An acknowledgement, but not really a correction

A few days ago I wrote a post (what matters is the radiative imbalance) in which I claimed that a post by David Stockwell was wrong. David made a few comments on my post, claiming that I had made a mistake. The exchange didn’t end particularly well, but – in the interests of honesty – I’m going to acknowledge something. To be clear though, what David concludes in his post is still incorrect, but I did misunderstand something that he was saying.

In David’s post he refers to a continuous top-of-the-atmosphere forcing of 1 Wm-2 and suggests that this is consistent with IPCC estimates. The only IPCC estimate he mentions in his post is the change in radiative forcing since 1750 (the change for the last 50 years – the period considered by David – is just slightly more than 1 Wm-2). Hence, I assumed that he had confused the TOA imbalance with the change in forcing. It seems that this may not be correct and that he did indeed mean a TOA imbalance. Admittedly, he did make it difficult to realise this, partly because he refers to a paper by Meehl & Hansen (which I cannot find) and partly because he calls it a continuous TOA forcing, which doesn’t really make sense (i.e., it’s not expected to be constant).

So, what David appears to be actually referring to is the TOA imbalance suggested by climate models. This is illustrated in the figure below, taken from Hansen et al. (2011), which shows how the expected TOA imbalance changes with time and with response function. Most climate models assume a slow response function and hence predict that, since about 2000, the TOA imbalance should have been about 1 Wm-2. What David is claiming is that his analysis of the ocean heat content data suggests it is actually 0.27 Wm-2, much smaller than that predicted by climate models. He concludes that this implies a lower climate sensitivity than climate models would predict. However, what David has done is compute the average for the last 50 years, and compared it to what would be expected for the last decade or so. It’s clear, from the figure below, that the TOA imbalance is expected to have been increasing with time, and hence the average for the last 50 years would be expected to be quite a bit lower than the current value.

Global mean surface temperatures (left-hand panels) and TOA energy imbalance (right hand panel) for 3 different possible response functions.

Global mean surface temperatures (left-hand panels) and TOA energy imbalance (right hand panel) for 3 different possible response functions.


So, yes I may well have misunderstood (justifiably so, I would argue) what David was referring to in his post. No, it doesn’t mean that what David was suggesting (climate sensitivity is much lower than expected) is correct. However, as part of this exchange I did come across the paper by Hansen et al. (2011) which appears to be an excellent analysis of our current understanding of climate science and climate modelling. It is rather long, so I haven’t read it all, but what I have read seems excellent and I certainly recommend it as a very good resource.

David, however, doesn’t think particularly highly of the Hansen et al. (2011) paper (Honest Jim: The science is not settled). This has already been rebutted by Geoff Davies but I thought I would make one comment, related to the figure above. In his criticism, David Stockwell highlights the following paragraphs from Hansen et al. (2011)

Our principal conclusions, that the slow response function is unrealistically slow, and thus the corresponding net human-made climate forcing is unrealistically large, are supported by implications of the slow response function for ocean mixing.

If the negative aerosol forcing is understated by as much as 0.7 W/m2, it means that aerosols have been counteracting half or more of the GHG forcing.In that event, humanity has made itself a Faustian bargain more dangerous than commonly supposed.

David, interprets this as an indication of a problem with the GCMs. In a sense this is true, but this is discussed in quite some detail in Hansen 2011. The basic issue seems to be that the rate of heat uptake in the deep ocean is higher in the models than is observed. Yet, these models seem to still be doing a reasonably good job of matching the rise in global surface temperatures. Most of these models, however, assume a slow response function. This means, if I understand it correctly, that the system responds slowly to changes in forcings and means, essentially, that a large amount of energy needs to go into the oceans so as to reach equilibrium.

