What matters is the radiative imbalance

I started this blog because I was getting frustrated by how often I saw scientific claims being made, with regards to global warming, that were just simply wrong. I was following, and partially involved with, a brief exchange between Joanne Nova and Michael Brown, an astronomer at Monash University. Joanne eventually responded to Michael Brown with the following suggestion

So, yes, the radiative imbalance is what matters. The problem, though, is that the article to which Joanne links is simply wrong. I know it’s more than a year old, but I thought I would briefly discuss it again here as I think it illustrates a major issue with this whole debate.

The basic premise of the article, written by someone called David Stockwell, is that one can use ocean heat content data (from, for example, Levitus et al. 2012) to determine how much energy has accrued in the climate system in the last 50 years. Dividing this by the surface area of the Earth and the time (in seconds) then gives an estimate of the average top-of-the-atmosphere (TOA) energy imbalance (in Wm-2). This is essentially correct and the calculation gives a TOA energy imbalance of about 0.27 Wm-2.

The article then goes on to basically say that this is considerably smaller than the continuous top-of-atmosphere forcing of 1 Wm-2 – presented by the IPCC – and, hence, that this mild forcing is consistent with the lower estimates from Lindzen, Spencer, Loehle and himself. Here’s the problem (and this was explained extremely clearly by Tom Curtis in the comments to Stockwell’s article): the 1 Wm-2 is not the continuous top-of-atmosphere forcing, it is the change in radiative forcing (anthropogenic only) over the time interval considered. If the surface temperature did not change over that time interval, then the TOA energy imbalance would indeed be at least as big as this change (likely bigger because of additional forcings and feedbacks), but the surface temperature does change. Hence, the actual TOA imbalance is much smaller than the change in radiative forcing. As also pointed out by Tom Curtis in the comments, the actual TOA imbalance, at time t, is given by (from a paper by Winton et al. 2010)

where ΔF is the change in radiative forcing, ΔT is the change in surface temperature, and λ is the climate feedback factor (basically representing how much a certain change in forcing will influence surface temperatures). Therefore, that the surface temperature also rises while the radiative forcing increases means that the TOA imbalance does not (and should not) match the expected change in radiative forcing.

So, Joanne, did I find your link helpful? Not really; it, sadly, just further confirmed my view that a number of those who are skeptical of the science of global warming don’t actually understand the underlying physics particularly well. What was quite remarkable about this particular article was that Tom Curtis very clearly explained why the comparison was wrong, and yet even Roger Pielke Sr (who was also commenting) would not acknowledge the error. Maybe the author has since acknowledged his mistake (the article was written last year) but, if not, I find this incredibly frustrating. The comparison is very obviously wrong and any credible scientist should be willing to at least consider this and, ideally, actually accept their error.

In truth this whole issue may not actually be trivial (the concept of radiative balance can get confusing and I’ve certainly made some mistakes myself) but it’s not that complicated. If we even disagree about the basics (and this is remarkable in that it really shouldn’t be something we’re disagreeing about) how can we hope to actually have sensible discussions about those aspects that are much more complicated than this. Furthermore, that someone can’t even get this right does beg the question of why anyone should take anything they say (with respect to global warming at least) seriously? And, as usual, if I’ve made some kind of mistake, feel free to point it out in the comments.

This entry was posted in Climate change, Climate sensitivity, Global warming, IPCC and tagged , , , , , , , , , . Bookmark the permalink.

