Thursday 7 July 2016

Is it time to freak out about the climate sensitivity estimates from energy budget models?

Estimates of climate sensitivity using simple energy budget models tended to produce lower values than many other methods. Consequently they were loved by the mitigation sceptical movement, who seemed to regard these as the most robust of all methods. Part of their argument is the claim that these are “empirical” estimates, conveniently forgetting the simple statistical model the method uses, that they still require information from physical global climate models for the forcings, and that global climate models output also fit the “empirical” temperature change (and many other observed changes).

Before the last IPCC report the estimate for equilibrium climate sensitivity was between 2°C and 4.5°C with a best estimate of 3°C. I do not know of any explicit statement, but I have the feeling that the new studies with low estimates from energy budget models were the reason why the last IPCC report reduced the lower bound to 1.5°C. Since the reasons for the discrepancies were not understood the last IPCC report no longer gave a best estimate for equilibrium climate sensitivity.

The equilibrium climate sensitivity is defined as the equilibrium change in global mean near-surface air temperature after doubling the atmospheric concentration of carbon dioxide.

A Nature News and Views by Kyle Armour (2016) showed this week that three assumptions made in the simple energy budget models lead to strong biases.

1. This week Mark Richardson and colleagues (2016) showed that the temperature change is underestimated because we have few measurements in regions where the change is large, especially the Arctic. This masking problem creates a bias of 15%.

Furthermore, over the ocean, empirical estimates do not use the air temperature, but use the sea surface temperature instead; the water temperature is a much smoother field and can thus be estimated using many fewer samples, which is good because observations over the oceans are sparse. Above sea ice the air temperature is used. Thus this also means that the decrease in the ice cover need to be taken into account. The temperature trend of the air temperature over the ocean is also higher than the trend of the sea surface temperature. Both effects make the "observed" trend 9% smaller.*

2. Climate change is mainly due to increases in carbon dioxide concentrations, but also warming due to increases in methane concentrations, cooling due to increases in aerosols (small airborne particles) and changing due to land use changes. Half a year ago Kate Marvel and colleagues showed that these forcings do not have the same global effect as carbon dioxide and that, as a consequence, the energy balance models are biased low. Marvel and colleagues estimate that this makes the estimates of energy balance models 30% too low.

3. Kyle Armour and colleagues (2013) previous work showed that in the early warming phase climate sensitivity appears smaller than the true value you would get if you would wait till the system has returned to equilibrium. This leads to an underestimate of 25%.

Taking all three biases into account the best estimate from the energy balance models from around 2°C estimate becomes 4.6°C**; see Figure 1b of Armour (2016) reproduced below.

Climate sensitivity estimated from observations1 (black), and its revision following Richardson et al. (blue) then following Marvel et al. (green), and in red the revision for the time dependence (Armour). The grey histogram shows climate model values.

The equilibrium climate sensitivity from global climate models is about 3.5°C***, which is close to the best estimate from all lines of evidence of about 3°C. The "empirical" estimate of 4.6°C is now thus clearly larger than the ones of the global climate models.

Is that a reason to freak out? Have we severely underestimated the severity of the problem?

Probably not, there are many different lines of evidence that support an equilibrium climate sensitivity around 3, with a likely range from around 2 to about 4.5. That the simple energy balance models might now suggest a best estimate of around 4.6°C does not really influence this overall assessment. It is just one line of evidence.

That the energy balance climate sensitivity is minimally above the upper bound does not change this. These energy balance models have not been studied much and the biases are so large that the correction need to very accurate, while they are currently mostly based on single studies. It is quite likely that this value will still change the coming years. If this value still holds after a dozen more studies you may want to consider freaking out a little. How uncertain this bias corrected climate sensitivity is is illustrated by its wide distribution in the above graph with a 95% uncertainty range of 2.5-12.8°C.

[UPDATE. Gavin Schmidt mentions on twitter that it should also be studied whether these three factors are fully independent. While they seem to relate to different aspects there could be a link because spatial patterns and forcing efficacy are strongly related. Thus it would be valuable to make a study that considers all three biases in combination.]

The promotion of the cherry picked climate sensitivity of 2°C, or lower, was disingenuous. A similar promotion of a value of 4.6°C would be no better. (Someone promoting a climate sensitivity of 12.8°C deserves a place in statistical Purgatory.)

