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Lindzen and Choi Unraveled

Filed under: — group @ 8 January 2010

Guest Commentary by John Fasullo, Kevin Trenberth and Chris O’Dell

A recent paper by Lindzen and Choi in GRL (2009) (LC09) purported to demonstrate that climate had a strong negative feedback and that climate models are quite wrong in their relationships between changes in surface temperature and corresponding changes in outgoing radiation escaping to space. This publication has been subject to a considerable amount of hype, for instance apparently “[LC09] has absolutely, convincingly, and irrefutably proven the theory of Anthropogenic Global Warming to be completely false.” and “we now know that the effect of CO2 on temperature is small, we know why it is small, and we know that it is having very little effect on the climate”. Not surprisingly, LC09 has also been highly publicized in various contrarian circles.

Our initial reading of their article had us independently asking, how we could have missed such explicit evidence of the cloud feedback as shown in LC09? Why would such a significant finding have gone undiscovered when these feedbacks are widely studied and recognised as central to the projections of climate change? We discovered these common concerns at a meeting last year and then teamed up to address these questions.

With the hype surrounding the manuscript, one would think that the article provides a sound, rock solid basis for a reduced climate sensitivity. However, our examination of the study’s methods demonstrates that this is not the case. In an article in press (Trenberth et al. 2010 (sub. requ.), hereafter TFOW), we show that LC09 is gravely flawed and its results are wrong on multiple fronts. These are the major issues we found:

  • The LC09 results are not robust.

    A goal of LC09 was to quantify the cloud feedback by examining variability in top-of-atmosphere (TOA) radiative fluxes in the tropics as it relates to variability in mean sea surface temperature (SST). To do this they examine only tropical data. In general, they find that during periods of higher-than-normal SST, the radiation emitted and reflected to space by the earth goes up as well, cooling the Earth and amounting to an overall negative climate feedback. To show this, they select intervals of warming and cooling (in a time series of monthly averaged values) and compare fluxes at their endpoints (see Figure). They didn’t provide an objective criterion for selecting these endpoints and in some instances (see their Fig. 1), the selection of these intervals actually appears to be quite odd.


    Fig. 1: Warming (red) and cooling (blue) intervals of tropical SST (20°N – 20°S) used by LC09 (solid circles) and an alternative selection proposed derived from an objective approach (open circles) (TFOW, 2010).

    The result one obtains in estimating the feedback by this method turns out to be heavily dependent on the endpoints chosen. [edit] In TFOW we show that the apparent relationship is reduced to zero if one chooses to displace the endpoints selected in LC09 by a month or less. So with this method the perceived feedback can be whatever one wishes it to be, and the result obtained by LC09 is actually very unlikely. This is not then really indicative of a robust cloud feedback.

  • LC09 misinterpret air-sea interactions in the tropics

    The main changes in tropical SST and radiative fluxes at TOA are associated with El Niño-Southern Oscillation (ENSO) and are not necessarily indicative of forced variability in a closed system. ENSO events cause strong and robust exchanges of energy between the ocean and atmosphere, and tropics and subtropics. Yet LC09 treat the tropical atmosphere as a closed and deterministic system in which variations in clouds are driven solely by SST. In fact, the system is known to be considerably more complex and changes in the flow of energy arise from ocean heat exchange through evaporation, latent heat release in precipitation, and redistribution of that heat through atmospheric winds. These changes can be an order of magnitude larger than variability in TOA fluxes, and their effects are teleconnected globally. It is therefore not possible to quantify the cloud feedback with a purely local analysis.

  • More robust methods show no discrepancies between models and observations

    In TFOW, we compute correlations and regressions between tropical SSTs and top-of-atmosphere (TOA) longwave, shortwave and net radiation using a variety of methods. LC09 found the observed behavior to be opposite from that of 11 atmospheric models forced by the same SSTs and conclude that the models display much higher climate sensitivity than is inferred from ERBE. However, in our analysis comparing these relationships with models, we are unable to find any systematic model bias. More importantly, the nature of these relationships in models bears no relationship to simulated sensitivity. That is, the metric developed by LC09 is entirely ineffective as a proxy for simulated sensitivity.

  • LC09 have compared observations to models prescribed with incomplete forcings

    The AMIP configuration in the model simulations used by LC09 have incomplete forcings. The AMIP protocol started off a test only of how an atmospheric model reacts to changes in ocean temperatures, and so models often only use the ocean temperature change when doing these kinds of experiments. However, over the period of this comparison, many elements – greenhouse gases, aerosols, the sun and specifically, volcanoes changed the radiative fluxes, and this needs to be taken into account. Some models did this in these experiments, but not all of them.

    For instance, the dominant source of variability in the reflected solar flux arises from aerosols associated with the eruption of Mount Pinatubo in June of 1991 yet all but 2 model simulations examined by LC09 omit such forcings entirely. Other radiative species are absent from the models altogether. It is thus obviously inappropriate to expect such model simulations to replicate observed variability in TOA fluxes.