42 Responses to What matters is the radiative imbalance

  1. Something that I considered putting in the post, but thought I’d add here instead, is a calculation to see what sort of TOA imbalance one might expect. If one assumes a transient climate response of 1.5oC, then that tells you how much the surface temperatures will have changed by over the time interval over which CO2 doubles. CO2 will have doubled, relative to what it was in 1850, by about 2050 (so, it takes about 200 years). The land and atmosphere have a mass of around 1019 kg and a specific heat capacity of 1000 J kg-1K-1. This means the total energy in the land and atmosphere will have risen by about 1.5 x 1022J. The oceans have a heat capacity 100 times greater than this, so the energy in the oceans (and hence the overall energy) will have risen by about 1.5 x 1024 (in order to maintain equilibrium between the different parts of the climate system). If you divide this by the time take (200 years) and by the surface area of the Earth, you get 0.5 Wm-2. So, a rough back-of-the-envelope calculation suggests that you would expect an average TOA imbalance of about 0.5 Wm-2. Seems pretty close to what is determined using OHC data, to me at least. Bear in mind, of course, this is just a rough calculation.

  2. As has been pointed out to me, even if the basic idea in Stockwell’s article was correct, comparing a long term average of the TOA imbalance with the value at some instant in time is not a particular good way to validate, or not, the fundamentals of AGW.

  3. Sou says:

    I only discovered David Stockwell today by a different route. He was one of the few people, along with the authors themselves, who cited a silly study quoted by a trio of fake sceptics on WUWT. I had to look him up. Like Jo “Nova”, it turns out he’s a committed science denier and an anti-mitigation lobbyist and, as with Jo “Nova”, I very much doubt he’d ever admit that he misrepresents science (or admit to any mistakes he makes about climate stuff no matter how obvious).


    NOD32 won’t let me onto his landshape.org website, asserting that “The web page is on the list of websites with potentially dangerous content”. (Which is pretty funny when you find out that he “moved to the San Diego Supercomputer Center at University of California San Diego in 1997.”)

    I trust NOD32 more than I trust David Stockwell 🙂

  4. Amazing. I always assume that if one can present a clear explanation as to why something is wrong, that it will be accepted and acknowledged. To me, acknowledging an error is an illustration of scientific objectivity and assuming that you never make one is arrogance. It’s clear that I’m both naive and overly optimistic.

  5. BBD says:

    Not to mention honest.

    The contrast is evident.

  6. Good grief. Is he actually a climate scientist? That seems so absurd I’m starting to doubt that I understand this properly. He can’t be that wrong, can he?

    Having said that, he did on Twitter this year, I think, make the same point about AR5. He ignored my tweet that tried to point out that these were changes in radiative forcings since 1750. Although, maybe he just didn’t notice. I imagine he’s quite busy, what with trying to get the AGU to accept his minority report.

  7. > Is he actually a climate scientist?

    I think so:


    There must be some misunderstanding.

    Or maybe it’s a just vocabulary thing [1].

    [1] http://neverendingaudit.tumblr.com/post/31268600509

  8. Could be just vocabulary. He’s just redefining what various things means? Seems quite a common strategy as far as I can tell.

  9. Michael Brown says:

    Just had another look at Stockwell’s post and noticed Tom Curtis left an extensive comment on this very topic.

  10. Thanks, he did indeed. I used quite a lot of what Tom said in the post (properly credited I hope) but missed that particular one. It’s quite hard to keep up with Tom 🙂

  11. Michael Brown says:

    Interesting that Stockwell is now posting on viXra (arXiv backwards).

    viXra has some pretty amusing pseudoscience posts, and my personal favourite is….

    viXra:1212.0050 [pdf] submitted on 2012-12-07 11:30:22

    Gravitational Ejection of Earth’s Clouds
    Authors: Fran De Aquino
    Comments: 5 Pages.
    It is shown that, under certain circumstances, the sunlight incident on Earth, or on a planet in similar conditions, can become negative the gravitational mass of water droplet clouds. Then, by means of gravitational repulsion, the clouds are ejected from the atmosphere of the planet, stopping the hydrologic cycle. Thus, the water evaporated from the planet will be progressively ejected to outerspace together with the air contained in the clouds. If the phenomenon to persist during a long time, then the water of rivers, lakes and oceans will disappear totally from the planet, and also its atmosphere will become rarefied.
    Category: Climate Research

