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.

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Notes

* 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.

References

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.

Are climate models running hot or observations running cold?

“About thirty years ago there was much talk that geologists ought only to observe and not theorise; and I well remember some one saying that at this rate a man might as well go into a gravel-pit and count the pebbles and describe the colours. How odd it is that anyone should not see that all observation must be for or against some view if it is to be of any service!”
Charles Darwin

“If we had observations of the future, we obviously would trust them more than models, but unfortunately…"
Gavin Schmidt

"What is the use of having developed a science well enough to make predictions if, in the end, all we're willing to do is stand around and wait for them to come true?"
Sherwood Rowland

This is a post in a new series on whether we have underestimated global warming; this installment is inspired by a recent article on climate sensitivity discussed at And Then There's Physics.

The quirky Gavin Schmidt quote naturally wanted to say something similar to Sherwood Rowlands, but contrasted to Darwin I have to agree with Darwin and disagree with Schmidt. Schmidt got the quote from to Knutson & Tuleya (thank you ATTP in the comments).

The point is that you cannot look at data without a model, at least a model in your head. Some people may not be aware of their model, but models and observations always go hand in had. Either without the other is nothing. The naivete so often displayed at WUWT & Co. that you only need to look at the data is completely unscientific, especially when it is in all agony their cherry picked miniature part of the data.

Philosophers of science, please skip this paragraph. You could say that initially, in ancient Greece, philosophers only trusted logic and heavily distrusted the senses. This is natural at this time, if you put a stick in the water it looks bent, but if you feel with your hand it is still straight. In the 17th century British empiricism went to the other extreme and claimed that knowledge mainly comes from sensory experience. However, for science you need both, you cannot make sense of the senses without theory and theory helps you to ask the right questions to nature, without which you could observe whatever you'd like for eternity without making any real scientific progress. How many red Darwinian pebbles are there on Earth? Does that question help science? What do you mean with red pebbles?

In the hypothetical case of observations from the future, we would do the same. We would not prefer the observations, but use both observations and theory to understand what is going on. I am sure Gavin Schmidt would agree; I took his beautiful quote out of context.

Why I am writing this? What is left of "global warming has stopped" or "don't you know warming has paused?" is that models predicted more warming than we see in the observations. Or as a mitigation sceptic would say "the models are running hot". This difference is not big, this year we will probably get a temperature that fits to the mean of the projections, but we also have an El Nino year, thus we would expect the temperature to be on the high side this year, which it is not.


Figure from Cowtan et al. (2015). Caption by Ed Hawkins: Comparison of 84 RCP8.5 simulations against HadCRUT4 observations (black), using either air temperatures (red line and shading) or blended temperatures using the HadCRUT4 method (blue line and shading). The shaded regions represent the 90% range (i.e. from 5-95%) of the model simulations, with the corresponding lines representing the multi-model mean. The upper panel shows anomalies derived from the unmodified RCP8.5 results, the lower shows the results adjusted to include the effect of updated forcings from Schmidt et al. [2014]. Temperature anomalies are relative to 1961-1990.

If there is such a discrepancy, the naive British empiricist might say:

• "the models are running hot", 

but the other two options are:

• "the observations are running cold" or
• "the comparison is not fair".

And every of these three options has an infinity of possibilities. As this series will show, there are many observations that suggest that the station temperature "observations are running cold". This is just one of them. Then one has to weigh the evidence.

If there is any discrepancy a naive falsificationist may say that the theory is wrong. However, discrepancies always exist; most are stupid measurement errors. If a leaf does not fall to the ground, we do not immediately conclude that the theory of gravity is wrong. We start investigating. There is always the hope that a discrepancy can help to understand the problem better. It is from this better understanding that scientists conclude that the old theory was wrong.

Estimates of equilibrium climate sensitivity from the recent IPCC report. The dots indicate the mean estimates, the horizontal lines the confidence intervals. Only studies new to this IPCC report are labelled.

Looking at projections is "only" the last few decades, how does it look for the entire instrumental record? People have estimated the climate sensitivity from the global warming observed until now. The equilibrium climate sensitivity indicates how much warming is expected on the long term for a doubling of the CO2 concentration. The figure to the right shows that several lines of evidence suggest that the equilibrium climate sensitivity is about 3. This value is not only estimated from the climate models, but also from climatological constraints (such as the Earth having escaped from [[snow-ball Earth]]), from the response to volcanoes and from a diverse range of paleo reconstructions of past changes in the climate. And newly Andrew Dessler estimated the climate sensitivity to be 3 based on decadal variability.