  • LC09 incorrectly compute the climate sensitivity

    By not allowing for the black body radiation (the Planck function) in their feedback parameter, LC09 underestimate climate sensitivity. Using the correct equations, LC09 should obtain a feedback parameter and climate sensitivity of -0.125 and 0.82 K, respectively, rather than their values of -1.1 and 0.5 K.  In contrast, TFOW results yield a positive feedback parameter and greater sensitivity estimate, though we also caution that this approach is not a valid technique for estimating sensitivity, as a closed and therefore global domain is essential (though not by itself sufficient). Lastly, LC09 fail to account for variability in forcings in estimating sensitivity.

While climate models are known to struggle with many aspects of tropical climate, especially in regards to its coupled variability, the problems claimed by LC09 are not among them. Forster and Gregory [2006] and Murphy et al. [2009] address changes in the energy budget with surface temperatures for a much larger domain and present a much more complete and defensible analysis and discussion of issues. They demonstrate that recent observed variability indeed supports a positive shortwave cloud feedback. So the feedbacks from processes other than the Planck function response are clearly positive in both observations and models, in contrast to LC09’s conclusions. Moreover, it is not appropriate to use only tropical SSTs and TOA radiation for feedback analysis as the transports into the extratropics are substantial. Any feedback analysis must also recognize changes in ocean heat storage and atmospheric energy transport into and out of the tropics which are especially large during ENSO events. While the tropics play an important role in determining climate sensitivity, simplistic and arbitrary analyses of tropical variability can be grossly misleading.


References

Forster, P. M. F., and J. M. Gregory (2006), The climate sensitivity and its components diagnosed from Earth Radiation Budget Data, J. Clim., 19, 39–52
Lindzen, R. S., and Y.-S. Choi (2009), On the determination of climate feedbacks from ERBE data, Geophys. Res. Lett., 36, L16705, doi:10.1029/2009GL039628.
Murphy, D. M., S. Solomon, R. W. Portmann, K. H. Rosenlof, P. M. Forster , and T. Wong (2009), An observationally based energy balance for the Earth since 1950, J. Geophys. Res., 114, D17107, doi:10.1029/2009JD012105.
Trenberth, K. E., J. T. Fasullo, Chris O’Dell, and T. Wong, (2010): Relationships between tropical sea surface temperature and top-of-atmosphere radiation. Geophys. Res. Lett., 37, doi:10.1029/2009GL042314, in press.


61 Responses to “Lindzen and Choi Unraveled”

  1. 1
    Simran says:

    Thanks for the post.

    As you say in the fourth dot-point, Lindzen does not account for black-body radiation in his rather strange definition of the feedback parameter. As I see it, a positive feedback parameter (by the definition in the paper) would imply a runaway greenhouse situation, or at least some sort of local super-greenhouse effect. Thus, to extrapolate the positive slope of all the model regressions to a global feedback parameter would indicate thay are all in runaway greenhouse situations – clearly this is not the case.

    Is that correct or am I missing something here? If the net TOA outgoing radiation reduces with increasing temperature, the temperature in these models should increase without bound.

  2. 2
    Robert Reiland says:

    Isn’t the recent paper on low-level cloud feedbacks (http://www.sciencemag.org/cgi/reprint/325/5939/460.pdf) by Amy C. Clement et al. also relevant to this subject? They measured a net positive feedback from low-level clouds over the Northeast pacific.

  3. 3
    Ben Lawson says:

    When all you have is a hammer, everything looks like a nail… Maybe Lindzen should visit a bigger hardware store, preferably outside of the tropics.

  4. 4
    Spencers says:

    “They didn’t provide an objective criterion for selecting these endpoints and in some instances… the selection of these intervals actually appears to be quite odd… The result one obtains in estimating the feedback by this method turns out to be heavily dependent on the endpoints chosen… with this method the perceived feedback can be whatever one wishes it to be…”

    I suppose this is a polite way of saying that Lindzen and Choi fell victim to confirmation bias: the all too common pitfall of trying lots of things that don’t produce the result you are sure is correct, and finally finding something that does what you expect and publishing it. It would have been good for everyone if the problems had been caught in review before publication, but even things that seem obvious in retrospect can take a while to see.

  5. 5

    All this ignores what seems far more important which is that heat permanently taken into the deep ocean, say deeper than 100 meters so it does not have any effect on emissions from the ocean surface, has no part in anybody’s arguments about “feedbacks.”

    Has anyone calculated the effect on surface temperature due of heat disappearance from that surface, where that disappeared heat is the increase in ocean heat content shown on this site at “Updates — on 28 Dec 2009? If that effect was added to the temperature record shown on the same post, what would that temperature record look like?

