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All IPCC definitions taken from Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Annex I, Glossary, pp. 941-954. Cambridge University Press.

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How sensitive is our climate?

What the science says...

Select a level... Basic Intermediate Advanced

Net positive feedback is confirmed by many different lines of evidence.

Climate Myth...

Climate sensitivity is low

"His [Dr Spencer's] latest research demonstrates that – in the short term, at any rate – the temperature feedbacks that the IPCC imagines will greatly amplify any initial warming caused by CO2 are net-negative, attenuating the warming they are supposed to enhance. His best estimate is that the warming in response to a doubling of CO2 concentration, which may happen this century unless the usual suspects get away with shutting down the economies of the West, will be a harmless 1 Fahrenheit degree, not the 6 F predicted by the IPCC." (Christopher Monckton)


Climate sensitivity is the estimate of how much the earth's climate will warm in response to the increased greenhouse effect if we double the amount of carbon dioxide in the atmosphere.  This includes feedbacks which can either amplify or dampen that warming.  This is very important because if it is low, as some climate 'skeptics' argue, then the planet will warm slowly and we will have more time to react and adapt.  If sensitivity is high, then we could be in for a very bad time indeed.

There are two ways of working out what climate sensitivity is. The first method is by modelling:

Climate models have predicted the least temperature rise would be on average 1.65°C (2.97°F) , but upper estimates vary a lot, averaging 5.2°C (9.36°F). Current best estimates are for a rise of around 3°C (5.4°F), with a likely maximum of 4.5°C (8.1°F).

The second method calculates climate sensitivity directly from physical evidence, by looking at climate changes in the distant past:

adapted fig 3a

Various paleoclimate-based equilibrium climate sensitivity estimates from a range of geologic eras.  Adapted from PALEOSENS (2012) Figure 3a by John Cook.

These calculations use data from sources like ice cores to work out how much additional heat the doubling of greenhouse gases will produce.  These estimates are very consistent, finding between 2 and 4.5°C global surface warming in response to doubled carbon dioxide.

It’s all a matter of degree

All the models and evidence confirm a minimum warming close to 2°C for a doubling of atmospheric CO2 with a most likely value of 3°C and the potential to warm 4.5°C or even more. Even such a small rise would signal many damaging and highly disruptive changes to the environment. In this light, the arguments against reducing greenhouse gas emissions because of climate sensitivity are a form of gambling. A minority claim the climate is less sensitive than we think, the implication being we don’t need to do anything much about it. Others suggest that because we can't tell for sure, we should wait and see.

In truth, nobody knows for sure quite how much the temperature will rise, but rise it will. Inaction or complacency heightens risk, gambling with the entire ecology of the planet, and the welfare of everyone on it.

Basic rebuttal written by GPWayne

Update July 2015:

Here is the relevant lecture-video from Denial101x - Making Sense of Climate Science Denial

Last updated on 5 July 2015 by skeptickev. View Archives

Printable Version  |  Offline PDF Version  |  Link to this page

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Further reading

Tamino posts a useful article Uncertain Sensitivity that looks at how positive feedbacks are calculated, explaining why the probability distribution of climate sensitivity has such a long tail.

There have been a number of critiques of Schwartz' paper:


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Comments 301 to 350 out of 386:

