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Sensible Questions on Climate Sensitivity

Filed under: — group @ 15 August 2017

Guest Commentary by Cristian Proistosescu, Peter Huybers and Kyle Armour


Two recent papers help bridge a seeming gap between estimates of climate sensitivity from models and from observations of the global energy budget. Recognizing that equilibrium climate sensitivity cannot be directly observed because Earth’s energy balance is a long way from equilibrium, the studies instead focus on what can be inferred about climate sensitivity from historical trends. Calculating a climate sensitivity from the simulations that is directly comparable with that observed shows both are consistent. Crucial questions remain, however, regarding how climate sensitivity will evolve in the future.


The recent papers, by Kyle Armour (hereafter A17) and by us (Proistosescu and Huybers, 2017) (hereafter PH17), build on a large literature documenting the time-dependence of climate feedbacks in models. They make quantitative apples-to-apples comparisons between the climate sensitivities simulated by CMIP5 models and those inferred from global energy budget observations.

[Aside: For brevity, we refer to the global energy budget constraints as “observations”. In reality, these constraints are not purely observational; they combine surface and ocean temperature observations over the recent transient evolution of the climate system with model-based estimates of historical radiative forcing and of the global energy imbalance during early-industrial climate. Further, inference of climate sensitivity from these observations rely upon a physical model that entails some strong simplifications.]

Because feedbacks may change over time as patterns of warming evolve, observations made today do not necessarily provide estimates of the long-term, equilibrium climate sensitivity (ECS). Rather, they constrain a quantity that we call the inferred (A17), or instantaneous (PH17), climate sensitivity (ICS). The two studies were performed independently using distinct methodologies, and both find that ICS values are systematically lower than ECS values within CMIP5 models. Moreover, they find that model-derived ICS values are consistent with ICS values inferred from observations.

Figure shows model Equilibrium Climate Sensitivity (ECS, blue, from PH17), compared with observationally- and model-derived Inferred/Instantaneous Climate Sensitivity (ICS, black and red). Circles denote medians, while the line denotes the 5-95% confidence interval. Solid lines indicate published estimates, dashed lines indicate PH17 and A17 values with Nic Lewis’ comments taken into account, and dot-dashed lines indicate PH17 and A17 values with both the Lewis correction and the Richardson et al (2015) correction.

Of mountains and molehills

Nic Lewis has posted some criticisms of both papers (A17 critique, PH17 critique) where he proposes changes to these studies that supposedly render the models and data again in disagreement. The criticisms focus on the treatment of radiative forcing within the models which is used in the calculation of ICS values. We approach these criticisms by exploring their implications for the resulting ICS estimates, without necessarily implying agreement.

For A17, Lewis suggests that one should (i) assume that CO2 forcing increases slightly faster than logarithmically with CO2 concentration, rather than linearly, as is traditional[1], and (ii) estimate model CO2 forcing values by a different method[2]. Accounting for these two effects increases model-mean and median ICS by ~0.1°C. For PH17 the suggestions are to (i) adjust historical forcing to account for the average pre-industrial volcanic forcing[3], (ii) rescale the radiative forcing associated with a CO2 doubling for each model when calculating ICS[4], and (iii) better account for the difference between instantaneous and effective radiative forcing, a point that was raised in PH17. While the last suggested adjustment almost certainly conflates time-dependence of feedbacks with stratospheric and tropospheric adjustment, we nonetheless explore the impact of adding Lewis’ upward correction of 0.1°C.

[1]A17 employed the standard assumption that CO2 forcing increases linearly with the logarithm of concentration, while recent work suggests that CO2 forcing might increase slightly faster than linearly. Assuming this forcing nonlinearity decreases model ICS by 0.04°C, on average.

[2]A17 estimated CO2 forcing using linear regression of global radiative imbalance on global temperature over years 1-5 of each model’s abrupt CO2 quadrupling simulations. This choice was made to avoid forcing estimates being biased by the nonlinear relationship between radiative imbalance and temperature that typically emerges beyond year 5. Using years 1-20 for this calculation, as Lewis suggests, seems unwise to us. But doing so increases model ICS by 0.09°C, on average. A third suggestion was to include additional CMIP5 models in the analysis; while we do not do so here, we estimate that including them would bring model-mean ICS back to near the A17 value since most of the additional models are variants of those already included that happen to have low ICS.

