Where the complex climate models go wrong

By Christopher Monckton of Brenchly

Joe Born (March 12) raises some questions about our paper Why models run hot: results from an irreducibly simple climate model, published in January in the Science Bulletin of the Chinese Academy of Sciences.

To get a copy of our paper, go to scibull.com and click on “Most Read Articles”. By an order of magnitude, our paper is the all-time no. 1 in the journal’s 60-year archive for downloads either of the abstract or of the full text.

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Mr Born says that he is not sure he should take on trust our assertion that the Planck or instantaneous climate-sensitivity parameter is about 0.31 Kelvin per Watt per square meter; that we “obscure” the influences on the fraction of equilibrium temperature response attained in a given year; that we have used that fraction “improperly”; that we have incorrectly assumed a steep initial increase in temperature response; that we have relied on a model generated by a step-function representing the effects of a sudden pulse in CO2 concentration rather than one in which concentration increases by little and little; that it is “not clear” how we have determined that the 0.6 K committed but unrealized global warming predicted by the IPCC was not likely to occur; that our model should have taken more explicit account of the fact that different feedbacks operate over different timescales; that we were wrong to state that in an electronic circuit the output voltage transits from the positive to the negative rail at loop gains >1; and that our discussion of electronic circuitry was “unnecessary”.

Phew! I shall answer each of these points briefly.

First, however, Mr Born’s essay is predicated on a fundamental assumption that is flat wrong. He says that increasing CO2 concentration raises the optical density of the atmosphere, in turn raising the effective altitude [so far so good],

“and, lapse rate being what it is, reduces the effective temperature from which the Earth radiates into space, so less heat escapes, and the Earth warms”.

No. The characteristic-emission layer – the “altitude” from which the Earth appears to radiate spaceward, and at which, uniquely in the climate system, the fundamental equation of radiative transfer applies – is the locus of all points at or above the Earth’s surface at which incoming and outgoing radiation are equal. In general, the mean altitude of the locus of these balance-points rises as a greenhouse gas is added to the atmosphere. Thus far, Mr Born is correct.

His fundamental error lies in his assertion that the increase in the Earth’s characteristic-emission altitude reduces the effective temperature at that altitude, “so less heat escapes, and the Earth warms”.

The truth, which follows from the definition of the characteristic-emission layer and from the fundamental equation of radiative transfer that applies uniquely at that layer, is that the Earth’s effective radiating temperature is unaffected by a mere change in the mean altitude of that layer. It is not, as Mr Born says it is, “reduced” as the altitude increases.

The radiative-transfer identity, first derived empirically by the Slovene mathematician Stefan and demonstrated theoretically five years later by his Austrian pupil Ludwig Boltzmann, equates the flux density at the characteristic-emission layer with the product of three parameters: the emissivity of that layer; the Stefan-Boltzmann constant; and the fourth power of temperature.

Now, the flux density is constant, provided that total solar irradiance is constant (which, averaged over the 11-year cycle, it broadly is), and provided that the Earth’s albedo does not change much (it doesn’t). Emissivity is as near constant at unity as makes no difference; and the Stefan-Boltzmann constant is – er – constant. It necessarily follows that the temperature of the emission layer is constant unless any of the other three terms in the equation changes – and none of them changes much, if at all, merely in response to an increase in the mean altitude of the characteristic-emission layer.

Precisely because the effective radiating temperature at the characteristic-emission layer is near-constant under an increase in the mean altitude of the characteristic-emission layer, and precisely because the lapse rate of atmospheric temperature with altitude is very nearly constant under that increase, it is the surface temperature, not the effective radiating temperature at the characteristic-emission altitude, that rises in response to that increase in altitude.

Many of the subsequent errors in Mr Born’s understanding appear to flow from this one.

So to the individual points he makes.

First, the value of the Planck parameter. We stated in our paper that we had accepted the IPCC’s stated value. We might also have explained that we did not take it on trust. Indeed, the first of many fundamental errors in the climate modelers’ methodology that I identified, back in 2006, was the mismatch between the official value 0.31 K W–1 m2 and the Earth’s surface value 0.18 K W–1 m2 that was implicit in Kevin Trenberth’s 1997 paper on the Earth’s radiation budget.

As our paper explains, to a first approximation the Planck parameter is simply the first differential of the fundamental equation of radiative transfer – i.e., 0.27 K W–1 m2. However, allowance for the Hölder inequality obliges us to integrate the differentials latitude by latitude, based on variations in both radiation and temperature. That brings the value up by about one-sixth, to 0.31 K W–1 m2.

To verify that the modelers had done this calculation correctly, I asked John Christy for 30 years’-worth of satellite mid-troposphere temperature anomaly data in latitudinal steps of 2.5 degrees and spent a weekend doing the zenith angles, frustal geometry and integration myself. My value for the Planck parameter agreed with that of the IPCC to three decimal places. And, precisely because all of the parameters in the fundamental equation of radiative transfer are as near constant as makes no difference, the Planck parameter is not going to change all that much in our lifetime.

Next, Mr Born says we “obscure” the influences on the fraction equilibrium temperature response attained a given number of years after a radiative perturbation. Far from it. We begin by making an elementary point somehow not stated by Mr Born: that if there be any feedbacks (whether net-positive or net-negative) operating on the climate object, then the instantaneous and equilibrium temperature responses to a given radiative perturbation will not be identical, and there will be some pathway, over time to equilibrium, by which the temperature response will increase (with net-positive feedbacks) or decrease (with net-negative feedbacks) compared with the instantaneous response.

We continue by explaining the IPCC’s values – in its 2007 and 2013 reports – for the principal temperature feedbacks. We further explain that the response to feedbacks over time is not linear, but (assuming the IPCC’s strongly net-positive feedbacks) follows a curve in which, typically, half the approach to equilibrium occurs in the first 100 years, and the remainder occurs over the next 3000 years (see e.g. Solomon et al., 2009). We also provide a simple table of values over time that are unlikely to introduce too much error. The table was derived from a graph in Gerard Roe’s magisterial paper of 2009 on feedbacks and the climate. Far from obscuring anything, we had made everything explicit.

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Mr Born goes on to say we had used the fraction of equilibrium temperature response “improperly”. However, it is trivial that in all runs of our model that concerned equilibrium sensitivity (and most of them did) that fraction is simply unity. In those runs that concerned instantaneous sensitivity (some did), that fraction is simply the ratio of the Planck to the equilibrium sensitivity parameter. In those runs that concerned transient sensitivity, we were dealing with sub-centennial timescales, so that up to half of the equilibrium response should have been evident. All of this is uncontroversial, mainstream climate science. Admittedly, it is very badly explained in the IPCC’s documents: but not the least value of our paper has been in explaining simple concepts such as this one.

