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.
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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.
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Monckton of Brenchley says:
As a general point, however, we should note that the formula for computing a temperature increment from an certain change in emissions is
Delta_T = A * ln(C_final / C_initial) where C_initial and C_final are the initial and final concentrations, respectively and A is a constant that is adjusted to give the desired sensitivity value for a doubling of concentration. The fact that A = 1 happens to work for your desired transient no-feedbacks sensitivity is just a numerical coincidence of the fact that ln(2) just happens to be close to your desired value of 0.7 (in Celsius).
I wanna know where the rabbit is. It’s cold, and I’m getting hungry.
============
Monckton of Brenchley says:
September 29, 2011 at 12:28 pm
To David Hoffer: No, I don’t have the math wrong. Read carefully! I was talking of transient no-feedbacks sensitivity, not equilibrium no-feedbacks sensitivity, so 0.7 K this century (compared with 1.2 K in total by a couple of millennia hence) is correct. >>>
My mistake. I always use equilibrium because it reduces the debate to one number. By using transient, I find that it introduces additional concepts that distract from my main argument, which is that we have a forcing subject to the law of diminishing returns and no plausible feedback mechanism that could possibly substantiate a linear, let alone an exponential, increase in termperature.
Keeping it so simple puts the warmists in a tough bind. Claiming feedbacks that increase exponentially is just plain old silly. Claiming feedbacks that are high enough to make anything over 500 PPM significant would have resulted in something disastrous at 350 PPM. If they claim something lower to account for the lack of warming we’ve seen so far…. well then the whole thing is insignificant by their own account then.
That’s why (I think) presenting it this way makes tghem run and hide. Joel Shore took a shot at my math, but even using his numbers and calculations, he failed to propose any feedback mechanism that would result in linear temperature increases. He’s the one with the PhD in physics, not me. But he didn’t step up, and neither has anyone else I’ve posed the problem to.
Rgds,
dmh
Monckton of Brenchley says:
September 29, 2011 at 12:28 pm
To David Hoffer: No, I don’t have the math wrong. Read carefully! I was talking of transient no-feedbacks sensitivity, not equilibrium no-feedbacks sensitivity, so 0.7 K this century (compared with 1.2 K in total by a couple of millennia hence) is correct.
Could you provide a citation where the IPCC uses this value?
To Joel Shore, – You really must not impute motives to me that do not exist. You say I took the logarithm of the proportionate increase in CO2 concentration with an implicit coefficient of 1 because that came close to what you call my “desired” value of 0.7 K for transient, no-feedbacks climate sensitivity. That kind of insinuation really won’t do, and it’s not the first time you’ve done it. Please desist.
I do not have any “desired” values. I merely take the values the IPCC starts with and draw conclusions from them. The IPCC’s function for the radiative forcing from an increase in CO2 concentration is 5.35 times the logarithm of the proportionate increase: thus, 5.35 ln[C(b) / C(a)], where C(a) is the unperturbed concentration. In response to the CO2 doubling expected by the end of this century, the forcing is thus simply 5.35 ln 2, or 3.708 W/m2.
To get a transient, with-feedbacks climate sensitivity from this, we multiply by 0.5 K/W/m2, the 1900-2100 transient sensitivity implicit in and derivable from any or all six of the IPCC’s emissions scenarios. And that gives 1.854 K. To remove the feedbacks, we divide by the IPCC’s implicit central estimate of the overall feedback gain factor G = 2.8, giving 0.66 K.
Since 0.66 is very close to the natural logarithm of 2 (which is 0.69) , one can take a short cut by obtaining the transient no-feedbacks climate sensitivity for the doubling of CO2 concentration this century simply as the logarithm of 2, because the coefficient 5.35 x 0.5 / 2.8 is close to unity; and similarly, of course, for the transient, no-feedbacks sensitivity in response to any increase in CO2 concentration other than a doubling one takes the logarithm of the proportionate increase C(b)/C(a). It’s as simple as that. It has nothing to do with what I “desire”, and everything to do with the IPCC’s own methods, which I have merely simplified without significant loss of accuracy.
It is increasingly evident that, even if one uses the IPCC’s methods, the warming we’re going to cause is a whole lot less than it imagines. Even if the IPCC were right about expecting an equilibrium warming of 3.26 K in response to a doubling of CO2 concentration, rather than the 1 K which is really the theoretical maximum, it would still be about an order of magnitude cheaper to do nothing about it (except to adapt in a focused way to any adverse consequences that might arise) than to spend trillions shutting down the economies of the West in an attempt to control the climate that will have no more chance of success than that of King Canute, who knew perfectly well – as should all of us by now – that all such attempts are expensively futile..