  1. I'll have a post on that paper next week, DSL. I wouldn't say they've constrained climate sensitivity - more accurately they showed that models with climate sensitivity below 3°C don't simulate cloud changes very well, so climate sensitivity is likely on the high end.
  2. dana1981 - Actually, it's that those models with low sensitivity don't simulate humidity changes very well, not clouds. They note that clouds are a more difficult phenomena to observe, too. Fasullo and Trenberth 2012 (described here) appears to be much in the same vein as Spencer and Braswell 2011, where they examined how climate models matched observations, although S&B 2011 was clearly refuted due to poor technique and the exclusion of models they themselves tested which refuted their conclusions.
  3. KR @302 - yes, to be precise Fasullo and Trenberth are looking at relative humidity changes in the subtropics, which are related to subtropical cloud formation. Anyway, more details in the post next week.
  4. I'll stand corrected, but in my book anything that narrows the range of "likely" is constraining. Would it be fair to say that we have less confidence in the lower sensitivity models now?
  5. DSL @304 - yes, the lower sensitivity models don't simulate subtropical humidity well, so they merit less confidence.
  6. Using a GCM to predict/verify sensitivity is flawed and hubris. We have a lot of known unknowns in the GCMs. They are not established science, but SWAGs. Assuming the climate is ever in equilibrium as the basis for a calculation is absurd. It is never, ever, in equilibrium. If it were, we would not see the changes that have occurred in the past. Until science has a better handle on clouds (and many other second-order feedbacks), any attempts to quantify sensitivity are relying on guessing about past events, but not on understanding why.
  7. Try reading the intermediate or advanced version of the article (or the appropriate chapter in the IPCC report). You will see that there are empirical studies of climate sensitivity. Read deeper into the papers and you will see that noone assumes climate is in equilibrium - the utility of term does not require it. Your comments on cloud feedbacks would have been justified for TAR but they are far better quantified now. Note also that models are doing a pretty good job of estimating temperature trends, even something as primitive as that used by the Broecker in 1975 ("Climatic change; are we on the brink of a pronounced global warming?" Science, v 189, n 4201, p 460-3, 8 Aug. 1975") which got temp for 2010 better good.
  8. Hey, so I was linking your excellent version of Knutti and Hegerl graphic used in this post and noticed that it uses a potentially confusing notation both here and in the original paper.  The 90% confidence interval is labelled "very likely" and the 66% confidence interval is labelled as "likely."  That's sensible from a science perspective, but a bit confusing in that values from the 66% region are more likely to be the drawn values than those in the 66-90% interval.  Not sure there's any way to better label the figure, but I thougt I'd just put that out there to see if there's a less confusing way of doing so....

  9. Paul,

    The 90% interval is from 5% to 95% so it includes the 66% confidence interval.  Therefore it is more likely to occur since if the 66% occurs the 90% must also occur.

  10. Michael, I'm well aware of that.  My point is that if one didn't go digging through to the original article AND understand IPCC terminology AND frequentist statistics, the graph would seem to be confusing.  

    If it were labelled for example "66% confidence interval" and "90 % confidence interval" one wouldn't have to go chasing footnotes to understand it....


  11. Paul from VA @310.

    You are right that it is confusing, but because it is actually more confusing than you say, as it also refers to "the most likely value."

    The caption for Figure 4 (in the Advanced version of this post) says "The circle indicates the most likely value. The thin colored bars indicate very likely value (more than 90% probability). The thicker colored bars indicate likely values (more than 66% probability)." The original Knutti & Hegerl paper sort of copes with this by talking of "most like values" and "likely ... and very likely value ... ranges" (my emphasis) but I would consider this poor description for a Review Article where the audience is very likely less attuned to the underlying science and so more reliant on the actual descriptions presented. And at SkS the audience is even less steeped in the science (although it is an advanced level SkS post).

    The problem is also encountered in the other Knutti & Hegerl figure used in the advanced level post (SkS figure 6) where the terms "most likely warming" and "likely range" cope reasonably well. Yet if this is an advanced level post I would have thought the concept of a confidence interval would be preferable as suggested @ 310.

  12. Paul and MA,

    This discussion seems to me to come down to how useful the IPCC terms are in a scientific paper.  These terms have been discussed a lot beore and some people do not like them.  On the other hand, people also did not like using numbers before the IPCC adopted the current terms.  It seems to me extremely likely that the scientists reading the review paper are familiar with these terms, the paper is not intended for a lay audience.  Most of the users here at SkS are also familiar with these terms.  They are not perfect, but they are what we currently have.  I imagine that if we switched to new terms someone else would complain.  It is difficult to please everyone.

    Perhaps you could write a new post that explains things better?  Good explainations are always welcome.

  13. Long time lurker, first time poster here.David Wasdell of the Apollo-Gaia project claims climate sensitivity is closer to 7.8 deg C per CO2 doubling.'s his mistake, if any? It's based on palaeoclimate data but doesn't fit the lower palaeoclimate sensitivities given elsewhere.
  14. Jutland @313, the 7.8 deg C value is for the Earth System Climate Sensitivity, ie, the change in temperature for an initial doubling of CO2 after all feedbacks, including slow responding feedbacks from ice sheets, etc, have stabilized.  The value is similar to other reasonable estimates, but the Earth System Response will take several thousands of years to stabilize.  The value is therefore largely irrelevant to temperatures over the next century or so.  Further, provided we do stop emitting CO2 at some point in the next century, equilibriation of CO2 concentration between the surface and deep oceans will reduce CO2 concentrations to about 50% of their peak increase over preindustrial values, so that the Earth System Response would be to a much lower overall CO2 concentration.