  6. 6
    David B. Benson says:

    Jim Bullis, Miastrada Co. (5) — The deep ocean is much deeper than that. First there is the so-called seasonally mixed layer (at least annually) and then the rest of the mixed layer down the to main thermocline. The bottom of the mixed layer is at various depths in different parts of the ocean, but possibly around 500 meters is representative. The entire mixed layer participates in eventually setting the SSTs, with a characteristic time of about 5–10 years, I think. The deep ocean redistributes heat on a very much longer time scale. Interestingly, it seems that it usually sends heat from the SH to the NH!

  7. 7

    David B. Benson,

    I did not say how deep the ocean was. I said “deeper than 100 meters” would be where heat would have no effect on emissions.

    But your details are relevant and I would tend to agree with you about the 5-10 year time frame. Imagine what the air temperature would be if the ocean heat content had not increased. I imagine it would be somewhat hotter and that is the question that I think is important.

    I imagine the specific heat of air and the specific heat of water would be the main parameters for the calculation, of course the temperature of various layers would then be needed. I recall some conversation about this from some time past, but the recent “Updates –” post of 28 Dec reminded me of it and reinforced my contention that this is important.

    The record portrayed in the referenced document is for 700 meters which I think might be ok for starters, but if we were to do this right we need much deeper data and maybe a lot more samples.

  8. 8
    Jim Prall says:

    Further to Jim Bullis’ question in #5, I know we are very short of direct measurement of the heat content of the deep oceans. There are the free-floating Argos drifter buoys that can dive and surface autonomously, reaching a maximum depth of 2000m. This data should give us some help in constraining the heat content and fluxes into the deep ocean, but online in outline form.
    One other way I could see trying to constrain the overall heat flux into the world oceans would be sea level rise – strictly just that portion attributable to thermal expansion, excluding added meltwater runoff from glaciers and ice sheets. Since we have only coarse estimates of the latter, I’m not sure how precise a constraint this could offer – maybe only some degree of upper limit?

  9. 9
    cumfy says:

    Thanks for the analysis Kevin et al.

    I had considerable reservations along many of the same lines, which I summarised in August:
    http://www.realclimate.org/?comments_popup=930 (#127)

    Which includes some JRA budget maps to illustrate the issues of meridional and latent heat variability swamping OLR variation.

  10. 10
    David B. Benson says:

    Jim Bullis, Miastrada Co. (7) — Ok, 700 meters for the average mixed layer depth. Now the entire heat content of the atmosphere is the same as 2.5 meters of ocean, so water heat content is all but 0.36% of the total. Somehow I think the deep ocean can be ignored on the centennial scale.

  11. 11
    Thomas says:

    I fail to see the relevance of 5,6, and 7 to the question raised by LC09, which is “how does TOA radiation balance vary as a function of SST?” If we were able to get a closed system (irregardless of heat storage) then you would be able to compute longterm sensitivity based upon that function. The problem with LC09, is that they would need to have used globally averaged surface temperature, and globally averaged TOA fluxes, as otherwise they might simply be detecting say that locally warm spots are cloudier than their surroundings (which because anomalously warm areas would likely have stronger convective activity than cooler regions I would expect). So I would say LC09 falls down, because the (claimed) correlation of cloudiness with SST anomalies, may be due to anomalous tropical versus extratropical temperature differences. Of course the issues of cherry picking a few data points, and avoiding data contaimination from volcanic aerosols are also significant.

    Even if we had a whole earth that we could experiment with, and were able to adjust average surface temperature, we would want to adjust the temperature slowly enough so that the atmosphere (and cloudiness) has come into quasi equilibrium with the new boundary conditions. Otherwise our data may be affected by temporal variations of TOA caused by the adjustment process itself. I.e. any perturbation to the climate system is likely to result in both a transient, and a time invariant response, and we want to be sure the transient has died off before concluding that the measurement is of the long term change to the equilibrium.

  12. 12

    One of the tricks (in the positive sense) scientists should always use is to sit back and think: now I have this result, what change in the experiment could reverse it? That they failed to do this is worse than confirmation bias: it’s sloppy technique. I’m surprised an experience MIT academic could get this so badly wrong.

  13. 13
    Doug Bostrom says:

    David B. Benson says: 8 January 2010 at 9:28 PM

    “…the entire heat content of the atmosphere is the same as 2.5 meters of ocean, so water heat content is all but 0.36% of the total.”

    I’ve wondered about that proportion and the answer (thank you) is truly staggering.

    It makes me think (and I’m obviously not the first) that some of the variation we see in global air temperature is simply thanks to variances in opportunities for heat to leak into sea water. There’s just such huge capacity there. With that size of sink a thermal rearrangement of water in the oceans of relatively small scale could make a large difference in air temperature.

    Wow.

  14. 14

    I thank you for this concise debunking of this paper.

    But it bothers me that the absolutist whack-job idiocy of Lindzen and Choi is given even a modicum of respect necessary to evaluate their paper.

