## I’m confused about Kummer & Dessler

I wrote a post recently about the new Kummer & Dessler paper on Equilibrium Climate Sensitivity (ECS). It was based on the earlier work of Shindell et al. (2014). The basic premise is that more land mass in the northern hemisphere (NH) means that it should be more sensitivity to changes in radiative forcing that the southern hemisphere (SH). However, aerosol, ozone and land-use forcings are also bigger in the NH than the SH (and have a cooling influence). This inhomogeneity in these forcings means that the change in temperature, ΔT, for a given globally averaged change in radiative forcing, ΔF, will be smaller than if all the forcings were homogeneous.

However, these inhomogeneities should reduce with time (as the GHG forcing increases and the aerosol – and other – forcings decrease). Therefore, if you use an energy budget method to estimate the transient climate sensitivity (TCR), you will underestimate the TCR unless you compensate for this inhomogeneity. Shindell et al. (2014) suggest using a correction factor, E, in front of the aerosol, ozone and land-use forcings, as shown below

My understanding of the Kummer & Dessler paper, is that they essentially apply the same correction to the ECS equation (I know they actually use an integral form, but I think it’s the same basic equation). So, to determine the ECS, you can use

where Q is the system heat uptake rate – the energy imbalance. However, Troy Masters has a blog post that seems to suggests that this efficacy factor shouldn’t be applied to the ECS calculation. I also had a discussion about this with Fred Moolton on my earlier post. My feeling is that Troy has a point, but I haven’t quite worked out what he’s done in his analysis.

To try and understand this, I modified my two-box model so that it considered the two hemispheres independently. I then set it up so that one was more sensitive than the other and modified the forcings so that there was an inhomogeneous component. It was fairly straightforward to show that this inhomogeneity would reduce the change in temperature compared to if the forcings were homogeneous – and, hence, illustrating that simple energy budget estimates would underestimate the TCR.

However, when I considered the ECS, the simple method didn’t underestimate the ECS. What seemed to be happening is that the reduction in ΔT produces a smaller Planck response (negative feedback) which means that the energy imbalance, Q, is greater when the forcings are inhomogeneous than when they’re not. This seems to compensate for the reduced ΔT and suggests that one shouldn’t apply the efficacy factor when estimating the ECS using an energy budget method.

Let me make a few extra comments, though. Kummer & Dessler is written by people who are clearly experts in this field. It is, therefore, quite possible that I’ve misunderstood something about this situation. Secondly, it’s not completely obvious that it really matters. Even without the efficacy factor, Kummer & Dessler get an ECS of 2.3K with a range from 1.6 – 4.1K. This is already quite consistent with other estimates. If they were to include the temperature correction suggested by Cowtan & Way, it would increase slightly, making it even more consistent. It’s also quite likely that these energy budget estimates don’t capture some non-linearities which would mean that they may well under-estimate the ECS anyway. As I think is suggested in this comment by James Annan to a Nic Lewis post, the linear assumption in the energy budget estimate means we should probably regard this as en effective climate sensitivity, rather than a true representation of the equilibrium climate sensitivity.

So, essentially, I’m confused about Kummer & Dessler and I’ve written this post mainly to, hopefully, illustrate an element of skepticism. I could also, of course, be illustrating my ignorance, but that’s a risk one should be willing to take 🙂

Update : As I mention in this comment, I think I’ve resolved my confusion. I had assumed that the reason for the different sensitivities in the two hemispheres was simply because of different heat contents. This – I think – is incorrect. There may be some effect from this, but it’s also because of different feedback responses. If one considers this, then the efficacy factor should apply also to the ECS, as well as to the TCR.

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### 33 Responses to I’m confused about Kummer & Dessler

1. jsam says:

No true “climate sceptic” is uncertain. 🙂

2. BBD says:

This is one of those occasions when an email to the corresponding author (Andrew Dessler, in this case) would probably be hugely helpful in establishing if Troy’s analysis is well-founded or not.

3. BBD says:

That said, as you point out, does it matter?

Even without the efficacy factor, Kummer & Dessler get an ECS of 2.3K with a range from 1.6 – 4.1K. This is already quite consistent with other estimates. If they were to include the temperature correction suggested by Cowtan & Way, it would increase slightly, making it even more consistent. It’s also quite likely that these energy budget estimates don’t capture some non-linearities which would mean that they may well under-estimate the ECS anyway.

If we are looking at the effective climate sensitivity rather than equilibrium sensitivity (as you go on to emphasise further) then there doesn’t seem to be much disagreement with the persistently central ECS estimate of ~3C/2xCO2.