Next Mr Born says we have incorrectly assumed a steep initial increase in temperature response (one can see this steep initial response quite clearly in Roe’s graph). Mr Born may or may not be right that there should not be a steep initial increase; but, like it or not, that is the assumption the IPCC and others make. We provided worked examples in the paper to show this. In short, Mr Born’s quarrel on this point is not with us but with the IPCC.

Furthermore, once we had calibrated the model using the IPCC’s assumptions and had obtained much the same sensitivities as it had published, we then adopted assumptions that seemed to us to be less inappropriate, and ran the model to reach our own estimates of climate sensitivity: around 1 K per Co2 doubling.

One of those assumptions, attested to by a growing body of papers in the literature, some dozen of which we cited, is that temperature feedbacks are probably net-negative. Here, for instance, is a graph from Lindzen & Choi (2009), showing the predictions of 11 models compared with measurements from the ERBE and CERES satellites:

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Given the probability that temperature feedbacks are net-negative, we ourselves had not assumed a strong initial temperature increase: for that assumption, made by the IPCC, depends crucially on strongly net-positive feedbacks, some of which – such as water vapor – are supposed to be quick-acting. However, the ISCCP data appear to suggest no increase in column water vapor in recent decades, and even something of a decrease at the crucial mid-troposphere altitude:

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Mr Born complains that in determining the fraction of equilibrium temperature response at any given year we relied on a model generated by a step-function representing the effects of a sudden pulse in CO2 concentration rather than one in which concentration increases by little and little. So we did: however, as the paper explains, we tested the model to ensure that the results it generated over, say, 100 years were much the same as those of the IPCC. It generated broadly similar results.

As it happens, I had first come across the problem of stimuli occurring not instantaneously but over a term of years when studying the epidemiology of HIV transmission. My then model, adopted by some hospitals in the national health service, overcame the problem by the use of matrix addition, but sensitivity tests showed that assuming a single stimulus all at once produced very little difference compared with the time-smeared stimulus, merely displacing the response by a few years. Similar considerations apply to the climate.

Besides, our model is just that – a model. If Mr Born does not like our values for the fraction of equilibrium temperature response attained after a given period, he is of course free to choose his own values by whatever more complex method he may prefer. But, unless he chooses values that depart a long way from mainstream climate science, the final sensitivities he determines with our simple model will not be vastly different from our own estimates.

Next, Mr Born says it is “not clear” how we have determined that the 0.6 K committed but unrealized global warming predicted by the IPCC was not likely to occur. On the contrary, it is explicitly stated. We assumed ad argumentum that all warming since 1850 was anthropogenic, ran our model and found that the variance between its predicted warming to 2014 and the observed outturn was nil, implying – as explicitly stated in the paper, that there is no committed but unrealized global warming in the pipeline. See table 4 of our paper.

Interestingly, the official answer of the “hokey team” to our point is that we should have assumed that more than all the warming since 1850 was manmade. On that point, we disagree. For They cannot at once argue that the hefty increase in solar activity between the Maunder Minimum 0f 1645-1715 and the near-Grand Maximum of 1925-1995 had no influence on global temperature, but that the decline in solar activity since its peak in 1960 is so great that it would have caused significant cooling in the absence of anthropogenic forcings over the period.

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Mr Born also complains that our model should have taken more explicit account of the fact that different feedbacks operate over different timescales. Well, our transience fraction may be tuned at will to take account of that fact. And we even presented a table of values of that fraction over time to take account of a mainstream, conventional distribution of temperature feedbacks and their influences over time. If Mr Born disagrees with Dr Roe’s curve, he is of course entirely free to substitute his own. We presented not tablets of stone but a model.

Next, Mr Born devotes much ink but not much light to his assertion that we were wrong to state that in an electronic circuit the output voltage transits from the positive to the negative rail at loop gains >1. We consulted the reviewed literature; a process engineer with three doctorates, who also consulted the literature; a doctor of climatology specializing in feedback analysis as applied to the Earth’s climate; and a Professor ditto (the last two being among the top six worldwide in this highly specialist field). I also discussed the question of the response-versus-loop-gain curve with a group of IPCC lead authors at a talk I gave at the University of Tasmania three years ago.

Not one of these eminent advisers agrees with Mr Born. That, on its own, does not mean he is wrong: but it does mean that the point we raise is at least respectable.

The Bode feedback-amplification equation is entirely clear: at loop gains >1 the equation mandates that the temperature response becomes negative. In an electronic circuit one can of course – as Mr Born does at rather tedious length – find ways of making the circuit oscillate even in the absence of loop gains >1, and one can find ways of making it not oscillate even at loop gains >1.

However, the equation actually used in the climate models (including ours) is, like it or not, the Bode system-gain equation. Mr Born carefully plots only that part of the graph of the equation below a loop gain of 1:

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However, our paper plots the graph both sides of a loop gain of unity. A loop gain of 1 is equivalent to the feedback sum of 3.2 Watts per square meter per Kelvin in Mr Born’s graph, for in the climate the loop gain is the product of the feedback sum and the Planck parameter, and the Planck parameter is the reciprocal of 3.2.

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On reading Mr Born’s piece one would think the point we had raised was both trivial and inappropriate. However, the specialists whom we consulted, and the equation itself, suggest that our point is both non-trivial and substantial.

Indeed, the Professor, until I debated the issue with him before a learned society somewhere in Europe a couple of years back, was a true-believer in the profitably catastrophist viewpoint. When I displayed the full plot of the Bode equation he went white.

He wrote to me afterwards, sending me a paper in which he had himself urged caution in the use of Bode in climate modeling. A few weeks ago he got in touch again to say he has thought about the matter ever since and has now concluded – damn you, Monckton – that I am right, and that in consequence climate sensitivity cannot be more than 1 K and may be less.

He has submitted a paper for peer review. If that paper is published, and if it proves correct, the science will indeed be settled – but in a direction entirely uncongenial to the profiteers of doom.

One of the IPCC lead authors in Tasmania interrupted my talk when I showed the full Bode graph and said: “Have you published this?” No, I replied. “But you must,” he said. “This changes everything!” Yes, I said, I rather think it does.

If the Bode equation is inappropriate for loop gains >1, then it may also be inappropriate for loop gains <1. It may – at least in its unmodified form – be the wrong equation altogether. And without it one cannot get away with claiming the absurdly high and unphysical sensitivities the IPCC profits by asking us to believe in.

At minimum, tough asymptotic bounds to constrain the behavior of the equation at the singularity should be imposed. That, at any rate, is what the very small variability of global temperature over the past 810,000 years would suggest: and, on that point, Mr Born surely agrees with us.

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The hokey team have responded to this point by saying that the paleoclimate record (showing temperature varying by only 3.5 K either side of the long-run mean over the past 810,000 years) demonstrates high net-positive feedback in response to very small forcings over the period.