  12. Don’t know why he has to go to viXra. Even the arXiv allows amusing postings


  13. Tom Curtis says:

    I have been rereading Stockwell and Pielke’s posts, and trying to make more sense of what Pielke wrote. His formula, “global radiative imbalance = global radiative forcing + global radiative feedback” could be interpreted as just Winton et al’s “N (t) = R(t) – lambda*T(t)”, only with N (and R) being positive up, rather than positive down as in Winton’s formula. Such an interpretation means that Pielke adopting a non-standard convention without specifying that he is doing so, and is poor form. However, it still cannot make sense of his claim that:

    “[W]hat the Levitus et al data shows is that the global radiative feedback is negative (and this necessarily would include the water vapor, sea ice etc radiative feedbacks). That is

    global radiative feedback < global radiative forcing."

    For a start, with “global radiative feedback” being interpreted as lambda *delta T, necessarily “global radiative feedback” is less than “global radiative forcing” until the new equilibrium temperature is reached. How that can be a problem for the IPCC is beyond explanation.

    More puzzling, the planck response (ie, the response with zero additional feedbacks) results in a lambda of 3.1 Wm^-2 C^-1. For a delta T of 0.7 C, that represents an increase of outgoing LWR of 2.16 W/m^2, significantly greater than the 1.72 W/m^2 forcing calculated in AR4. As there is still a top of atmosphere energy imbalance, it follows that lambda must be significantly less than 3.1 Wm^-2 C^-1, ie, that net feedbacks are positive rather than negative. Indeed, simple calculation shows the central estimate of the feedback from the Levitus data of lambda = 1.6 Wm^-2 C^-1, ie, that the climate sensitivity for a doubling of CO2 is 2.3 C.

    In essence, Pielke was (at best) interpreting evidence of net positive feedbacks as evidence of net negative feedbacks; and no “skeptic” seems to have been able to pick him up on it.

  14. I agree, I find it all very odd. It’s examples like this that flabergast me. I even tweeted Roger’s post yesterday and Gavin Schmidt responded by saying it is definitely wrong and it’s been pointed out many times before. So, it appears that a senior, professional climate scientist has fundamentally mis-interpreted the relationship between the rise in OHC and climate sensitivity and is claiming that there is problem with the IPCC report. Implicitly (or maybe even explicitly) he is suggesting a much lower climate sensitivity than expected. It’s been pointed out that he’s wrong. It’s seem very clear that he’s wrong and yet he has not acknowledged this and others (Joanne Nova for example) are still using this to argue for lower climate sensitivities. It’s just remarkable. This is the kind of thing that I assumed a rational discussion could resolve quickly. Clearly not and, as you say, no “skpetic” appears to have noticed the error or, if they have, pointed it out. It’s hard to be charitable when I see things like this.

  15. BBD says:

    There’s no need to be charitable. A sustained refusal to admit error does not merit a charitable response. Misrepresentation such as we get from Jo “Nova” doesn’t deserve a charitable response.

    These people are being unbelievably irresponsible and deserve the hard side of the hand.

  16. Has anyone tried to contact Senior about this?

  17. Gavin Schmidt implied that it had been pointed out many times, but I don’t know if anyone actually has. Comments on his posts are not open, as you probably know. Maybe I’ll tweet him this post.

  18. Tom Curtis says:

    willard, Pielke Snr participated in the original discussion at Niche Modelling, and in fact responded directly to my comment where I quoted Winton et al. If he thought it was just a difference in formulation, he had ample opportunity to say so, and to clarify the confusion. So, I would consider him to have been “contacted”.

  19. Thanks, Tom.

    Could you post his response here? Strangely, Disqus don’t load the comments here.

    In any case, clarification would seem to be in order, if the disagreement rests on basic stuff.

  20. Willard, does this link work?


    If not, I can probably put them here but am not sure if that violates some basic principle of blogging.

  21. Disqus comments are now loading. Thanks.


    So this is where the famous Joule gambit comes in:

    If one could measure the heat content changes of the climate system (which is mainly in the oceans) with an accurate enough spatial resolution, one can obtain the climate imbalance at that time. Monthy (or annual) averages are used because the data do not have a fine enough temporal (and likely spatial) resolution for shorter time periods.

