Troy's Scratchpad

October 30, 2014

Combining recent instrumental sensitivity estimates with paleo sensitivity estimates

Filed under: Uncategorized — troyca @ 7:46 pm

In the last couple years, there have been quite a few papers using the instrumental period to estimate equilibrium*** sensitivity, with most of them finding best estimates heavily concentrated near the lower end of the IPCC 1.5K – 4.5K assessed "likely" range.  Examples include Aldrin et al. (2012), Ring et al. (2012), Otto et al. (2013), Lewis (2013), Skeie et al. (2014), Masters (2014), Loehle (2014), and, more recently, Lewis and Curry (2014).  I think this general theme stems from a few factors: 1) the lower-than-expected increase in surface temperatures at the turn of the century, 2) a decrease in estimates of the magnitude of the anthropogenic aerosol cooling offset, and 3) more constrained estimates of OHC in recent years.

Many people argue that these studies indicate that sensitivity is less than previously thought, and that policies and risk analysis should reflect the downgraded estimates.  Critics, on the other hand, often point to paleo evidence to dismiss the impact of these studies on our current expectations of CO2-induced warming.  Therefore, I thought it would be interesting to combine the latest estimates of sensitivity from PALAEOSENS (2012), which I take to represent synthesized evidence from paleo estimates, with my (admittedly ad-hoc) synthesized evidence from a few of these recent instrumental era estimates with published distributions.  This Bayesian approach of combining different lines of independent evidence is nothing particularly new, having been done by Annan and Hargreaves (2006), but I was curious to see how it would shake out with these recent estimates.  Here are the results:


Numerically, the result of the “combined” evidence is a median of 2.1 K, a “likely” (68%) range of 1.5-2.9 K, and a “very likely” (95%) range of 1.1K-3.9K.  There are a few caveats here: first, I used WebPlotDigitizer to quickly digitize the values from the aforementioned studies, which is a nifty tool, but obviously not perfect.  Second, your results for this kind of method are always going to be affected by the studies chosen, although I think the “Instrumental Mean” line – with its mode and median between 1.5 and 2.0 K – is probably a fair representation of the evidence from these type of studies.  And finally, it could be argued that there are structural uncertainties in our knowledge that permeate both the paleo and instrumental estimates, such that these lines are not truly “independent”, and the resulting uncertainty ranges should be wider. 

Script for this post can be found here.

***these methods range from assuming effective=equilibrium sensitivity (e.g. Otto et al 2013) to explicitly considering the modeled differences (e.g. Masters 2014).  


  1. 1. If one uses the latest HITRAN data instead of something from the last millennium then all your figures have to drop by about 30% because the best estimate of the direct effect of CO2 is not about 1C but about 0.6C for a doubling.

    2. The ice-age records show that there exists very strong negative feedbacks in warm interglacial periods for any warming.

    3. All the estimates of sensitivity basically use the same period of strong temperature rise from 1970-2000 and are therefore all biased by a single event (which happens to coincide with the period when we were cleaning up the atmosphere from the various anti-pollution acts).

    So, I’ve confident the effect of doubling CO2 is below 1C

    Comment by Scottish Sceptic — October 31, 2014 @ 2:04 am

    • Hi Scottish:

      1. If one uses the latest HITRAN data instead of something from the last millennium then all your figures have to drop by about 30% because the best estimate of the direct effect of CO2 is not about 1C but about 0.6C for a doubling.