There are many other lines of evidence for an equilibrium climate sensitivity around 3, from basic physics, to global climate models, various climatic changes in the deep past and the climate response to volcanoes. Before accepting values far away from 3 we would need to understand the physics of the feedbacks that produce such deviations.

Figure 1 Ranges and best estimates of ECS based on different lines of evidence. Bars show 5-95% uncertainty ranges with the best estimates marked by dots. Dashed lines give alternative estimates within one study. The grey shaded range marks the likely 1.5°C to 4.5°C range as reported in AR5, and the grey solid line the extremely unlikely less than 1°C, the grey dashed line the very unlikely greater than 6°C. Figure taken from figure 1 of Box 12.2 in the IPCC 5th assessment report (AR5). Unlabeled ranges refer to studies cited in AR4. The figure in the review article by Knutti and Hegerl (2008) presented by Skeptical Science is also a very insightful overview.

The likely range of possible climate sensitivity values has been between 1.5°C and 4.5°C since the 1979. That does not sound like much progress. However, we now have many more lines of evidence and those lines have been much better vetted. Thus we can be more sure nowadays that this range is about right. A large part of the uncertainty comes from cloud and vegetation feedbacks. Having worked on clouds myself, I know that these are very difficult problems. Thus I am not hopeful that the uncertainty range will strongly decrease the coming decade or maybe even decades.

We will have to make decisions in the face of this uncertainty. Like any decision in a complex world.


* The temperature trend of the air temperature over the ocean is 9% higher than the trend of the sea surface temperature in the CMIP5 models. For most models the top layer is 10 m deep. For those models with a higher vertical resolution the trend is only 8% higher. The difference is small and not statistically significant, but the effective resolution of numerical models is normally larger than the nominal resolution, thus I would not be surprised if studies with dedicated high resolution models may lead to estimates that are a few percent points lower.

** If we simply combine all these biases: 1.24 (Richardson) * 1.30 (Marvel) * 1.25 (Armour) we get that the simple energy balance models are biased by as much as a factor 2. Taking this into account could suggest increasing the best estimate from the energy balance models from around 2oC to around 4oC. Because of the uncertainty around the estimates and the thick tails, the estimate becomes 4.6°C. See Figure 1b of Armour (2016).

*** The ensemble of global climate models of the CMIP5 project have an average climate sensitivity of 3.5°C with a 95% uncertainty range of 2.0-5.6°C (Geoffroy, et al. 2013).

**** Many thanks to Kyle Armour and And Then There’s Physics for many helpful hints and comments. Any errors are naturally mine.

Related reading

Nature Geoscience: Impact of decadal cloud variations on the Earth’s energy budget. A physical explanation of why climate sensitivities estimated from recently observed trends are probably biased low.

An oldie from Science in 2004: Three Degrees of Consensus explains the various ways to estimate climate sensitivity and why it may have been more luck than wisdom that the first estimate of the range of the climate sensitivity still holds.

Skeptical Science: How sensitive is our climate?

Climate dialogue: Climate Sensitivity and Transient Climate Response

Fans of Judith Curry: the uncertainty monster is not your friend

Tough, but interesting for scientists: Andrew Dessler talk at Ringberg15 on why the equilibrium climate sensitivity exceeds 2°C.


Armour, Kyle C., 2016: Projection and prediction: Climate sensitivity on the rise. Nature Climate Change, News and Views, doi: 10.1038/nclimate3079.

Armour, Kyle C., Cecilia M. Bitz and Gerard H. Roe, 2013: Time-Varying Climate Sensitivity from Regional Feedbacks. Journal of Climate, doi: 10.1175/JCLI-D-12-00544.1

Geoffroy, O., D. Saint-Martin, G. Bellon, A. Voldoire, D.J.L. Olivié and S. Tytéca, 2013: Transient Climate Response in a Two-Layer Energy-Balance Model. Part II: Representation of the Efficacy of Deep-Ocean Heat Uptake and Validation for CMIP5 AOGCMs. Journal of Climate, 26, pp. 1859- 1876, doi: 10.1175/JCLI-D-12-00196.1.

Marvel, K., G.A. Schmidt, R.L. Miller and L.S. Nazarenko, 2015: Implications for climate sensitivity from the response to individual forcings, Nature Climate Change, 6, pp. 386-389. 10.1038/nclimate2888.

Richardson, Mark, Kevin Cowtan, Ed Hawkins and Martin B. Stolpe, 2016: Reconciled climate response estimates from climate models and the energy budget of Earth. Nature Climate Change, doi: 10.1038/nclimate3066. If you cannot read this article at Nature, you can go there via The Guardian, which has a special link that allows everyone to read (not download) the article. See also the News and Views on this article by Kyle Armour.