    Far more relevant to the immediate future (ie, next 100-200 years) are the Transient Climate Response and the Charney Climate Sensitivity, which the Apollo-Gaia project shows as 3 C (close to IPCC central estimates).  The only policy relevant impact of the Earth System Response is that it shows that a stable solution to the problem of global warming will require zero net anthropogenic emissions.  Merely reducing emissions to 20% of current values is not a stable long term response. 

  15. Jutland@313

    The biggest mistake in that booklet is their application of Earth System Sensitivity, which by their own definition works in millenial timescale, to the problem of AGW mitigation, which works on a century (or couple of centuries) timescale. The ESS by thier own definition, is a speculative measure, based on inaccurate deep-paleo data. You cannot expect ESS to play out fully within the mitigation timeframe (until say 2100) IPCC is concerned about. Beyond the timeframe of few centuries, the CO2 level may drop signifficantly due to ocean invasion, so most of the ESS feedbacks may not (and likely will not) play out. The same applies to Hadley & Hansen sensitivities: their positive feedbacks are not rellevant within the timeframe considered. By the same token, the rock weathering negative feedback does not play out within interglacial cycles of 100ky, therefore we don't talk about it while considering Milankovic forcings. While taking about this century, Charney sensitivity is the only one that we can be certain to play out.

    Even more erroneour (actually ridiculous for me) is their calculation of Earth System Sensitivity in this booklet.

    Check out the figure 8 on age 13. They claim ESS being far more accurate than other sensitivities, because it's derived from "high precision mathematics". That's just pathetically ridiculous. They don't mention how imprecise their input data is: just few points of highly uncertain values from 100 or 40 milion years ago. I'm sorry but if you are trying to estimate ESS from so highly uncertain old data (even ignoring the paleo-expert assertions that Earth sensitivity was different at that time due to continental configurations, etc.), your "high precision mathematics" won't help you to find the precise parameter you're looking for.

  16. Tom @314 and Chriskoz @ 315Thank you both for your helpful and swift replies. I had suspected something must be awry as he had published it online rather than in a peer-reviewed journal, but I am not a scientist, so could not work out what it might be. Incidentally, as this is the first day I've posted may I say what a valuable resource this site is, I very much appreciate it. For many years I *thought* I understood the greenhouse effect, because I understood those simple diagrams which show a single-layer atmosphere with equivalent arrows emerging out, one into space and one back to the ground. Then I read a piece by John Houghton which talked about the adiabatic lapse rate and how the greenhouse effect would be impossible if the lapse rate didn't exist. And I realised that I didn't really understand the greenhouse effect at all, because the lapse rate wasn't on those over-simple diagrams. This site was one of the ones I used to read up on it to improve my understanding, and it was the first place I thought of for help when I was reading Wasdell's paper, so thank you very much.
  17. "There are some of us who remain so humbled by the task of measuring and understanding the extraordinarily complex climate system that we are skeptical of our ability to know what it is doing and why." Dr John R Christy

  18. Well-quoted, Earthling.  I, too, am "skeptical" of John Christy's ability to know what the climate is doing and why.

  19. @316, you mean I've got more reading to do? 

  20. Stub for Klapper to move conversation from Guardian to SkS where he believes there are more informed commenters than me. 

  21. Klapper: "....or where is the missing 0.5W/m2 between models and reality?"

    Rob: "Really? Who've you asked about this one?"

    Klapper: "You for a start. However, while you've dismissed this as irrelevant, you're not very knowledgeable about greenhouse physics (your repetitive references to the irrelevent heat seeking missile examples says a lot), and I think this is time to take this argument over to Skeptical Science where there are more knowledgeable posters to discuss/argue the point."

    Just to pick up the conversation with Klapper.

    I don't know why you're asking me questions like this that are best answered by people who are experts in the field. All I can do is try to read the relevant research and give my non-professional opinion. 

    What I'm asking you is, on all these questions you're asking, which you seem to think are evidence of a failed theory of AGW, who are the experts you're asking? You say they're not answering these questions, but are you actually asking anyone who actually would best know the answer?