    When they say that “absolutely, convincingly, and irrefutably proven the theory of Anthropogenic Global Warming to be completely false.” – it sets off all kinds of alarms.

    [Response: Note this was said about LC09, not by them. I doubt that Lindzen would have gone that far. – gavin]

    The issue they argue is not as benign as plate tectonics, or even helio-centrism – where failing to accept science is harmlessly foolish. It is not even the doubt of tobacco causing cancer, where a few million people will die sooner from diseases caused by tobacco. Anthropogenic Global Warming climate models cannot exclude human extinction, and hence deserves a type of serious consideration that excludes such dolts.

    We face tremendous survival risks, and it is no less than dangerous treason to civilization for dangerous fools to ask us all to live for today while devaluing the future. They use bad science to declare a defeat to thermodynamics – treason to logic.

    Thank you for debunking them – it is civil of you to read their article. However, this is not tobacco, not cold fusion, not even creationism, this is planetary sustainability for humans. Their ethics are slimy.

    Now that our military and CIA are seriously scrutinizing climate change, it begins to take on the feeling of a war. About time.

  15. 15
    Edward Greisch says:

    It is easy to be fooled by a sufficiently complex mathematical function or algorithm. That has happened innumerable times before. It is too easy to draw a trend line through a graph that looks like scattershot to me. The papers analyzed are much too complex for me and almost everybody else to understand in anything close to real time. The “various contrarian circles” look and sound as scientific as anything else if you don’t stay anchored to a few simple truths. Those simple truths would be the 1859 Tyndall experiments, etc. It is very easy for almost everybody to be fooled by the contrarians otherwise.

    Thank you, RC, for pointing out what happens if you change the chosen points by a small amount. This is one of those cases where I am willing to trust RC’s analysis. My own knowledge of the 1859 Tyndall experiments tells me who to trust. The basics must be taught.

    It is rather unusual for RC to post 2 articles at once. The 2 articles do compliment each other. I wondered at first why you didn’t combine them. For once, I looked at the articles referenced in the main articles as well. It is necessary this time. The New York Times article’s point that we are discussing the size of the climate sensitivity, not whether there is one, is important. Have Lindzen and Choi created anything that will eventually result in a more precise and robust number for climate sensitivity? I think the answer is yes, even if it is only another straw man to shoot down.

    Thanks again to John Fasullo, Kevin Trenberth, Chris O’Dell, Gavin Schmidt and the other posters who have added clarifications.

  16. 16
    meteor says:

    I don’t understand

    in the figure 1b of TFOW, you find (in red and blue) a greater slope than LC09.
    this slope in W/m2.°K is the inverse of climate sensitivity.
    So, if my understanding is good, greater the slope in your graph, smaller is the sensitivity.

    (net flux N = – deltaT/sensitivity)

    can you explain or rectify please?

  17. 17
    meteor says:

    adding to my post

    the legend of your graph (fig1b) is not clear.
    Is the dotted red regression is original LC09 or the modified?
    If it is the original, the sensitivity of LC09 is very low but if it is the black one it is the contrary.
    So can you give us a clear legend?

  18. 18
    cumfy says:

    #11
    “The problem with LC09, is that they would need to have used globally averaged surface temperature, and globally averaged TOA fluxes..”

    This is an interesting point which I took a look at a while back using the
    global temperatures and fluxes from:
    http://www.ncdc.noaa.gov/oa/climate/research/anomalies/index.html
    http://www.cgd.ucar.edu/cas/Trenberth/trenberth.papers/i1520-0442-21-10-2297.pdf

    Essentially a peak-to-peak global temperature variation of 4K is driven by a 10PW (20 Wm-2 global equivalent) all-flux TOA.

    It is interesting to observe that the LC09 derived sensitivity of 0.2K/Wm-2 is almost identical to the bulk sensitivity derived from the seasonal variation in global mean temperature/ heat flux (4K/20Wm-2)=0.2K/Wm-2(!) (Note the global analysis is closed both in area and total heat budget)

    When the analysis is repeated to eliminate potential bias of asymmetry in distribution of TOA SW by sampling at the equinoxes rather than solstices a figure more like 0.3K/Wm-2 is derived.

    These figures represent lower bounds on sensitivity, as equilibrium is not achieved nor any account of lag given.

    What, however intrigues me, is that no one uses the data from seasonal varaition in global temperature/heat flux, to *properly* analyse sensitivity. (eg Fasullo/Trenbreth who have produced numerous other important papers on the data)

    This approach has a particular advantage over ongoing analysis of our ad hoc CO2 experiment with the planet:

    The forcing rate from the seasonal cycle(40 Wm-2/1y =40Wm-2y-1)is 1000 times larger than GHG rate (4 Wm-2/100y =.04Wm-2y-1).
    Thus, the measurability of the effects produced are 3 orders of magnitude greater than those from direct GHG forcing.

