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 0.8^{o}C since 1750. Using *F* = σ *T*^{4}, 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

Δ*Q* = Δ*F* – λ Δ*T*,

where Δ*Q* is the radiative imbalance, Δ*F* is the radiative forcing (measured relative to 1750), Δ*T* 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 CO_{2} produces a change in radiative forcing of 3.7 Wm^{-2} which alone causes a rise in temperature of 1^{o}C. If you take Roger’s numbers (Δ*Q* = 0.71 Wm^{-2}, and Δ*F* = 2.29 Wm^{-2}) and add that Δ*T*=0.8^{o}C, then you get that λ = 1.975 Wm^{-2} per ^{o}C. This is then 0.506^{o}C per Wm^{-2} which means the equilibrium surface temperature would rise by 1.9^{o}C due to a doubling of CO_{2}. This is actually lower than more detailed estimate using the same technique (e.g., Otto et al. get around 2^{o}C) and lower than other estimates (paleo-climatological and modelling estimates are close to 3^{o}C). 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.

The sad thing is that for the purposes of Watts and Crew it really doesn’t matter if Pielke is wrong. They simply don’t care. They don’t care about Pielke or his embarrassment of his own reputation and they don’t care about science. Many plates of spaghetti have been slung from the table at WUWT and despite all it having slid off without leaving a trace on science itself it’s still left a big stain on the wall of the public mind. Doubt in the public mind is all that matters to Watts.

Members of the public as encounter Pielke’s invention as it is repeated endlessly in a myriad of newspaper and broadcasting reader forums and the like will find their eyes crossing as they try to absorb the details but the actual payload will be successfully delivered: “scientists are in complete disagreement.”

Wotts, having the opportunity to read Pielke’s views in a fuller context, I withdraw my earlier claim that he has made a mistake. Rather, I have been misinterpreting him as talking about feedback to the temperature response of a giving forcing, whereas he has been talking about the feedback in radiative terms to a given forcing.

It should be noted that discussing climate sensitivity in terms of a feedback on temperature responses is by far the most common convention. Thus AR5 defines a “climate feedback” as follows:

(My emphasis)

Taking the standard formula, ΔQ = ΔF – λ ΔT, we can define “radiative feedback” as – λ ΔT, and obtain Pielke’s formula. That is not so strange given that ΔF is positive is the upward radiation at the TOA reduces, while λ ΔT results in an increase in upward radiation at the TOA with increasing temperature. Rewriting the equation to align the signs of the terms produces Pielke’s equation.

We then find that,

expressing feedbacks in radiative terms, a feedback is positive, if and only if, the downward radiative imbalance at the TOAincreasesas a result of the effects of the feedback. Therefore, if increasing surface temperature reduces the downward radiative imbalance, it must be a negative “radiative feedback”.The obvious corollary is that there is a positive “radiative feedback” only if you have a runaway greenhouse effect. Indeed, even a zero “radiative feeback” will necessarily result in a runaway feedback response in temperature as the energy imbalance will increase temperature, but will never close the energy imbalance.

Translating this into a temperature feedback, however, we find that the temperature response to a doubling of CO2 with no temperature feedbacks is 1.2 C. Therefore, any temperature response greater than 1.2 C indicates a positive temperature feedback; and any less indicates a negative temperature feedback. A temperature response of 1.2 C indicates λ = 3.08 W m^-2 C^-1. If λ is more than that, you have a negative temperature feedback, whereas if it is less you have a positive temperature feedback. With λ = 0.1, for example, you require a 37 degree increase in GMST to achieve equilibrium for a doubled CO2 content –

but that would still constitute a negative “radiative feedback”. Indeed, unless λ =<= 0, the "radiative feedback" is negative.On this understanding, Pielke is not committing a blunder (which makes me much happier). He is, however, being needlessly obscure and positively inviting misinterpretation. He no where on the WUWT post discusses the implications of positive "radiative feedback", nor the relationship between "radiative feedback" and "temperature feedback". As nearly all discussions of climate sensitivity are in terms of temperature feedback, that has probably left most WUWT readers with the impression that the latest data indicates a temperature response to doubling of CO2 < 1 C. Nor does he discuss the expected temperature response of the data (taking it at face value), but merely chides the IPCC for not themselves doing so. (I believe the IPCC do in fact discuss it, and probably at length; but base their climate sensitivity estimates on more than just three datum points.)

Further to your calculation of climate sensitivity based on IPCC AR4 data, the IPCC states that the warming from 1901-1912 to be 0.89 C. Further, from figure 5.8a the mean reconstructed temperature (and the simulated temperature with lower solar variability) is about 0.2 C lower than that. Plugging those figures into the equation yields λ = 1.55, or a climate sensitivity for a doubling of CO2 of 2.4 C. The error margins are, of course, very wide indeed.