Accordingly, I consulted an eminent geologist who said the positive and negative forcings over so long a timescale were very substantial. So I consulted another geologist. He said the same.

Mr Born’s final point is that our discussion of electronic circuitry was “unnecessary”. Not so. The models use an equation taken from electronic circuitry, where it represents a real event, the phase-transition of the voltage from the positive to the negative rail at a loop gain of unity, and misapply it to the climate, which is an object in a class to which that equation does not apply, especially at the very high loop gains implicit in the IPCC’s estimates of climate sensitivity.

There are two principal reasons why the Bode equation – unless it is modified in some fashion analogous to Mr Born’s modification of a circuit to prevent its output from behaving as it would otherwise do – does not apply to the climate.

First, as temperature feedbacks and hence loop gain increase, there comes no moment at which the effect of the feedbacks is to reverse the output and push temperatures down, though that is what the Bode equation in the form in which it is applied to the climate models mandates.

Secondly, in an electronic circuit the output [voltage] is a bare output: it does not act to equilibrate the circuit following the perturbation amplified by the feedback. In the climate, however, an increase in surface temperature is precisely the mechanism by which the object self-equilibrates, and the Bode equation simply does not model this situation.

For these reasons, we considered it important to raise an early red flag about the applicability of the Bode equation. We are not the first to have done so, but as far as we know our brief treatment of the problem is more explicit than anything that has been published before in the reviewed literature.

I have a further paper on the Bode question in the works that has passed review by an eminent expert in the field (I don’t know who, but the journal is in awe of him). The paper will be published in the next few months.

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At no point did that reviewer (or any reviewer) question the validity of the point we raised. On the contrary, he said that the paper was a good definition of a real problem. The paper describes the problem in some detail and raises questions designed to lead to a solution.

Readers who have struggled through to this point may now like to read our paper in Science Bulletin for themselves. There is, perhaps, not a lot wrong with it after all.

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380 thoughts on “Where the complex climate models go wrong

      • seems like quite an increase from around 1700 to the late 20th century, if I’m looking at your chart the correct way, leif.
        Now, that doesn’t mean that the increase in temperature we have experienced is caused by this increase….

      • Mr Svalgaard’s first graph does not go back to 1645: indeed, it excludes not only the entire Maunder Minimum but also the rapid recovery in solar activity from 1715-1745. His second graph appears to show a not inconsiderable increase in solar activity between the Maunder Minimum of 1645-1715 and the near-Grand Maximum of 1925-1995.
        Furthermore, there is considerable historical and even artistic evidence of exceptional cold on both sides of the Atlantic during the Maunder Minimum, consistent with the Little Ice Age. What does Sami Solanki think? His 2005 paper described the Maunder Minimum as the period of least solar activity since the last Ice Age 11,400 years previously, and the near-Grand Maximum of 1925-1995 as almost the most active period in 11,700 years.
        Does Dr Solanki accept the subsequent revisions that appear to have been made to the sunspot and other solar activity records? And, if we are now claiming that we know better how many sunspots there were in 1645-1715 than some of those who were observing them at the time, how many more revisions must we endure? The seemingly speculative revisions to the sunspot record are beginning to look like the questionable revisions to the early 20th-century global temperature record. Every adjustment to the record seems to be an adjustment designed to minimize the influence of natural forcings, so as to maximize the apparent impact of anthropogenic influences.

      • From a talk to be given at the International Astronomical Union’s general assembly in August:
        The new Sunspot and Group Numbers: a full recalibration
        Clette, F., Svalgaard, L., Cliver E.W., Vaquero, J.M., Lefèvre, L.+ more authors:
        After a 4-year research effort, we present here the first end-to-end revision of the Sunspot Number since the creation of this multi-secular reference index of solar activity by Rudolf Wolf in 1849 and the simultaneous re-calibration of the Group Number (Hoyt and Schatten 1998), which leads to the elimination of the past incompatibility between those two independent but equivalent data sets. […]
        The new Sunspot Number series definitely excludes a progressive rise in average solar activity between the Maunder Minimum and an exceptional Grand Maximum in the late 20th century.
        If you have problems with this address the issue as presented in Space Science Reviews last year:
        http://www.leif.org/research/Revisiting-the-Sunspot-Number.pdf
        instead of regurgitating obsolete claims from old papers.

      • Mr Svalgaard’s first graph does not go back to 1645: indeed, it excludes not only the entire Maunder Minimum but also the rapid recovery in solar activity from 1715-1745.
        What is so typical of your sleights of hand, you ignore that most of your ‘hefty’ increase took place from 1749 on:
        http://www.leif.org/research/Monckton-Flaw-5.png
        but what else can one expect from an activist.

      • What a shame that Mr Svalgaard is not keeping the tone scientific. Let us, please, avoid mere yah-boo.
        My reproduction of the Hathaway graph shows a far greater increase in solar activity from around 1695-1735 than thereafter. That period also coincided with the most rapid rate of increase in the entire Central England temperature record. Thereafter, the Hathaway shows solar activity as quite stable until it began to increase in the 20th century. And over the period of stable solar activity the Central England temperature was also stable. Then the Sun became more active – according to Hathaway’s graph, at any rate – and, sure enough, Central England temperature also showed increases, no doubt enhanced somewhat by CO2 emissions in the late 20th century.
        There does, therefore, seem to be some degree of correlation between changes in solar activity as indicated by sunspot number and changes in surface temperature (assuming, as one may, that the Central England temperature is not an altogether unworthy proxy for global temperature). So the point I made in the head posting was not altogether unmeritorious.

        • It is hard, when you consistently ignore the science and persists with false statements [for whatever reason]. You claim:
          My reproduction of the Hathaway graph shows a far greater increase in solar activity from around 1695-1735 than thereafter.
          The English sentence is muddled; you seem to have lost your facility of clear expression. One interpretation is that you are saying that solar activity from 1695 to 1735 increased ‘far’ more than from 1735-2000 [‘thereafter’], but as everybody can see
          http://www.leif.org/research/Monckton-Flaw-6.png
          comparing the green and blue boxes that that is not the case. Another interpretation is that you claim that activity in the green box is ‘far’ greater than in the blue box. Either way, you are way off base. Now, is that deliberate or just sloppiness or perhaps plain ignorance? You make the call. The standard interpretation is that activity increased dramatically from ~1700 until recently. This is now being seriously challenged.
          [corrected link, see below .mod]

      • The actual quote “Interestingly, the official answer of the “hokey team” to our point is that we should have assumed that more than all the warming since 1850 was manmade. On that point, we disagree. For They cannot at once argue that the hefty increase in solar activity between the Maunder Minimum 0f 1645-1715 and the near-Grand Maximum of 1925-1995 had no influence on global temperature, but that the decline in solar activity since its peak in 1960 is so great that it would have caused significant cooling in the absence of anthropogenic forcings over the period”
        Assuming your chart is correct and M2nckton’s is not. Looking at above chart increase from about ~1680 to 1750 50 to 120, decrease 1850 to 2000 120 to 140. Leif are you suggesting that the increase in your own graph between 1680 to 1750 had no affect on temperature but that the non change from 1850 to 2000 absent from CAGW would have caused a drop? Otherwise, I really fail to see your point. The AGW crowd needs to explain what would have caused a drop in temperatures since 1850, before they can say that Monckton should have used a negative number. Your chart does nothing to change that argument. Now perhaps it would have been clearer if it was stated in that way. And, since I don’t know what the actual hockey team statement was I do not know if they mentioned the sun or not as the change that would have lowered temperatures. If they didn’t it is somewhat a strawman argument. If they did then all Monckton needs to do to satisfy you would be to use your second chart as a source, correct?