  22. Rob Honeycutt @321, there has been a recent paper by Smith et al (Feb, 2015) on "Earth's energy imbalance since 1960 in observations and CMIP5 models".  For your discussion with Klapper, the key graphs are figs 3 a and b.

    "Earth's energy imbalance. (a) Time series of 5 year running mean N and Ht (as Figure 2, second panel) for 21 CMIP5 coupled model simulations (N in green, Ht in orange, ensemble mean in thick lines) compared with Ht from MOSORA (red) and No (blue, see text). Black squares (diamonds) show where differences between MOSORA and No (CMIP5) are significant with 90% confidence. (b) N averaged over different periods in No (blue, with 1 sigma uncertainties) compared to the CMIP5 models (green, box showing the mean ±1 sigma and whiskers showing the range) and estimates from the IPCC fifth assessment (red) [Rhein et al., 2013, Box 3.1]. Numerical values are given in Table S3."

    To interpret that, No is the net downward energy flux at the Top of the Atmosphere (ie, TOA energy imbalance) determined from observations, being the net difference between satellite observed outgoing long wave radiation and incomeing short wave radiation benchmarked against ocean heat content data from July 2005 to June 2010.  Ht MOSORA is the ocean heat content from a Met Office reanalysis.  That makes it semi-emperical, being emperical over those zones of the ocean of which we have observations, but using a computer model constrained to the emperical values over those zones where we have observations to fill in those zones in which we do not have observations.  Ho and Ht CMIP5 are the multimodel mean equivalents.

    Several things are worth noting in Fig 3a.  First, No (ie the TOA energy imbalance) from observations and models match closely except for the period of 1972-82.  They certainly match well over the last decade, although the observed No is slightly less than the modelled No in that period (of which more later).  Second, TOA energy imbalance and OHC should match closely, and do for the models.  There are, however, wide disparities between them in observations.  That indicates there are more problems with the observations than there are with the model/observation comparison.  (For what it is worth, the problems with observations probably relate to the limited region of the ocean in which OHC is directly observed, coupled with problems in the reanalysis.)

    Fig 3b is much simpler, and simply shows a direct mean TOA energy imbalance comparison between models and observations over various periods.  As you can see, the observations are statistically indistinguishable from the models for all periods.  More importantly, "the missing 0.5W/m2 between models and reality" is seen to be a fiction.  The actual difference over the most recent decade is 0.11 W/m^2.  The 0.5 figure is based on old figures from CMIP 4 and far less accurate observations, and even then is exagerated by rounding.  That Klapper is still using it shows he is clinging to old data simply because it is convenient for his message.

    The paper also has some interesting information about the cause of the discrepancy between models and observations, encapsulated in Fig 4:

    As you can see, the discrepancy between model and observed short wave radiation (ASR) is greater and more persistent than the discrepancy in longwave radiation (OLR) after 2000.  Ergo the primary cause of the 0.11 W/m^2 discrepancy between models and observations is the reduced observed shortwave radiation compared to the models.  At least part of the explanation of  that is that the models cease to use historical data from about 2000 onwards, and hence do not include the short wave forcing from a series of recent volcanoes.  If that forcing were included, the discrepancy between models and observations would be smaller, possibly non-existent.

    (Note to Rob - I've spelt out in detail a number of points I know you know quite well for the benefit of Klapper and other potential readers.)

  23. Perhaps Tom Curtis might use this recent study to add to the "It's the Sun" post, a counter to the myth that the Earth's temperature still is catching up to the increased input from the Sun that happened before around 1960?  The counter to the myth is that if the myth is true, energy imbalance should be decreasing since then, as the increased outgoing radiation due to the Earth's higher temperature increasing compensated for the now-stable input from the Sun.  Pretty please?

  24. @Rob Honeycutt #321:

    "... who are the experts you're asking?..."

    You, and Tom Curtis and if not direct me to the peer-reviewed research that you know of. I admit I have in the past used Skeptical Science as a sounding board for ideas I have, since after a few back and forths on the numbers I can normally see if there is a concrete reason to reject the reason or not.