    [[Heresy Alert]]
    I have to say my suspicions are that there may be people cogniscent of the likely outcome of such an analysis — and that it is rather on the low side to be politically expedient to publish on.
    [[End Heresy Alert]]

    I do though, look forward to someone producing a credible analysis along these lines, hopefully sooner rather than later.

  19. 19
    Tim McDermott says:

    From the first bullet:

    The result one obtains in estimating the feedback by this method turns out to be heavily dependent on the endpoints chosen. [edit] In TFOW we show that the apparent relationship is reduced to zero if one chooses to displace the endpoints selected in LC09 by a month or less.

    emphasis added.Gavin is getting tougher, he even edits guest contributions!

    [Response: There was a sentence in there that the authors didn’t feel was justified, and they asked me to remove it. The [edit] tag was to demonstrate that I’d edited the piece since the original post. – gavin]

  20. 20
    H Hak says:

    Haven’t checked this again but believe your objections to LC09 are similar to Roy Spencer’s concerns earlier.

  21. 21

    Doug Bostrom #13,

    You get the point. Now consider that it is widely thought that a modest increase in temperature of air at the surface will cause much heightened weather activity, and of course that would mean greater winds that would cause faster vertical mixing of the ocean and faster uptake of the heat. It seems that this would significantly moderate the temperature at the global surface. As a control system problem, this system should operate to keep the temperatures at the surface fairly low.

    I am sure that the climate modelers have some way to estimate how higher winds would cause greater vertical mixing of the oceans. From the data plots of the post “Updates –” 28 Dec, it looks like this has not been adequately done. I also am aware of the separation of the ocean modeling and the atmospheric modeling work, with perhaps not enough interaction. Further, the ocean modeling did not seem to put enough attention on vertical mixing (Monterey code). So, maybe an adjustment of this part of the model would be interesting. It could be important since it might set the stage for the next 20 years of wrangling over what it all means.

    (For my part, I hark back to a previous career in underwater sound research where the study of this process was a primary matter of interest. Because it determines whether a surface ship sonar detects a submarine before the sub sinks the ship, there is a need for general knowledge of the vertical temperature gradient and that is why we have massive amounts of XBT data from the last 50 years or more. There is an annual effect of higher thermoclines after a summer season and extensive vertical mixing after a winter season that makes the “thermocline” zero for a significant depth.)

    #8 Jim Prall,

    The data tells us where the heat goes; we do not control the data or constrain anything about the sea level. The data just tells us how badly things are going. Of course, if you look at the whole picture, controlling CO2 would do the job, but after that the only thing we can do about rising sea level is build dikes.

    #10 David Benson,

    The question is not about the entire heat content of either body. The question is, how much would the ocean temperature increase in order to take down an incremental temperature increase in the atmosphere. It should be possible to get a rough sense of things if we just talk about an ocean top layer of about 100 meters. This would be a fairly short term process. For deeper regions, the vertical mixing is much slower, but in the time frames of a few years it seems like there would be enough of that vertical mixing, although a slow process, to matter in the heat accumulation picture.

    As a control system problem (control systems was another previous career), the slow rate of vertical mixing would act as a time constant which would limit the system’s ability to null out the surface temperature on a short time basis, and thus there might be a constant temperature offset prevailing. However, in this concept that constant temperature offset would still be much less than the temperature if that control system did not exist.

  22. 22
    David B. Benson says:

    Doug Bostrom — Yes, and that’s just down to 700 meters. Then there is the deep ocean…

  23. 23
    Babelsguy says:

    Someone above claimes that an increased SST would increase convection.

    I always thought bigger temperature differences in layers of water would rather reduce convection?

    Could someone knowledgeable please clarify?

    Cheers

    Babelsguy

    [Response: Atmospheric convection. – gavin]

  24. 24
    Babelsguy says:

    Whoops, that should only apply if the warmer water layers are on top, of course….

  25. 25
    Completely Fed Up says:

    I think you misspell “Hearsay” here:

    [[Heresy Alert]]
    … blah blah blah …
    [[End Heresy Alert]]

    It’s often the case that when someone calls what they’re about to say “heresy”, they don’t believe it is but want to make out that they’re “on the edge” as it were.

    What a rebel.

    Or minstrel.

    Mmmm. Chocolate…

  26. 26
    Ray Ladbury says:

    Cumfy, estimating climate sensitivity using annual variation is not all that straightforward–how long is the delay from onset of forcing to equilibrium (or do you reach equilibrium at all) and what does sensitivity over such a short time even mean? Certainly, you aren’t having much effect below the first few meters of the ocean.

    I mean after all, the diurnal variation is even greater, if short-term measurements were meaningful, why not use that!?