        • My point is that solar activity has very little to do with the climate and that Monckton could really have benefited from not invoking an un-substantiated solar connection, and that with a [we think now] unrealistic and obsolete view of said activity. CO2 and CAGW have little or nothing to do with this. Neither his model, nor IPCC’s rely on solar activity being a major driver.

      • Even with the corrected SPN there is a variation in TSI on the order of 1 +/- 0.5 Wm-2 with a long duration. That would produce roughly a 0.25 to 0.35 Wm-2 imbalance depending on your choice of reference. So somewhere between 25% and 50% of the climate change could easily be solar on century time scales.

      • “After a 4-year research effort, we present here the first end-to-end revision of the Sunspot Number ”
        OK. So you have “revised”, in other words, “changed”, or “altered”, or “fudged, because these days we know better than those stupid old people”, the data to fit with what you believe the numbers should be?
        I have read some of what you have written, Leif, and I cannot see that you make out your case convincingly. You seem to have fallen into the trap of many a practitioner, in many a field, of trying to find something new in the same old data. When, in fact, sometimes the same old data is exactly that – and should just be left alone.
        The most obvious example is your extrapolation backwards from present measurement techiques, via satellites and improved telescopes, to your “knowing” what error margins to apply to observations centuries ago.
        You do this with a level of assurance which is entirely unscientific. You also present this data as the best available evidence, rather than being truthful – namely, that it’s just your own model of what you think might be the case.
        Your pomposity works against you at every turn. If you think history will remember you, you are sadly mistaken, because history (at least in the sciences) only remembers the hubrists as fools. It’s the truly great scientists, who questioned their own theories and invited others to debunk them, who are remembered down the ages.
        Which do you want to be, Leif?

    • Leif Svalgaard March 16, 2015 at 2:00 pm
      “For They cannot at once argue that the hefty increase in solar activity between the Maunder Minimum 0f 1645-1715 and the near-Grand Maximum of 1925-1995 had no influence on global temperature, ”
      Except that there very likely was no such ‘hefty’ increase and no Grand modern Maximum

      So their objection was invalid either way?

      • “As solar activity is not a parameter in Monckton’s ‘model’, he should never have brought it up”
        You forget, Leif, that everything you do is only a “model”. You are not an experimental scientist – you are a “modeller”. You, in fact, spend your entire life taking data and other peoples’ models and reintepreting them.
        You are a “modeller”. And you are trying to convince us that your interpretation – your “models” – are better than everyone else’s.

        • I am concerned with observations [counting of sunspots] having counted more than 60,000 of them. Monckton is the modeler. But there is nothing wrong with models as such, as models are condensations of our knowledge. Data without a model to interpret them do not mean anything.

      • The solar proxy data and temperature proxy data correlate too well to simply be a coincidence. Seriously Dr. Svalgaard, if not solar variability then what do you think causes the minor temperature fluctuations (like the ones inferred during the Holocene) on this planet? Are you of the same opinion of the hockey team that these past temperature variations did not even occur or do you attribute some other cause?
        http://www.nature.com/ngeo/journal/v7/n4/full/ngeo2094.html

      • captdallas2 0.8 +/- 0.2 March 17, 2015 at 6:25 am
        Even with the corrected SPN there is a variation in TSI on the order of 1 +/- 0.5 Wm-2 with a long duration. That would produce roughly a 0.25 to 0.35 Wm-2 imbalance. So somewhere between 25% and 50% of the climate change could easily be solar on century time scales
        No, a 1 W/m2 change in TSI over a long enough period produces a temperature change of 1/1361/4 = 0.000184 of 288K = 0.05 K which is totally in the noise.
        .

    • Apparently lsvalgaard has a mental block, or is purposely obfuscating total increase with rate of increase.
      A greater Rate of increase is clearly demonstrated in Mocktons graph as occurring during the Maunder Minimum. Chopping off the Maunder Minimum and then saying it’s not so is as disingenuous as illogical.

      • As activity goes up from zero the rate of increase is infinity, but the rate of increase is not important. What is important is the amount of increase. If I had nothing in my pocket and I get a dollar, the rate [defined as (new amount – old amount)/old amount] is infinite, but the amount is only 1 dollar. If I then get 100 dollars, the amount increased by 100 dollars, but the rate is no longer infinite.
        As solar activity is not a parameter in Monckton’s ‘model’, he should never have brought it up, especially since he fancies obsolete data. That is all.

      • Leif:
        you posted a chart which seems to indicate a significant increase in solar activity from the late 18th century to the late 20th century…Is this a correct interpretation of the graphic you posted?

        • No, the correct interpretation is that solar activity rose to about equal heights in the 18th, 19th, and 20th centuries, and that there therefore is not a linear, progressive increase over that time. I’l show that inconvenient truth again:
          http://www.leif.org/research/SSN-Since-1749.png
          The conclusion of the recalibration paper [ http://www.leif.org/research/Revisiting-the-Sunspot-Number.pdf ] is:
          “Regarding the impact of the new SN recalibration, the most prominent implication is the significant reduction of the upward trend in the average amplitude of solar cycles that was present in the original GN series between the 18th and the late 20th century. The recalibrated series indicates that 11-yr peak SNs during the 18th and 19th century were comparable to those observed during the recent interval of strong activity during the second half of the 20th century. The scenario of the initial post-Minimum recovery is still uncertain, as the exact amplitude of the first cycles of the 18th century remains difficult to establish given the scarcity of observations over that period. Still, the vanishing upward trend over the last 250 years questions the existence of a modern “Grand Maximum” in the 20th century […] which resulted primarily from the erroneous transition between Wolf and Wolfer in the Hoyt and Schatten GN time series. As this “Grand Maximum” concept rests on the occurrence of out-of-range amplitudes of the solar cycle, it is definitely contradicted by the re-calibrated and reconciled SN and GN series.”