[3]Temperature change is considered as an anomaly with respect to pre-industrial climate. Thus, volcanic forcing should also be considered as anomalies with respect to the average pre-industrial forcing. The issues of pre-industrial volcanic forcing can be largely avoided by considering the same averaging interval as in Lewis and Curry (2015), raising model ICS by an average of 0.1°C.

[4]Radiative forcing PH17 inferred from the CMIP5 models (which averages 3.9 W/m2) is larger for a doubling of CO2 than the estimate generally used elsewhere, including in Lewis’s estimates (3.7 W/m2, ref. AR5 TS & 9.7.1, which relies on a subset of the CMIP5 models). In order to make results comparable, PH17 rescaled radiative forcing to the commonly-used AR5 value.

In the figure, we show both the original A17 and PH17 estimates of model ICS, and versions that take into account Lewis’s suggestions. The most notable change is that the PH17 model-median ICS estimate increases from 2.5 to 3.0°C, while the 5-95% credible interval narrows from 1.6 to 4.2°C to a range of 2.2 to 4.0°C. This shift is primarily in response to rescaling radiative forcing using model specific values, and it leads to better agreement between the median values of PH17 and A17. However, regardless of the methodology used, or whether or not Lewis’ suggestions are accounted for, the core results still hold: model values of ICS are consistent with observational ICS values.

Should we be concerned by the remaining offset?

Although consistent, the ranges of historical and model based ICS values do not completely overlap. However, there are additional effects that could be taken into account that would make the estimates more congruent. When sampled in a manner consistent with observations, by accounting for spatial coverage and differences between sea-surface and near-surface-air temperatures, changes in model temperature over the historical period are reduced by a median of 19% (i.e. Richardson et al (2015)). A proportional correction to model ICS is illustrated in the figure. Additionally, there is significant uncertainty in the magnitude and efficacy of non-CO2 forcing agents. There is enough uncertainty in fact, that accounting for the efficacy can broaden the range of observational ICS to easily contain all model estimates (Figure 1).

Furthermore, while model-median ICS is based on the forced response in a model ensemble, the observational ICS depends on a single realization of Earth’s warming, the details of which are sensitive to the phase of natural variability affecting the pattern of surface warming over the periods considered. Thus, the observed estimate of ICS is almost certainly perturbed from its expected value (i.e., what would be obtained from perfect knowledge of an infinite ensemble of Earth histories). Recent evidence suggests that observed temperature patterns in recent decades, associated with a cooling of the East Pacific, can lead to a more negative cloud feedback than that seen in the historical response in models over the same period. It seems important to determine whether the inability of models to simulate these recent patterns is indicative of model deficiencies or simply a consequence of natural variability.

Since both estimates have differing sources of uncertainty, demanding agreement between the best-estimate historical ICS and best-estimate model ICS would constitute over-fitting. Additionally, given the fact that the model ensemble is an ensemble of opportunity, we don’t expect the model range to cover the full uncertainty range. Still, it is worth considering the lack of model coverage in the range of low ICS. This discrepancy may reflect that while low values of ICS are allowed by observational constraints (associated with a low aerosol forcing), it is challenging to construct climate models that produce such low ICS values, as it requires a more-negative cloud feedback that is difficult to reconcile with current mechanistic understandings. Better constraints on historical aerosol forcing and forcing efficacy might go a long way towards understanding the plausibility of low ICS values (e.g. Marvel et al, 2016).

What is the magnitude of ECS? (hint:≠ICS)

An important core finding of A17 and PH17 is that values of ICS drawn from the historical record are not sufficient to constrain values of ECS. Indeed, within models, ICS and ECS differ as the strength of radiative feedbacks change over time as patterns of surface temperature evolve with warming. PH17 demonstrated that portions of the climate system that respond over centennial timescales (such as the southern oceans) are important amplifiers of climate sensitivity in the models – a slow-mode response leading to values of ECS that are higher than the values of ICS that reflect more transient warming. Increasing sensitivity over time seems to be associated with a low-cloud feedback excited by warming in the Eastern Equatorial Pacific and Southern Ocean. This slow-mode response (and thus ECS) is essentially unconstrained by global energy budget observations because warming in these regions has been small, possibly held back by upwelling water from the ocean interior.