If this is wrong, then how can the models still be matching the observed rise in surface temperatures? A possibility, according to Hansen et al. (2011), is that they’re ignoring the effect of aerosols. Aerosols have a negative forcing, and hence the overall forcing in the models is higher than it is in reality. This compensates for the slow response function, allowing the models to match the surface warming. What Hansen et al. (2011) suspect is that the actual response function should be faster (i.e., the system responds more quickly and less energy goes into the oceans – as suggested by observations) but the overall forcing is lower due to the influence of aerosols. This, however, shouldn’t be seen as a good thing because the aerosols tend to be short-lived and hence their influence on the overall forcing (reducing it) could change and therefore – if this were to happen – the overall forcing could increase.

So, maybe one could argue that the climate models are not quite correctly representing the climate system. However, this appears to be (at least if I understand Hansen et al 2011 correctly) because they’re underestimating the influence of aerosols. This suggests that the response function is faster than some models have been assuming and hence that the climate can respond faster to changes in forcing. Accurate estimates of the TOA imbalance could constrain this uncertainty and, as pointed out by Hansen et al. (2011)

If Argo data are complemented with adequate measurements of climate forcings, we will argue, it will be possible to assess the status of the global climate system, the magnitude of global warming in the pipeline, and the change of climate forcing that is required to stabilize climate.

So, I’ll end this rather long post there. The main point of this was to at least acknowledge that I may have misunderstood something about David Stockwell’s post, that I referred to earlier, and to highlight the Hansen et al. (2011) paper that appears to be a very thorough summary of our understanding of the climate system.

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18 Responses to An acknowledgement, but not really a correction

  1. BBD says:

    The loss of the Glory satellite was a disaster for this endeavour. The apparent lack of a replacement mission is borderline incomprehensible.

  2. Yes, I believe Hansen has been quite critical of the lack of a satellite that can actual constrain the aerosol influence.

  3. anthony says:

    I’m still confused by what you are trying to say. Let’s clear up a couple of things.

    Firstly, you say:

    “However, what David has done is compute the average for the last 50 years, and compared it to what would be expected for the last decade or so.”

    My understanding is that David uses the SAME time spans as Levitus 2012 and Hansen 2011.

    Both Levitus and Hansen find a lower CS than is reported by AR4 which David refers to at the beginning of his blog article. So it is not David who is finding a lower CS but Levitus and Hansen. It should also be noted that AR5 reduces its range for ECS.

    Secondly is not a reduced ECS consistent with the temperature response from increasing CO2? I tried to make this point to Tom Curtis when David wrote his blog article but something seems to have been lost in translation.

    As to “continuous TOA forcing”; I don’t think David meant this as an average but that it was continuous or are you suggesting CO2 forcing is Discontinuous? Anyway, if ECS is reducing TOA forcing must be reducing, although as regards the TOA imbalance, Knox and Douglass have found this to be negative:

    http://www.pas.rochester.edu/~douglass/papers/KD_InPress_final.pdf

    Also of interest is K&D’s response to Nuccitelli et al’s criticism of their paper:

    http://www.sciencedirect.com/science/article/pii/S037596011201119X

    As for ECS and revision downwards by AR5 see also Nic Lewis’s analysis at your namesake:

    http://wattsupwiththat.com/2012/12/19/why-doesnt-the-ar5-sods-climate-sensitivity-range-reflect-its-new-aerosol-estimates/

  4. dbostrom says:

    The Glory mission was a travesty from end to end in terms of placement in orbit. Glory was intended to gather data that is absolutely critical to helping us understand the future we’re creating; data from Glory could have helped shape the quality of life for generations to come. Despite the compelling value of the mission it was put in the fumbling hands of a launching scheme built around recycled ballistic missile boosters, already an indication of twisted priorities, then further budgeted into oblivion as evidenced by –two– missions (Orbiting Carbon observatory, “OCO” –and– Glory) succumbing to the same silly problem of not being able to eject its aerodynamic shroud.

    If anything OCO was an even more tragic outcome than Glory.