      • Leif:
        1) thanks for responding and clarifying, and
        2) the graph I was referring to actually went back a few more decades, (lsvalgaard, 7:52 pm) to the beginning of the 18th century, when the index seemed to be much lower. It appears that the idex went from around 70-80 to around 130…That does seem to be a substantial increase, I might not be capable of reading your chart, but thats what it looks like when the page loads on my computer… now,i dont believe in cherry picking, so i accept your explanation.
        thanks again.
        david

        • There are almost no observations during 1730-1750, so any sunspot number values for that interval are highly uncertain which means that there is very little hope of comparing earlier counts with newer counts using overlapping observers. In 1722, George Graham in London discovered that the geomagnetic declination [the amount by which a compass needle deviates from pointing true north] varied during the day. In order to even observe this, solar activity [Extreme Ultraviolet radiation to be precise] must have been comparable to modern values.
          Foukal & Eddy [yes, that Eddy!] note that the observations of the ‘red flash’ at solar eclipses in 1706 and 1715 implies that “a significant level of solar magnetism must have existed even when very few spots were observed, during the latter part of the Maunder Minimum”, see Slide 27 of http://www.leif.org/research/Another-Maunder-Minimum.pdf

      • Leif:
        I reread your response to me, and I have to ask,
        why did you change my question?
        here is the wording in my post to you:
        ” you posted a chart which seems to indicate a significant increase in solar activity from the late 18th century to the late 20th century…”
        And here are the terms of your response:
        “and that there therefore is not a linear, progressive increase over that time”
        I never inferred a “linear, progressive increase”
        Looking at the pseudo sinusoidal nature of the time series you presented to us, its hard to imagine that any thinking person would infer some linear increase.
        i merely noted that your own chart seemed to show that solar activity had increased from the early 18th century to the late 20th century. Do you feel this isn’t the case, that solar activity levels of those two time periods are roughly equivalent?
        Im aware that it seems highly unlikely that variance in TSI over this period is responsible for changes in temperature, but one wonders what to make of the graphical data you presented.
        Im curious…what other observations in the sunspot index do you discount?
        If the time series you present is flawed to the degree that you seem to conclude, why present the chart?
        An increase of about 120% from its low in the early 18th century to say, 1990 may be an artifact of poor observations in the early 1700’s, if so, why present the data in the first place?

        • I changed it because your question was incomplete. You might as well have said between 1996 and 2001 where it went from almost zero to 120, a more than 1000% increase. Or from 1705 to 2008 where there is a 500% decrease. In determining long-term trends you should make the comparison of extended periods. Our conclusion was that there is little difference between the 18th, 19th, and 20th centuries.
          its hard to imagine that any thinking person would infer some linear increase
          Yet, that is what Monckton’s graph is intended to show.
          what other observations in the sunspot index do you discount?
          We do not discount any observations, on the contrary we try to use all the observations available. But raw observations do not take into account differences in telescopes, observer acuity, and method of counting. We try to assess these factors [as did Wolf and Hoyt & Schatten].

    • I’ve given up trying to find correlations. The average global temperature doesn’t correlate with anything – TSI, sunspots, cosmic rays or anything else. We are looking at a random walk that has expanding excertions over expanding time scales. The only exception must be between the Earth’s orbit and ice ages.

      • Yep. And Earth’s atmospheric ability to over long term and short term spans of time to increase/decrease absorption of SWIR deep into oceans, along with our oceans’ varying ability to mix, layer, pile it up, and distribute this stored potential heat is the most likely source of our temperature trends. The entire ocean has an overturning circulation measured in 100’s of years while several shorter surface cycles are greater than 50 years, while still others are decades long, and still others can make a complete cycle in less than 5 years.
        Given that the oceans are a HUGE MASSIVE heat distributing system, the puny addition of ppm anthropogenic CO2, or the puny addition of a tiny fraction increase of a small fraction of solar radiation we sit in the path of, is a comparative nonstarter for me.

  1. That seems like a very good defence.
    But I would like to hear Joe Born’s reply to this reply. I do hope he asks to write a post here.
    Pedant’s corner.
    It’s the “National Health Service” not the “national health service”. That matters to some of us. Obviously tweaking noses is part of the game, hence “hokey”, but why pick more fights at once than necessary.

    • Thank you for getting back on track. Excellent post Mr. Monckton. I am sorry the entire post was immediately sidetracked by an agenda barely if at all, cogent to the message of your post. The solar affect on climate is indeed a different matter entirely, and involves far more then simple TSI equations. It is a worthy subject to discuss, (at another time) but was certainly not the intent of your post, nor is your post in anyway dependent on which version of the solar record is used.
      Lately at WUWT I have noticed the initial response is more often a thread diversion by some with an agenda.

      • Bingo.
        I have noticed the same.
        It’s like a person looking to purchase a car pointing out to a used car salesman the high-mileage on a car and the oil stain underneath it and the car salesman asking why they didn’t notice the radio works and the steering wheel is included free.

    • MCourtney
      March 16, 2015 at 2:08 pm
      That seems like a very good defence.
      But I would like to hear Joe Born’s reply to this reply. I do hope he asks to write a post here.
      ———————-
      That is not a good defence, but actually a very confusing and paradoxical one,,,,,as far as I can tell.
      Where the complex climate models go wrong.
      By Christopher Monckton of Brenchly
      I my self accept respect and acknowledge the Moncton’s work and struggle in this one.
      As far as I can tell Monckton has done a good job in pointing out where and how the complex climate models are or go wrong.
      As far as I can tell Joe Born did not challenge or tried to show any fault as far as this goes up to this point.
      But where Monckton goes wrong and paradoxically wrong is when he tries to right that wrong with his simpler model.
      And that is what Joe Born reply was about, if I did not misunderstand Joe, that is.
      You see is all about the feedbacks.
      There is where and when the Moncton’s paradox is borne, so to speak.
      In principle AGW has no problem or any paradox when it claims and propagates that CO2 emissions and RF become a climate changer in the anthropogenic era.
      Their assumption of the feedbacks support the claim that RF becomes a climate changer when actually it was not such as previously in the terms of natural climate change.
      Moncton does a good job on showing that the assumption of their feedbacks is wrong because such feedbacks are wrong, so to speak.
      But when Monckton tries to right that wrong, by somehow claiming and showing better feedbacks, different ones than the AGWers than Monkton goes in a paradoxical position, because simply Monckton is relying in the same principle that CO2 and RF are a climate changer.
      At that point he is in contradiction with the very basics of Climatology, where RF is not considered as a climate changing force……..and unless he accepts that he is an AGWer he must accept that he is in contradiction with Climatology.
      If he somehow accepts that he is an AGWer, probably a lukewarmer or a BAGWer (Benign) then he has to face his own paradox, where RF is a climate changing force but in the same time it is not a climate changing force.
      Monckton says:
      “Mr Born’s final point is that our discussion of electronic circuitry was “unnecessary”. Not so. The models use an equation taken from electronic circuitry, where it represents a real event, the phase-transition of the voltage from the positive to the negative rail at a loop gain of unity, and misapply it to the climate……..”
      The electronic circuitry in question firmly holds and propagates the main AGW principle, the RF being (becoming) the main driving force of climate change.
      The other thing is that while Monckton can rightly claim that his simple model can point out where the complex GCMs go wrong still it will be not wise to even imply that his simple model can or does do what actually the GCM “beasts” can do. These two kinds are worlds apart.
      Even in their wrong the GCMs are very very beautiful, the ugliness remains with the human misinterpretation of that wrong.
      I my self see that that wrong is the best ever we could have ever expected or imagined from GCMs.
      We mostly learn through our errors…..and that one is a superb beautiful error, on my view that is.
      cheers

