by Rud Istvan
If climate sensitivity is high, then modest GHG increases cause significant warming. If it is low, then significant GHG increases will not. Analysis of the IPCC assessment of sensitivity provides another window into the ‘government-climate research’ complex and its propensity to overstate future warming, misrepresent findings, and dismiss challenging evidence.
Equilibrium climate sensitivity (ECS) is the total eventual temperature response of surface temperature to a radiative perturbation. For anthropogenic global warming (AGW), the principal perturbation is from rising atmospheric CO2 concentration. The IPCC comparison norm is a doubling of CO2 (in the range of scenario SRES A2), the so-called ΔT2x. Doubling CO2 produces a directly increased forcing of 3.7w/m2 according to 3rd IPCC TAR. Zero feedback ΔT0 can be calculated using the Stefan-Boltzmann law. ΔT0 has been canonically calculated as 1°C. 
GCMs have multiple positive and negative feedbacks such as water vapor, lapse rate, and clouds. ECS is therefore an emergent property of the overall climate system, and of its models. Different feedbacks operate on different time scales. Since there can be no certainty about the future of any complex nonlinear dynamic system, ECS may be described as a probability density function (PDF). Substantial work since IPCC AR4 has gone into better PDF estimation (e.g. using improved Bayesian approaches). Recent research suggests that the high ECS ‘fat tail’ of IPCC AR4 is extremely unlikely, and that ΔT2x is not more than 4°C with 95% confidence.
ECS provides an important check on overall GCM realism. IPCC AR4 WG1 9.6 describes several ways climate observations can be used to constrain (i.e. ‘quality control’) GCM ECS. There is a revealing incongruity in the last paragraph of summary 9.6.4: “Results from studies of observed climate change and the consistency of estimates from different time periods indicate that ECS is very likely larger than 1.5°C with a most likely value between 2°C and 3°C. …Nevertheless, constraints from observed climate change support the overall assessment that the ECS is…a most likely value of approximately 3°C.” Which is the same value essentially since the 1979 Charney Report. The AR4 consensus selected the top value from the most likely range, perhaps because the IPCC AR4 GCMs mean ECS is 3.2.  This suggests consensus ‘high’ bias in several interesting ways.
The simplest energy balance description of ECS is a climate sensitivity parameter λ such that
ΔT = λ * ΔF
where T is a new equilibrium temperature in °C, sensitivity λ is a constant expressed as °C/(w/m2), and F is radiative forcing in w/m2. Zero feedback with doubled CO2 λ0is 0.3°C/(w/m2).
The other simple way to calculate climate sensitivity is by netting all positive and negative feedbacks ‘ƒ’ around ΔT0. It is the climate system’s amplifier gain.
ΔT = ΔT0 / (1-ƒ)
Obviously net positive ƒ causes nonlinearly increasing ΔT gain, while net negative ƒ damps asymptotically toward no temperature change. This model of ECS grows explosively as ƒ approaches 1, so has observational bounds.
The gain parameterization can be rearranged for an ECS ‘S’:
S = ΔT/ΔT0 = ΔT/1°C = ΔT = 1/(1-ƒ)
The consensus 4th IPCC value for SRES A2 is ΔT of 3.4°C for the 21st century.  SRES A2 has CO2 slightly more than doubling, specifically from about 380ppm in 2000 to about 860ppm in 2100. That is about a (860/380)=2.26 times increase in CO2 over the present atmospheric concentration.
Linear approximation calculates an AR4 consensus of ([2.0/2.26]*3.4) 3°C for a doubling of CO2. S = 3 corresponds to ƒ = (2/3) 0.67, and λ = (3/3.7) 0.8°C/(w/m2).