4. BBD,
Yes, maybe I should send an email.

5. Andrew Dessler says:

I think a useful clarification is that we can think of the efficacy as composed of two terms: 1) a part due to heat capacity and 2) a part due to differing climate sensitivity (lambdas) from two different forcings. Part 1 disappears for the ECS calculation, but part 2 does not. I did a simple illustration of the lambda effect in Mathematica here: https://www.dropbox.com/s/3f03srn1jxuani1/simpleCalcV1.pdf

Our paper does not make an argument about how big this effect is, it just notes that it’s possible to resolve disagreements among various estimates of ECS if this is important.

6. Hi Andrew,
Thanks for the comment. I guess I’m still a little confused as to why part 1 disappears for the ECS, but I’ll have a look through the document in your link and see if I can solve my confusion.

7. Fred Moolten says:

Thanks to the link to the Annan/Fasullo/Lewis discussion, including their Guest Blog pieces and the subsequent comments. In my view, James Annan comes across as the most logical and objective of the three. Lewis and Fasullo are also worth reading, but their biases appear to color their conclusions to some extent.

8. Andrew Dessler says:

Unfortunately, my doc does not explain why part 1 disappears, just why part 2 does not. I’ll have to put something together illustrating part 1 …

9. Andrew,
Thanks, that would be interesting. I’m still confused, but that isn’t necessarily all that surprising 🙂

10. Steve Bloom says:

Fred, research results can have a biasing effect. But perhaps there’s some substantive reason you don’t like what Fasullo says?

11. Fred Moolten says:

Steve – I generally do like Fasullo’s take on these issue, but I think he’s done some cherry picking to support his views. Lewis is much more guilty of this. In any case, readers can look at the discussions and judge for themselves.

12. A couple of interesting things about the Kummer & Dessler paper. Nic Lewis has pointed out, that the paper uses temperatures reference to 1880-1899 but forcings relative to 1750. They should be relative to the same period and so – I think – correcting for this would reduce the E = 1 ECS estimate – probably back towards what Otto et al. (2013) got. I will add that Nic Lewis seems particularly good at catching these types of errors in papers (assuming he is correct). Doing so is very good. What would also be good, though, is if he could sound a bit less like a pompous ass when he points these out. I also think that Nic Lewis may be one of the last people on the planet who should be advising others to be more skeptical – unless he’s being intentionally ironic.

I think I may have also resolved my issue with Kummer & Dessler. The system heat uptake rate Q can be estimate using

$Q = \Delta F - \left( \epsilon \sigma T^3 - W \right) \Delta T$,

where ΔF is the change in forcing, the first term in the brackets represents the Planck response, with an emissivity, and W is the feedback (in Wm-2K-1). When I was doing my check with my two-box model, I was assuming that all that the inhomogeneity acts to do is increase the forcing in the hemisphere with the higher heat content and reduce it in the hemisphere with the lower heat content – hence it acts to reduce ΔT. But, I was assuming that it did not influence the feedback response W. Therefore a smaller ΔT means that the second term in the above equation is smaller and the system heat uptake rate increases when the forcing is inhomogeneous compared to when it is homogeneous.

However, if the inhomogeneity also acts to change the feedback response, then my test was wrong. If so, that would explain why the efficacy factor should be applied to both the TCR and ECS equations. I’m not sure if I have resolved this, but this could be the reason why I was finding that it didn’t seem to apply to the ECS equation, but did to the TCR equation.

13. Oh, hope you all noticed that I put LaTeX directly into my above comment. Expect more equations in my posts in future, now that I no longer have to do them in Equation Editor in Word, save them as a picture and them upload them to WordPress 🙂

14. Andrew Dessler says:

Yes, Nic Lewis correctly points out an error in our description of the forcing. That will be corrected in final published version. However, this will INCREASE our inferred climate sensitivities. It is quite trivial to understand this: to correct the zero issue, we will reference out temperature to 1750 instead of the late 19th century. This will increase the temperature values in that time series, and it will therefore increase the integral of temperature. Since the integral of temperature is in the denominator of the lambda equation, that will decrease lambda and increase ECS. I calculate an upper limit increase of 20% (it’s uncertain because we don’t really know how much T increased between 1750 and the late 19th century).

15. Andrew,
Thanks, I wasn’t sure which way it would go. I was having some trouble following the discussion between Troy and Fred on Troy’s blog.