  25. @Tom Curtis #322:

    "...First, ...the TOA energy imbalance...from observations and models match closely except for the period of 1972-82"

    Where would you get observations from 1972 for the TOA energy imbalance? For that matter exactly how accurate are the current observations for the TOA imbalance? There's an post over at the Guardian on the water vapour/climate change story by "MaxStavros" which claims the satellite numbers in raw form show an imbalance of 6.5W/m2 at the TOA. Since we know that is impossible the number has been adjusted down to something more believable. I can understand the instruments on the satellite are precise but not accurate, but that means the "observations" are not that reliable. I'm guessing the most reliable number is ocean heat, but that is true only since the ARGO era, from 2004 or 2005. From the NODC data, the warming rate of the oceans, corrected to global area, is about 0.5 W/m2. This is close to other estimates. The following example is ocean plus melting, plus land, but since most of the heat goes into the oceans we would expect the ocean only and total should be close (and they are).

    Here's a quote from Jame Hansen et al 2012 at the NASA website: "We used other measurements to estimate the energy going into the deeper ocean, into the continents, and into melting of ice worldwide in the period 2005-2010. We found a total Earth energy imbalance of +0.58±0.15 W/m2 divided as shown in Fig. 1"

    Here's the problem with an energy imbalance of +0.58W/m2: the models show a much larger TOA energy imbalance. The GISS model shows +1.2W/m2, and the CMIP5 ensemble mean is +1.0 W/m2 for the 2000 to 2015 period.


    [JH] Link activated.

  26. Klapper... The Smith etal paper that Tom links to bears reviewing, especially the summary and conclusions. This sums up some of the things I've been attempting to state with regards to the relationship between observations and models, where I've said that it's reasonable to conclude that the models are better representing the climate system and our observations are challenge our ability to "close the Earth's energy budget."

    What I see you doing (or at least believe I see you doing) is getting stuck in down in the weeds of our observations, assuming they have to be somehow correct. I think that's a misdirected approach. As I've said several times in our conversation so far, there are lots of uncertainties in the empirical evidence and the models are there to contrain those uncertainties. 

  27. Klapper - It is wholly unreasonable to discard ocean heat content data prior to 2005. While the XBT data has higher uncertainties than ARGO, and there have been several calibration issues with it that are recently resolved, the sampling back to the 1960's is more than sufficient to establish long term growth in ocean heat content. There simply isn't enough deviation in temperature anomalies over distance to reject long term warming of about 0.6C/decade even with sparse XBT sampling. 

    For details on this, including evaluating the standard deviation of anomalies against distance, see the Levitus et al 2012, specifically the "Appendix: Error Estimates of Objectively Analyzed Oceanographic Data", which speaks directly to this matter. The uncertainty bounds from Levitus et al are shown in Fig. 2 here. And they are certainly tight enough to establish warming. 

  28. @Rob Honeycutt #326:

    "...assuming they have to be somehow correct..."

    Oh I don't assume they have to be correct at all. You can take the Net observations (satellite) from the Smith paper and throw them in the trashcan. However, that's not true of the ARGO data. Our knowledge of ocean heat is much much better since 2005 or 2004 than pre 2005 or 2004.

  29. @KR #327:

    The problem is the XBT data only go down to 700 m. If I had tried to use only 0-700 heat gain as my metric, I would be jumped on big time since I was "ignoring" the deeper ocean. The amount of sampling below 700 m prior to the ARGO network is extremely sparse, as noted in the Smith et al paper, particularly in the southern ocean.

  30. @Tom Curtis #322:

    "...That Klapper is still using it shows he is clinging to old data simply because it is convenient for his message..."

    Absolutely not true (and an unecessary cheap shot to boot). I extracted the multi-run per model ensemble mean numbers from KNMI data explorer, CMIP5 rpc4.5 scenario. I also checked one individual run from the GISS EH2 model, same emissions scenario (although it makes no real difference between the scenarios in the 2005 to 2015 period).

    I used the rlut, rsdt, and rsut variables (absolute values, not anomalies) to calculate my net. I'm looking into the difference between my Net TOA imbalance and Smith et al, but not tonight.

  31. Klapper - The XBT data does go to (and through) 2000 meters. Yes, XBT data back to the 1950's is sparse below 700 meters, but it is still data, and uncertainties due to sparse sampling are considerably smaller than the ocean heat content trends over the time of observations. 