  2. The difference between solar activity from the Maunder Minimum/Dalton Minimum in contrast to the Modern Maximum is very significant.
    Some of the reasons why the models are off are because they neglect or assign wrong relative importance to the following items:
    Geo -Magnetic Field Strength Of The Earth.
    Solar Variability and Associated Secondary Effects. Way underestimated.
    CO2 ‘S Role– far to much importance.
    Initial State Of The Climate- probably wrong or incomplete.
    Lack Of Understanding Of Feedbacks. Especially clouds.
    Aerosols – The models do not address them properly.
    This is why even in hindsight the models can not get it right and why basic atmospheric predictions they made such as the hot spot in the lower troposphere in the tropics and a more zonal atmospheric circulation pattern in response to global warming have not come to pass.

    • The difference between solar activity from the Maunder Minimum/Dalton Minimum in contrast to the Modern Maximum is very significant.
      The evidence favors that it is not. See also e.g.
      http://www.leif.org/EOS/2011GL046658.pdf
      “the best estimate of magnetic activity, and presumably TSI, for the least‐active Maunder Minimum phases appears to be provided by direct measurement in 2008–2009”

      • Leif,
        Your “evidence” seems to change as the years go by. Perhaps you should alter your attitude towards what is “evidence” and “fact”, and admit that what you are producing is just another “model”?
        A degree of humility does all who call themselves scientists a whole lot of good, from time to time. I’ve read your opinions for many years now, and I believe that you have lost – or at least misplaced – that essential trait recently.

      • Model, model, model, model. That entire paper, Leif – with the exception of modern numbers – is based on modelled outputs. As the years go by, you seem to become more and more sure of your models, rather than less sure of them.
        Now, that’s what I’d expect of an econometrician, not a scientist.

  3. Sounds like not a single comment modifies a single claim, conclusion, position extrapolation.
    Really? Perfection at first go?

    • In response to Mr Proctor, i shall of course be happy to address any particular scientific defect he may conceive that he has come across in our paper. However, the paper was very thoroughly peer-reviewed by three diligent reviewers, ironing out many defects. And I have responded in a surely considered, careful and well-evidenced way to the queries raised by Mr Born. I do not claim perfection, but – for the reasons carefully enunciated in the head posting, I am not sure that Mr Born’s criticisms of our paper are well founded.

    • Doug, really? We have been subject to numerous studies that say the end of the world as we know it will occur in the next five to ten years since the 1990’s. The proposed models to date only barely work if the past is cooled and the present relies on an increasingly fewer number of rural temperature measurement stations that are approximated by urban centers hundreds to thousands of kilometers away (i.e., UHI writ large).
      Do you believe, or do you not believe, that the older models were “perfect” when first proposed? If you do, then say so now or just go away.

    • What a nonsensical statement, making a contradictory comment does not automatically require modifications to a claim or conclusion. Making a well supported strong argument can lead to modification absent a stronger response.
      The challenge to one item in the article has been responded to in substance and as an attempt at misdirection. Perhaps you would like to re-read the comments and see if it modifies your bias.
      We’ll leave discussion of perfection to theologians. Yes. Really.

      • Alx, Doug said “Sounds like not a single comment modifies a single claim, conclusion, position extrapolation.
        Really? Perfection at first go?” What challenge did he make to one specific item? None in this specific post by Doug. I see that in later posts he got busy with specific issues. Also, what is my bias? The truth is that previous model projections do not conform to observable reality and this is acknowledged by those who made the models. If reality met, or exceeded model projections, my perspective would be different. But the bottom line is that a tremendous amount of energy can not be accounted for and either the previous models are wrong or the temperature measurement devices are wildly inaccurate. Which is it?

      • Alx, on second read I may have wrongly concluded that you were addressing my comment and not Doug’s original post. If I was wrong, apologies,

  4. All of these machinations are unnecessary with the simple summary that the absorptive spectrum for CO2 is already dominated by H2O, and that H2O changes phases as gas, liquid and solid at normal temperatures. The energy absorbed and released in these phase changes is so huge it drowns out all other Atmospheric gasses. It’s called the water cycle! Meanwhile. CO2 only changes phases at MINus 109 degrees, a temperature rarely attained anywhere on Earth. See my blog “How in the universe can CO2 control the Earth’s Weather … At Paullitely.com

    • And add the fact that gaseous CO2’s emissivity is a paltry 0.0017, at least 400 times lower than water vapor. My analogy is that you have a car parked in the middle of a Texas desert at noon in July. The car is painted flat black (water vapor) and it absorbs quite a bit of radiation. The inside of that car is going to get really hot. On top of that black paint you place two drops of light grey paint (CO2) and it only absorbs a fraction of what water vapor will. It is NOT going to make that car any hotter… since both materials are absorbing the same wavelengths from the same energy field at the same time… and water does it so much better. Gases at the pressures found in the vast majority of our atmosphere are not really very good at holding on to heat and are really non radiators until you get close to vacuum pressures. A dry desert at night is a good example. It gets cold FAST without water vapor… and even if the CO2 could radiate at surface pressures (it can’t) that 15µm photon’s energy level is around -80°C so the only thing its warming up is space.

  5. Lord Monckton,
    When was the latest update on the length of the pause? I have been anxiously awaiting that and I am curious if it has seen any changes lately.