I use ECS point estimates while IPCC dealt in PDFs and ‘likely’ values. WG1 10.5.1 box 10.2 figure 2 has the most likely IPCC S (green) at 3 (P(0.5)=3) and the GCM S (blue) at 3.2. I just calculated the IPCC’s consensus ECS must be S = 3. WG1 9.6.4 said the best estimate was 3. Although 9.6.4 also said the most likely value was between 2 and 3, which the AR4 10.5.1 graphic definitely does not say. In a lawyerly way, we have again just shown the consensus ‘high’ bias, and a bit of graphical misrepresentation.
S (and translation to/from λ) can be used to evaluate the overall net GCM feedback ƒ. Modeled values of ECS should correspond to inferred values from observation.
There are at least three ways that S can be estimated:
- Bayesian GCM
- Inferred ƒ
- Inferred S
There may be studies in addition to those cited below where this has been or can be done. Please email them, as I wish to avoid selection bias. There are also papers that are very tempting, but which cannot fairly be used. 
Annan (footnote 2) showed that uniform priors do not take full advantage of actual climate knowledge, and result in greater probability of a high S.
Annan published his resulting PDF’s in his Figure 2. He did not discuss the resulting most likely S of 1.8-1.9. Enlarge the figure digitally to verify this; dotted is prior, solid is posterior. These are far below 3, and outside the AR4 9.6.4 most likely band. The paper gives a long discussion about this method and how it constrains unrealistically high values. Nothing about what the improved estimation otherwise says about the consensus S. (I read the paper twice to make sure).
Using a blend of uniform and informed priors, Tomassini found S using the Bern 2.5D GCM of around 2 to 2.3. Case f is with (dashed) and without (solid) ocean heat (Levitus 2005) in the prior.
Using expert priors, Aldin estimated a mean S of 2°C with a mode of about 1.9. The PDF is
A possible criticism is that Aldin uses a simpler climate model than those above.
Forster’s study of ERBS radiation budgets estimated the observed net radiative feedback at 2.3w/m2 above ΔT0 3.7w/m2.  This implies S=([3.7+2.3]/3.7) = 1.6. A much more sophisticated evaluation of this paper reached essentially the same conclusion using very different methods.
This is important because GCMs are not involved. The authors said,
“If our results are accurate, it could mean either that there is little or no positive water vapor feedback and a neutral cloud feedback or it could imply that the longwave cloud feedback is negative… [compared to GCMs]”. Both suppositions can be shown directionally correct compared to observation, since all GCMs have roughly constant UTrH and positive cloud feedback. (Both are at variance with observed trends since 1975. The directionally correct answer is lower but still positive water vapor feedback and neutral to negative cloud feedback.) Climate Etc. followers also know this important paper’s result was improperly ‘transformed’ by AR4 to misleadingly indicate higher sensitivity and a worrisome ‘high S’ fat tail.
A different study of radiative satellite data found the observed imbalance was 0.9W/m2.  The 4th IPCC’s consensusnet imbalance is +1.6W/m2. Using the same reasoning as for Forster, the inferred S is about 1.7. A potential criticism is this study’s short observational period.
Chylek used the Vostok ice cores to estimate that λ was about 0.49, and S was 1.3-2.3 with 95% confidence.  The analysis covered both a warm to cold period, and a cold to warm period, each thousands of years long and capturing all feedbacks. It followed their paper using satellite data to infer infer a similar ECS. Chylek’s study was criticized by a comment from Hargreaves and Annan for using paleoclimate starting and ending points. Hargreaves and Annan pointed out that the accepted method was to use averages, did so, and found S =2.4. And then they said, “ The resulting climate sensitivity is in line with most energy balance analyses of paleoclimate data”. That is simply not true. The comment specifically referenced Hansen 1993 , who says ice age paleoclimate gives S =3. So does Knutti’s review, below (footnote 27), available prior to the comment. Even more telling, Hargreaves and Annan closed with: “The authors have not presented any significant evidence to challenge existing estimates of climate sensitivity”. Yet the comment itself does, and ignored the fact. Hargreaves and Annan also ignore their own Bayesian finding of S ≈ 1.9. Chylek published a 2009 open letter to the climate research community saying it had “substituted the search for truth with an attempt to prove one point of view.” 
