Kummer & Dessler on Climate Sensitivity

I’ve finally had a chance to read the new Kummer & Dessler paper The impact of forcing efficacy on the equilibrium climate sensitivity (ECS). It’s an analysis of climate sensitivity that uses energy budget estimates and also considers (as suggested by Drew Shindell – and others) that aerosol, ozone and land use forcings are inhomogeneous. I discussed Drew Shindell’s work in an earlier post and the basic idea is that the northern hemisphere (NH) should – because of all the land mass – warm faster than the southern hemisphere (SH). However, the aerosols and ozone are not well-mixed and have a larger effect in the NH than in the SH. This means that the global temperature response is smaller than it would be if these forcings were homogeneous (well-mixed).

One can correct for this by adding some factor, E, to these inhomogeneous forcings, e.g.,
The equation above is for the transient climate response (TCR), while Kummer & Dessler compute the ECS, but one can apply the same correction to estimates of the ECS. To get the ECS, Kummer & Dessler use an integral form of the following equation
where N is the energy imbalance, F is the change in radiative forcing, and dT is the change in surface temperature. They then solve for λ, which has units of Wm-2K-1. Inverting λ and multiplying by 3.7 Wm-2 gives the equilibrium temperature after a doubling of CO2.

Their results are shown in the table below. Assuming there’s no inhomogeneity in the forcings (E = 1) gives an ECS of 2.3K with a range from 1.6K to 4.1K. Assuming an efficacy factor of 1.33 gives an ECS of 3.0K, and an efficacy factor of 1.5 gives an ECS of 3.5K.

credit : Krummer & Dessler (2014)

credit : Krummer & Dessler (2014)

I should add, however, that Troy Masters did an analysis that suggested that the inhomogeneity correction may not be as large as suggested by Shindell. I haven’t quite worked out the significance of what Troy has illustrated, but as I see it, it’s fairly clear that E has to be greater than 1. It seems that it can’t be bigger than 1.5. What Troy’s done may well suggest that E is closer to 1 than to 1.5. However, even with E = 1, Kummer & Dessler get an ECS of 2.3K (range 1.6K – 4.1K). So, even if the inhomogeneity is only a 10% effect, it’s still acting to adjust the energy budget estimates back towards being quite similar to estimates using other methods (paleo, GCMs). Also, I think the Kummer & Dessler E = 1 estimate doesn’t include the Cowtan & Way temperature correction, which would increase the ECS further.

So, essentially it seems that as we consider these energy budget estimates in more detail we’re finding that the various corrections are acting to adjust these estimates so that they become more consistent with other estimates. This is good scientifically (it’s useful to have multiple methods that give similar results) but not necessary comforting. We certainly shouldn’t be pleased that the original energy budget estimates are likely to be underestimating climate sensitivity. We also shouldn’t – as some seem to do – argue that we should be optimistic and hope that these lower estimates are correct. Wishful thinking isn’t going to have any effect on reality.

Anyway, I’ll finish with a short video in which Andrew Dessler explains their recent paper.

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28 Responses to Kummer & Dessler on Climate Sensitivity

  1. BBD says:

    Thanks for the overview of Krummer & Dessler. It’s interesting – and necessary – to see the way that this study (and many others) show that estimates of ECS much below ~3C/2xCO2 are invariably the result of methodological shortcomings of one sort or another. Lukewarmers aren’t holists when it comes to the evidence. It’s also interesting to see who they affiliate with (eg. Lewis; Masters; Spence; Lindzen).

  2. I also came across this discussion paper today that seems to be trying to decompose the recent temperature record into an anthropogenic component, volcanoes, solar, ENSO and AMO. What always confuses me about such analyses is that seem to mix forcings (anthro, solar, volcanoes) with variability (ENSO, AMO) and so it’s not clear to me that it’s methodologically sound. Also, I have a feeling that some think that the AMO is forced, rather than some kind of internal variability, but I haven’t quite worked out the implications of that.

  3. BBD says:


    it’s not clear to me that it’s methodologically sound

    I share your doubts. Not least because IIRC the AMO may be influenced by anthropogenic aerosols as well as by GHG forcing, to complicate matters still further. Damned if I can find the reference though. Sorry.

  4. BBD says:

    However, I *did* manage to find a useful post by Tamino on the way the global warming (surface temperature) signal does leak into the AMO, which might be helpful if you are thinking about this.

  5. BBD,
    Thanks. Tamino’s post is really useful. I hadn’t quite considered it like that, but it does make sense. There is no reason to expect that the anthropogenic signal is purely linear, so removing a linear trend and assuming that what remains is the AMO could well mean that some of the anthropogenic forcing has essentially leaked into the AMO and one would then underestimate the anthropogenic influence.

