By Christopher Monckton of Brenchley
My commentary written for Remote Sensing on the empirical determination of climate sensitivity, published by the splendid Anthony Watts some days ago, has aroused a great deal of interest among his multitudes of readers. It is circulating among climate scientists on both sides of the debate. Several of Anthony’s readers have taken the trouble to make some helpful comments. Since some of these are buried among the usual debates between trolls on how awful I am, and others were kindly communicated privately, I have asked Anthony to allow me, first and foremost, to thank those readers who have been constructive with their comments, and to allow his readers the chance to share the comments I have received.
Joel Shore pointed out that Schwartz, whose paper of 2007 I had cited as finding climate sensitivity to be ~1 K, wrote a second paper in 2008 finding it close to 2 K. Shore assumed I had seen but suppressed the second paper. By now, most of Anthony’s readers will perhaps think less ungenerously of me than that. The new .pdf version of the commentary, available from Anthony’s website (here), omits both Schwartz papers: but they will be included in a fuller version of the argument in due course, along with other papers which use observation and measurement, rather than mere modeling, to determine climate sensitivity.
Professor Michael Asten of Monash University helpfully provided a proper reference in the reviewed literature for Christopher Scotese’s 1999 paper reconstructing mean global surface temperatures from the Cambrian Era to the present. This, too, has been incorporated into the new .pdf.
Professor Asten also supplied a copy of a paper by David Douglass and John Christy, published in that vital outlet for truth Energy & Environment in 2009, and concluding on the basis of recent temperature trends that feedbacks were not likely to be net-positive, implying climate sensitivity ~1 K. I shall certainly be including that paper and several others in the final version of the full-length paper that underlies the commentary published by Anthony. This paper is now in draft and I should be happy to send it to any interested reader who emails monckton@mail.com.
A regular critic, Lucia Liljegren was, as all too often before, eager to attack my calculations – she erred in publishing a denial that I sent her a reference that I can prove she received; and not factually accurate in blogging that “Monckton’s” Planck parameter was “pulled out of a hat” when I had shown her that in my commentary I had accepted the IPCC’s value as correct. She was misleading her readers in not telling them that the “out-of-a-hat” relationship she complains of is one which Kiehl and Trenberth (1997) had assumed, with a small variation (their implicit λ0 is 0.18 rather than the 0.15 I derived from their paper via Kimoto, 2009); and selective in not passing on that I had told her they were wrong to assume that a blackbody relationship between flux and temperature holds at the surface (if it did, as my commentary said, it would imply a climate sensitivity ~1 K).
A troll (commenter on WUWT) said I had “fabricated” the forcing function for CO2. When I pointed out that I had obtained it from Myhre et al. (1998), cited with approval in IPCC (2001, 2007), he whined at being called a troll (so don’t accuse me of “fabricating” stuff, then, particularly when I have taken care to cite multiple sources, none of which you were able to challenge) and dug himself further in by alleging that the IPCC had also “fabricated” the CO2 forcing function. No: the IPCC got it from Myhre et al., who in turn derived it by inter-comparison between three models. I didn’t and don’t warrant that the CO2 forcing function is right: that is above my pay-grade. However, Chris Essex, the lively mathematician who did some of the earliest spectral-line modeling of the CO2 forcing effect, confirms that Myhre and the IPCC are right to state that the function is a logarithmic one. Therefore, until I have evidence that it is wrong, I shall continue to use it in my calculations.
Another troll said – as usual, without providing any evidence – that I had mis-stated the result from process engineering that provides a decisive (and low) upper bound to climate sensitivity. In fact, the result came from a process engineer, Dr. David Evans, who is one of the finest intuitive mathematicians I have met. He spent much of his early career designing and building electrical circuitry and cannot, therefore, fairly be accused of not knowing what he is talking about. Since the resulting fundamental upper limit to climate sensitivity is as low as 1.2 K, I thought readers might be interested to have a fuller account of it, which is very substantially the work of David Evans. It is posted below this note.