    In general, our choices in allocating resources to produce “man rated” launch systems produces peculiar outcomes and is at the same time exemplary of our (human) bizarre attitude to hazards and risks. If a booster has a single living person at the top of the system then we’re extremely (and rightly so) scrupulous about engineering out as much as possible single points of failure and the like. A single life is assigned huge value. Conversely, if we’re launching something on which many lives depend– a weather satellite for instance– then standards are hugely relaxed; it’s not considered as important to preserve many lives as it is a single life.

  5. Tom Curtis says:

    David Stockwell attempts to gloss over his errors in a post on the other thread, to which the post here is a response. He wrote:

    “It is simple. I quoted the figure you think I erroneously used at the top of my article (1.6W/m2 from the IPCC). I then when on to compare an estimate of the modelled continuous forcing produced by Hansen of 0.6W/m2 with the measured from the ocean effective continuous forcing of 0.3W/m2.

    It is, of course, not that simple. In fact, what he did was to quote the IPCC estimate of radiative forcing, and then provide his own definition of radiative forcing – a definition that differs substantially from that used by the IPCC. His definition reads:

    “Remember a forcing is an imbalance that causes heating, like a hot plate heating a saucepan of water. While the forcing continues, the temperature of the water will continue to rise. Global warming is the theory that increases in anthropogenic CO2 in the atmosphere are producing a radiative imbalance, or forcing, causing the earth to warm dangerously.”

    (My emphasis).

    David’s definition equates to that of the TOA energy imbalance, rather than to the IPCC’s definition of radiative forcing, which reads:

    “Radiative forcing is the change in the net, downward minus upward, irradiance (expressed in W m–2) at the tropopause due to a change in an external driver of climate change, such as, for example, a change in the concentration of carbon dioxide or the output of the Sun. Radiative forcing is computed with all tropospheric properties held fixed at their unperturbed values, and after allowing for stratospheric temperatures, if perturbed, to readjust to radiative-dynamical equilibrium. Radiative forcing is called instantaneous if no change in stratospheric temperature is accounted for. For the purposes of this report, radiative forcing is further defined as the change relative to the year 1750 and, unless otherwise noted, refers to a global and annual average value. Radiative forcing is not to be confused with cloud radiative forcing, a similar terminology for describing an unrelated measure of the impact of clouds on the irradiance at the top of the atmosphere.”

    David attempts to escape one of the criticisms directed against him, ie, of comparing TOA energy imbalances with radiative forcings without distinguishing between them by saying he merely quoted the IPCC figure on radiative forcings, but in fact compared energy imbalances. That does not wash, however. The reason it does not wash is that if we accept his claim, then he has deliberately misrepresented the IPCC by quoting the IPCC “radiative forcing”, and then misdefining it. Either David was confused about radiative forcings in the later part of his blog post, thinking he was talking about radiative forcings when in fact he was talking about energy balances; or he deliberately introduced a non-standard definition of radiative forcing in discussing the IPCC claims on radiative forcing without noting the fact, thereby trying to mislead his readers.

    Now, being fair, his blogpost may have just been slovenly and confused rather than deliberately deceptive. However, in practice the only way to distinguish between honest and dishonest mistakes is that the authors of the former take pains to correct the mistake. Absent such a correction, ie, a clear update to his blogpost stating that he has used a non-standard definition of forcing, and that the quoted IPCC forcing is distinct from, and not expected to match in value the “forcings” he later discusses in his post, the correct conclusion is that the deception is deliberate; or at the very best, that he did in fact commit the error of confusing radiative forcings with TOA energy imbalance in his initial post (as he has been criticized for), and that his later response distinguishing between the IPCC figure which he merely “quoted” and the “forcings” he actually discusses is an ad hoc evasion designed to allow him to avoid admitting error.