  6. BBD says:

    This, I think, is what did for Tung & Zhou (2013). Dumb Scientist wrote it up at SkS.

  7. Thanks, that’s really good. I had thought about something similar myself, but DumbSci has said it better than I could have.

  8. Thanks BBD and Anders. Our debate continued on two SkS articles by Dr. Tung; I only finished my long-delayed implementation of Dr. Tung’s simulation last month.

    TL;DR: I don’t think the AMO is understood well enough to regress temperatures against it without absorbing some of the nonlinear human influence.

  9. Pingback: The Climate Change Debate Thread - Page 4092

  10. BBD says:


    Thanks for the update. I read the two posts by Dr Tung and the exchanges in comments with great interest. And little real sense that his replies carried the weight of a killing blow.

  11. BBD says:

    Sorry, not very clear – I read the SkS posts at the time. So I missed your comment on 19 April 2014.

  12. Almost everyone missed it because I took so long to finish my comment. I did enjoy talking with Dr. Tung, especially in contrast to most of the “debates” I suffer through.

  13. BBD says:

    At least he knew whereof he spoke and there actually was a debate. And my belated thanks for pursuing the issues with T&Z13 as you did – publicly, politely, and effectively. We weren’t then introduced.


  14. KR says:

    The discussion with Dr. Tung was very rewarding – while in the end I (personal opinion) was not convinced by his arguments, it was delightful to have a polite and frank exchange.

    Thanks for the pointer to Werf and Dolman 2014, ATTP – that looks like a very interesting comparison of various anthropogenic forcing and AMO inputs and their effect on TCR estimates.

  15. dana1981 says:

    A point worth clarifying – the study says that ECS is 3°C if the aerosol + ozone forcing efficacy is ~1.33, which is indeed less than the 1.5 in Shindell’s paper. In fact Krummer & Dessler specifically state,

    At least some of the high efficacy of aerosols and ozone [in Shindell] was due to nature of the transient runs he analyzed, but his analysis nevertheless clearly showed that, in the models at least, the efficacy of aerosol and ozone forcing was significantly greater than 1.0.

  16. Fred Moolten says:

    re the AMO, Isaac Held an others have shown that during intervals of rapidly rising ocean heat content, a contribution to warming from internal unforced variability must necessarily be much smaller than the forced component.

    Re Krummer and Dessler:
    At the risk of seeming boringly repetitious, I think it’s worthwhile recalling that if a value of λ based on observations from past decades, or any similar non-equilibrium interval, is used to derive a sensitivity extimate, what it yields is not ECS but “effective climate sensitivity”(eff-CS). This is because the calculation assumes that λ is constant during an interval of warming (the defining assumption of eff-CS), thereby allowing λ derived from non-equilibrium conditions to be used to calculate the equilibrium value. Another way of stating this is that it assumes a linear relationship between temperature change and radiative restoring, the extent to which a radiative imbalance imposed by a forcing is reduced. In fact, there is no a priori reason why this assumption should be true, and considerable reason to think that it substantially overestimates the equilibrium value of λ, and thus underestimates ECS. Two important papers on this point are Armour et al 2013
    and Andrews et al 2012 .

    The extent of the disparity is currently hard to estimate and is subject to uncertainties in forcing data and forcing efficacy. Nevertheless, I believe that at this point, the most appropriate approach is simply to use the term eff-CS to refer to estimates derived from non-equilibrium conditions, and ECS for estimates based on paleoclimate data or models constrained by observational data on water vapor, albedo, clouds, and other short and medium term feedbacks. Unfortunately, a number of recent papers reporting eff-CS estimates have referred to them as ECS; examples include the widely cited Otto et al. These papers at times include a tacit acknowledgment that their estimates may be at the low end of a possible range, but it would be less confusing in my view if they simply refrained from terming them ECS.

  17. Dana,
    Thanks, a good point.

    Yes, I agree. These energy budget estimates indeed assume that λ is constant over the warming period and that this value will be appropriate for the entire period over which CO2 doubles. As you say, this assumption may well be questionable.

    As an aside, Troy Masters has an interesting post about this paper in which he seems to be arguing that applying the Shindell correction to the ECS is questionable. I haven’t managed to quite work through what he is suggesting but I do wonder if he doesn’t have a point. It’s not obvious to me that the influence of the inhomogeneities on the ECS will be the same as on the TCR. On the other hand, maybe it does apply to both – i just need to find some time to have a look at what Troy is suggesting and maybe try a few things with my toy, two-box model.