    Again, I would refer you to Levitus et al 2012, in particular Fig. 1 and the supplemental figure S10, which shows the 0-2000m 2-sigma uncertainties, variances, and trends for each ocean basin. We have enough data to establish long term OHC trends with some accuracy. 

  32. Klapper - My apologies, S10 in Levitus et al is for the thermosteric component, while S1 shows the OHC (1022 J). Again, there is sufficient data to establish a long term trend against sampling uncertainties 0-2000m. 

  33. Klapper @328...  Just to trying to simplify things here, so your key issue is that measured changes in OHC data (W/m^2) do not match model results for TOA imbalance. 

  34. Given the preceding thread at the Guardian prior to the start here at SKS, was a thread discussion beginning here and running to 7,000 words of comment with nothing resolved, I would suggest a little discipline is required here at SKS to prevent it becoming another pantomime.

    The issue to hand is "the missing 0.5W/m2 between models and reality." Such a quantity was identified @322 as having been "based on old figures from CMIP 4 and far less accurate observations, and even then is exaggerated by rounding."

    This is refuted @330 as being "absolutely not true" because the missing 0.5W/m2 is apparently a different 0.5W/m2 to that identified @322, and for which we await a full description.

    Looking back at the Guardian thread, the 0.5W/m2 appears here as the difference between study-based "heat gain in the measurable part of the ocean .. in the range of 0.3 to 0.6 W/m2" yielding a "best guess at ocean heat gain (of) 0.5W/m2" and "Models show(ing) the imbalance at the top of the atmosphere through this period as being 1.0 W/m2."

    So what period? What models? Is the TOA 1.0 W/m2 anything to do with the "TOA energy imbalance projections from the models (of) ... currently about 1.0 to 1.2 W/m2" mentioned in the Guardian thread here?

    Please let us not spend many thousands more words without a grip on what is being discussed.

  35. Klapper - you are proposing to ignore OHC pre-Argo because there is only data to 700m. However, if you wish to postulate that the huge change in OHC 0-700m does not mean energy imbalance, then you must also be proposing that there could somehow cooling of the 700-2000 layer to compensate for warming in the upper layer.

    I would also be interested in your opinion on the Loeb et al 2012  paper in claiming that models and observations are at odds.

  36. Scaddenp - We do have XBT data below 700m, just rather less of it. Which is how the ocean heat content analyses going back to the 1950s have been done.

  37. @MA Rodger #334:

    To cross-check my model vs actual comparison for TOA energy imbalance I extracted at the KNMI Data Explorer site data from the CMIP5 Model Ensemble RCP 4.5 (all runs) the variables rsut, rlut, and rsdt, monthly data. I averaged the monthly global data into annual global numbers and calculated the TOA energy imbalance per year as rlut + rsut - rsdt.

    To compare to a published number, in this case I'll use the Hansen et al number from the GISS website linked above, I averaged the years from my model extraction data, in this case 2005 to 2010. The GISS number for global TOA energy imbalance of 0.58 W/m2 +/- 0.15. This agrees with other published estimates of similar time periods.

    The average I get from my CMIP5 RCP 4.5 ensemble annual data, 2005 to 2010 inclusive is 0.92 W/m2. The models appeart to be running too hot by a substantial amount.

    My next experiment will be to compare these TOA CMIP5 data to OHC over a longer period, say 2000 to 2014 inclusive. Or maybe just OHC from 2005 to 2014 since the ARGO spatial density was essentially full coverage after 2004 or 2005. We can likely agree that the global energy imbalance dominantly present in the ocean heat gain, although some of the imbalance goes into the atmosphere and melting continental ice.

  38. Klapper - 5 to (at most) 15 year periods are short enough that statistical significance is lacking, and that the model mean is expected to differ from short term variations such as ENSO. 

    I don't think you can make any significant conclusions from such a short period of data. 

  39. Klapper/everyone - I'll note that many of Klappers issues with model fidelity have been discussed at great length over on the Climate Models show remarkable agreement with recent surface warming thread. And on that thread Klapper was shown (IMO) that his arguments did not hold. 

    This appears to be yet another search for a (notably short term, and hence statistically insignificant) criteria with which to dismiss modeling. 

  40. Klapper @337:

    1)  Did you compute (∑rlut x 1/n) + (∑rsut x 1/n) - (∑rsdt x 1/n) or (∑(rlut + rsut - rsdt)) x 1/n?