      I am not sure what you mean about the “direct effect” of CO2, but I am presuming you mean the “no feedback” scenario (idealized Planck response), in which case I am assuming you believe the HITRAN data to show a reduction in the forcing per CO2-doubling? Current estimates use about 3.7 W/m^2…are you suggesting it is closer to 2.2 W/m^2? First of all, I find this hard to believe, given that there is a history of validating the line-by-line radiative transfer codes used to derive the CO2 forcing against this HITRAN database… do you have a reference? Second, a reduction in the estimates of the WMGHG forcing would actually *increase* the instrumental estimates of sensitivity, not decrease them. The reason for this is that these estimates tend to use some variation of an energy balance model in their method, where ECS = F_2xCO2 / [(F_hist – Q_hist) / T_hist]. Fixing Q_hist and T_hist at 0.8 K and 0.5 W/m^2 (which is about what is used in these estimates), a reduction in F_2xCO2 from 3.7 W/m^2 to 2.2 W/m^2 would also mean reducting F_hist (or which a large component is WMGHG forcing) from 1.95 W/m^2 to 0.85 W/m^2 (that is, a larger proportion is offset by aerosols), resulting in a “most likely” estimate for ECS of ~5K!

      2. The ice-age records show that there exists very strong negative feedbacks in warm interglacial periods for any warming.

      PALAEOSENS provides a synthesis of a large collection of studies about various periods in the past. I have not studied paleo sensitivity in any detail myself, but surely you can see why, given the lack of support in your comment here, I don’t really see what I can do with your statement. Do you have some work quantifying the sensitivity over these various periods?

      3. All the estimates of sensitivity basically use the same period of strong temperature rise from 1970-2000 and are therefore all biased by a single event (which happens to coincide with the period when we were cleaning up the atmosphere from the various anti-pollution acts).

      You seem to be arguing here that the bulk of the rise from 1970 to 2000 was due to a reduction in the cooling offset of the aerosol forcing, and therefore this should result in lowered instrumental estimates. To this I have a couple objections:

      1) There are studies that have examined the change in aerosol forcing with this “brightening” (e.g. Cherian et al (2014) for Europe –, and it is possible to compare the global change in aerosol forcing against that of WMGHG over the time period. Moreover, most studies indicate that the forcing change resulting from the reduction in U.S. + European aerosols was offset by increasing aerosols over Asia. So I would be curious to see a credible estimate of the aerosol forcing change since 1970 suggesting it dwarfed the WMGHG forcing.

      2) If you were able to find #1 to be the case, I would note that of the instrumental studies included, one examines the time from 1950 to the most recent decade, while the other two examine from the 19th century to present. Even if you postulate that the global aerosol forcing change is positive from 1970 to present, there is no arguing that globally the aerosol forcing is negative relative to pre-industrial times. If you thus make the case that the magnitude of the aerosol forcing is stronger than that suggested by IPCC estimates (which you would need to for it to be responsible for the temperature rise), this will again *increase* the estimated ECS over the instrumental period, because of the overall decrease in F_hist from the energy balance estimate above.


      Comment by troyca — October 31, 2014 @ 12:15 pm

  2. According to Gavin Schmidt the primary CO2 absorption bands are saturated:

    When you plug that into the solar spectrum you get this:

    The models use hitran for the approximately logarithmic diminution in effect with increase on concentration, but I do not believe they have factored in Beer’s saturation.

    Comment by gymnosperm — October 31, 2014 @ 9:26 pm

    • As I did to the above commentor, I would ask you, what value do you then expect for the forcing from a doubling of CO2? I would be very surprised to find such a simple mistake, as the LBLRTMs have been extensively tested again databases like HITRAN, and such a mistake would affect applications far more ubiquitous than that those in climate science. Regarding Beer-Lambert, Science of Doom has a good post on why including emission is necessary if you are going to attempt to model the radiative forcing vs. concentration relationship:

      Comment by troyca — November 3, 2014 @ 7:38 am

      • Apparently the standard logarithmic relationship assumed between CO2 concentration and forcing is likely to be revised to make forcing decrease more slowly than logarithmically, but only modestly. A weaker CO2 band that is not saturated becomes more significant.

        Comment by niclewis — November 5, 2014 @ 10:43 am

      • Sorry, I meant increase more slowly than logarithmically

        Comment by niclewis — November 5, 2014 @ 10:45 am

      • Thanks Nic, interesting…any idea of the degree of the change? I am assuming we are not talking about anything that drops the 280->560 concentration change below 3 W/m^2?