Schmittner’s paleoclimate data from the last glacial maximum estimates a median sensitivity of 2.3°C, as well as constraining the likely range to 1.7-2.6. There is now the usual critique on grounds that the findings don’t agree with the consensus value of S=3, and so are suspect. The 2011 ‘consensus’ paper cited in support of this view gives improper values and has many things biased ‘high’. As a specific example, ΔT0 is given as 4w/m2 when the IPCC TAR value is 3.7. As another specific example, the peak Eemian temperature is shown as 1°C above the present when other proxies have it regionally as much as 6°C higher, and Vostok shows 3°C. (Yet again showing proxy selection bias.) They even criticize Schmittner for only going from cold to warm (like AGW itself).
Schwartz used ocean heat data from Levitus (2005) to observationally (and erroneously) calculate ΔT as 1.1°C±0.5 without reliance on GCMs.  The period covered was 125 years. The finding was so surprising that he critiqued several possible error sources himself.
This provoked three responses. One pointed to ocean data quality to basically dismiss the result. Levitus (2009 and 2012) continues to refine the ocean heat data; those refinements do not alter the corrected conclusion of this paper.
The second pointed out a problem in the calculation of relaxation time, and offered a corrected version (that also agrees with other findings). Schwartz republished with the correction and found λ = 0.51 and S = 1.9. That is how good science should work.
The third was a response from Foster et al. (with Mann as senior author). They plugged Schwarz’ observational findings into GCM GISS-ER, and reproduced his results! So they argued Schwartz’ data were wrong, because “this model is known to exhibit a true equilibrium climate sensitivity of 2.7 C under doubled CO2 conditions.” They then did a similar thing for his time scale parameter using a 14 GCM ensemble. They said, “the estimates of time scale produced by this method are generally unrealistically low in comparison to the known behavior of the models in response to changes in GHG forcing.” They in effect said twice in one comment that the GCM models are trustworthy, and evaluation of 125 years of actual climate observations isn’t. Schwartz’ reply says much: “It is questionable whether measurements should be rejected because they do not agree with models.”
This comment finally referencing a (then new) sensitivity review by Knutti, saying Schwartz’ result was inconsistent with other observational data. Knutti’s review has the most likely S from a century of instrumental observation at about 2.3, and from the last millennium’s proxies at about 2.1. Only the review’s paleoclimate data supported S=3. The new Chylek (corrected) and Schmittner paleoclimate work suggests S=2.3-2.4. All three classes of observations are closer to Schwartz’ corrected 1.9 than to the consensus value of S=3. It apparently never occurred to these commenters that the review’s observational judgments implied that GCMs are oversensitive.
If you have been checking footnotes, you know I have excluded Lindzen and Choi’s corrected 2011 paper that finds S = 0.7. Sea surface temperature is not just a response to radiative imbalance. It is also a function of ocean oscillations like PDO and AMO. Over most of their observational period, AMO was in a cold minimum and PDO was declining. Both would (if uncorrected) result in underestimation. Which appears to have been the case to some degree.
GCMs are oversensitive. IPCC future warming forecasts are too high. IPCC AR4’s own sensitivity discussion irrefutably illustrates this ‘high’ bias.
The consensus places unshakable faith in simulation models that provably do not correctly reproduce the most important two feedbacks. For both of the principal atmospheric feedbacks there is a ‘high’ bias in simulation compared to observation that collectively explain why S is also too high. Forster and Gregory pointed this out half a decade ago. Don’t damn the data. Fix the models.
JC comment: Rud Istvan emailed me this post several days ago, we have gone back and forth on this several times and I have done some light editing. Rud is author of the forthcoming book Arts of Truth. This is a guest post, and the views presented here are those of Rud Istvan.