  6. Anthony, I’m always willing to be corrected if wrong, but according to David’s post he has used the increase in ocean heat content over the last 50 years to determine the average flux into the climate system (0.27 Wm-2). He has then compared this to values from Hansen. The 1 Wm-2 is a model prediction for the last 10 years or so (since about 2000). Hansen also computes the flux using the OHC but the periods considered (see Fig 14) are either 1993-2008 or 2005 – 2010. So, essentially, David appears to have compared a 50 year average with averages for a recent decade. It’s not surprising that David’s average is less than those he compares to, as the energy imbalance is expected to increase with time.

    I don’t know why you say Hansen found a lower CS than AR4. The number he quotes regularly in his 2011 paper is an ECS of around 3 degrees per doubling of CO2.

    No, a reduced ECS is not consistent with a temperature response to increasing CO2. The ECS is the equilibrium temperature (considering fast feedbacks only) after a doubling of CO2. The temperature has to rise as a consequence of increased CO2 and so a temperature rise, alone, does not imply anything with respect to the ECS.

    As far as the continuous issue is concerned, David said continuous top-of-the-atmosphere forcing is 1 Wm-2. Well, it’s not continuously 1 Wm-2. It increases with time. It may have been almost constant since about 2000, but it hasn’t been constant since 1963.

    Yes, Douglass & Knox do find a negative forcing. However, they too are likely wrong. Firstly they consider only the 0-700m OHC so do not consider the total increase in OHC. Secondly, they compute the gradient of the OHC and then subtract the geothermal flux (0.087 Wm-2). This is incorrect. The OHC alone determines the energy imbalance. You don’t subtract the geothermal flux. Furthermore, the OHC is associated with about 90% of the energy imbalance and so one should really increase it by about 10%. So, the only reason that Douglass & Knox get a negative flux is because they don’t consider the full increase in OHC and because they, incorrectly, subtract the geothermal flux. You simply need to look at the OHC data for the last few decades to see that there are no extended periods when it was decreasing.

    As far as the revised ECS estimates are concerned. Yes, I am aware of them. They’re very interesting bits of work but have their own caveats. Firstly, the ranges are consistent with earlier work and so one cannot use them to claim that the ECS is lower. The IPCC has extended the range downwards, but has not presented a best estimate. The ECS estimates are also very sensitive to uncertainties in the OHC data and to possible aerosol influences. If aerosols are acting to reduce the energy imbalance (as suggested in Hansen 2011) then if this effect were to reduce, the ECS estimates using the methods of Lewis and Otto et al. would rise. So, I know that there are newer, observationally based ECS estimates but I wouldn’t bank on their lower estimates turning out to be correct. It would be good if it were so, but I suspect most climate scientists have more confidence in the paleo-climatological evidence suggesting an ECS of 3 degrees per doubling.

  7. Indeed, I should probably have acknowledged a little less given that David actually refers to a top-of-the-atmosphere forcing.

  8. Tom Curtis says:

    anthony writes:

    “My understanding is that David uses the SAME time spans as Levitus 2012 and Hansen 2011.”

    To begin with, it is not at all clear that David is referring to Hansen 2011. David in fact refers to “Meehl and Hansen”, but provides neither link, date nor title of the paper(s) in question. A cynic might suggest that that obscurity is a defense against what David knows to be inevitable refutation, particularly has David has been asked for references, and not bothered to provide them. Indeed, rather than provide references, he employed a false charge of his disputant (Wotts) going off topic to terminate the conversation.

    Despite his reticence, however, it is probable that he was referring to two separate papers – Meehl et al, (2011), and either Hansen et al (2005), or more likely Hansen et al (2011). My confidence that he is referring to two separate papers is increased in that the only four papers which have both Hansen and Meehl as co-authors have Ben Santer as lead author, and do not appear to discuss either TOA energy imbalance or ocean heat content.

    David wrote:

    “The paper by Levitus et al. uses the array of ARGO floats, and other historic ocean measurements, to determine the change in the heat content of the ocean from 0 to 2000m, and so derive the actual net radiative forcing that has caused it to warm over the last 50 years.