Hereward Corley pointed out that the reference to Shaviv (2008) should have been Shaviv (2005). Nir Shaviv – another genius of a mathematician – had originally sent me the paper saying it was from 2008, but the version he sent was an undated pre-publication copy. Mr. Corley also kindly supplied half a dozen further papers that determine climate sensitivity empirically. Most of the papers find it low, and all find it below the IPCC’s estimates. The papers are Chylek & Lohman (2008); Douglass & Knox (2005); Gregory et al. (2002); Hoffert & Covey (1992); Idso (1998); and Loehle & Scafetta (2011).
I should be most grateful if readers would be kind enough to draw my attention to any further papers that determine climate sensitivity by empirical methods rather than by the use of general-circulation models. I don’t mind what answers the papers come to, but I only want those that attempted to reach the answer by measurement, observation, and the application of established theory to the results.
Many thanks again to all of you for your interest and assistance. Too many of the peer-reviewed journals are no longer professional enough or unprejudiced enough to publish anything that questions the new State religion of supposedly catastrophic manmade global warming. Remote Sensing, for instance has still not had the courtesy to acknowledge the commentary I sent. Since the editors of the learned journals seem to have abdicated their role as impartial philosopher-kings, WattsUpWithThat is now the place where (in between the whining and whiffling and waffling of the trolls) true science is done.
The fundamental constraint on climate sensitivity
A fundamental constraint rules out strongly net-positive temperature feedbacks acting to amplify warming triggered by emissions of greenhouse gases, with the startling result that climate sensitivity cannot much exceed 1.2 K.
Sensitivity to doubled CO2 concentration is the product of three parameters (Eq. 1):
- the radiative forcing ΔF2x = 5.35 ln 2 = 3.708 W m–2 at CO2 doubling (Eq. 2), from the function in Myhre et al. (1998) and IPCC (2001, 2007);
- the Planck zero-feedback climate sensitivity parameter λ0 = 0.3125 K W–1 m2 (Eq. 3), equivalent to the first differential of the fundamental equation of radiative transfer in terms of mean emission temperature TE and the corresponding flux FE at the characteristic-emission altitude (CEA, one optical depth down into the atmosphere, where incoming and outgoing fluxes are identical), augmented by approximately one-sixth to allow for latitudinal variation (IPCC, 2007, p. 631 fn.);
- the overall feedback gain factor G (Eq. 4), equivalent, where feedbacks are assumed linear as here, to (1 – g)–1, where the feedback loop gain g is the product of λ0 and the sum f of all unamplified temperature feedbacks f1, f2, … fn, such that the final or post-feedback climate sensitivity parameter λ is the product of λ0 and G.
The values of the first two of the three parameters whose product is climate sensitivity are known (Eqs. 2-3). The general-circulation models, following pioneering authors such as Hansen (1984), assume that the feedbacks acting upon the climate object are strongly net-positive (G 1: the IPCC’s implicit central estimate is G = 2.81). In practice, however, neither individual temperature feedbacks nor their sum can be directly measured; nor can feedbacks be readily distinguished from forcings (Spencer & Braswell, 2010, 2011; but see Dessler, 2010, 2011).
Temperature feedbacks – in effect, forcings that occur because a temperature change has triggered them – are the greatest of the many uncertainties that complicate the determination of climate sensitivity. The methodology that the models adopt was first considered in detail by Bode (1945) and is encapsulated at its simplest, assuming all feedbacks are linear, in Eq. (4). Models attempt to determine the value of each distinct positive (temperature-amplifying) and negative (temperature-attenuating) feedback in Watts per square meter per Kelvin of original warming. The feedbacks f1, f2, … fn are then summed and mutually amplified (Eq. 4).
Fig. 1 schematizes the feedback loop:
Figure 1. A forcing ΔF is input (top left) by multiplication to the final sensitivity parameter λ = λ0G, where g = λ0f = 0.645 is the IPCC’s implicit central estimate of the loop gain and G = (1 – g)–1 = 2.813 [not shown] is the overall gain factor: i.e., the factor by which the temperature change T0 = ΔF λ0 triggered by the original forcing is multiplied to yield the output final climate sensitivity ΔT = ΔF λ = ΔF λ0 G (top right). To generate λ = λ0 G, the feedbacks f1, f2, … fn, summing to f, are mutually amplified via Eq. (4). Stated values of λ0, f, g, G, and λare those implicit in the IPCC’s central estimate ΔT2x = 3.26 K (2007, p. 798, Box 10.2) in response to ΔF2x = 5.35 ln 2 = 3.708 W m–2. Values for individual feedbacks f1–f4 are taken from Soden & Held (2006). (Author’s diagram from a drawing by Dr. David Evans).