    • In response to Cold in Wisconsin, the latest graph – including data to the end of February 2015 – shows no global warming for 18 years 3 months. Now that weakish el Nino conditions appear to be intermittently present, I should expect the length of the Pause to shorten over the coming months. However, if the el Nino is followed by a la Nina the Pause may begin to lengthen again at the end of this year.
      Meanwhile, I am in future gong to include the changes in sea temperature measured by the ARGO bathythermographs in my monthly round-up. This will show that in the 11 full years oif the ARGO record the rate of increase in ocean temperature – which, over a sufficiently long period, will be perhaps the most reliable indicator of the long-run temperature trend – is equivalent to just 0.2 Celsius degrees per century, notwithstanding record increases in CO2 emissions.
      I did send the graphs to Anthony as usual, but he did not publish them. I suspect he may be waiting for another uptick in the length of the Pause. My own feeling is that the monthly data and six-monthly comprehensive updates should be published whichever way the trend is going. However, Bob Tisdale now does a mid-month update here which will give you some of the information also to be found in my own monthly updates – though I think it is not as visually clear as my presentation of the data.

      • Mr. Monckton, regarding the ARGO bathythermographs, do you have any concern regarding their accuracy in that they move, and therefore are continually measuring disparate areas of the ocean, both latitude and longitude, as well as changing locations relative to ocean currents?

      • In response to David A, the ARGO bathythermographs are the least ill-resolved method we have. But one should not place too heavy a reliance on their results: for each buoy has to cover 200,000 cubic kilometers of ocean. How reliable is such sparse coverage likely to be? Willis Eschenbach puts it thus: ARGO is the equivalent of taking a single temperature and salinity profile to represent the whole of Lake Superior – less than once a year.
        The truth is that the ocean is really too big for us to measure its temperature changes with sufficient precision even to establish the direction of a trend, let alone its magnitude. ARGO is merely an indication.
        I am less concerned about the fact that the buoys move about. In view of the extreme variability of temperature change in different parts of the ocean, the major problem is that the coverage is woefully insufficient to draw precise conclusions.

  6. As one can see the data shows clearly their is a solar /climate correlation. Leif’s own data further supports this. Read below.
    http://jonova.s3.amazonaws.com/graphs/model-trend/scaffetta-2013-mwp-fig23.gif
    Now if one looks at this chart(in the above) the bottom one with the blue temperature curve and compares it to the latest study showing the solar secular cycle one will see a good correlation between global temperature and the solar secular cycle.
    The solar secular cycle trend from 1610-2010, and the absolute values of the solar secular cycle trend correlating with the global temperature trends (1610-2010), and absolute values of the global temperature.
    The solar secular cycle trend also shows a distinct increase in solar activity from the period 1930-2005 period, versus the period from 1650-1930 in that the solar secular cycle through out that period of time never exceeds 125 ,in contrast to being above 125 from the 1930-2005 period of time, with a peak of 160!
    In addition if one examines the data, at times when the solar secular trend breaks 100 on the down slide the global temperature trend is down although the global temperature value starting points may differ most likely due to other climate items superimposed upon the global temperature trend such as the state of the PDO,AMO or ENSO.
    During the times when the solar secular trend broke 100 those being the period 1660 -1720 and 1780-1830 both corresponding to the Maunder Minimum and Dalton Minimum ,the global temperature trend is in a definitive down trend. In addition even from the period 1880-1905 when the solar secular cycle approaches the 100 value, the global temperature trend is slightly down once again.
    Then on the other hand, when the solar secular cycle trend exceeds 125 from 1930 -2005 the temperature trend is up and shoots really up when the great climatic shift takes place in 1978 which is when the PDO ,shifted from it’s cold to warm phase.
    The data from the above shows quite clearly that when the solar secular cycle breaks 100 on the down slope look for a global temperature cooling trend to begin from what ever level the global absolute temperature is at, and when the solar secular cycle rises and breaks through 100 on the upside look for a global temperature trend to rise from what ever level the global absolute temperature is at.
    A general rule I see is when the solar secular cycle exceeds 125 global temperatures trend up or are at a higher level and when it breaks 100 on the downside global temperatures trend down or are at a lower level.
    If this latest solar information is correct and that is a big if ,but if it is correct, it shows the climate is more sensitive to primary ,and the secondary effects associated with solar variability.
    In addition my low average value solar parameter criteria for cooling may be able to be adjusted up some , due to this latest information.
    One last note, it looks like around year 2010 the solar secular cycle trend finally broke 100 n the down swing which would be the first time since 1830, when the solar secular cycle broke 100 on the up swing and had since stayed above that level until year 2010.
    THE GRAPH SHOWING THE SOLAR SECULAR CYCLE IS ON PAGE 13 OF THE PDF I HAVE SENT . LOOK BELOW.
    http://www.leif.org/EOS/Maunder-Minimum-Not-So-Grand.pdf

    • From your link: “the solar activity from 1609 to 1723 was not dramatically different
      from that over the past 300 yr”,
      contradicting your assertion that “The difference between solar activity from the Maunder Minimum/Dalton Minimum in contrast to the Modern Maximum is very significant.”
      so enough of this nonsense.

    • “Leif’s own data supports it…”
      I think that it should be made clear here that :eif’s “data”, as presented is not “data”, but his own “model” of the data.
      It may be right, it may not. However, you should not present what Leif produces as “data” – it plainly is not that.

      • Anto, is there an observation/count of sunspots you consider to be data or are you saying that all observation counts are models?

  7. More data, and this is why AGW theory will be obsolete before this decade ends and why the models will never work. The models are being fed erroneous data and wrong data without proper weighting of data and in some cases just omitting the data completely.
    https://climateaudit.files.wordpress.com/2015/01/md99-2275_jiang2015_1.png
    More data which shows since the Holocene Optimum from around 8000BC , through the present day Modern Warm Period( which ended in 1998) the temperature trend throughout this time in the Holocene, has been in a slow gradual down trend(despite an overall increase in CO2, my first chart ), punctuated with periods of warmth. Each successive warm period being a little less warm then the one proceeding it.
    My reasoning for the data showing this gradual cooling trend during the Holocene ,is Milankovitch Cycles were highly favorable for warming 10000 years ago or 8000 BC, and have since been in a cooling cycle. Superimposed on this gradual cooling cycle has been solar variability which has worked sometimes in concert and sometimes in opposition to the overall gradual cooling trend , Milankovitch Cycles have been promoting.
    Then again this is only data which AGW enthusiast ignore if it does not fit into their scheme of things. I am going to send just one more item of data and rest my case.
    http://www.murdoconline.net/wordpress/wp-content/uploads/2011/01/gisp2-ice-core-temperatures.jpg

    • I am not sure that Mr del Prete’s final graph is appropriate, since the data are not brought up to the present. It looks, by eye, as though the data run only to about 1850, and there has been getting on for 1 K of warming since then.
      But his point about the apparent correlation between high levels of solar activity and high global temperature may have some force. i have seen several analyses indicating that the time-integral of solar activity is quite a good predictor of temperature change. However, I have not yet seen this done in the peer-reviewed literature.