        Comment by troyca — November 6, 2014 @ 8:01 am

      • I’m not sure, but I think it is a fairly minor change

        Comment by niclewis — February 25, 2015 @ 8:05 am

  3. Oops, that would be EARTH spectrum.

    Comment by gymnosperm — November 1, 2014 @ 7:29 am

  4. I have qualms about combining paleo ECS estimates with modern ones. I don’t see the justification for assuming that the property (ECS) is the same for the glacial state as for the current state. An analogy: suppose that you estimated the slope of a response curve by taking two nearby measurements and drawing a chord between them, and someone else did the same. If the curve is (say) tan(x), and your measurement is near x=0 while theirs is near x=45 degrees, the results are not directly comparable. The assertion that climate sensitivity is the same in a world with vast permanent ice, and presumably much less greenery and a much larger seasonal variation in sea ice, seems to be a mere assumption rather than being backed by evidence.

    Comment by HaroldW — November 2, 2014 @ 1:47 pm

    • Harold,

      I don’t disagree with your points re different responses under different conditions. This is certainly a limitation of palaeo estimates, and I think you can get into plenty of subjective / judgment calls not only in which specific studies to include within meta-analysis, but how to assess the relative strengths of various methods. That being said, part of what you see in the above combining of instrumental + paleo is that despite people claiming that “paleo says this about sensitivity”, it really does provide a relatively weak constraint / wide distribution. I believe in the upcoming decades we will reduce the primary uncertainties in the instrumental methods (aerosol forcing + OHC estimates), so those will provide the stronger constraints going forward.

      Comment by troyca — November 3, 2014 @ 7:26 am

  5. Troy, I agree with the concept of what you have done (and have carried out a similar exercise myself), but I have a few comments:

    1. The recent lower instrumental estimates do not generally depend on the hiatus. Aldrin 2012, Lewis 2013, Otto 2013, Skeie 2014, Lewis & Curry 2014 all produce much the same median ECS estimates when using data ending at 2000 (Aug 2001 for Lewis 2013; it uses no later data).

    2. The reduction in consensus (IPCC) aerosol forcing estimates impacted the Otto 2013 and Lewis & Curry 2014 ECS estimates, but I beleive not any of your other instrumental estimates. Indeed, the higher AR4 aerosol forcing estimates used as Bayesian priors increased the Aldrin 2012 and Skeie 2014 ECS estiamtes beyond where their observational data gave a best fit.

    3. The more constrained OHC estimates may have reduced ECS uncertainty ranges, but I do not think they have reduced the median ECS estimates from instrumental studies.

    More importantly, your method of combining instrumental and paleo estimates isn’t really valid. Bayesian updating requires the multiplication of a (posterior) PDF from one source – used as a prior – with an independent likelihood function (not a PDF) from a different source. One could argue that the roughly Gaussian paleo estimate warrants a uniform prior so that its likelihood function would have been the same share as the PDF.
    But in any case Bayesian updating isn’t valid in a case like this, in my view. It provides an ill defined result that in general will depend on which source is used to provide the PDF and which source to provide the likelihood function. See my 2013 paper Modification of Bayesian updating where continuous parameters have differing relationships with new and existing data. arXiv Rep., 25 pp at

    BTW, minor point, in IPCC parlance “very likely” means 90% probable (5-95%) not 95% and “likely” means 66% (17-83%) not 68%.

    Comment by niclewis — November 5, 2014 @ 11:10 am

    • Hi Nic,

      Given #1-3, what do you suppose the reason is for the lack of low estimates of sensitivity prior to the last few years?

      I suppose I am being a bit cavalier in describing the method above as Bayesian updating (and I confess that, short of some extensive study, your paper is over my head). If I understand, your point is essentially that some sort of synthetic instrumental likelihood function is going to look different than that synthetic instrumental PDF (whereas the paleo likelihood function and PDF could be relatively the same), so which is chosen as the prior will matter. That being said, my expectation is that the uncertainty resulting from these differences is relatively minor compared to the uncertainty in choosing which lines of evidence are independent, which studies go into each line of evidence, and how to create a synthesis of each line of evidence, but perhaps that is incorrect.