    “The heat content of the world ocean for the 0-2000 m layer increased by 24.0×1022 J corresponding to a rate of 0.39 Wm-2 (per unit area of the world ocean) and a volume mean warming of 0.09ºC. This warming rate corresponds to a rate of 0.27 Wm-2 per unit area of earth’s surface.”

    To compare these figures, say the continuous top-of-atmosphere forcing is 1Wm-2, a figure given by Meehl and Hansen and consistent with the IPCC estimates. The forcing of the ocean from a TOA forcing of 1Wm-2 is a lower 0.6m-2 due to losses, estimated by Hansen.

    The direct quote from Levitus allows us to nail down the period in question. It is 1957.5-2010.5 in the 0-2000 meter pentadal data, and estimating the trend on the data shows a globally averaged mean energy imbalance over the full data range of 0.272 W/m^2. In contrast the 1993.5-2003.5 trend shows a globally averaged mean energy imbalance of 0.422 W/m^2. That approximates to the period discussed in Hansen et al, (2005). Approximates, of course, because the data are pentadal averages, so that the end values are influenced by data outside the strict 1993-2003 period discussed by Hansen et al. Despite problems with the low resolution of the data, however, it is clear that the trend is different from 0.272 W/m^2 and that consequently, if David was referring to Hansen et al (2005), he compared different periods with different expected trends.

    If, as is more likely, David was comparing to Hansen et al (2011), the situation is still worse. That is because in addition to specifying the periods of interest, Hansen et al (2011) actually explicitly makes the comparison over those periods. They write:

    “Argo era observed planetary energy imbalances are 0.70 W/m^2 in 2003-2008 and 0.59 W/m^2 in 2005-2010. Slow, intermediate, and fast response functions yield planetary energy
    imbalances 0.95, 0.59 and 0.34 W/m^2 in 2003-2008 and 0.98, 0.61 and 0.35 W/m^2 in 2005-2010.

    Observed planetary energy imbalance in 1993-2008 is 0.74 W/m^2, assuming the Lyman
    et al. (2010) upper ocean heat storage, but only 0.51 W/m^2 with the Levitus et al. (2009) analysis. The calculated planetary energy imbalance for 1993-2008 is 1.06, 0.74 and 0.53 W/m^2 for the slow, intermediate and fast climate response functions, respectively.”

    The Levitus 2012 data show equivalent trends to Levitus 2009 over those periods.

    The disparity between the observed trends over the periods of interest and the 0.27 W/m^2 quoted by David show categorically that he was comparing disparate periods. If he was quoting Hansen from Hansen et al (2011), he did so in the full knowledge that he was doing so in that he drew Hansen’s figures from sentences which contained immediate comparisons to the observational data. It follows that, because he knew the predicted data, he also had at least read the compatible observed data and knew it to be very different from the data for the full period which he quoted from Levitus et al (2012). I hope, for his reputation, that he can quickly provide an alternate source for his data which does not so starkly call into question his honesty.

    Turning to Meehl et al, the situation is even worse. Meehl et all discuss the average TOA energy imbalance for eight decades with negative trends drawn from model runs covering the period 2005-2100. The 1 W/m^2 TOA energy imbalance is not that for any historical period, therefore, but an average over the forthcoming century. It is thus literally impossible that David has compared like with like in the case of Meehl et al, both because of the disparity of time periods (10 years vs 60 years) and because the time periods in Meehl et al are all future time periods for which we have no observational record.

    I have covered this issue in some detail so that you, anthony, have no excuse for your continued defense of David’s shockingly flawed post. If you bother checking the references, you know that David was entirely inaccurate in his analysis, and inaccurate in such a way that raises serious doubts about his honesty. If you are any skeptic at all, you will now require of David a full retraction on the original page so that casual readers will not be deceived by his garbage. I await, with interest, your reaction.