The modelers’ attempts to identify and aggregate individual temperature feedbacks, while understandable, do not overcome the difficulties in distinguishing feedbacks from forcings or even from each other, or in determining the effect of overlaps between them. The methodology’s chief drawback, however, is that in concentrating on individual rather than aggregate feedbacks it overlooks a fundamental physical constraint on the magnitude of the feedback loop gain g in Eq. (4).
Paleoclimate studies indicate that in the past billion years the Earth’s absolute global mean surface temperature has not varied by more than 3% (~8 K) either side of the 750-million-year mean (Fig. 2):
Figure 2. Global mean surface temperature over the past 750 million years, reconstructed by Scotese (1999), showing variations not exceeding 8 K (<3%) either side of the 291 K (18 °C) mean.
Consistent with Scotese’s result, Zachos et al. (2001), reviewing detailed evidence from deep-sea sediment cores, concluded that in the past 65 Ma the greatest departure from the long-run mean was an increase of 8 K at the Poles, and less elsewhere, during the late Paleocene thermal maximum 55 Ma BP.
While even a 3% variation either side of the long-run mean causes ice ages at one era and hothouse conditions at another, in absolute terms the temperature homeostasis of the climate object is formidable. At no point in the geologically recent history of the planet has a runaway warming occurred. The Earth’s temperature stability raises the question what is the maximum feedback loop gain consistent with the long-term maintenance of stability in an object upon which feedbacks operate.
The IPCC’s method of determining temperature feedbacks is explicitly founded on the feedback-amplification equation (Eq. 4, and see Hansen, 1984) discussed by Bode (1945) in connection with the prevention of feedback-induced failure in electronic circuits. A discussion of the methods adopted by process engineers to ensure that feedbacks are prevented in electronic circuits will, therefore, be relevant to a discussion of the role of feedbacks acting upon the climate object.
In the construction of electronic circuits, where one of the best-known instances of runaway feedback is the howling shriek when a microphone is placed too close to the loudspeaker to which it is connected, electronic engineers take considerable care to avoid positive feedback altogether, unless they wish to induce a deliberate instability or oscillation by compelling the loop gain to exceed unity, the singularity in Eq. (4), at which point the magnitude of the loop gain becomes undefined.
In electronic circuits for consumer goods, the values of components typically vary by up to 10% from specification owing to the vagaries of raw materials, manufacture, and assembly. Values may vary further over their lifetime from age and deterioration. Therefore engineers ensure long-term stability by designing in a negative feedback to ensure that vital circuit parameters stay close to the desired values.
Negative feedbacks were first posited by Harold S. Black in 1927 in New York, when he was looking for a way to cancel distortion in telephone relays. Roe (2009) writes:
“He describes a sudden flash of inspiration while on his commute into Manhattan on the Lackawanna Ferry. The original copy of the page of the New York Times on which he scribbled down the details of his brainwave a few days later still has pride of place at the Bell Labs Museum, where it is regarded with great reverence.”
One circuit parameter of great importance is the (closed) feedback loop gain inside any amplifier, which must be held at less than unity under all circumstances to avoid runaway positive feedback (g ≥ 1). The loop gain typically depends on the values of at least half a dozen components, and the actual value of each component may randomly vary. To ensure stability the design value of the feedback loop gain must be held one or two orders of magnitude below unity: g <0.1, or preferably <0.01.
Now consider the common view of the climate system as an engine for converting forcings to temperature changes – an object on which feedbacks act as in Fig. 1. The values of the parameters that determine the (closed) loop gain, as in an electronic circuit, are subject to vagaries. As the Earth evolves, continents drift, sometimes occupying polar or tropical positions, sometimes allowing important ocean currents to pass and sometimes impeding or diverting them; vegetation comes and goes, altering the reflective, radiative, and evaporative characteristics of the land and the properties of the coupled atmosphere-ocean interface; volcanoes occasionally fill the atmosphere with smoke, sulfur, or CO2; asteroids strike; orbital characteristics change slowly but radically in accordance with the Milankovich cycles; and atmospheric concentrations of the greenhouse species, vary greatly.