Since you’re commenting, have I roughly corrected my confusion about the efficacy in the ECS estimates. If I have, my error was in thinking that the reason the inhomogeneity influenced temperatures was simply because of the difference in heat content of the two hemispheres. Having thought about this a little more, my sense is that my misunderstanding is that the two hemispheres also have a difference feedback responses and so the inhomogeneity can influence the temperature response without necessarily influencing the system heat uptake rate. Of course, I could still be confused – but I’m getting used to that 🙂

16. troyca says:

Hi Andrew,

Yes, Nic Lewis correctly points out an error in our description of the forcing. That will be corrected in final published version. However, this will INCREASE our inferred climate sensitivities. It is quite trivial to understand this: to correct the zero issue, we will reference out temperature to 1750 instead of the late 19th century.

I think you correction here is quite problematic. In the accepted version of the paper, your methods section describes referencing all time-series to the 1880-1900 baseline, which is the version of the methods that the reviewers accepted. Why not simply reference the forcing series to that same 1880-1900 baseline (which actually has a lower RF relative to 1750 due to high volcanic activity), which is readily available, as described in the paper? This would greatly reduce your estimate of ECS, but it would be performing the actual calculation that was accepted by the reviewers.

To switch to referencing all series to 1750 is problematic because

a) none of the major temperature series used in your paper (GISS, HadCRUT, NCDC) span back prior to 1850, so you would be relying on much sparser data and/or proxy reconstructions. Since the abstract begins with “Estimates of the Earth’s equilibrium climate sensitivity (ECS) from 20th-century observations…”, this would not longer be quite as accurate – you would no longer be relying primarily on 20th century observations, but instead on proxies a century and a half prior to the 20th century. Moreover, the studies you mention (e.g. Otto et al) that you are trying to reconcile are all base-lined to the end of the 19th century, not the mid 18th century.

b) KD14 implicitly assumes an N = 0 over the baseline period. There are studies that indicate that N over 1880-1900 may be close to 0, in which case it may be okay, but the same cannot be said for 1750…it was almost certainly positive as it still hadn’t equilibrated from the sharp rise in solar irradiance from the late 17th century to the mid 18th century. Accounting for a positive N in the baseline period obviously lowers the ECS estimate.

17. Troy,
Thanks, I think I now understand your discussion with Fred better than I did before.

18. Andrew Dessler says:

ATTP: Yes, the efficacy effect here is due to different climate sensitivities from the different forcers.

Troy: thanks for your comments. First, we’ve run our proposed changes by the editor, so changing the paper is not an issue. Second, I am very grateful when people point out errors and opportunities for clarification of our results. I want the paper to be as correct and clear as possible. That said, I’m a little bit surprised about the doggedness of the criticisms of our baseline choice (particularly when the alternative suggestions are equally uncertain). The answer we come up with for the ECS assuming efficacy = 1 is similar to previous calculations (e.g., Otto). So to the extent that errors exist, I see no reason to think they’re terribly important. We’ve recently estimated that the range of various assumptions for how to do the baselining introduces an uncertainty of ~20%, within the overall uncertainty of the quantity (1.6-4.1 K). And the exact ECS value is not even the main point of trying to make in the paper. The main point of the paper is that efficacy can have a big effect on the inferred ECS and provides a way to bridge the gap between various estimates. That does not change with any choice of baseline.

19. Fred Moolten says:

I’m curious about the value of N in 1750. Reconstructions (Marcott et al, Mann et al), if I read them correctly, show that temperature in 1750 had been declining for decades, although with ups and downs, and only subsequently trended upward into the mid to late 1800s.. The reliability of these proxy data can be questioned, but they appear consistent with a negative N in 1750. Is there solid evidence for a positive N from a reliable combination of solar and aerosol evidence?

20. I’m also interested in N in the 1700s. I don’t have a good proof of this, but I’d assumed that it was unlikely that changes in natural forcings could produce a long-lived, substantial energy imbalance. Is there a chance that the energy imbalance in 1750 could have a magnitude (negative or positive) much bigger than 0.1 Wm-2.

21. troyca says:

Hi Andrew,

I don’t want to seem like I am harping on this, so I will not pursue this further if you do not wish. However, I want to clarify that I am not advocating for one particular baseline in a vacuum. Rather, I am saying that the KD14 correction should use 1880-1900 as the baseline *in this case* instead of 1750 because:

1) It is what the paper’s method accepted by reviewers said it was doing

2) It is more relevant to the 20th century estimate studies referenced in the abstract and paper, which use the late 19th century as a baseline.

3) The three temperature sets KD14 uses (GISS, HadCRUT, and NCDC) all cover 1880-1900, as do the IPCC forcings, so the data is readily available. However, none of the temperature datasets extend back to 1750, so I am not sure what you would use in that case (do you plan on splicing proxies from the earlier period with temperatures from the instrumental period)?