    2)  The IPCC uses just one model run per model in calculating multi-model means for a reason.  Failing to do so allows a few models with unusually large numbers of runs to be more heavilly weighted in the absence of evidence that those models are superior, and indeed, regardless of any evidence of their superiority or inferiority.  In particular, one model with multiple runs is the GISS model ER, which you have previously stated has a TOA energy imbalance from 2000-2015 of 1.2 W/m^2 - ie, it is at the high end of the CMIP 5 range, and above the CMIP 5 multi-run mean as calculated by you.  There is reason to think this distorts your result.

    3)  5 years is too short a time for such comparisons for reasons given by KR.  What are your results for 2000-2010 for comparison with the Smith et al data?  Indeed, what are your results for all of the Smith et al periods as shown in the second panel of the first graph in my post @322?

    4)  Why do you use the multi-model (really multi-run) mean rather than the multi-model median as do Smith et al?  In this case where damage functions are not a factor, using the median as the central estimate makes sense (IMO) in that it is less subject to distortion by outliers.  Is their some reason why you preffer it despite this disadvantage?

    5)  I ask you to forgive me for not responding to your earlier posts.  I had an extensive response prepared and lost it in the attempt to post it.  Unfortunately I have been ill since then, and not had the energy for recomposing a similarly extensive response.  I am also considering whether or not to download the data from KNMI for direct comparison before more detailed response (which will take more energy and concentration).

  41. Klapper @337.

    You are getting your  0.58 W/m2 +/- 0.15 from Hansen et al (2012) , a paper which states:-

    "The fact that Earth gained energy at a rate 0.58 W/m2 during a deep prolonged solar minimum reveals that there is a strong positive forcing overwhelming the negative forcing by below-average solar irradiance. "

    I would suggest that such a quote is difficult to ignore, although you apparently do overlook it. It sort-of adds weight to the comment by KR @338. From memory, the negative solar forcing through those years between cycle 23 & 24 was something like -0.13W/m2, reducing your mismatch from the range 0.19-0.49 W/m2 to 0.06-0.36 W/m/2, considerably reduced from the originally stated 0.5 W/m2.

    The paper goes on to say:-

    "Measured Earth energy imbalance, +0.58 W/m2 during 2005-2010, implies that the aerosol forcing is about -1.6 W/m2, a greater negative forcing than employed in most IPCC models." and "Most climate models contributing to the last assessment by the Intergovernmental Panel on Climate Change (IPCC, 2007) employed aerosol forcings in the range -0.5 to -1.1 W/m2."

    Again, here is very relevant data you overlook. If these AR4 models underestimate negative aerosol forcing, you would expect them to run with a greater TOA imbalance. And if they did so in AR4, would more recent models be expected now to conform to Hansen et al (2012)? Or is that a bit of an assumption on your part?

  42. @KR #338:

    "I don't think you can make any significant conclusions from such a short period of data".

    The quality data for OHC only begin since the ARGO system reached a reasonable spatial density (say 2004 at the earliest). However I will look for some longer OHC/global heat gain data/estimates to match longer periods, say a 15 year period from 2000 to 2014 inclusive. The average for that period is a TOA energy imbalance of 0.98W/m2 from the CMIP5 ensemble (multi-runs per model) mean rcp4.5 scenario.

  43. @Tom Curtis #340:

    "..The IPCC uses just one model run per model in calculating multi-model means for a reason."

    Yes very egalitarian of them. An argument could be made for using the other ensemble which says, the better resource supported models have more runs and are probably more realistic than the less resourced models. However, it doesn't make much difference, as the 2005 to 2010 average TOA imbalance changes from 0.92 to 0.90W/m2 with the one run per model ensemble.

    "..What are your results for 2000-2010 for comparison with the Smith et al data?"

    The 2000 to 2010 average TOA energy imbalance is +0.95W/m2.

    ".. rather than the multi-model median as do Smith et al?"

    I would have to download all the models, a very tedious process, and create my own median; KNMI only options a mean in their ensemble exports.

  44. @MA Rodger #341:

    ".. reducing your mismatch from the range 0.19-0.49 W/m2 to 0.06-0.36 W/m/2, considerably reduced from the originally stated 0.5 W/m2"

    You're forgetting the originally stated comparison was to OHC, not global energy imbalance (although as noted OHC pretty much is the bulk of the energy imbalance). In any case, even reduced, the numbers support my hypothesis the models run too hot.