Otto, A., F.E.L. Otto, O. Boucher, J. Church, G. Hegerl, P.M. Forster, N.P. Gillett, J. Gregory, G.C. Johnson, R. Knutti, N. Lewis, U. Lohmann, J. Marotzke, G. Myhre, D. Shindell, B. Stevens, and M.R. Allen, 2013: Energy budget constraints on climate response", Nature Geoscience, 6, pp. 415-416. 10.1038/ngeo1836.


  1. Excellent read.

    "The promotion of the cherry picked climate sensitivity of 2°C, or lower, was disingenuous. "


  2. Hi Victor,

    Nice post.

    The 9% difference between air and SST reported warming includes an effect from changing sea ice. Air only warms <5% more than the water below (exact number depends on the model), but the switch from measuring air temperatures over ice to measuring water temperatures when ice retreats boosts the effect to about 9%. It turns out this is mainlym related to how the anomalies are calculated.

    Limited space in the paper means we couldn't dwell on this too much, but a more detailed explanation is in Cowtan et al. 2016 which we cite.

  3. JCH, thanks.

    MarkR, space is even more limited in blog posts. :) I already tend to write too long posts by mentioning all those "important" details. I thought the change in ice cover was the smaller effect and skipped it. If it is about half, maybe I should add it.

  4. Nice post, Victor. Another interpretation of how the new energy-budget constraints fit into the broader picture is that the upper bound on climate sensitivity must come from something else. That is, both models and energy-budget constraints allow sensitivity > 4.5 C, so we must rely on those other lines of evidence (e.g., paleoclimate, emergent constraints, etc) to rule out this high tail.

  5. Kyle, agree. That is what I hinted at with my tongue in cheek remark: "Someone promoting a climate sensitivity of 12.8°C deserves a place in statistical Purgatory."

    That upper limit estimate is just that we do not have enough information to restrain the energy balance models, not a real upper bound, which will have to come from other considerations.

    If there were an interaction between the forcing efficiency and the time-dependence, is there any reason to expect that to reduce the ECS bias or increase it or does it need a separate study to even guess the sign of the effect?

  6. The short answer is that I'm not sure. My suspicion is that some portion of the Marvel et al result may actually be due to feedback time-dependence, even though they (and I) have framed it in terms of forcing efficacy. This would mean that their forcing efficacy revision may not be totally independent of the time-dependent feedback revision, so that they can't be simply combined as I've done here. So, for now, you can take the 'Marvel et al' curve above as a conservative estimate if you'd like (giving ECS = 3.9 C with a 2.1-10.7 C 95% range, by my estimate, when combined with the Richardson et al result). But note also that I've not included uncertainty in my 'time dependence' correction here (I've used the model average of 25%, while the range across models is about 0 to 100% based on work I'm about to submit); so, that too is a conservative estimate.

    We definitely need additional studies to examine forcing efficacy, feedback time-dependence, and their possible relation, and with more models to get a sense of the robustness of the results. I'm working on this, and it sounds like Gavin and collaborators are too.

  7. Hi Kyle,
    What would your personal guess of ECS be?

  8. Nice post, but:

    I realize I'm a broken record on this point, but the stable global temperature implied by ECS isn't something that can ever exist in the real world, primarily because ECS omits carbon feedbacks. Even speaking in terms of ESS (earth system sensitivity) is somewhat misleading since, unlike in past climates, we won't be in anything resembling an equilibrium climate state until we're on the other side of the peak. At this point we'll be lucky if that peak temperature is less than +5C, even if we manage to limit the CO2 concentration directly resulting from our emissiobs to a doubling (doubtful).

  9. An ECS around 4 C seems reasonable to me; it's very likely above 2 C, but we have little information about the upper bound at the moment. It will be interesting to see if consensus emerges as these new results are examined more closely and combined with other lines of evidence.

  10. Steve, good point about other feedbacks. The ECS values discussed here exclude carbon cycle feedbacks, ice sheet feedbacks, and feedback nonlinearities that might arise if warming becomes large enough.

  11. Thanks for the reply. Do you think 3C ECS is reasonable as well?

  12. Michael, Kyle just wrote on twitter: "3C is still consistent with new studies, but 4-5C is too. Other evidence needed to rule out high ECS values."