To me, it seems like a no-brainer that you would do the calculations originally described in the paper, for the reasons above. If it makes little difference after you change this, so much the better!

However, Nic claims that by using the 1880-1900 baseline for forcings, in accordance with what it says in KD14, one actually gets 1.5 K ECS for the median estimate, and even if the full Shindell efficacy of 1.5 applied (which we know it does not) one gets < 2 K median estimate. I do not think this issue is irrelevant – for instance, at ClimateDialogue, John Fasullo is arguing that the IPCC should not have lowered the lower bound of the likely ECS estimate below 2K, citing KD14 in support of this. However, if Nic is correct and the method/data described in KD14, when applied correctly, actually shows an estimate < 2K, this would obviously be an argument against John's position. Similarly, our host noted in his first post on your paper:

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).

But obviously, this would not be true if Nic is right and a correction to the KD14 method results in an estimate < 2K. Moreover, your statement above would seem to be in conflict if Nic is right on this matter:

The main point of the paper is that efficacy can have a big effect on the inferred ECS and provides a way to bridge the gap between various estimates. That does not change with any choice of baseline.

If a 1.5 efficacy leads to a < 2K median ECS for the 1880-1900 baseline, this would mean it is a small bridge for a very large gap, right? So there generally seems to be conflicting claims here: Nic is saying that using the 1880-1900 baseline for forcings, as described in KD14, results in a median estimate of 1.5 K for ECS when E= 1.0. Per your last comment, you say only 20% of your uncertainty (1.6K to 4.1K), 2.3 K median comes from baselining choices, so assuming 1880-1900 produces the lowest ECS estimate, this would seem to imply that using the 1880-1900 baseline for Forcing (while leaving everything else the same) produces a median estimate of 2.3K – (20% * (2.3K – 1.6K)) = 2.16K. Is this correct? If not, what number to you get for ECS when baselining forcing to 1880-1900? Hopefully we can quickly hash out these remaining technical discrepancies, but as I mentioned above, I will let it rest if you want me to stop bugging you.

22. I’d be quite keen to see the numbers for a 1880-1899 baseline. If you consider the standard Otto et al. calc (which was baselined to 1860-1879) it essentially got an ECS of 2 degrees. If I look at the figures in their supplementary information, it doesn’t look as though changing to an 1880-1899 baseline should make much difference. However, it did use a system heat uptake rate of 0.65 Wm-2 and I suspect that Nic may be using the lower values from a recent paper, the authors of which I can’t remember.

23. Fred Moolten says:

Troy – If you’re still following this here, I’m looking forward to your future discussion of ECS vs EFS. You’ve been scrupulous in acknowledging that these don’t necessarily mean the same thing, but not everyone else has been equally forthright. Regarding the above commentary, an EFS below 2 K would not necessarily conflict with John Fasullo’s assertion that ECS should exceed 2 K.

24. Yes, as I think I said on Troy’s blog, I would also be interested in that discussion. I don’t know enough about possible non-linearities, but it does seem possible that there could be quite a difference between the EFS and the ECS. Having said that, the uncertainties in some of the forcings are sufficiently large that this may not be the case.

25. Andrew Dessler says:

Thanks for everyone’s comments. In response to Troy’s questions, here are some new calculations that I’ve done. I’ve used 1890-1900 as the zero period and zeroed both forcing and temperature during that time. The resulting ECS is 2.1 K (for efficacy = 1), once again consistent with every other calculation of this quantity. The reason that it’s very close to the result we already got (2.3 K) is because forcing over this period is very close to zero (-0.1 W per square meter), so the forcing time series is not adjusted much, and the temperature adjustments are also similar.

If I use the period 1880-1900 and follow the same recipe, I do indeed get much lower numbers, consistent with what Nic Lewis got. So why are the numbers so different? The reason is that you should only zero both forcing and temperature if the system is in radiative equilibrium. Given the strong volcanic activity early in the 1880s, that constraint is not satisfied and the answer you get from Lewis’ calculation is almost certainly low biased. (if you have another explanation for the difference, I’d like to hear it)

You could get around that problem by, instead of zeroing the forcing, setting it to be the amount of forcing yet to be expressed in the temperature. This will have the effect of increasing Lewis’ ECS and I suspect would bring his estimate into agreement with mine if done correctly.