Key research targets should be improving understanding of (i) how the east-west temperature gradient in the Pacific Ocean will evolve in the future, and (ii) how low-level cloud (and other) feedbacks will respond, in turn. Zhou et al (2017) suggest that feedbacks can vary with the surface warming pattern, at least on decadal timescales. Yet, it is not known whether the magnitude by which feedbacks evolve within the models is realistic. A major challenge going forward is to develop instrumental observations capable of constraining these processes. Another potential path to better understanding slow-mode contributions to ECS is to explore paleoclimate changes occurring over timescale where the climate has had more time to fully come into equilibrium (e.g., PALAEOSENS).

As usual, it will be the interplay between theoretical exploration and observational analysis that will build our understanding of climate sensitivity. Lewis’ comments have helped to sharpen consideration of the topic, but we need not make mountains of difference out of molehills. Model ICS estimates strongly overlap with observed ICS uncertainty ranges, and proposed alterations involve only small modifications. More interesting at this point is to explore how future warming could diverge from historical patterns, and how climate feedbacks in the future might be different from those at present.


We thank Nic Lewis and Gavin Schmidt for comments on a draft of this post. We want to note that on the basis of as-of-yet unpublished research, Nic disagrees with our use of the Kummer and Dessler upward correction of observational ICS due to aerosol efficacy.


  1. K.C. Armour, "Energy budget constraints on climate sensitivity in light of inconstant climate feedbacks", Nature Climate Change, vol. 7, pp. 331-335, 2017.
  2. C. Proistosescu, and P.J. Huybers, "Slow climate mode reconciles historical and model-based estimates of climate sensitivity", Science Advances, vol. 3, pp. e1602821, 2017.
  3. C.A. Senior, and J.F.B. Mitchell, "The time-dependence of climate sensitivity", Geophysical Research Letters, vol. 27, pp. 2685-2688, 2000.
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  5. P.M. Forster, "Inference of Climate Sensitivity from Analysis of Earth's Energy Budget", Annual Review of Earth and Planetary Sciences, vol. 44, pp. 85-106, 2016.
  6. M. Richardson, K. Cowtan, E. Hawkins, and M.B. Stolpe, "Reconciled climate response estimates from climate models and the energy budget of Earth", Nature Climate Change, vol. 6, pp. 931-935, 2016.
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  10. J.R. Kummer, and A.E. Dessler, "The impact of forcing efficacy on the equilibrium climate sensitivity", Geophysical Research Letters, vol. 41, pp. 3565-3568, 2014.
  11. K. Marvel, G.A. Schmidt, R.L. Miller, and L.S. Nazarenko, "Implications for climate sensitivity from the response to individual forcings", Nature Climate Change, vol. 6, pp. 386-389, 2015.
  12. C. Zhou, M.D. Zelinka, and S.A. Klein, "Impact of decadal cloud variations on the Earth’s energy budget", Nature Geoscience, vol. 9, pp. 871-874, 2016.
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  15. K.C. Armour, J. Marshall, J.R. Scott, A. Donohoe, and E.R. Newsom, "Southern Ocean warming delayed by circumpolar upwelling and equatorward transport", Nature Geoscience, vol. 9, pp. 549-554, 2016.
  16. . , "Making sense of palaeoclimate sensitivity", Nature, vol. 491, pp. 683-691, 2012.

56 Responses to “Sensible Questions on Climate Sensitivity”

  1. 51

    No one has responded to my query. Why not? I’m not a climate change denier. I’ve studied the data I’m capable of understanding and, for me, human induced climate warming is a fact. But it is also a fact that for the last million or so years the climate has been fluctuating with some regularity, with relatively short warming periods followed by much longer and increasingly colder years culminating in increasing glaciation and then warming again – all in approximately 100,000 year cycles. Study of these cycles leads one to believe that we should have been heading into a colder climatic period for the last few hundred years. That we are not speaks to a significant alteration of these cycles, best explained by human burning of fossil fuels and forest clearing. But if these facts are not accounted for we are likely to underestimate the sensitivity of our climate to atmospheric carbon dioxide. I’d appreciate some response.