In the Neoproterozoic, 750 Ma BP, CO2 concentration (today <0.04%) was ~30%: otherwise the ocean’s magnesium ions could not have united with the abundance of calcium ions and with CO2 itself to precipitate the dolomitic rocks laid down in that era. Yet mile-high glaciers came and went twice at sea level at the equator.
As in the electronic circuit, so in the climate object, the values of numerous key components contributing to the loop gain change radically over time. Yet for at least 2 Ga the Earth appears never to have endured the runaway greenhouse warming that would have occurred if the loop gain had reached unity. Therefore, the loop gain in the climate object cannot be close to unity, for otherwise random mutation of the feedback-relevant parameters of vital climate components over time would surely by now have driven it to unity. It is near-certain, therefore, that the value of the climatic feedback loop gain g today must be very much closer to 0 than to 1.
A loop gain of 0.1, then, is in practice the upper bound for very-long-term climate stability. Yet the loop gain values implicit in the IPCC’s global-warming projections of 3.26[2, 4.5] K warming in response to a CO2 doubling are well above this maximum, at 0.64[0.42, 0.74] (Eq. 8). Values such as these are far too close to the steeply-rising segment of the climate-sensitivity curve (Fig. 3) to have allowed the climate to remain temperature-stable for hundreds of millions of years, as Zachos (2001) and Scotese (1999) have reported.
Figure 3. The climate-sensitivity curve at loop gains –1.0 ≤ g < +1.0. The narrow shaded zone at bottom left indicates that climate sensitivity is stable at 0.5-1.3 K per CO2 doubling for loop gains –1.0 ≤ g ≤ +0.1, equivalent to overall feedback gain factors 0.5 ≤ G ≤ 1.1. However, climate sensitivities on the IPCC’s interval [2.0, 4.5] K (shaded zone at right) imply loop gains on the interval (+0.4, +0.8), well above the maximum loop gain that could obtain in a long-term-stable object such as the climate. At a loop gain of unity, the singularity in the feedback-amplification equation (Eq. 4), runaway feedback would occur. If the loop gain in the climate object were >0.1, then at any time conditions sufficient to push the loop gain towards unity might occur, but (see Fig. 2) have not occurred in close to a billion years (author’s figure based on diagrams in Roe, 2009; Paltridge, 2009; and Lindzen, 2011).
Fig. 3 shows the climate-sensitivity curve for loop gains g on the interval [–1, 1). It is precisely because the IPCC’s implicit interval of feedback loop gains so closely approaches unity, which is the singularity in the feedback-amplification equation (Eq. 4), that attempts to determine climate sensitivity on the basis that feedbacks are strongly net-positive can generate very high (but physically unrealistic) climate sensitivities, such as the >10 K that Murphy et al. (2009) say they cannot rule out.
If, however, the loop gain in the climate object is no greater than the theoretical maximum value g = 0.1, then, by Eq. (4), the corresponding overall feedback gain factor G is 1.11, and, by Eq. (1), climate sensitivity in response to a CO2 doubling cannot much exceed 1.2 K. No surprise, then, that the dozen or more empirical methods of deriving climate sensitivity that I included in my commentary cohered at just 1 K. If that is indeed the answer to the climate sensitivity question, it is also a mortal blow to climate extremists worldwide – but good news for everyone else.
References
Bode, H.W., 1945, Network analysis and feedback amplifier design, Van Nostrand, New York, USA, 551 pp.
Chylek, P., and U. Lohman, 2008, Aerosol radiative forcing and climate sensitivity deduced from the last glacial maximum to Holocene transition, Geophys. Res. Lett. 35, doi:10.1029/2007GL032759.
Dessler, A.E., 2010, A determination of the cloud feedback from climate variations over the past decade, Science 220, 1523-1527.
Dessler, A.E., 2011, Cloud Variations and the Earth’s Energy Budget, Geophys. Res. Lett. [in press].
