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Feature: Checking their homework

August 2009

For decades now we have heard how global warming is going to get us, how a doubling of atmospheric carbon dioxide will lead to scary amounts of warming. How's that working out?

First, a couple of boring numbers:

The IPCC (alt: IPCC) and the European Environment Agency both provide the formula for calculating change in radiative forcing (ΔF) in W/m2. For carbon dioxide (CO2) this formula is given as ΔF = αln(C/Co) where C and Co are the current and pre-industrial concentrations of CO2, respectively and α = 5.35. Some would immediately argue this overstates average net forcing from increasing atmospheric CO2 and we'd tend to agree but the inflated value is not important, at least, not yet -- call it an inbuilt "safety margin," if you like.

Atmospheric CO2 is presented in parts per million by volume (ppmv). There is no universal standard for what we mean by a doubling of CO2 and various numbers are used, most commonly 560 (2x280 -- the common pre-Industrial revolution reference) and 600 (2x300 -- presumably benchmarked from early in the Twentieth Century).

Since most people seem to conceive the situation as two times "natural," which we take to mean immediately pre-Industrial Revolution, we'll be using the former. From the above formula then, the change in forcing from a doubling of pre-Industrial Revolution atmospheric CO2 = 5.35 x ln(560/280) 3.7 Wm-2.

According to the National Academies' Climate Change Science: An Analysis of Some Key Questions (2001), doubling CO2 (to 600 ppmv) would lead to a forcing of about 4 W/m2, so we guess these figures are close enough for our purposes here.


"The sensitivity of the climate system to a forcing is commonly expressed in terms of the global mean temperature change that would be expected after a time sufficiently long for both the atmosphere and ocean to come to equilibrium with the change in climate forcing. If there were no climate feedbacks, the response of Earth's mean temperature to a forcing of 4 W/m2 (the forcing for a doubled atmospheric CO2) would be an increase of about 1.2 °C (about 2.2 °F). However, the total climate change is affected not only by the immediate direct forcing, but also by climate “feedbacks” that come into play in response to the forcing."

"As just mentioned, a doubling of the concentration of carbon dioxide (from the pre-Industrial value of 280 parts per million) in the global atmosphere causes a forcing of 4 W/m2. The central value of the climate sensitivity to this change is a global average temperature increase of 3 °C (5.4 °F), but with a range from 1.5 °C to 4.5 °C (2.7 to 8.1 °F) (based on climate system models: see section 4). The central value of 3 °C is an amplification by a factor of 2.5 over the direct effect of 1.2 °C (2.2 °F). Well-documented climate changes during the history of Earth, especially the changes between the last major ice age (20,000 years ago) and the current warm period, imply that the climate sensitivity is near the 3 °C value. However, the true climate sensitivity remains uncertain, in part because it is difficult to model the effect of feedback. In particular, the magnitude and even the sign of the feedback can differ according to the composition, thickness, and altitude of the clouds, and some studies have suggested a lesser climate sensitivity."

Climate Change Science: An Analysis of Some Key Questions, pp 6-7,
Committee on the Science of Climate Change
National Research Council

"Climate models calculate outcomes after taking into account the great number of climate variables and the complex interactions inherent in the climate system. Their purpose is the creation of a synthetic reality that can be compared with the observed reality, subject to appropriate averaging of the measurements. Thus, such models can be evaluated through comparison with observations, provided that suitable observations exist. Furthermore, model solutions can be diagnosed to assess contributing causes of particular phenomena. Because climate is uncontrollable (albeit influenceable by humans), the models are the only available experimental laboratory for climate. They also are the appropriate high-end tool for forecasting hypothetical climates in the years and centuries ahead. However, climate models are imperfect. Their simulation skill is limited by uncertainties in their formulation, the limited size of their calculations, and the difficulty of interpreting their answers that exhibit almost as much complexity as in nature."

Climate Change Science: An Analysis of Some Key Questions, p 15,
Committee on the Science of Climate Change
National Research Council

So, how's that working out in the real world? How could we tell?

The Carbon Dioxide Information Analysis Center provides Recent Greenhouse Gas Concentrations, complete with increased radiative forcing. Going by the July 2009 update Earth is already experiencing three-fourths of the increased forcing estimated from 2xCO2 (2.99 W/m2) from greenhouse gas changes alone.

Now, observations tell us that Earth responds quite rapidly to forcing changes, for example the range from 12 °C-15.8 °C and back each year as the greater land mass of the northern hemisphere receives more and less solar forcing with the changing seasons:

According to the IPCC's AR4 assessment for policymakers, "The total temperature increase from 1850 – 1899 to 2001 – 2005 is 0.76 [0.57 to 0.95] °C", so three-fourths of the expected forcing has delivered three-fourths of a degree warming...

Given that black carbon has been "blamed" for a percentage of estimated warming, as has solar activity and lets not forget land use change with only about one-third of estimated warming due to changes in atmospheric carbon dioxide, the chances of 2xCO2 delivering even 1 degree warming would appear, um... limited, much less the rather imaginative 3 °C proposed above.

And since carbon dioxide increases have so little effect on global mean temperature it should be obvious that spending fortunes restricting carbon dioxide emissions will also have irrelevantly small effect.


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