      I would be curious to see the results of your exercise in combining various lines of evidence. From a glance at the assessment of the last IPCC AR5 report, my impression is that they tended to use an “inclusive” assessment that was more along the lines of an average of the study distributions, rather than taking the product of independent methods. This tends to grant larger probabilities to higher-end sensitivities, and IMO does not properly devalue “low information” study results.

      Comment by troyca — November 6, 2014 @ 9:08 am

      • Hi Troy

        You ask what I think the reason is for the lack of low estimates of sensitivity prior to the last few years. I can tell you why the instrumental period ECS estimates cited in AR4 were all high, as follows:

        Andronova and Schlesinger (2001) was affected by an error in its computer code that substantially biased upwards its estimate for ECS – it seems by ~0.9°C for the case with a realistic set of forcings included.

        Gregory et al. (2002) used a very high estimate of aerosol forcing, derived from an unsuitable GCM-based detection & attribution study, and also the erroneous Levitus et al 2000 ocean heat content dataset (an “arithmetical error” – reported by James Annan but no action taken).

        All the other studies apart from Forster and Gregory (2006) had results stated using unsuitable uniform priors for ECS and, often, also for ocean diffusivity. That gave them very fat upper tails as well as increasing their median estimates. If the Forster and Gregory (2006) results had not been restated on that basis, the median ECS estimate would have been 1.6 rather than 2.3°C.

        Knutti et al. (2002) used a very weak statistical method and found that their observational constraints did not enable a well constrained ECS estimate to be produced; they did place a lower limit of 1.2°C on ECS, but that figure was biased upwards by use of the same erroneous OHC dataset as Gregory et al. (2002).

        Frame et al (2005): statistical errors, ocean heat content miscalculation, use of GHG attributable warming derived from an unsuitable GCM-based detection & attribution study. See Lewis (2014) J Climate

        Forest et al (2002 and 2006): multiple statistical errors, poor experimental design, use of data ending in 1995: see Lewis (2014) J Climate, where a revised ECS best estimate of 1.6 C waas obained when using the full model simulation runs to 2001, better experimental design and correct statisitical methods.

        I made a crude attempt a few months ago at seeing how much a paleo estimate fitted by a shifted lognormal distribution with 10-90% range of 1-6 K (as per AR5) and a median of 2.86 K (my notes indicate this related to AR5 Fig. 10.20b and was a mean, but I’m not offhand sure what of) alters the ECS median and ranges from Lewis & Curry 2014. Roughly speaking, it increased the 5%, 17%, 50% and 83% points all by about 0.1 C, but significantly reduced the 95% ECS point. However, I didn’t estimate a noninformative prior distribution for the combined estimate, so these results may be some way out. I must try doing so.

        I agree that AR5 used crude methods of combining various lines of evidence, and evidence from different studies within each line of evidence, and did not adequately devalue ‘low information’ study results..

        Comment by niclewis — November 8, 2014 @ 3:03 pm

      • Thanks Nic, that is a pretty comprehensive dissection of some of those older studies, and I also re-read your “Sensitive Matter” paper as well and saw your criticisms WRT the AR5 studies.

        Regarding the affect of a palaeo prior on your LC14 results, I am surprised that it only increased most of those percentile estimates by ~0.1 K.

        Comment by troyca — November 13, 2014 @ 7:59 am

      • Hi Troy, I’ve now done a more accurate assessment using a computed noninformative prior, and find a rather larger increase in ECS at the 50% and 83% when adding the paleo information, and a modest increase rather than a significant decrease of the 95% point. But the effects of adding the paleo information are still fairly modest.

        Comment by niclewis — November 27, 2014 @ 1:04 pm

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