  13. Thanks, Victor. I know ECS is the warming associated with a doubling of CO2. Is that roughly the warming that would take place in the latter half of the century?

  14. Under a business as usual scenario the values are similar, which may lead some people to confuse them, but these two number are by definition fundamentally different.

  15. Climate Sensitivity Estimated From Earth's Climate History, James E. Hansen and Makiko Sato:
    "Our best estimate for the fast-feedback climate sensitivity from
    Holocene initial conditions is 3 ± 0.5°C for 4 W/m2 CO2 forcing (68% probability)."


    "The Earth system sensitivity relevant to humanity now is the sensitivity of the present climate state to a positive (warming) forcing. That sensitivity is not as great as for a negative forcing, but it is much larger than the 3°C fast-feedback climate sensitivity."

    It seems we eventually catch up to Hansen. Perhaps we should consider freaking out :)

  16. To respond more to Michael, Victor's post is mainly about the equilibrium climate response, which is how much we will eventually warm (due to fast feedbacks only) if we double atmospheric CO2. As others have pointed out, this does ignore slow feedbacks, which will also become relevant on multi-century scales, and the system sensitivity (ESS) may well be above 4C.

    However, for the next century (till 2100, say) what is probably relevant is the transient climate response, which is between 1C and 2.5C and is the amount we will have warmed at the instant when we have doubled atmospheric CO2.

    However, an issue with this is that it doesn't really tell us how to relate this to our emissions. There is another metric called the Transient Response to Cumulative Emissions (TCRE) which is between 0.8C and 2.5C per 1000 GtC. We've emitted about 600GtC and warmed by about 1C, so a reasonable best estimate would be about 1.7C per 1000 GtC. Therefore, how much we will probably warm by 2100 depends on how much we emit by 2100. If we emit another 400GtC, we will probably reach 1.7C. If we emit another 1400 GtC, we will warm by more than 3C (relative to pre-industry).

    We're currently emitting 10GtC/yr, so to keep below 2C (50% chance) would require emitting no more than about 500GtC, and to keep below 1.5C would require emitting no more than about another 250GtC. In other words, having a reasonble chance (50%) of keeping below 2C would require no more than 50 years of current emissions, and less if emissions continue to rise.

  17. Somewhat amusing that Hansen et al 1988 used an ECS of 4.2 C and has been taking stick for it ever since.

    Time to revise all those blog posts, although as Hansen pointed out, for the difference between 3 and 4.2 to show up you have to go out more than 20 years.

  18. Eli, 4.2°C still sounds a bit high to me. But I would not be surprised if the next IPCC report would give 3.5°C as best estimate of the ECS, if the current results for the energy balance models still holds, we still have many studies showing faster than expected changes in several other climate systems and the models with the higher sensitivities are still the ones with the most realistic cloud properties.

  19. andthentheresphysics, thanks. I should also have added to my answer to Michael that the temperature in 2100 depends on what humanity does, while the climate sensitivity is physics and does not depend on human action.

  20. So what would be a good probable range for ECS? 2.5-4.5?

  21. If nothing unexpected is published, I would expect that the lower bound will go up. My feeling is that 1.5°C is too low for our current understanding.

    I would not dare to give numbers for the probable range out of the blue. That would require gathering all the evidence we currently have, similar to the previous review of Knutti and Hegerl (2008). That is work.

    1. Hi Victor,
      So does any of this impact the finding that adhering to the Paris Agreement results in temp. rise of 2.3-3.5C by 2100?

  22. From my perspective the Republican PR machine's obsession with the "Climate Sensitivity number" is nothing but another smooth cynical distraction. It's not like people have any benchmark to help us understand precisely what this or that number actually means in terms of its ultimate impact.

    What we do know is the observed transition over the past half century when compared with the previous centuries. Aren't those changes scary enough to know that we have invited profound disruption into our lives and should do everything in our power to slow it down?

  23. I argue above that the climate sensitivity is still 3°C like it has been for decades. How should that staying the same make a difference for projections of the future?

  24. When ECS2x is discussed, it amazes me that Schmittner, Urban, Shakun, Mahowald, Clark, Bartlein, Mix, and Rosell-Melé seldom comes up. See and the figure reproduced therein. That's from:

    Science 09 Dec 2011:
    Vol. 334, Issue 6061, pp. 1385-1388
    DOI: 10.1126/science.1203513

    and it was a full Bayesian treatment. There's a kind of follow-up investigation at


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