    The use of heat in Joules as the metric avoids any need to focus on a global average temperature trend at one x-y level (e.g. the surface).

    Please refer to these papers […]

    Then the comment pielkes all the way down [1] from there.


    Not sure how this response is responsive. And it seems that Alex Harvey has the same impression:

    [Alex] So you are saying that Prof. Pielke’s formula is just plain wrong?

    [Tom] Yes.

    Then we get to Peter & Judy. But Senior reappears:

    [The formula for radiative imbalance that I present] is just a statement of the conservation of heat in Joules. The radiative imbalance is a result of a difference in the heat input and heat output of the climate system system. The components of the heat input and output can be expressed as direct and indirect radiative forcing as we did in the report. […]

    Followed by some handwaving. Then there’s davids99us who tries to make some sense out of this hurly burly, after which Senior comes back to ask Tom to summarize what Tom said a few times already, i.e.

    [David & Senior] actually take the net radiative forcing relative to 1750 in 2006 and treat it as the TOA energy imbalance, ignoring the evolution over time. […]

    Once again, the TOA imbalance does not equal the radiative forcing relative to a particular time period plus the feedbacks. […] Given that the choice of 1750 as the baseline for radiative forcing is a convenience only, taking Stockwell’s equation literally would mean that the TOA imbalance could as easilly be determined from the radiative forcing relative to the last glacial maximum, and be approximately 8 W/m^2 plus feedbacks.

    With my emphasis and my omission of needless words. I would not say this conversation has been felicitous. Senior should meet Tom’s argument more squarely than that.

    Something needs to be settled here.


    [1] http://init.planet3.org/2009/08/pielkes-all-way-down.html

  22. I am mostly with Tom Curtis, of whom I have not heard before that I recall. He has parsed this mess admirably.

    I disagree in a quibbling way that “Prof. Pielke’s formula

    global radiative imbalance = global radiative forcing + global radiative feedback

    is just plain wrong”

    It’s only sort of wrong in my opinion.

    It seems to express conservation of energy using screwy definitions. I believe he means that the total forcing is the sum of the direct forcing according to some definition and its amplification or attenuation by unforced processes. This is little more than a tautology, like saying the cash in my wallet is the sum of the bills in my wallet and the coins, those being the only two forms of cash in this country.

    But that is not what we mean by “global radiative imbalance”, and that is not what we expect to see piling up in the ocean. If one assumes that it is what is balanced by ocean heat, it’s at that point that the peculiar definition becomes wrong. Further, conflating this quantity with radiative imbalance as normally construed, one can construct a naive model wherein the system is insensitive to forcing, as Tom explains.

    It seems on first blush correct (I have not followed this debate in detail but it is consistent with what I read in the comments at the link) that RPSr makes the “false assumption that the TOA imbalance at a time, t, is [at] least equal to the forcing at t relative to some earlier time”.

    If that is what RPSr is doing, calibrating the sensitivity from integrating the coupled forcing and comparing to the heat content of the ocean, he is indeed making an error that a reasonably proficient undergraduate in ocean or atmosphere sciences ought to be able to avoid.

    This would not be the first time.

  23. Thanks, Michael. I do find this quite remarkable, partly because it would appear to the kind of issue that could be resolved quite easily. It would seem amazing if someone like RPSr could give it some thought and, ideally, correct any error. If this is, incorrectly, being used to argue for a low climate sensitivity then one could take a step back and think a bit more about what getting this wrong means. It would seem like an incredible step in the right direction. If it’s not the first time RPSr has made this kind of mistake, then I’m probably being optimistic if I think he would ever acknowledge this error (or at least address it).

  24. Tom Curtis says:

    MTobis, thankyou for the complement on my parsing.