  27. 27
    David B. Benson says:

    Jim Bullis, Miastrada Co. (21) — I have only begun to realize how imprtant the vertical mixing in the upper ocean (down to the main thermocline) is, and how difficult it is for me to discover what is known about it and so the extent to which it is adequately parameterized.

    However, simple two box models suggest that the seasonally mixed layer contributes about 20% and the rest of the mixed layer about 80% with a characteristic time of somewhere between 5 and 10 years. I’ll admit that is rather crude, but agrees with the global temperature products fairly well.

    I would quite like to have a better conceptual model, but nothing more complex appears to be adequately trainable (to detemine the constants). In any case, it is clear that the heat content lies in the ocean so that, for simplicity, the temperature of the air above can be ignored.

  28. 28

    Edward Greisch 15,

    As I understand it, if we limit our truth to the 1859 Tyndall experiments we can all be secure in the knowledge that saturation of CO2 has occurred as far as attenuation of IR radiation and there is no real chance of doing anything about it. If that were true, we would have already exprienced catastrophic warming since almost no emitted energy of IR in the CO2 band would be escaping.

  29. 29
    cumfy says:

    Re26
    Ray
    Of course you raise valid questions, and of course very little of climate science is particularly straightforward. That should not prevent the search for analyses which shed light.

    1. 6 months is not a particularly short period and there is significant change in the principal positive feedback -(tropospheric water vapor) from January to July. The apparent lag between forcing and temperature response is of the order 1 month. It seems feasible therefore, that a significant proportion of the (quasi)equilibrium temperature is attained.

    2. Ocean heat storage is of the order 10^23J each year
    http://www.cgd.ucar.edu/cas/Trenberth/trenberth.papers/i1520-0442-21-10-2313.pdf. Global ocean SST mean varies on the order 0.5C. To store this energy at 0.5C about 130m of the global ocean is required:
    (10^23) / (3.6 * (10^14) * 0.5 * 4.2 * (10^6)) = 132.275132

    In practice only about a third of the ocean (ie Southern Ocean) effectively acts as the capacitor for this heat, as through symmetry all the NH ocean is “cancelled out” by an equal area of SH ocean.

    Thus at 0.5C ~400m of this residual SH area is required to store 10^23J. Maybe the temperature differences are higher, but even at 5C one would require 40m. Lets say 50m at 4C.

    3. I come back though to the central strength of a seasonal analysis of global temperature/heat flux:

    The measurement effects are of the order 1000 times greater since
    the forcing rate from the seasonal cycle(40 Wm-2/1y =40Wm-2y-1)is 1000 times larger than GHG rate (4 Wm-2/100y =.04Wm-2y-1)

    I think that the potential benefits and leverage of such an approach far outweigh the potential difficulties of “interpretation”.

    PS
    I am very interested in any data/articles you have on global diurnal temperature variation. Naturally any model would accurately account for and explain such variation, and as such the global diurnal variation should be describable in terms of the global sensitivity.

    PPS
    Just discovered: An observationally based energy balance for the Earth since 1950 D. M. Murphy et al which I am chewing over.

  30. 30
    Completely Fed Up says:

    cumfy, if 6 months is quite long when it comes to changing the oceans, why does it take ~800 years for a warmer surface to make the ocean bulk release CO2?

  31. 31
    Ray Ladbury says:

    Cumfy, have you looked at this post by Tamino?

    http://tamino.wordpress.com/2009/08/17/not-computer-models/

    Tamino uses a 30 year response time for the oceans–not sure how much you could get that to respond to a yearly oscillation. You will likely underestimate the sensitivity significantly.

  32. 32
    David B. Benson says:

    Wunsch, C. and R. Ferrari, 2004, Vertical mixing, energy, and the general circulation of the ocean
    Clear exposition as one expects from Carl Wunsch. Unfortunately, this review seems not to answer my questions about vertical ocean profiles other than to remind me about stratification. Still, the care in energy balances was certainly worth the reading effort.

  33. 33
    Doug Bostrom says:

    Jim Bullis, Miastrada Co. says: 9 January 2010 at 3:18 PM

    (For my part, I hark back to a previous career in underwater sound research where the study of this process was a primary matter of interest. Because it determines whether a surface ship sonar detects a submarine before the sub sinks the ship, there is a need for general knowledge of the vertical temperature gradient and that is why we have massive amounts of XBT data from the last 50 years or more. There is an annual effect of higher thermoclines after a summer season and extensive vertical mixing after a winter season that makes the “thermocline” zero for a significant depth.)

    Interesting. Presumably some of that was classified; I sure hope some of it is published now. Any idea? Kind of remindful of the reactivated intel remote sensing recycling effort.

  34. 34
    Steve Bloom says:

    cumfy: “Naturally any model would accurately account for and explain [global diurnal temperature] variation, and as such the global diurnal variation should be describable in terms of the global sensitivity.”

    Now pull the other one, it’s got bells on.

