we will exceed 6C or 1000 PPM CO2 which was one definition of CAGW that I offered in an earlier post.
b = matrix(CO2_VAL>1000,x,x) + matrix(DT_VAL>6,x,x) > 0
And the answer is …
Given our current knowledge of fossil fuel resources and climate sensitivity, there is a
8.6% 10% chance that if we burn all the fossil fuels available to us that temperatures will rise above 6C and/or atmospheric CO2 concentrations will exceed 1000 PPM.
Addendum: Moving the Goalposts
My original ‘intuition’ for the 6C and 1000 PPM CO2 limits were my (faulty) understanding of the maximums for the Cenozoic climate. My understanding was faulty. Cenozoic maximums appear to be more like 12C warmer than present with CO2 concentration peaking around 1200+ PPM CO2. There is essentially 0% chance that we will exceed either without additional feedbacks not accounted for in the ECS I have used here.
However, I have also seen how the climate ran at a max of about 4C warmer with a CO2 concentration near or below 500 PPM CO2 for the last 30 million years or so. We could use this as a marker of a critical threshold, if there is compelling evidence that the modern biosphere will fair poorly under Paleogene climatic conditions.
There is a 45% probability will exceed 4C warming and a near certainty that will exceed 500 PPM CO2. There is a 50% probability will exceed 4C warming and a near certainty that will exceed 500 PPM CO2.
20120528 I consider this whole BOE (“Back of Envelope”) series a work in progress and will be regenerating the charts now and then. They are date stamped if you want to save one off for some reason.
20120529 The code is now available here