Douglass, D.H., and R.S. Knox, 2005, Climate forcing by the volcanic eruption of Mount Pinatubo, Geophys. Res. Lett. 32, doi:10.1029/2004GL022119.
Douglass, D.H., and J.R. Christy, 2009, Limits on CO2 climate forcing from recent temperature data of Earth, Energy & Environment 20:1-2, 177-189.
Gregory, J.M., R.J. Stouffer, S.C. Raper, P.A. Stott, and N.A. Rayner, 2002, An observationally-based estimate of the climate sensitivity, J. Clim. 15, 3117-3121.
Hansen, J., A., Lacis, D. Rind, G. Russell, P. Stone, I. Fung, R. Ruedy, and J. Lerner, 1984, Climate sensitivity: analysis of feedback mechanisms, Meteorological Monographs 29, 130-163.
Hoffert, M.I., and C. Covey, 1992, Deriving global climate sensitivity from paloeclimate reconstructions, Nature 360, 573-576.
Idso, S.B., 1998, CO2-induced global warming: a skeptic’s view of potential climate change, Clim. Res. 10, 69-82.
IPCC, 2001, Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change [Houghton, J.T., Y. Ding, D.J. Griggs, M. Noguer, P.J. van der Linden, X. Dai, K. Maskell and C.A. Johnson (eds.)]. Cambridge University Press, Cambridge, United Kingdom, and New York, NY, USA.
IPCC, 2007, Climate Change 2007: the Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, 2007 [Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Avery, M. Tignor and H.L. Miller (eds.)], Cambridge University Press, Cambridge, United Kingdom, and New York, NY, USA.
Kimoto, K., 2009, On the confusion of Planck feedback parameters, Energy & Environment 20:7, 1057-1066.
Lindzen, R.S., 2011, Lecture to the American Chemical Society, Aug. 28.
Loehle, C., and Scafetta, N., 2011, Climate change attribution using empirical decomposition of climatic data, Open Atmos. Sci. J. 5, 74-86.
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.
Myhre, G., E. J. Highwood, K. P. Shine, and F. Stordal, 1998, New estimates of radiative forcing due to well mixed greenhouse gases, Geophys. Res. Lett. 25:14, 2715–2718, doi:10.1029/98GL01908.
Paltridge, G., 2009, The Climate Caper, Connor Court, Sydney, Australia, 110 pp.
Roe, G., 2009, Feedbacks, Timescales, and Seeing Red, Ann. Rev. Earth. Planet. Sci. 37, 93-115.
Schwartz, S.E., 2007, Heat capacity, time constant, and sensitivity of Earth’s climate system, J. Geophys. Res. 112, D24So5, doi:10.1029/2007JD008746.
Schwartz, S.E., 2008, Reply to comments by G. Foster et al., R. Knutti et al., and N. Scafetta on “Heat Capacity, time constant, and sensitivity of Earth’s climate system”, J. Geophys. Res. 113, D15015, doi: 10.1029/2008JD009872.
Scotese, C.R., A.J. Boucot, and W.S. McKerrow, 1999, Gondwanan paleogeography and paleoclimatology, J. African Earth Sci. 28:1, 99-114.
Shaviv, N., 2005, On climate response to changes in the cosmic-ray flux and radiative budget, J. Geophys. Res., doi:10.1029.
Soden, B.J., and I.M. Held, 2006, An assessment of climate feedbacks in coupled ocean-atmosphere models. J. Clim. 19, 3354–3360.
Spencer, R.W., and W.D. Braswell, 2010, On the diagnosis of radiative feedback in the presence of unknown radiative forcing, J. Geophys. Res, 115, D16109.
Spencer, R.W., and W.D. Braswell, 2011, On the misdiagnosis of surface temperature feedbacks from variations in Earth’s radiant-energy balance, Remote Sensing 3, 1603-1613, doi:10.3390/rs3081603.
Zachos, J., M. Pagani, L. Sloan, E. Thomas, and K. Billups, 2001, Trends, Rhythms and Aberrations in Global Climate 65 Ma to Present, Science 292, 686-693.
I’d like as much input from process control folks as is possible! Seems like they could hold the key regarding CAGW.