To Phil, – You ask for a citation in the IPCC’s documents for the value ~0.7 K for 21st-century transient climate sensitivity to a CO2 doubling in the absence of temperature feedbacks. My previous message explains the math. But one can also demonstrate it very simply, thus. The equilibrium no-feedbacks climate sensitivity is simply the radiative forcing 5.35 ln 2 = 3.708 W/m2 multiplied by the Planck parameter 0.3125 K/W/m2, giving 1.159 K. The IPCC’s values for the transient and equilibrium climate-sensitivity parameters respectively are 0.5 and 0.879 K/W/m2, The first is derivable from all six of the IPCC’s emissions scenarios (p. 803, Fig. 10.26); and the second is simply the IPCC’s explicit multi-model mean central estimate for equilibrium warming at CO2 doubling of 3.26 K, divided by the radiative forcing of 3.708 Watts per square meter (Myhre et al. 1998; IPCC, 2001, 2007). So, to convert from equilibrium to transient no-feedbacks sensitivity to a CO2 doubling in the 21st century one merely multiplies the equilibrium value 1.159 K by 0.5/0.879, giving 0.66 K. The small discrepancy between this value and the 0.69 K arrived at by my rule of thumb of simply taking the logarithm of 2 and calling it Kelvin is, I hope, not too unacceptable. Any questions, let me know.
davidmhoffer said:
Perhaps this post of mine http://wattsupwiththat.com/2011/09/27/monckton-on-pulling-planck-out-of-a-hat/#comment-755311 where I address that point showed up from moderation only after you wrote this? At any rate, your math was indeed wrong…and with corrected math, it is clear that one doesn’t need any dramatic feedback mechanisms to get a linear temperature increase, just a fairly steady but not particularly large increase in our CO2 emissions, as has so far been the case…and which those who propose doing nothing to curb our emissions even in the face of growing pressures to exploit large coal and tar sands reserves are no doubt fine with.
Monckton of Brenchley says:
And, given the confusion of some commenters in this thread regarding how to compute logarithmic growth correctly, I thought it was important to make very explicit your simplification in taking advantage of this “close to unity” coincidence so that people didn’t start to believe one could simply use the formula you wrote down (i.e., assuming a constant outside the logarithm of exactly 1) with impunity in situations where this coincidence does not occur. That was the main point that I was trying to make.
Monckton of Brenchley:
I don’t believe in your economic alarmist fantasies about “shutting down the economies of the West” because they have no support from economic studies…and because it makes no sense to believe that market economies can be so successful in coping with real resource scarcity but if we impose some artificial resource scarcity on fossil fuels (by putting a cost on dumping greenhouse gases into the atmosphere) then the economies will just shrivel up and die. In fact, the artificial resource scarcity that we would be imposing is actually more flexible than real resource scarcity because it allows fossil fuels to still be used abundantly provided that the necessary technology is developed and used to sequester the emissions of CO2.
To Joel Shore: No, your earlier post plainly accused me of getting stuff wrong so that I could reach my “desired value”. Other posters have warned you that this nasty habit of making unwarrantable accusations – particularly when, as in this case, I was able to prove your nasty little accusation baseless – is something you need to get rid of.
Monckton of Brenchley: For the record, here is my entire post ( http://wattsupwiththat.com/2011/09/27/monckton-on-pulling-planck-out-of-a-hat/#comment-755316 ) you are talking about (minus the part that quotes you):
Somehow I can’t see the part where I said your were getting stuff wrong in this particular case. And I used the term “desired” in the context of how A is determined given any sensitivity value that one might believe to be correct.
I have rightly criticized you for being wrong before when you are wrong. In this particular case, I was just noting that the approximate correctness of your formula was due to a numerical coincidence and hence one should not assume that one can just assume A=1 whenever one is computing a temperature rise due to some increment in CO2 concentration from some equilibrium or transient climate sensitivity with or without feedbacks.
(I am frankly agnostic as to your estimate of a 0.7 C transient climate sensitivity for the no-feedbacks case. I think your way of going between equilibrium and transient sensitivity is a bit simplistic but probably not too bad as a rough approximation.)
Thanks for that Anthony, I have republished this on the UKIP Scotland Blog
Monckton of Brenchley,
The discussion you have/had with Lucia started with your assertion (in your paragraph 3) that the Planck parameter lambda0 has a value of 0.15 W-1 K m^2.
In that post, you gave no clear definition, only a reference to Kimoto, and Lucia has made the argument that filling in Kimoto’s formula’s with current radiation numbers (from K&T) and then blindly plugging it into the equilibrium sensitivity formula is not going to get you the right result.
In this post, you adhere to a more conventional definition of lamba0, which refers to the Planck response of planet Earth without feedbacks. This definition is used by most climate scientists (including Lindzen) and makes much more physical sense than Kimoto’s, simply because to get the gray-body response of planet Earth, you need to be at least above the troposphere. Besides that, for equilibrium state, lambda0 is easy to calculate, since the planet as a whole needs to be in radiative balance with space, independent of the surface temperature. You correctly point out that the value, calculated as such, is 0.3125 W-1 K m^2.
Now may I point that using lambda0==0.3125 and the “IPCC central estimate” of the feedback parameters which you quote at 2.1 W/m^2/K, the resulting equilibrium temperature increase at the surface for 2xCO2 will be : 3.7*(0.3125)/(1-2.1*0.3125) = 3.36 C, and not 0.8 K that you obtained.
So it seems that your problem was rooted in the fact that you used the wrong Planck parameter formula and incorrectly filled it with invariant radiation numbers. Which was exactly what Lucia was explaining. Switching to the definition used by climate scientists (such as Lindzen) solves your problem.
Thank you for your contribution to the debate