  2. 52

    CWD 51,

    What was your question? I’m sorry, but I think I missed it. I’ll answer if I can.

  3. 53
    Mal Adapted says:

    C.W. Dingman:

    No one has responded to my query. Why not?

    Your query is fine, but your assumption that someone is obliged to respond is problematic. Probable reasons no one has are: nobody read it, nobody who read it has had time to craft a good answer, or nobody who read it is able to craft a good answer and doesn’t want to give a misleading one.

    I’m in the last category by default, but it sounds like you may be referring to the longest of the three Milanković cycles, identified by Serbian geophysicist and astronomer Milutin Milanković in the 1920s as the astronomical forcing for the Pleistocene ‘Ice Ages’. I can assure you that the scientific consensus on AGW is cognizant of those, and all other long-term cycles apparent in paleoclimate data. Since the Mark I eyeball is notoriously easy to fool, climate scientists have developed domain-specific statistical methods, that verify the 100ky cycle.

    Reliance on climate-specific statistical methods is a potential stumbling block for laypersons, but it can be overcome by education if you’re willing to cover all the ground along the way. If you’re new to the science supporting the AGW consensus, you can find out about Milanković cycles and much more in the highly recommended book The Discovery of Global Warming, written for educated non-specialists by physicist and historian of science Spencer R. Weart and published by the American Institute of Physics. I predict it will answer many of your questions. I found the paperback version very easy to absorb, while the online version is more detailed, and is updateable.

  4. 54


    I think that the slogans are those executive summaries that you are relying on to say distributed energy systems work, but only in pilot studies to my knowledge, is rooftop solar going to work in the north where days are short and snow cover lasts for months, and finally when you do the math on the extent of batteries and solar and wind it becomes mind numbingly large. Try this reference:
    What references do you have to say that those systems can replace the existing energy system?

  5. 55

    Roger Caiazza, it is not the responsibility of New York state to singlehandedly end climate change–rather a lucky thing, since New York state *can’t*. Actually, no single jurisdiction can, not even the national government of China.

    New York’s responsibility is to clean up *New York’s* emissions. Since the atmosphere is a global commons, New York must trust that other jurisdictions also act to clean up theirs. Of course, New York might wish to verify this–and luckily, 190+ nations have agreed to verification measures. It’s this thing called the “Paris Accord.” Perhaps you’ve heard of it?

    It’s annoying to have to rely on the good faith of others, of course. But then, others are also relying on the good faith of New York.

    (Sadly, the good faith of the US, not so much.)

  6. 56

    Dingman and Milankovitch
    It’s thought that summer insolation at 65deg N latitude drives or at least correlates with the onset and termination of ice ages. It’s possible to calculate this value 1MM years into the past and future. If you take a close look you’ll find that we are due to approach a local minimum in that insolation value in about 1000 years, after which the value will increase and it will not drop below the 1000 year value for about 50,000 years.

    Ganopolsky, et al (Nature, Vol 529, pp200-) studied the relationship between insolation at this latitude and ice age onset/termination, and also CO2 levels. They found that there is a curve defining the relationship between these variables. Below the curve an ice age can be initiated but above it, it cannot. As CO2 increases lower, more extreme insolation levels are required to initiate and sustain an ice age. Based on this relationship they conclude that at and above today’s CO2 levels there will be no ice age for at least 100kyr. Their analysis also suggests that even without our perturbation of greenhouse gases, there would not have been an ice age (or complete deglaciation either) for at least 50kyr.

    Now you may protest – why should this cycle be so different from every other cycle in the last million years? Well it just IS. Orbital cycles are chaotic. They don’t repeat exactly the same way. We just happen to be living in the highest prolonged period of 65N latitude summer insolation in the last 800,000 years. (It will happen again in 400,000 years, for even longer!) One factor is that we are in or entering a period of low orbital eccentricity, which reduces the difference between north and south summers and winters. We live in very fortunate times.