  9. anthony says:

    OK, when you say David has used a 50 year time span of OHC to arrive at a forcing figure which is less than the IPCC figure for forcing you mean Levitus 2012 has used a 55 year time span:

    http://www.agu.org/pubs/crossref/pip/2012GL051106.shtml

    Levitus 2012 is fairly unambiguous:

    “We provide updated estimates of the change of heat content and the thermosteric component of sea level change of the 0-700 and 0-2000 m layers of the world ocean for 1955-2010.”

    “The heat content of the world ocean for the 0-2000 m layer increased by 24.0×1022 J corresponding to a rate of 0.39 Wm-2 (per unit area of the world ocean) and a volume mean warming of 0.09ºC. This warming rate corresponds to a rate of 0.27 Wm-2 per unit area of earth’s surface.”

    So Levitus 2012 has provided an average forcing of 0.27Wm-2 since 1955.

    David has compared that with the IPCC forcing of 1.6Wm-2 since 1750. That is the proper comparison not the shorter periods quoted from Hansen although they are of interest.

    In fact Tom has gone to some lengths to illustrate that the CO2 forcing varies from time to time based on Hansen’s papers; that is trivial, no one is disputing that; but the point David was making is over the period of maximum AGW, since 1955, Levitus 2012, the most up to date study gives a forcing less than the IPCC which David refers to at the beginning of the paper.

    Was the forcing less or more at 1750 or 1955? The point I tried to make is that it is also trivial that CO2 forcing declines with concentration:

    The temperature response also declines:

    http://c3headlines.typepad.com/.a/6a010536b58035970c0115707ce438970b-pi

    That leads onto the issue of ECS and radiative balance. In respect of these aspects I gave you Nic Lewis’s article previously which you have not commented on; so I’ll do it again:

    http://wattsupwiththat.com/2012/12/19/why-doesnt-the-ar5-sods-climate-sensitivity-range-reflect-its-new-aerosol-estimates/

    Lewis concludes:

    “The best estimate of the change from 1871–1880 to 2002–2011 in decadal mean adjusted forcing, net of the Earth’s heat uptake, is 2.09 − 0.43 = 1.66 W/m². Dividing that into the estimated temperature change of 0.727°C and multiplying by 3.71 W/m² gives an estimated climate sensitivity of 1.62°C, close to that from reworking Gregory 02.

    Based on the estimated uncertainties, I compute a 5–95% confidence interval for ECS of 1.03‑2.83°C – see Appendix 3. That implies a >95% probability that ECS is below the IPCC’s central estimate of 3°C”

    As to your dispute with David about TOA forcing, OHC and radiative imbalance I’ll let David respond to that but in the meantime Pielke Snr has done an overview of the issue referencing AR5 and the Levitus and Hansen papers:

    http://wattsupwiththat.com/2013/10/21/radiative-forcing-radiative-feedbacks-and-radiative-imbalance-the-2013-wg1-ipcc-report-failed-to-properly-report-on-this-issue/#more-95999

  10. Anthony, I think you’re actually not correctly describing what David did but you’re making exactly the mistake that I thought David had made. You say

    So Levitus 2012 has provided an average forcing of 0.27Wm-2 since 1955.

    David has compared that with the IPCC forcing of 1.6Wm-2 since 1750. That is the proper comparison not the shorter periods quoted from Hansen although they are of interest.

    So, yes there is no dispute that the actual calculation that David has done using the Levitus data is correct (it is) the issue is the comparison that is then made. Comparing this with the IPCC forcing of 1.6Wm-2 is incorrect. The 0.27 Wm-2 since 1955 is the average rate (per square metre) that energy has entered the oceans (and hence the climate system). The 1.6 Wm-2 since 1750 is the change in forcing since 1750. As Tom has pointed out earlier, these are not actually quantities that one should compare. The analogy that I’ve already made is that this is like comparing the average speed of a car in a drag race with its final speed and then being surprised that they aren’t the same.

    Before we go further, it would be good to clarify this one thing.

  11. anthony says:

    I agree, which is why I referred you to Nic Lewis’s post where he reaches a similar CUMULATIVE forcing of 1.66Wm-2.