So what’s the right thing to do? Given the discussion above, I think it’s clear that Lewis’ numbers are really a lower limit. I would argue that our approach of zeroing in 1750 (assuming radiative equilibrium at that point and then assuming a range of temperature changes between 1750 and 1880 of, e.g., +/-0.1 K) is a good approach, but I would also acknowledge that zeroing over 1890-1900 is probably as good.

26. Steve Bloom says:

Given the announcement just a few days ago that we’ve passed a major climate tipping point, there’s a vast irony in the effort by some to massage into being a low climate sensitivity. They’re missing the point, rather on purpose.

27. troyca says:

Thanks Andrew, that clarifies things!

28. Rob Painting says:

Steve – It’s true that lower climate sensitivity estimates make little to no difference to potentially catastrophic outcomes, such as mass coral bleaching and ocean acidification. And, under business-as-usual scenarios, may delay warming by only a couple of decades, but it is nevertheless a scientifically interesting question.

I think you have to differentiate between the nonsense appearing on contrarian blogs and the mainstream media – where low climate sensitivity is falsely used to infer there’s nothing to worry about, and earnest discussions such as this and at Troy’s blog. I’m enjoying to back-and-forth anyway.

29. Joshua says:

It’s nice to see an honest-to-god discussion discussion taking place between people who know what they’re talking about – sharing alternate perspectives. No identity aggressive or identity protective to distract from the scientific debate.

It is perhaps worthy of note that in a related discussion over at Troy’s crib, Nic Lewis broke into a similar discussion to imply that Fred is unable to accept the possibility of errors or flaws in peer reviewed literature, an implication that doesn’t pass the most basic skeptical scrutiny.

It would be helpful if “skeptics” would realize that boilerplate, identity aggressive rhetoric is counterproductive, and their insistence on such only marks them as “skeptics” (with quotes).

30. Joshua,
It has been an interesting discussion, I’ve certainly clarified my confusion.

I found Nic’s first comment at Troy’s scratchpad unfortunate – hence my rather snarky inference in my earlier comment. I will add, though, that I thought his later comments were better and more of the form that I would hope such discussions would take.

31. Fred Moolten says:

Joshua – I agree with the comment by And Then There’s Physics. Our various personalities can’t help intruding at times into vigorous debate, but I’m content to see temporary flareups calm down quickly rather than escalate. It’s what happened in this instance, and differs from the standard scenario on Judith Curry’s blog, which is one reason I don’t comment there as often as I once did.

A more important reason I’ve been spending some time here and on Troy’s blog is that I’m learning a lot from my interactions with others and the discussions in general. Maybe I’m misremembering previous experience, but I think opportunities to learn from informed discussion were greater on Climate Etc in the past than recently.

32. Joshua says:

Fred and Anders –

Yes, I agree that Nic’s tone changed, and in the specific context that is more important. A useful discussion ensued.

Within the general frame, however, it was an example of one of the many counterproductive patterns that roil discussion of climate change: a counterproductive tendency to conclude that someone thinks peer review is infallible just because they don’t agree with criticisms of a particular peer reviewed publication.

Yes, our various personalities (and perhaps more importantly, our biases, preconceptions, and conditioned habits of pattern recognition) can’t help but intrude. Of that there is no doubt. But the tribal war dance will continue to the extent that we don’t own up to our habits and examine the reasons why we over-reach, injudiciously, as Nic did to start with in that thread. I happen to think Nic has something important to add to the discussion of climate change, but it becomes more difficult for me to assess his input (particularly as I am someone not able to evaluate the technical components of his input) if he isn’t open acknowledging how his input is often accompanied by the very same attributes that he criticizes in others.- in other words how his personality intrudes just as do those of others.

Fred – as for Climate Etc. – I have seen it said a number of times that the technical discussions were more fruitful earlier in its lifespan. Indeed, I have looked back at some of the very earlier threads – many of which you contributed to actively – and; it does seem to me that there was relatively more respectful give and take on technical issues and less politicization, tribalization, identity aggression and identity protection, etc. I think that such an assessment is easily biased (nothing is ever as “good as it used to be”), but there is probably a functional bottom line in that you can say that for whatever reason, you would not learn from engaging there now to the extent that you once did. Maybe that’s because you’ve changed, but I would guess that the reason is more that the forum has change. And I have to wonder if the arc of Judith’s trajectory within the climate wars context might not be at least partially explanatory. Certainly, Pekka,- who in my impression was another person who once engaged there in more good faith discussion of the sort we’ve seen in this thread – has suggested that he has seen a shift in Judith’s orientation, and I would speculate that shift has been towards an orientation that might certainly be associated with a degradation of the discussions at her blog.

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