Bart has some very interesting input on the threads over at Climate Audit, referencing negative feedback. Most of it is over my non-science/math head, but a lot of the right kind of heads seem properly intrigued.
Sir Monckton,
Okay, first let me appologize for misspelling your name in the previous thread. I’m sorry for that, but I don’t think it’s any worse than the electric bill I have received for the past year addressed to Garg Swift, despite numerous attempts to get them to fix it. lol.
Second, since the bulk of this post seems to address very issue I was having such a lively discussion about on the other thread, thank you for taking the time to illuminate your application of engineering principles to climate feedback.
Please understand that I’m not trying to be a pain in your rear. I agree with the conclusion, but I do not agree that the method above is a good way to reach that conclusion. All your other points and methods are much stronger.
My reasoning for feeling uncomfortable with the use of the engineering feedback theory is that it is grossly oversimplified for use in climate analysis. For example, as Willis has been arguing recently, clouds may have a powerful damping effect on feedbacks. That does not mean that the feedbacks are not strong though. It is possible to have multiple and offsetting feedbacks, and I do not think the way your equation above handles the problem is comprehensive enough in this context.
Please be patient with me, I’m not trying to say you are wrong. It’s more of a technical burr under my saddle, rather than claiming that you made an error. It looks like your method supports your conclusions, but in this case it might be that correlation is not the same as causality.
I offer your figure 2 as evidence. You pointed out that the temperature stays within a relatively narrow range. I agree that there is some mechanism which appears to damp the system and allow it to stay within relative equilibrium (as opposed to a runaway feedback). On the other hand, notice how the temperature swings rapidly (in geological time) from max to min and spends very little time in the middle range. Does that look like a system with or without feedbacks?
The data paleo data seems to indicate an on/off switch effect very much like a system with strong positive/negative feedbacks. You can see the same kind of thing when you look at aerodynamic feedback effects, which might be a better fit in this context. You can get feedback on the pressure over a wing, where turbulence can amplify the drag, but there’s a finite limit on how much amplification you can get.
Here’s one paper that talks about an effect similar to what I’m talking about.
Modulation of wind ripples…
As you can see, there it is possible to have a strong positive feedback and also have a boundary on the extent of the magnitude of the feedback.
Once again, thank you for the elaborate explanation of your feedback gain limit theory. I have very little issue with any of the other brilliant points you have made. I just don’t see that this one method is valid in this context.
free the mails.
lucia says:
September 27, 2011 at 2:35 pm
Christopher,
I would be happy to write a post engaging what you claim and publish the contents of my emails to you and yours to me in their entirety.
======================================================
You could have made a modicum of inquiry, first.
I’d be happy not to care about your e-mail wars.
Reverse engineering is tricky enough without assumptions that can easily be verified or refuted. Unless you can show where you asked and Monckton refused to answer, your protests hold no value.
James
Sorry again,
I’ve been reading too much George R. R. Martin. I meant to say Lord Monckton in my previous post. There’s too many Sir’s in this book. lol
Sincerely,
Gary
Lord Monckton, please don’t lump Lucia Liljegren with troll detractors. While not labeling her so directly, you appear to do so by inference in your above post.
It has been my experience that Ms. Liljegren seeks truth through rigorous means. She is equally brutal to all who seek to use math and science to bolster their political opinions. I would venture therefore that if she was critical of your math, there was good reason for it.
I had a structural geology prof as a senior who was rumored to have never issued a first class on his final exam (He was an Imperial trained doctorate and one of Ramsay’s students). I got a high second class on his exam and was the top in my class. I felt cheated a bit at the time, because I had studied very, very hard.
Years later when I returned to academia for graduate studies I took graduate level structural geology courses (from another student of Ramsay coincidentally) and aced all my exams and projects – not because I studied particularly hard, but because I actually remembered all the stuff from years before, taught by that stern, uncompromising nit-picker, who demanded complete rigor.
I think of Lucia in the same way as I think of that prof from Imperial so many years ago – If you come up against her you better be prepared.
BTW, like Ramsay, he was a Scot.
At some point the coffin is so full of nails that it becomes entirely metallic.
steven mosher says:
September 27, 2011 at 4:25 pm
Steven , that’s a bit obscure. Care to fill in the blanks? Is it regarding Lucia’s misunderstanding, which she (properly and correctly) acknowledged above?