    The issue is what figure for climate sensitivity does that forcing give and Lewis concludes a lower CS than the IPCC. Hansen of course, As Tom notes, finds a higher CS.

    More to the point let me ask you what accumulated forcing does Levitus’s averaged annual forcing of 0.27Wm-2 give for the period from 1955-2010? The resolution of that makes the comparison between Levitus 2012 and the IPCC figure from 1750 more relevant.

  12. I’m trying to think of how best to answer the question in your last paragraph. Firstly, the 0.27Wm-2 is not a forcing (as per the IPCC definition) it is simply an average of the energy imbalance. So, to a certain extent, I think the question doesn’t really make sense. Let me see if I can explain why. The 0.27 Wm-2 tells you the average rate (per square metre) that energy has been accumulating in the climate system (or, more correctly, about 90% of the total). Given a time interval (1955-2010) and this value, one can then calculate how much energy has accumulated in the system.

    The change in forcing since 1750 (1.66 Wm-2 quoted by David in his post) is the change in radiative forcing due to direct anthropogenic effects since 1750. If nothing else had changed since 1750, then this would be the energy imbalance (i.e., today energy would be accruing at a rate of 1.66 Wm-2). However, as Tom has pointed out in a number of places, the surface temperature has risen also since 1750. So, the energy imbalance is then the difference between this change in forcing and the “effective” change in forcing due to this temperature increase. Basically
    TOA = ΔF – λ ΔT.

    So, going back to your question, given a change in forcing one can’t really say anything about the expected average energy imbalance because to do so requires that you know λ which is, essentially, an estimate of the climate sensitivity.

    However, I think you can do the following. An ECS of 3 degrees per doubling is 0.75oC per Wm-2. That means that λ = 1.3333 Wm-2 per oC. If I consider the period 1750 to 2005, then ΔF = 1.66 Wm-2, and ΔT=0.8oC. If I plug these numbers in to the equation above I get an energy imbalance (today roughly) of 0.6 Wm-2. So an ECS of 3 degrees is consistent with the energy imbalance we measure today.

    To a certain extent, a problem that I’m having with this discussion is that there is a confusion between changes in forcings and energy imbalances (and also time intervals). It does make it quite hard to have such a discussion if we aren’t even really in agreement as to what the various quantities are and what the mean.

    I shall have to have another look at Nic Lewis’s paper. I don’t really have time to do so now, but will try to do so later.

  13. Okay, I see what Nic Lewis has done. It’s essentially the same calculation I’ve done but with different numbers. I will admit that some of my numbers are also not quite right. If you look at the Supplementary information for Otto et al. (2013) (a paper on which Nic Lewis is also an author) and look at Table 1, the numbers for the 2000s are ΔT=0.75oC, ΔF=1.95 Wm-2, and the total system heat uptake (essentially the energy imbalance) is 0.65 Wm-2. If you use these numbers to compute the ECS (as per Otto et al.) you get 2.1oC (and the range in Otto et al. is 1.2 – 3.9oC). So, for some reason, Otto et als. numbers differ from those in Nic Lewis’s WUWT post.

    A point I made earlier though, was that if something like aerosols is, temporarily, acting to reduce the system heat uptake (as some think) then that can have quite a large effect on estimates of the ECS using recent observations.

    However, I do think this discussion is drifting away from the original point of my post. The comparison that David makes between the 50 year average of the energy imbalance (based on OHC data) and numbers from either the IPCC (as you seem to think) or recent estimates (as per Hansen for example) is an incorrect comparison and cannot be used to infer (by itself) the climate sensitivity.

  14. Tom Curtis says:

    anthony, I am tired, and ill at the moment, so I will only respond to key points.

