I wasn’t going to write another post today but I’ve just come across a new Watts Up With That (WUWT) post by Roger Pielke Sr. The title of the post is Radiative Forcing, Radiative Feedbacks and Radiative Imbalance – The 2013 WG1 IPCC Report Failed to Properly Report on this Issue. I’ve got to say that I’m amazed by this post as it seems to be an incredibly embarrassing mistake for a professional climate scientist to make. It seems as though Roger Pielke Sr does not understand the difference between a radiative forcing an energy imbalance.
The basic premise of Roger’s post seems to be that the IPCC has reported that trhe radiative forcing change since 1750 is 2.29 Wm-2. On the other hand the IPCC reports that the average energy imbalance for the period 1971-2010 is 0.59 Wm-2 while for the period 1997-2010 it is 0.71 Wm-2. Just for completeness, the energy imbalance calculated for these periods is the average rate (per square metre) at which the Earth has been accruing energy. Roger then goes on to say
Thus, assuming that a large fraction of the global average radiative forcing change since 1750 is still occurring, the global average radiative feedbacks are significantly less than the global average forcings; i.e. a negative feedback.
Roger then includes the following relationship
Radiative Imbalance = Radiative Forcing + Radiative Feedbacks
and, if I understand him correctly, is suggesting that because the Radiative Imbalance is less than the Radiative Forcing that the Radiative Feedback is then negative. He’s then suggesting that the IPCC has got something fundamentally wrong.
However, Roger is so wrong that I am amazed that a climate scientist with Roger Pielke Sr’s credentials could actually have made such a mistake. As provided in a comment from Tom Curtis, the IPCC definition of a forcing is
“Radiative forcing is the change in the net, downward minus upward, irradiance (expressed in W m–2) at the tropopause due to a change in an external driver of climate change, such as, for example, a change in the concentration of carbon dioxide or the output of the Sun. Radiative forcing is computed with all tropospheric properties held fixed at their unperturbed values, and after allowing for stratospheric temperatures, if perturbed, to readjust to radiative-dynamical equilibrium. Radiative forcing is called instantaneous if no change in stratospheric temperature is accounted for. For the purposes of this report, radiative forcing is further defined as the change relative to the year 1750 and, unless otherwise noted, refers to a global and annual average value. Radiative forcing is not to be confused with cloud radiative forcing, a similar terminology for describing an unrelated measure of the impact of clouds on the irradiance at the top of the atmosphere.”
The important point is in bold. The radiative forcing is based on the change in irradiance assuming all tropospheric properties are held fixed, and it is measured relative to the year 1750. If the Earth’s tropospheric properties had indeed remained fixed since 1750, then the radiative imbalance would equal the radiative forcing (there shouldn’t be any feedbacks as the tropospheric properties haven’t changed). However, surface temperatures have risen by 0.8oC since 1750. Using F = σ T4, you can show that this corresponds to an increase in surface flux of about 4.3 Wm-2. If the radiative forcing has increased by 2.29 Wm-2 while the surface flux has increased by about 4.3 Wm-2, how can the feedbacks be negative (especially considering that the radiative imbalance is still 0.71 Wm-2).
The equation that Roger Pielke Sr should actually be using is
ΔQ = ΔF – λ ΔT,
where ΔQ is the radiative imbalance, ΔF is the radiative forcing (measured relative to 1750), ΔT is the change in surface temperature over the same time period, and λ is essentially the climate sensitivity. Basically, the rise in temperature acts to reduce the actual (current) forcing so that the current energy imbalance is determined by how much the radiative forcing has been reduced through the change in surface temperature that has also occurred since 1750.
In fact, one can actually go a step further. It is well accepted that a doubling of CO2 produces a change in radiative forcing of 3.7 Wm-2 which alone causes a rise in temperature of 1oC. If you take Roger’s numbers (ΔQ = 0.71 Wm-2, and ΔF = 2.29 Wm-2) and add that ΔT=0.8oC, then you get that λ = 1.975 Wm-2 per oC. This is then 0.506oC per Wm-2 which means the equilibrium surface temperature would rise by 1.9oC due to a doubling of CO2. This is actually lower than more detailed estimate using the same technique (e.g., Otto et al. get around 2oC) and lower than other estimates (paleo-climatological and modelling estimates are close to 3oC). However, the fundamental point is that even Roger’s own numbers suggest that feedbacks have to be positive.
This, in my opinion, is quite remarkable. This is a trivial mistake for a professional climate scientist to make. I have no real problem with people making mistakes. That’s perfectly fine and happens all the time (to me at least). However, for a high-profile climate scientist to claim that the IPCC have made some fundamental mistake when they haven’t, is something that I think needs to be addressed. Having said that, I believe that this error has been pointed out to Roger Pielke Sr a number of times (according to Gavin Schmidt at least), so I won’t be holding my breath.