  18. magnus w says:

    Without thinking to much… is it not so that the effect is on TCR and needs to take in to account when calculating ECS? ofc in the long run it might have another effect or perhaps stay the same depending on what happens with emissions…

  19. dana1981 says:

    Oh by the way, it’s Kummer, not Krummer.

  20. Dana,
    Thanks. I think I checked a number of times and still managed to get it wrong.

  21. Fred Moolten says:

    ATTP – Since you’ve read the Shindell and Kummer/Dessler (KD14) papers, I’m interested in your view of Troy Masters’ critique of KD14, which I find plausible but hard to evaluate, having seen only the abstracts of those papers. Troy’s argument appears to be the following:

    Shindell starts with the principle that a forcing over land (e.g., from aerosols) will induce a larger temperature response during the initial decades than a comparable globally distributed CO2 forcing, because the lower heat capacity of land allows the temperature to proceed faster toward equilibrium. This is why Shindell claims the effect on TCR would be amplified. However, as Troy notes, rate of approach to equilibrium has no effect on the ultimate equilibrium temperature. The latter is determined by the forcing F and the feedback parameter λ.,a parameter which in an energy budget model is assumed to be constant over time and temperature change, and which can be calculated from measurements of temperature change ΔT and ocean heat uptake (the latter as an index of planetary energy imbalance N). The energy budget equation is
    λ = (F – N)/ ΔT. If λ is constant, these measurements can be taken at any stage, the only difference being that closer to equilibrium, the temperature change will be greater and the residual energy imbalance smaller, leaving λ unchanged. For forcing from doubled CO2, the equilibrium temperature would be 3.7/ λ. For this reason, Troy argues that multiplying a given forcing by Shindell’s “efficacy factor” is unjustified.

    Of course, the above argument applies to estimation of what might more properly be called “effective climate sensitivity” (elsewhere Troy abbreviates it as EFS) than ECS, since EFS is based on assuming λ is a constant independent of time, whereas ECS allows λ to vary as the temperature response proceeds. In all likelihood, EFS is less than ECS.

    I find the argument persuasive to the extent that Troy accurately represents the description of both Shindell and KD14. My own reasons for thinking that the “ECS” values in Table 1 above should probably be increased is that almost all of them are actually EFS rather than ECS estimates. I believe Annan and Hargreaves is an exception, with its ECS estimate of 2.9 K.

  22. Fred,
    I haven’t quite worked out what Troy is suggesting. What I was trying to do today was to see if I could look into this using my simple two-box model. I got part way through doing it and then decided that cutting the grass and watching some of the cricket was a better way to spend my Sunday. I may have another go tommorrow.

    The one thing that I did consider is that it possibly depends on how one assumes the inhomogeneities evolve with time. Here’s my one thought. The basic way to calculate the ECS and TCR is to use

    TCR = F2x ΔT / ΔQ
    ECS = F2x ΔT / (ΔQH).

    The premise of the Shindell paper is that the northern hemisphere should warm faster than the south. If, however, the forcings are inhomogeneous, the effect on the NH is larger than on the SH and therefore for a given ΔF, ΔT will be smaller than if the forcings were homogeneous.

    This is where I think Troy may get something wrong (although I’m not sure). I think a fundamental point of the Shindel and Kummer & Dessler paper is that this inhomogeneity should reduce with time as the aerosol forcing get smaller and the GHG forcings get larger. Therefore the ΔT today (when the inhomogeneity is large) will underestimate the relationship between ΔT and ΔF. So, I think the efficacy argument applies to both the TCR and the ECS, but I want to try and check this tomorrow if I get a chance.

  23. Fred Moolten says:

    To add to the above discussion, Troy’s argument in its simplest formulation assumes that the feedback parameter λ is the same for the Northern and Southern hemispheres. However, if λ is substantially lower (higher sensitivity) in the NH, then an NH-dominated forcing would be expected to yield not only a higher TCR but also a higher ECS. The Armour et al paper provides support for this regional variation in λ. I don’t know whether Shindell actually made this claim in his paper.

  24. Fred Moolten says:

    PS – I’ve been able to see a draft of Shindell as well as his supplementary information. In addition to the faster warming due to the greater NH land mass, he also cites the greater positive feedback (equivalent to reduced λ) due to enhanced snow/ice albedo feedback, and includes an increase in ECS as one of the consequences of these NH/SH differences. I also think, however, that Troy is probably correct in claiming that using the entirety of Shindells’ efficacy correction to an ECS estimate is unjustified, since only part of that correction applies to equilibrium conditions.

    Parenthetically, I also note that Armour et al estimate a reduced λ from land that includes a smaller (less negative) Planck response. I’m not sure of the mechanism, but perhaps this is due to the lower average IR emissivity of land compared with water. Is there another mechanism for this?

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