Tom, I’m going to have to think about this. I can see if we define -λ Δ

Tas the radiative feedback then the equation is the same as Roger’s. Okay, so I can now see that the rise in temperature could be regarded as a negative radiative feedback. What’s confusing me though is Roger’s discussion of water vapour. I realise that it should produce a positive radiative feedback but am confused as to how Roger is concluding (I think) that it has to be negative. For example his post finishes withOne obvious issue, as far as I can tell, is that Δ

Qis anthropogenic forcings only and λ is the sensitivity to changes in anthropogenic forcings (i.e., the 3.7 Wm-2 is the adjusted forcing due to a doubling of CO2 and so doesn’t include feedbacks.) So, water vapour isn’t explicitly part of this equation. The feedbacks come from determining λ. If λ < 3.08 Wm-2 per oC doesn’t imply that there has to be a positive radiative feedback (without necessarily knowing what produces it). So, even though one can recast Roger’s equation to be the same as the one I’ve used here, I’m still not convinced that one can conclude that net radiative feedbacks are negative.Yes, I did realise that I could have gone and found numbers that were more correct but just wanted to show that even just plugging in Roger’s numbers would produce an ECS that was substantially bigger than 1oC.

You are correct about his comment on water vapour feedback, and cloud radiative feedback. In my comment, I was focused on correcting my error in interpreting Pielke and its ramifications, rather than on any particular errors by Pielke. However, when the IPCC state that the water vapour feedback and the cloud radiative feedback are positive, they are definitely talking in terms of the temperature feedback. They are asserting that, for a given initial perturbation of temperature, this will these feedbacks will result in a further perturbation such that the final temperature response will be larger than the initial perturbation.

Thinking this through, Radiative feedback = -λΔT. Assume that the radiative feedback is positive. It follows that -λΔT when ΔT is positive, and hence that to have a positive radiative feedback, λ must be negative. Now, if we breakdown λ, treating it as consisting of the sum λ(planck feedback) + λ(watervapour) + λ(lapse rate) + λ(cloud feedback) etc, then we see that if λ < 3.08 W m^-2 C^-1, then the sum of λ(watervapour) + λ(lapse rate) + λ(cloud feedback) etc must be negative, and hence their radiative feedbacks positive. (Parenthetically, I believe I have read a better treatment of this, but am too tired at the moment to look it up.) Or at least, that must be the case if we assume linear composition. That being the case, and given that λ on IPCC AR5 data is closer to 1.5 than to 3.05, it follows that the sum of all feedbacks excluding the planck response have a positive radiative forcing.

It appears, therefore, that Pielke is presenting evidence that the WV and Cloud radiative feedbacks are positive to motivate the belief that they are negative.

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Given that this post appears to be generating some interest, I should point out that Tom Curtis, above, is essentially correct and I did rather mis-interpret what Roger was saying in his post. If you want to read more then maybe my next post should be read in conjunction with this.

Yes, that’s certainly what I think I’m getting from this now. A net negative

Radiative Feedbackincluding the temperature response is not only what we would expect but also implies a positive feedback due to the other response.Here is how the 2007 IPCC WG1 SPM muddled this particular issue. In the caption to Figure SPM.2 they wrote

. “Global average radiative forcing (RF) estimates and ranges in 2005 for anthropogenic carbon dioxide (CO2 ), methane (CH4), nitrous oxide (N2O) and other important agents and mechanisms, together with the typical geographical extent (spatial scale) of the forcing and the assessed level of scientiﬁc understanding (LOSU)”

This caption certainly seems to indicate these are the forcing as of 2005.

Only in a footnote do they write

“Radiative forcing is a measure of the inﬂuence that a factor has in altering the balance of incoming and outgoing energy in the Earth-atmosphere system and is an index of the importance of the factor as a potential climate change mechanism. Positive forcing tends to warm the surface while negative forcing tends to cool it. In this report, radiative forcing values are for 2005 relative to pre-industrial conditions deﬁned at 1750 and are expressed in watts per square metre (W m–2).”

The obvious question is if they are actually presenting estimates of the changes since 1750, what is the current (2005 in that report) and 2013 in the current report radiative forcings?.Where does the water vapor radiative forcing fit in?

One does not simply accuse the IPCC of muddling an issue by raising obvious questions, unless these obvious questions are being rhetorical.

Also note that asking “where does the water vapor radiative forcing fit in” is less stronger than:

http://wattsupwiththat.com/2013/10/21/radiative-forcing-radiative-feedbacks-and-radiative-imbalance-the-2013-wg1-ipcc-report-failed-to-properly-report-on-this-issue/

***

Can I now say that Pielke Senior failed to refrain from using rhetorical questions?

willard (@nevaudit) – My question is not rhetorical. Both questions are the same.

“The IPCC failed to report on the global average radiative feedbacks of water vapor and clouds in terms in Watts per meter squared, and how they fit into the magnitude of the diagnosed global average radiative imbalance.”

“where does the water vapor radiative forcing fit in”

Instead of seeking to parse my comments, I suggest you, and others, provide your answers to them.

I’ve attempted answering this in these two comments on the other thread.

> Both questions are the same.

This FAILS to acknowledge that the sentence starting with “The IPCC FAILS to report” is not a question.

The only escape you have, dear Senior, is to claim that your FAIL claims presuppose questions the IPCC must answer.

Nevertheless, they are claims, in contradistinction to the “where’s vapor &c” question, if it is indeed a question.

And if that’s a question, then you FAIL to substantiate your FAIL claim, insofar as it FAILS to be more than a rhetorical device to adjunct “IPCC” with “FAIL”.

Please talk like a scientist.

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