    "..implies that the aerosol forcing is about -1.6 W/m2"

    Circular logic but that's a topic for whole discussion on itself. I'll say no more.

    "..would more recent models be expected now to conform to Hansen et al (2012)?"

    I'm using the more recent models (CMIP5) and they don't conform to Hansen et al 2012 (still too hot). I'm tempted to go get the AR4 model ensemble and try that also, but for now I'm off to work.

  45. Klapper @343:

    "The 2000 to 2010 average TOA energy imbalance is +0.95W/m2."

    1)  I need to make a correction.  I assumed that Smith et al presented a median value based on their use of a box plot.  In their supplementary information, however, they describe the central value as a mean, and the "first quartile" and "third quartile" values as being minus and plus one standard deviation respectively, with whiskers showing the range.  The values are given as 0.73 +/- 0.13 W/m^2 with a range from 0.43 - 0.97 W/m^2.  These values are stated as being the anomaly values with respect to the preindustrial era - anomaly values being used as a correction for model drift.

    2)  As noted before, the difference between observations and models over this period in Smith et al is 0.11 W/m^2.  Even using your uncorrected values, the difference between observed and modelled TOA energy imbalance from 2000-2010 is still only 0.33 W/m^2.  The +/- 2 sigma range of the observed TOA energy imbalance is 0.06 to 1.18 W/m^2.  So, even on your figures the discrepancy between mean model and mean observed TOA energy imbalance is substantially less than 0.5 W/m^2 (which as I said before, is a fiction).  Further, you are making a case that the models are shown to be seriously flawed because, the modelled TOA energy imbalance lies within error (actually, withing 1.2 SDs) of the observed value.  It may make a good emotive argument, but it is certainly not a scientific argument.

  46. Klapper - We have OHC data of reasonable quality back to the 1960s, as I noted here. What you are considering is far too short a period for statistical significance, hence too short to make broad statements about model fidelity. If you want to make any claims regarding the differences I would suggest using a sufficient amount of the available data. 

    You're arguing about short term unforced variations, not statistically significant long term climate trends, and your complaints about the XBT data don't change that fact. 

  47. Might suggest to one and all that this conversation about model fidelity shift to the appropriate thread on climate models?

  48. @Tom Curtis #345:

    "..So, even on your figures the discrepancy between mean model and mean observed TOA energy imbalance is substantially less than 0.5 W/m^2 (which as I said before, is a fiction)".

    You're ignoring my comment above in which I clearly stated the 0.5 W/m2 was the difference between OHC and the TOA model output. Here's my 2 most succinct posts from the Guardian on the source of the 0.5 W/m2 number:

    "All that being said, these studies would agree the heat gain in the measurable part of the ocean is in the range of 0.3 to 0.6 W/m2. If the best guess at ocean heat gain is 0.5W/m2, then where is the rest of the heat? Models show the imbalance at the top of the atmosphere through this period as being 1.0 W/m2. We know the atmosphere has limited heat capacity, and the troposphere hasn't shown significant warming since 2005 in any case. That leaves ice melting."

    "However, heat gain by the oceans right now might be 0.5W/m2, which is only 1/2 of the projected TOA energy imbalance, so while the oceans are warming, and the atmosphere very weakly so, together they don't account for the model predicted 1.0 to 1.2 W/m2 TOA net energy input."

    I concede in at least one post I used the OHC delta to TOA model as "shorthand" for the global energy delta to model TOA, but it's clear from my initial posts the source of the numbers. You're either not reading my full posts or you're deliberately ignoring the context.

  49. @Tom Curtis #345:

    "...anomaly values being used as a correction for model drift."

    Why don't you expand on what you think is going on here. I'm using the absolute numbers from the mean CMIP5 ensemble, which I think is the correct thing to do. What do you (and Smith et al) mean by "model drift"?

  50. @KR #347:

    "...We have OHC data of reasonable quality back to the 1960s"

    I've looked at the quarterly/annual sampling maps for pre-Argo at various depths and I wouldn't agree that's true for 0-700 m depth and certainly not true for 0-2000 m. There's a reason Lyman & Johnson 2014 (and other stuides) don't calculate heat changes prior to 2004 for depths greater than 700 m; they are not very meaningful.

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