    Just out of curiosity, why would you expect such a thing when models rather famously can’t do inter-annual variability and have achieved only the rough beginnings of doing inter-decadal variability? Then, even if there would ever be data sufficient for such a task (doubtful), there’s the slight problem that it will be many, many years before the kind of computing capacity needed might exist.

    Also, sensitivity is a model output, so we wouldn’t be describing such variation in terms of it.

    Anyway, you need to do more background reading on the science and less reasoning from first principles.

    One thing to read is this paper, which describes how radically different the climate was the last time CO2 was at present levels and there was sufficient time to reach equilibrium. Note that the models aren’t yet up to replicating that climate state, although it’s a problem that’s getting a lot of attention (inc. from Gavin).

    How quickly we will reach that state, BTW, especially given CO2 increases well beyond current levels, is the overwhelmingly most important question of our time, so I’m happy to see it being prioritized over trying to analyze diurnal variations.

  35. 35
    David B. Benson says:

    Ray Ladbury (31) — Tamino’s two box model has 1 and 30 year characteristic time components.

  36. 36

    27 David B. Benson,

    In my experience, the “seasonally mixed layer” is the only really mixed part and obviously it happens in less than a year. From there on down, it takes major events like hurricanes to get a little deeper from time to time. A Tsunami like that of a few years ago would do a massive amount of vertical pumping in a short time. On a general basis, maybe this starts to function on a 5 or 10 year basis world wide. But the Gulf Stream takes the warm water on a much deeper ride as it goes from its exit of the Gulf to deep ocean. The mixing is not vigorous but the vertical component over many miles of horizontal path must puts quite a lot of water downward. We only paid a little attention to currents at a mile depth, but even so, measurements showed that they were not zero. Here we get into the thermohaline circulation, which is another very sophisticated analysis, and validating this to the point of fully quantifying vertical mixing is not a simple job. Anyway, I look for more analysis of this in the future, but in the meantime, your 5 -10 year time constant looks reasonable.

    And I agree that this sort of fits what we see. But we are looking at an interval that is too short to make too much of it.

    33 Doug Bostrom,

    From my time on, there never was anything classified about ocean temperature gradients or other basic science. Military hardware is another matter. Much of the basic knowledge on this from WWII was pulled together in Summary Technical Report of Division 6, NDRC, 1946 and republished as NAVMAT P-9675, 1969 (Unclassified)

  37. 37
    Thomas says:

    cumfy’s idea is interesting, but flawed. The problem is that with seasonal changes the atmoshere is never at equilibrium (let alone the ocean). Clearly the equinoxes are not a good sample point, as that is near the time when seasonal changes are the greatest. The best times are probably January and July, when to some zeroth order approximation hemispheric temperatures are near equilibrium with the radiation, other times of year high latitudes are severely out of balance.

    But we still have a lot of problems, (1) ocean/land differences are near their greatest. Also seasonal surface albedo changes due to snow/ice and seasonal vegetation changes are still taking place. I doubt that once the sources of uncertainty are estimated that one would want to proceed with the excercise. Thats probably why no-one has done it (or published a paper based upon it).

  38. 38
    David B. Benson says:

    Jim Bullis, Miastrada Co. (36) — It seems there are many other slow mixing processes, down to the mixed layer depth and even in the deep ocean. For some attempts at two box models, see not only Tamino’s analysis, but other towards the end of the comments in
    http://tamino.wordpress.com/2008/10/19/volcanic-lull/
    http://tamino.wordpress.com/2009/08/17/not-computer-models/
    and also a bit towards the end of the open thread #17 there.

  39. 39
    Arthur Smith says:

    No, cumfy’s idea doesn’t address the main question at all, because diurnal and seasonal changes only affect *half the planet* at a time. GHG changes affect heat flow across the entire planet. A very different situation. Averaged across the whole planet, there is presumably close to zero average diurnal temperature change, because there’s close to zero change in total average incoming sunlight. Same with the seasons – in fact I believe we get slightly higher incoming solar energy during northern hemisphere winter, since Earth is slightly closer to the Sun at that point in its orbit.

  40. 40

    Now the question is will LC09 be included in the next IPCC review since McIntyre and McKitrick 2003, McIntyre and McKitrick 2005 were included in the last AR4 WGI Chapter 6 IPCC review.

    LC09, in the end, doesn’t have much to say, even though its author is a little more…shall we say credentialed and visible…than others.

  41. 41

    “Now the question is will LC09 be included in the next IPCC review since McIntyre and McKitrick 2003, McIntyre and McKitrick 2005 were included in the last AR4 WGI Chapter 6 IPCC review.

    LC09, in the end, doesn’t have much to say, even though its author is a little more…shall we say credentialed and visible…than others.”

    Errr, I meant published, not included.

