Guest Post by Willis Eschenbach
The IPCC says that the expected change in temperature arising from a change in forcing is equal to the change in forcing times the climate sensitivity. The IPCC provides values we can use to estimate the total human and natural forcing change since 1850. The IPCC also proves estimates for the climate sensitivity. These can be multiplied to provide the IPCC expected temperature change since 1850. The value derived (best estimate per IPCC numbers = 1.4 °C warming since 1850) is twice the observed warming (HadCRUT best estimate = 0.7°C warming since 1850).
Recently I became puzzled by what seems to be a glaring discrepancy in the official IPCC numbers. The IPCC estimate of climate sensitivity is +3 [+2 to +4.5] °C per doubling.
We also have the IPCC estimate of the change in forcing since 1750, in Watts per square metre (W m-2). The human contribution to that forcing is given by the 2007 IPCC Summary for policymakers as:
The understanding of anthropogenic warming and cooling influences on climate has improved since the Third Assessment Report (TAR), leading to very high confidence that the globally averaged net effect of human activities since 1750 has been one of warming, with a radiative forcing of +1.6 [+0.6 to +2.4] W m-2.
This represents the best estimate plus [lower and upper bounds].
Now, a doubling of CO2 is estimated by the IPCC to produce a change in forcing of 3.7 W m-2. So if we divide the climate sensitivity (in degrees per doubling) by 3.7, we will get the climate sensitivity expressed in units of degrees per W m-2. This gives us the result:
Climate Sensitivity = +0.8 [+0.5 to +1.2] degrees per W m-2.
Finally, we know that sensitivity times the change in forcing gives us the temperature change. Using the IPCC estimates of both, this gives us:
+0.8 [+0.5 to +1.2] degrees per W m-2 times +1.6 [+0.6 to +2.4] W m-2
= +1.3 [+0.4 to +2.2] degrees of warming from human activities since 1750. (Errors throughout have been assumed to add in quadrature.)
Now, we don’t have very good temperature data before 1850, so we need to adjust for that. However, there was very little human effect on the climate from 1750 to 1850. CO2 levels were only slightly lower in 1750 than in 1850, the industrial revolution was in its infancy, little fossil fuels were burnt, sulfur emissions were negligible, no fluorocarbons were emitted. Since the 1750-1850 anthropogenic contribution is very small compared to the total anthropogenic forcing, that IPCC based calculation of temperature change from humans of +1.3 [+0.4 to +2.2] degrees can be taken as the best estimate and bounds of the human caused temperature change since 1850.
For our final estimate, in addition to the human forcings since 1850 we need to add the natural forcings. The IPCC includes only one of these, solar forcing. The IPCC estimates that changes in solar forcing in the ~250 years since 1750 was 0.12 W m-2. For our rough calculations, we can make a crude but adequate estimate that three fifths of this change occurred since 1850. Adding solar forcing to the earlier equations makes the IPCC calculated temperature change from human and natural forcings combined since 1850 slightly greater, at +1.4 [+0.4 to +2.3] degrees.
Now, here’s the problem with that, and it’s a very big problem. According to the HadCRUT dataset (monthly dataset here, with notes here), the total temperature change 1850 – 2006 is +0.7 [+0.5 to +0.9] degrees. In other words, the world has warmed by around three-quarters of a degree (best estimate 0.7°C) since 1850. That’s nowhere near 2.3°C, the high end of what the IPCC says should have happened since 1850. It’s only half of the IPCC’s most likely number. It is just above the IPCC’s lower bound. So the IPCC method, using the IPCC numbers, way overestimates the historical temperature rise.
What can we conclude from this mismatch between observations and calculations? There are a number of possible explanations, in no particular order.
1. The sensitivity numbers are too high, and the forcing numbers are correct. If that is the case, the sensitivity is +1.5 [+0.5 to +2.4] degrees per doubling of CO2, a much lower and narrower range than the +3 [+2 to +4.5] range espoused by the IPCC.
2. The forcing numbers are too high, and the sensitivity numbers are correct. That gives us a calculated change in forcing since 1850 of +0.9 [+0.5 to +1.4] W/m2. Again this is much lower and more narrowly bounded than the canonical IPCC range of +1.7 [+0.7 to +2.5] W/m2 including solar. Note that in both this and the previous case, the relatively narrow bounds of the temperature observations have constrained narrow bounds on the underlying forcings or sensitivities.
3. Both the sensitivity and the forcing numbers are too high. This would limit possibilities to values such that the product of the two give us +0.7 [+0.5 to +0.9] degrees of warming. If the reductions were proportional, the forcing and the sensitivity would each need to be cut to about 70% of the IPCC numbers.
4. There are other mechanisms at play (e.g. cosmic rays, plankton aerosol production, thunderstorms) that the IPCC is not accounting for.
5. I’ve made a foolish mathematical mistake.
6. Climate may not obey a linear relationship between forcing and temperature change. My calculations are based on the IPCC assumption that a change in temperature can be calculated as a constant called “climate sensitivity” times the change in forcing. However, climate sensitivity may not be (and in my view is not) a constant. Instead, in my view climate sensitivity is a function of T, which changes the equation.
7. This is the “missing heat” that Trenberth referred to.
8. Something completely different that I haven’t thought of.
I couldn’t even begin to say which of those, or how many of those, if any of those, are actually going on …
Anyhow, that’s the oddity. If we multiply the IPCC historical forcing change since 1850 times the IPCC climate sensitivity to get the IPCC estimated temperature change since 1850, the result is nothing like the historical temperature change. The high IPCC estimate (2.3°C) is three times the actual change (0.7°C) since 1850. Clearly, something is wrong. Depending on which explanation we choose, we have different conclusions, none of which seems compelling.
Assistance and ideas welcome …