    I agree with you that my initial statement that “Prof Pielke’s formula … is just plain wrong” may have overstated the case. I attempt to make sense of the possibility that it was correct, but stated using unusual conventions above (Oct 17th). Unfortunately, if Pielke’s formula is not itself plain wrong, then his conclusions from the formula certainly are.

  25. SKS use the same figures as I do (0.6 vs 0.3W/m2) in a comprehensive discussion on the issue posted a month after my article – so I am wrong as you say I am then they must be wrong too;-) but I don’t think I am. they bring in figures from more sources yet still conclude that “the OHC issue is not entirely settled in either models or observational data,..”.

    I suggest the most obvious explanation for both the shortfall in heat accumulation and excess surface temperature rise in the models is the exaggeration of climate sensitivity to CO2. The recent revisions of the range of CO2x2 sensitivity downwards confirms this view.

  26. David, it’s not about your calculation of the rate at which heat has accumulated in the ocean. That’s correct. It’s your comparison of that with the change in radiative forcing over that time interval, which you’re interpreting as an illustration of a lower climate sensitivity. That is incorrect. You’ve essentially compared that average over some time interval with the different between the radiative forcing at the beginning and the end. This would be like comparing the average speed of a car in a drag race with it’s final speed (and being surprised that they aren’t the same).

    As Tom Curtis explains above, and as I try to explain in the first comment, the OHC rising at about 0.5 Wm-2 is entirely consistent with the expected climate sensitivities.

    If you really are serious about getting things right, you’ll give this some more thought because your claim that your calculation implies a lower climate sensitivity than others suggest is wrong.

  27. laterite says:

    You saying that I did doesn’t make it so. The figures that I use that you don’t quote show 0.6wm2 for modeled continuous forcing that comes from Hansen and 0.3wm2 for observations from Levitus (but you say 0.5wm2) whatever SKS uses these and other figures. The figure you and Tom Curtis are talking about, start to finish difference, is the total modeled forcing which I think was in Hansen is much bigger at 1.8wm2. So are SKS and Hansen using the figures wrongly?

  28. David, this is really a very simple thing. The radiative forcings quoted by the IPCC are the change in forcings. What you’ve calculated (using the OHC) is the average rate at which energy is accumulating in the system. Since surface temperatures rise while energy accumulates, the TOA energy imbalance (which determines the rate at which energy accumulates) is lower than the change in forcing over that time interval. You really can’t simply compare the average rate at which the energy accumulates with the change in forcing over that time interval to determine the climate sensitivity.

    A way in which to estimate climate sensitivity is

    TOA = ΔF – λ ΔT.

    Since 1970 ΔT = 0.6oC, ΔF=1.3 Wm-2, and (from your calculation) TOA = 0.3 Wm-2. That gives λ = 1.6 Wm-2C-1. The change in forcing due to a doubling of CO2 is 3.7 Wm-2 so that implies (divide 3.7 by 1.6) that the climate sensitivity is 2.3oC.

    So, your own calculation implies a climate sensitivity of 2.3oC, so doesn’t seem much lower than other estimates.

  29. It is simple. I quoted the figure you think I erroneously used at the top of my article (1.6W/m2 from the IPCC). I then when on to compare an estimate of the modelled continuous forcing produced by Hansen of 0.6W/m2 with the measured from the ocean effective continuous forcing of 0.3W/m2. The point is the comparison between the modelled heat accumulation and the actual heat accumulation as expressed in W/m2.Your calculation if the CO2 sensitivity implied by ocean warming is irrelevant to this comparison, and wrong as it attributes all the warming to CO2.

  30. And I have had some trouble finding the Hansen paper you quote (maybe you could give me a better reference). The only Hansen paper I can find that refers to a TOA imbalance of around 0.6 Wm-2 refers to an analysis of the period 2005 – 2010. If that is what you’re referring to, then you still seem to be comparing an average for a 50 year period with and average for a 5 year period. If I redo your basic calculation for the period 2005 – 2010, I get around 0.5 Wm-2 for the rate at which the ocean is accumulating energy – pretty close to that estimated by Hansen.