The outliers are the "instrumental" estimates. Not only do they scatter a lot and have large confidence intervals; that is to be expected because global warming has only increased the temperature by 1°C up to now. However, these estimates are on average also below 3. This is a reason to critically assess the climate models, climatological constraints and paleo reconstructions, but the most likely resolution would be that the outlier category, the "instrumental" estimates, are not accurate.

The term "instrumental" estimate refers to highly simplified climate models that are tuned to the observed warming. They need additional information on the change in CO2 (quite reliable) and on changes in atmospheric dust particles (so-called aerosols) and their influence on clouds (highly uncertain). The large spread suggests that these methods are not (yet) robust and some of the simplifications also seem to produce biases towards too low sensitivity estimates. That these estimates are on average below 3 is likely mostly due to such problems with the method, but it could also suggest that "the observations are running cold".

In this light, the paper discussed over at And Then There's Physics is interesting. The paper reviews the scientific literature on the relationship between how well climate models simulate a change in the climate for which we have good observations and which is important for the climate sensitivity (water vapour, clouds, tropical thunderstorms and ice) and the climate sensitivity these models have. It argues that:

the collective guidance of this literature [shows] that model error has more likely resulted in ECS underestimation.

Given that these "emergent constraint" studies find that the climate sensitivity from dynamic climate models may well be too low rather than too high, it makes sense to investigate whether the estimates from the "instrumental" category, the highly simplified climate models, are too low. One reason could be because we have underestimated the amount of surface warming.

The top panel (A) shows a measure for the mixing between the lower and middle troposphere (LTMI) over warm tropical oceans. The observed range is between the two vertical dashed lines. Every coloured dot is a climate model. Only the models with a high equilibrium climate sensitivity are able to reproduce the observed lower tropospheric mixing.
The lower panel(B) shows a qualitative summary of the studies in this field. The vertical line is the climate sensitivity averaged over all climate models. For the models that reproduce water vapour well this average is about the same. For the models that reproduce ice (cryosphere), clouds, tropical thunder storms (ITCZ) well the climate sensitivity is higher.

Concluding, climate models and further estimates of the climate sensitivity suggest that we may underestimate the warming of the surface temperature. This is certainly not conclusive, but there are many lines of evidence that climate change is going faster than expected as we will in further posts in this series: Arctic sea ice and snow cover, precipitation, sea level rise predictions, lake and river warming, etc. In combination the [[consilienceof evidence]] suggests at least that "the observations running cold" is something we need to investigate.

Looking at the way station measurements are made there are also several reasons why the raw observations may show too little warming. The station temperature record is rightly seen as a reliable information source, but in the end it is just one piece of evidence and we should consider all of the evidence.

There are so many lines of evidence for underestimating global warming that science historian Naomi Oreskes wondered if climate scientists had a tendency to "err on the side of least drama" (Brysse et al., 2013). Rather than such a bias, all these underestimates of the speed of climate change could also have a common cause: an underestimate of global warming.

I did my best to give a fair view of the scientific literature, but like for most posts in this series this topic goes beyond my expertise (station data). Thus a main reason to write these posts is to get qualified feedback. Please use the comments for this or write to me.

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Related information

Gavin Schmidt wrote the same 2 years ago from a modellers perspective: On mismatches between models and observations.

Gavin Schmidt's TED talk: The emergent patterns of climate change and corresponding article.

Climate Scientists Erring on the Side of Least Drama

Why raw temperatures show too little global warming

First post in this series wondering about a cooling bias: Lakes are warming at a surprisingly fast rate

References

Cowtan, Kevin, Zeke Hausfather, Ed Hawkins, Peter Jacobs, Michael E. Mann, Sonya K. Miller, Byron A. Steinman, Martin B. Stolpe, and Robert G. Way, 2015: Robust comparison of climate models with observations using blended land air and ocean sea surface temperatures. Geophysical Research Letters, 42, 6526–6534, doi: 10.1002/2015GL064888.

Fasullo, John T., Benjamin M. Sanderson and Kevin E. Trenberth, 2015: Recent Progress in Constraining Climate Sensitivity With Model Ensembles. Current Climate Change Reports, first online: 16 August 2015, doi: 10.1007/s40641-015-0021-7.

Schmidt, Gavin A. and Steven Sherwood, 2015: A practical philosophy of complex climate modelling. European Journal for Philosophy of Science, 5, no. 2, 149-169, doi: 10.1007/s13194-014-0102-9.

Brysse, Keynyn, Naomi Oreskes, Jessica O’Reilly and Michael Oppenheimer, 2013: Climate change prediction: Erring on the side of least drama? Global Environmental Change, 23, Issue 1, February 2013, Pages 327–337, doi: 10.1016/j.gloenvcha.2012.10.008.