The world wonders …
Thanks,
w.
I think they have been; check up-thread …
.
As one who built his first hi-fi amplifier kit more than half a century ago, and has a practical if amateur understanding of analog circuits, this made no sense to me at first:
It took a bit to realize that what was meant here is, in electronic terms, the effect of closing the feedback loop on the amplifier, that is, the ratio of the closed loop gain to the (theoretical) open loop gain of the amp. A typical power amplifier might have a (theoretical) open loop voltage gain of 10,000 — theoretical because it would fry both itself and anything it was connected to if it were run that way — with negative feedback applied to reduce the voltage gain to, say, 20 for a typical 50-watt audio amplifier. Thus the “closed loop gain” in normal electronic terms is 20, but the “closed loop feedback gain” as used here is 20/10,000 or .002 . Unfortunate terminology.
Forgive my interjecting here with such a maudlin comment, but it is this sort of post that keeps me coming back here — sometimes several times a day. Great stuff! Particularly the continuing excellent comments. Absolutely fascinating to see this aspect of science in action.
Many thanks to Sir Anthony and his merry band.
0.1? That seems to be the crucial figure. Where did it come from?
Looking through, I find, assertion:
“To ensure stability the design value of the feedback loop gain must be held one or two orders of magnitude below unity: g <0.1, or preferably <0.01.”
then a claim of practical backing:
“A loop gain of 0.1, then, is in practice the upper bound for very-long-term climate stability.”
and then it’s promoted to:
“the theoretical maximum value g = 0.1, “
But where did it come from? Is it to be found in the long list of references?
Thank you bold, Monckton. Your work is greatly appreciated.
http://epetitions.direct.gov.uk/petitions/2035
Christopher, that is a wonderful post. I’m sorry that personalities get in the way in the argument against this blight on humanity we call the CAGW hypothesis. Keep up the good work. While this post goes through the details of reaching the most sensible conclusion, to wit, the feed-backs can’t possibly be as dramatic as purported, else we’d have experienced runaway something or another in the past. I’m not sure your efforts will be properly appreciated. This avenue has been explored, and explored, and shown, and shown, and still the illogical persist.
Your methodical approach renders me useless in your search for more thoughts of sensitivities based on observations. But, I think an approach that may further your argument would be to define the percentage of energies of IR per bandwidth. The GHGs only absorb so much of the spectrum. A small portion of the IR spectrum, and most overlap. Given spherical shape of the earth, < 50% is re-emitted back to earth from any given GHG molecule and lessens as the elevation of the molecule increases. The 4 wavelength can only emit a small percentage of the total IR energy. And given the increase pant wetting of methane, the same could be said of the 3 wavelength. I'm engaged in other avenues at the time, so I haven't properly investigated the obvious questions. I don't know if the energy is evenly reflected by the earth per wavelength or what the distribution may be if it isn't. But, I think that's a way of presentation that may provide more force in the argument.
My best,
James Sexton
Nice apology Lucia. Basically, you made the assumption and went so far as to admit to making the assumption but then attempted to blame someone else for making an ass out of both you and your communicant.
Science should be nothing else unless first and foremost humbling.
The issue with the Schwartz approach is that there appear to be two relaxation times, as pointed out originally by Nicola Scafetta. Then how one combines them becomes an additional source of uncertainty.
Still Lord Monckton’s conclusion is right. In summary, none of the empirical approaches is althogether convincing, but taken together the body of evidence points to a climate senitivity around 1 degree for 2 x CO2. The uncertainty is still large, but there is a very high likelihood that sensitivity is far less than the IPCC’s model based determinations.
James Sexton says:
September 27, 2011 at 4:45 pm
lucia says:
September 27, 2011 at 2:35 pm
You could have made a modicum of inquiry, first…………
======================================================
Please note, my comment was made before Lucia’s comment towards the correspondence that led to her errors was posted at WUWT.
This is to her credit.
James
Does it look this will be the first year warmer than 1998? I always wonder when that will happen again so the climate religionists can say “see I told you so!”