    How is my calculation irrelevant and wrong? The only other warming is solar and that has dropped very slightly since 1970. If I included that, it would increase the climate sensitivity.

  31. laterite says:

    So you won’t admit you were wrong about your misunderstanding of the figures I used (which you parroted from Tom Curtis) so you try go OT. No time for such chatter. Bye

  32. David, seriously? I’ve asked you to provide me with a better reference for the Hansen paper you quote and you claim I’m going OT. I can’t be wrong about the figures you use because I don’t really know which figures you’re talking about (apart from the Levitus one). You don’t include any figures in your post. If you want to clarify which figures you are referring to I’d be happy to acknowledge if I am indeed wrong, but I can’t do so unless you actually point out which figures you mean.

  33. anthony says:

    Hansen’s paper is here:


    One of David’s analysis of it is here:


    An attempt of a rebuttal of David’s critique of Hansen’s paper by Geoff Davis is here:


    David’s response to Dr Davis is here:


  34. Thanks, but this is a slightly different issue to the one I address in this post. Over the past 50 years, the ocean heat content has risen at a rate consistent with an average TOA imbalance of around 0.3 Wm-2 (as correctly calculated by David in the post linked to above – in the tweet from Joanne Nova). David claims that this is less than half of IPCC estimates. Now I will accept that I had assumed that David was referring to the IPCC radiative forcing estimates (which was largely because this appeared to be what David was saying in his post). I will accept that he actually meant estimate from James Hansen which were consistent with IPCC estimates (also an odd thing to say since Hansen’s estimates are TOA imbalances, while IPCC estimates are changes since 1750). However, the numbers quoted by Hansen are for the period 1993 – 2008 and for the period 2005 – 2010. Hence David is comparing an average over the last 50 years either with an average for a 15 year periods (1993 – 2008) or for a 5 year period (2005 – 2010). Since Hansen computes his numbers using exactly the same method as David (i.e., by considering OHC data), the differences are simply because of different time intervals (unless one can show that Hansen has made a mistake, which I do not think is the case). So, that David gets an average TOA imbalance half that of Hansen is not because Hansen has over-estimated the climate sensitivities, it’s simply because the estimates consider different time intervals.

    Plus, the calculation I (and Tom Curtis) claim is the correct way to determine the TOA imbalance (given a change in forcing and a change in temperature) is essentially equivalent to the method used recently to determine climate sensitivities based on recent observations (Otto et al. for example), the results from which David claim proves his point.

  35. BBD says:


    Thanks for this debunking of Stockwell’s errors. Bookmarked thread for reference.

    I note that Stockwell failed to respond substantively to the critique of his errors and exhibited some ill grace in the process.

  36. chris says:

    I expect that the Hansen et al paper that David Stockwell refers to is Hansen et al (2005) “Earth’s energy imbalance: Confirmation and Implications Science 38, 1431-1435.


    This describes the modeled ocean heat accumulation of 6.0 W yr/m^2 during the decade 1993-2003 or 0.6 W/m^2/yr averaged over the ten year period.

    So, pretty much as you and Tom and Michael Tobis have described very clearly, this value of ocean heat gain is an average value for this 10 year period. In this paper Hansen et al also estimate the total forcing between 1880-2003 as ~ 1.8 W/m^2, of which they estimate that ~ 1 W/m^2 has been attenuated by the Earth warming response during that period, with 0.85 W/m^2 still remaining. Obviously there is still a very significant “unrealized” forcing since heat is continuing to be driven into the oceans at a prodigious rate.

    The similarities between these values and those that Stockwell quotes suggest that’s where his values come from. Difficult to understand why he can’t simply tell us ‘though!

  37. Thanks. Yes, I eventually did find that paper and, as you say, it’s very clearly for the period 1993-2003.

  38. Pingback: An acknowledgement, but not really a correction | Wotts Up With That Blog

  39. Pingback: Watt about David Stockwell? | Wotts Up With That Blog

Comments are closed.