  42. 42
    cumfy says:

    RE 39
    Arthur
    The *global* mean temperatures vary between 15.8C in July and 12C in January(paradoxical I know)See tables at:
    http://www.ncdc.noaa.gov/oa/climate/research/anomalies/index.html

    When Ray referred to the diurnal temperature variation being larger than the seasonal variation I presumed (in comparing apples with apples) he meant the global mean. But I do not have data for that. It seems feasible especially in NH summer as the highly continental Asian land mass varies between high and near zero insolation and typical continental local surface variation will be of the order 15-20C; whereas ocean will not vary by more than 0.25-0.5C.

    Land is very “fickle” in its insolation response. Ocean is constant.
    It is principally the asymmetries in their distribution, which produce the seemingly paradoxical response.

  43. 43
    David B. Benson says:

    It seems I was rather confused about the ocean mixed layer. First, the depth varies greatly in different parts of the ocean but the graphic in
    http://www.lodyc.jussieu.fr/%7Ecdblod/blt.html
    is probably representative. In any case, the idea is that this is the seasonally (at most annually) mixed layer.

    Deeper vertical mixing does occur, as indicated in the Wunsch/Ferrari paper mentioned above. Using just these two factors, a trained linear two box model of the system does quite well in reproducing global temperature product data, especially when ENSO is considered to be a forcing. (I previously gave the links.)

  44. 44
    Ray Ladbury says:

    Cumfy, Have you seen the analysis by Reto Knutti on determination of sensitivity via the annual cycle? It’s pretty good.

  45. 45
    cumfy says:

    Ray
    Thanks for the Tamino and knutti references.

  46. 46
    Ray Ladbury says:

    Cumfy, You are most welcome. I always love to recommend good work, and these two gentlemen continue to amaze with their high-quality output and understandable presentation.

  47. 47
    H. Tuuri says:

    Trenberth et al.:

    “They [LC09] didn’t provide an objective criterion for selecting these endpoints and in some instances (see their Fig. 1), the selection of these intervals actually appears to be quite odd.”

    http://www.mit.edu/~ysc/index.files/Lindzen&Choi2009GRL.pdf

    Looks like Lindzen and Choi have chosen periods where the sea surface temperature change is very fast. From Figure 1a in their paper, we see that Lindzen and Choi lack the ERBE data for certain periods of 1993 and 1998. That explains certain ‘odd’ endpoints in their intervals.

    Trenberth et al.:

    “In TFOW we show that the apparent relationship is reduced to zero if one chooses to displace the endpoints selected in LC09 by a month or less. So with this method the perceived feedback can be whatever one wishes it to be, and the result obtained by LC09 is actually very unlikely.”

    A naked eye estimate of the SST graph and ERBE graph in Figure 1a in the Lindzen and Choi paper gives a rough estimate for delta-Flux(W/m^2) per delta-SST. For example, the ERBE graph from late 1986 to early 1990 has a variation of delta-Flux around 3 W/m^2, while the sea surface temperature varies by about 0.5 K. This is consistent with what Lindzen and Choi say in their paper that delta-Flux(W/m^2) per delta-SST is roughly 6 W/m^2 per K (they call this ‘slope’). My naked eye does not see how moving the endpoints ‘by a month or less’ could change the figures much.

  48. 48
    Ray Ladbury says:

    H. Tuuri says, “My naked eye does not see how moving the endpoints ‘by a month or less’ could change the figures much.”

    That is why the naked eye is not considered a particularly accurate data analysis tool. The fact that selection of even slightly different intervals destroys the effect pretty much shows the effect isn’t there.

  49. 49
    H. Tuuri says:

    Ray (comment #48), if you look at Figure 1a of LC09, your naked eye should confirm what I see. The correlation between delta-Flux and delta-SST is very strong at least in the 1986 – 1990 period, and the ‘slope’ is roughly 6. The only way LC09 could be wrong is that their ERBE graph is incorrect. Some Googling revealed that LC09 are using the orbitally corrected ERBE data by Wong et al. from 2006. If the ERBE graph in LC09 Figure 1a is incorrect, please prove it.

    Thus, I do not understand how Trenberth et al. can do away with the correlation just by moving endpoints less than a month. I am eager to see their paper when it comes out.

    If LC09 are correct that delta-Flux per delta-SST is 6 W/m^2 per K, that is a surprising result. A simple black body radiation model would give just 4 W/m^2 per K. That is, the Earth would resist warming even stronger than a black body, which in turn would mean that a doubling of CO2 might warm the Earth less than 1 K.

  50. 50
    Chris O'Dell says:

    Turri,

    I’m sorry but you have to do the analysis for real, which we did. We tried varying a lot of things, and endpoints was one of them, and what really happens is that the slope result can change quite a bit. Are you looking at LW or SW or both? It is particularly in the SW where it matters (but both matter – see our table 1). Look at our paper. Reproduce our Table 1. If you do what we did and you always get what LC09 get, then okay. But you gotta bite the bullet and do the analysis first.


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