First, as always, I am captivated by the inimitable Monckton style, always great stuff.
I enjoyed the argument that the net feedback, if positive, cannot be more than about 0.1 from arguments regarding long-term temperature stability. I have noted this stability often, as it implies not positive feedback, not negative feedback, but the combination of the two that makes up a thermoregulatory system.
I have shown that in the tropics, this thermoregulation is achieved by a threshold-based system of changes of circulatory regimes. Climate sensitivity (lambda) varies greatly between these regimes, with the sensitivity being lower and lower with the passing of each successive threshold. I have shown that locally the response is strong enough to actually reduce the temperature despite strengthening sun. This means that at certain times and in certain regimes, the climate sensitivity lambda can actually be negative.
Unfortunately, this has huge implications for your argument. Your argument is based on the idea that the climate sensitivity lambda is a constant. But it is far from a constant—lambda is a wildly non-linear, threshold based function of temperature.
This means that your lovely delta-flog equation above, viz:
ΔT = ΔF λ = ΔF λ0 G
needs to have the substitution
λ = NonlinearF(T)
to give us
ΔT = ΔF * NonlinearF(T)
And that, my dear Lord, makes the entire equation unsolvable …
Keep up the great work, between your peregrinations and your gyrations you are always a source of great entertainment.
w.
PS – the existence of threshold based, self-organized criticality means the climate system can’t be analyzed using the whole classical feedback system you show in Figure 1. Threshold-based systems, particularly those involving emergent phenomena, are not describable as simple feedbacks of the type you propose.
Note to Willis and others, I just updated for the SECOND time, Monckton’s 4 equations, because not only did they get mangled in Open Office (converting from MS Word 2007) the free MSWord reader also failed to display them properly, and I used a screencap from that for the first edit.
I believe the four equations are correctly displayed and formatted now, if not please make a note in comments.
Just goes to show that if you get a science paper written in MS Word, and the math looks wonky, it may be format/conversion issues and program versions.
Legatus says @ur momisugly September 27, 2011 at 4:16 pm
“…A recent poster on this site, who works with observatories telescopes, pointed out that they make just such direct measurements of the infrared radiation….”
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It would be nice if you could give us a pointer to that comment or at least a name.
I find it curious that Christopher Monckton would appear to be troubled with the seemingly hostile tone of people who critique his work: He responds to one of the generally reasonable Lucia’s emails as
Without having seen the entire exchange (publicly anyway), it is clear, he is quick with the jibe and insult, which maybe a useful skill in disconcerting prospective car buyers if you are a used car salesman, but isn’t so useful if the purpose were to truthfully and accurately convey information that they had inquired about.
Moreover, he has his own propensity for letting fly the primary school ad hominems himself:
Given Monckton’s somewhat unusual visual appearance (which I agree should not be made fun of, regardless of whether it is related to an illness or otherwise), I do think it’s a bit odd he’s willing to be so cheeky in describing a critic as “an overcooked prawn”.
I would respectfully suggest that the above paragraphs, had they been written by Monckton’s critic as a comment on this blog aimed at the good Mr. Monckton, would not have passed moderation. I also respectfully request that Monckton be held to the same standards of fair play in his posts and comments on other posters on this blog that his respondents would and will be.
Great post and comments – thank you.
Mr Monckton
You might come up against heady resistance against your concepts merely because of a reflexive dislike of good English. I don’t think you should mind that.
Best
S
To Willis E.
Your argument strongly amplifies mine, but in a different way. I think we are on different pages of the same book here. I strongly agree with your points. Good post.
I just don’t understand all of this. The maths, yes, its still fairly easy to follow. STILL!!!! HOW MANY TIMES DOES IT HAVE TO BE SHOWN?
It is established regardless of how many misanthropist pinheads line up to dispute it. In the mean time, while we’re arguing over statistical acrobatics, people are getting burned in their homes and out of them. If that’s not enough, which it should be for any person, how long do we have to suffer through the impoverishment of our own communities to realize the real harm this hypothesis is doing? WTF?
So many people, for all their talents and abilities, can’t find a way to mathematically define the harm? It is because they’ve no desire to do so. This would require some introspection about their own beliefs and they don’t have the courage to do so.
James Sexton