    The most fundamental point with regard to your post is that you are using non-standard terminology and are getting yourself hopelessly confused as a result. Specifically, you are confusing radiative forcing, ie, the difference between upward and downward energy transfers at the TOA relative to a set year, and on the assumption that no feedbacks other than the restoration of radiative equilibrium in the stratosphere, with TOA energy balance, ie, the instantaneous difference between upward and downward energy transfers at the TOA. You confuse things by calling both of these distinct (if related) concepts by the same term, ie, “forcing”. They are not the same. Don’t believe me on this, look up the IPCC definitions of the two terms.

    Using the standard definitions, the radiative forcing from CO2 was 1.601 W/m^2 in 2003, the total radiative forcing from greenhouse gases was 2.58 W/m^2 (2.749 according to GISS), the total radiative forcing from all forcings was 1.588 W/m^2 according to GISS. In 2005, while accepting the GISS forcings as stated above, Hansen was estimating a TOA energy imbalance of 0.85 W/m^2. In fact, it was closer to 0.48 W/m^2, as determined from Levitus (2012) data. Please note that there is no contradiction between saying the radiative forcing in 2003 was 1.6 W/m^2, but that the TOA energy imbalance was 0.5 W/m^2. They are two distinct concepts.

    I will note that David has acknowledged this issue twice, now. Once here, and once in the original discussion (although he still insists on non-standard terminology, calling the radiative forcing the “effective forcing” and the TOA energy imbalance the “measured forcing”).

    Once you correct the terminology, you see immediately that the change in OHC is related directly to the TOA energy imbalance, not the radiative forcing be itself. Specifically, the total surface energy accumulation in a year equals the TOA energy imbalance over that year times the number of seconds in the year and the surface area of the Earth (by conservation of energy). Radiative forcing is related indirectly to the surface energy accumulation by the approximate formula given by Wotts, but the relation between the surface heat accumulation and radiative forcing is moderated by the change in outgoing energy due to increased surface temperatures.

    Given that, the appropriate comparison is between model estimates of the TOA energy imbalance and observational estimates of that balance based on observed changes in OHC. To make those comparisons, you need to compare over the same intervals used in the model estimates, ie, 1993-2003, 1993-2008, 2003-2008, and 2005-2010 (for the Hansen papers).

    I notice in a follow up post you add to your confusion by referring to an undefined “cumulative forcing”. I take it by that that you actually mean the radiative forcing, but the name is ill chosen in that you use “forcing” to mean the TOA energy imbalance, and the radiative forcing is not the cumulative TOA energy imbalance in any significant sense.

    Frankly, until you clarify your thinking by adopting the standard terminology, there is no point in discussing more interesting issues with you. It would be as fruitful as discussing geometry with somebody who insists means that a “square” is any closed figure or shape, all of whose vertices are formed by right angles.

  15. Tom Curtis says:

    Wotts, I think you will find that, at equilibrium, TOA = 0, hence ΔF – λ ΔT=0, so λ=ΔF/ΔT. Given that for a doubling of CO2, you have ΔF=3.7, and by stipulation ΔT=3, λ= 1.233. It follows that with ΔF = 1.66 and ΔT=0.8, the expected TOA energy imbalance is 0.67 W/m^2. Alternately, with a measured TOA imbalance of 0.6, λ = (1.66-0.6)/0.8 = 1.325, equivalent to a climate sensitivity for doubled CO2 of 2.8 C.

    Nitpicking, I know, but it illustrates the central point that anthony and David are correct in suggesting that central estimates of ECS based on this formula show a climate sensitivity less than 3 C per doubling. In fact, approached more rigorously, as in Otto et al, you get a central estimate of the ECS closer to 2 than to 3 (as you note below). Of course, as you also note, the uncertainties of this method are large. Large enough to encompass an ECS close to 4 (and I would argue that they are larger than the values quoted by Otto et al).

  16. Tom, yes you’re quite right. I took the 0.75oC per Wm-2 from Hansen’s paper but it should indeed be as you say. That’s the problem with doing quick back-of-the-envelope type calculations just before going into a meeting 🙂

  17. Pingback: Watt is up with Roger Pielke Sr | Wotts Up With That Blog

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