 For details see for example, CO2 no feedback sensitivity posted on Climate Etc 12/11/10. This is not settled. Fiedler derived 1.1°C in METR 5223, GCM Sensitivity Analysis, School of Meteorology, University of Oklahoma (2009), hereinafter Fiedler. 4th IPCC WG1 184.108.40.206 says GCMs calculate 1.2°C, which is a possible red flag. Differences involve ‘black’ versus ‘grey’ Earth. I use 1°C here for simplicity even though it may slightly overstate S.
 Annan and Hargreaves, On the generation…of probabilistic estimates of climate change, Climate Change 104:423-436 (2011)
 AR4 WG1 220.127.116.11 table 8.2. The median is also 3.2. The mode is 3.4.
 Cess (1990) at pubs.giss.nasa.gov
 Nothing new. See, for example, Torn and Harte, Missing Feedbacks, Asymmetric Uncertainties, Geophys. Res. Lett. 33: L10703 (2006). Fiedler, GCM Sensitivity Analysis (METR 5223), University of Oklahoma School of Meteorology, (2009). Lindzen and Choi, On the Observational Determination of Climate Sensitivity, Asia-Pacific J. Atmos. Sci. 47: 377-390 (2011). Curry, chapter 13 galley proofs (Thermodynamic Feedbacks), 2012.
 4th IPCC Table SPM 3
 Fiedler gives a precise method. The text uses simpler linear approximation.
 For example, Murphy et. al., An observationally based energy balance, J. Geophys. Res. 114: D17107 (2009). The authors expressly said, “the values used in this paper should not be interpreted in terms of equilibrium climate sensitivity.” Fair enough. (They followed the methods of Forster, but with a different goal.) But if one unfairly did, it would be about ([1.25/1.6]*3) an S of 2.3.
 Tomassini et. el., Robust Bayesian Uncertainty Analysis of Climate System Properties, J. Climate 20: 1239-1234.
 Aldrin et. al., Bayesian estimation of climate sensitivity, Envirometrics doi:10.1002/env.2140 (2012). See also the presentation from Norsk Regnesentral at nr.no/~Aldrin (2010)
 Forster and Gregory, The Climate Sensitivity…,J. Climate 19: 39-52 (2006)
 Fiedler’s method via λ calculates 1.5.
 Nic Lewis, IPCC’s Alteration of Forster and Gregory… posted on Climate Etc 7/5/2011
 Trenberth et. al., Earth’s Global Energy Budget, Bull. Am. Meteor. Soc. 90: 311-323 (2009)
 Chylek and Lohmann, Aerosol radiative forcing and climate sensitivity…, Geophys. Res. Lett. 35: L04804 (2008)
 Chylek et. al., Limits on Climate Sensitivity derived from recent satellite and surface observations, J. Geophys. Res. 112: D24S04 (2007)
 Hargreaves and Annan, Comment on CL08, Clim. Past. 5:143-145 (2009)
 Hansen et. al., How Sensitive is the World’s Climate? available at pubs.giss.nasa.gov
 His letter is available, for example, at thegwpf.org/opinion-pros-s-cons/218
 Schmittner et. al., Climate Sensitivity from …Reconstructions, Science 334: 1385-1388 (2011)
 See, for example, Skepticalscience/schmittner.
 Hansen and Sato, Paleoclimate implications… available at pubs.giss.nasa.gov
 For an excellent book length detailed overview compared to Hansen’s 2011 paper, see Prof. Antón Uriarte’s new e-book, Earth’s Climate History (2011). Worth every penny.
 Schwartz, Heat Capacity, Time Constant, and Sensitivity of Earth’s Climate System, J. Geophys. Res. 113: D15195 (2008) [corrected]
 Foster et. al., Comment on …Schwartz , J. Geophys. Res. 113: D15102 (2008)
 Knutti and Hegerl, The Equilibrium Sensitivity…, Nature Geocience/ngeo3387 (2008)