      • By far and away the easiest way to predict temperature is sunspot activity levels. And using past as probability, we can safely say we are at the tail end of the present Interglacial and the history of previous events shows us that another Ice Age will come at some point in the next +-4,000 years.

    • This chart by Richard Alley is very instructive. Look at the last year. It’s 95 years before 2000. That’s in 1905. The temperature is more than 1 C cooler than the Medieval Warm Period and 2 C and 2.5 C cooler than Roman and Minoan warm periods. It debunks Mann’s hockey stick. And yet Alley is a known AGW believer and resource person to Al Gore.

      • Dr. Strangelove says:
        The temperature is more than 1 C cooler than the Medieval Warm Period and 2 C and 2.5 C cooler than Roman and Minoan warm periods. It debunks Mann’s hockey stick. And yet Alley is a known AGW believer and resource person to Al Gore.
        Correctomundo. Alley has been constantly backing and filling, ever since he jumped on the climate gravy train. But his climbdown does not wipe away his previous work. Years ago Alley showed that CAGW is nonsense. It is still nonsense.
        Also, I wonder why “icanthelpmyself” would gratuitously throw out my name in this thread, where I’ve made no comments? It’s probably because I called him out on the Tim Ball thread for not knowing that latitude has an effect on temperature. He didn’t know that. He showed he’s a newbie on this whole subject, so please just disregard him. He has plenty to learn. He can start with learning the basics: that global warming has the greatest effect at night, and in winter, and at the higher latitudes.

      • Greenland is not The World.
        ==========
        there is no data series that samples “the world”. The satellites come close, but NASA prefers to not use them because even though its name includes NATIONAL … SPACE …, the satellite data doesn’t show the right message.
        Instead NASA gives us GISTEMP, a homogenized mix of ground station data run through a meat grinder., using raw materials supplied by different countries, with vastly different standards of data hygiene. What if McD’s made hamburger that way? Can you really mix road kill with prime grade A beef and not affect the flavor?
        Explain why it is that NASA satellites can measure the height of the ocean to 1mm, but they apparently cannot make a satellite to measure the temperature of the earth’s surface?
        How is it that a $19 hand held IR thermometer with laser pointer can accurately measure the temperature of objects remotely, but NASA with billions of dollars worth of satellites still relies on Peter Dufus to read the thermometer nailed to the local post office wall to calculate the earth’s average temperature?

      • “Greenland is not The World.”
        Show me your empirical data where Greenland is warming and the world is cooling for 100 years or longer. Mann’s hockey stick is from tree rings in the US. Al Gore’s 400,000-year temperature chart is from ice cores in Antarctica. Is US or Antarctica the world world? You can’t have it both ways. If you accept Mann and Gore, you should accept Alley. Or reject them all. But the problem with the hockey stick is Mann spliced tree ring proxy data and thermometer data to “hide the decline.”

      • (Another wasted effort by a banned sockpuppet. David spent a lot of time on that one. Comment DELETED. -mod)

      • By the way, what’s all these talk about temperature today being unprecedented? Both GISP and Vostok show so many points above the zero line (warmer than today) in last 10,000 years.

  8. If the Bode equation is inappropriate for loop gains >1, then it may also be inappropriate for loop gains <1. It may – at least in its unmodified form – be the wrong equation altogether. And without it one cannot get away with claiming the absurdly high and unphysical sensitivities the IPCC profits by asking us to believe in.

    But there is no suggestion that the Bode equation is inappropriate for loop gains >1 because that is a completely unstable system and no one, no even the IPCC, is suggesting that true net feedback is positive. If it were the world would be like Venus or the moon.
    There seems to be a lot of confusion because the IPCC talks about “net feedback” EXCLUDING the Planck feedback, which is strongly negative and overpowers all the rest put together. So there is not question of even approaching l loop gain of 1.
    Now you are correct that a simple linear feedback as represented cannot accurately represent the T^4 Planck feedback over a wide range. This can only be *approximated* as linear over a narrow range.
    The real issue is over whether the “net feedbacks” excluding Planck f/b either add to or reduce Planck f/b . The models *assume* net +ve that reduces Planck and the evidence is that they are wrong. That is why they run hot.

    • As Professor McKitrick pointed out in a recent lecture (and see also Monckton of Brenchley, 2008), the upper bounds of the IPCC’s values for the principal climate-relevant temperature feedbacks do exceed unity. And there is no theoretical reason why they should not do so. However, there is a theoretical reason why the Bode equation cannot possibly apply under such a regime: and if it does not apply to a feedback sum above unity the question does arise, like it or not, whether it is the right equation at all.
      The Planck “feedback” is not a feedback, but part of the reference-frame for determination not only of the direct warming to be expected in response to a forcing but also, et separatim, of the magnitude of the closed-loop gain. It should really be expressed, therefore, in units of Kelvin per Watt per square meter (see Roe, 2009, for a brief discussion).
      Our paper does explain how the Planck parameter is deployed in the climate-sensitivity equation. The net feedback sum is not added to or subtracted from the Planck parameter, as “Mike” suggests: it is multiplied by it.

    • Hello Mike
      The models run hot because the models are forced, “molested”, intentionally or not, then the assumption arises through a wrong interpretation, the AGW interpretation (the 3C CS),,,,,,,,,,,as far as I can tell GCMs basically simulate the climate and atmosphere functioning and do not assume such things like the assumption you point at.
      The assumptions generally are not a “cause” of warming in the GCMs but actually are after effects consequences.
      Of course I could be wrong……
      Cheers

  9. Where the complex climate models go wrong
    Guest Blogger / 1 hour ago March 16, 2015
    By Christopher Monckton of Brenchly

    Your post could have been much shorter if you’d just said where the complex climate models go right.8-)
    (A real sunset vs a CGI sunset. Which really inspires more awe?)

  10. Leif Svalgaard
    March 16, 2015 at 2:00 pm

    For They cannot at once argue that the hefty increase in solar activity between the Maunder Minimum 0f 1645-1715 and the near-Grand Maximum of 1925-1995 had no influence on global temperature,
    Except that there very likely was no such ‘hefty’ increase and no Grand modern Maximum:

    So, despite appearances, you are in agreement with Monckton: “They cannot at once argue that the hefty increase in solar activity between the Maunder Minimum …..”
    Either there was a grand max and it’s now cooling or there was no max and therefore it cannot now be evoked as a cause of cooling.
    As usual the hypocritical alarmists want it both ways: “solar was irrelevant during warming but is now the reason for the pause. “

    • Either there was a grand max and it’s now cooling or there was no max and therefore it cannot now be evoked as a cause of cooling.
      Although this subject is obscured by people being imprecise, I think the usual contention is that maximum solar activity means warming.

      • –Either there was a grand max and it’s now cooling or there was no max and therefore it cannot now be evoked as a cause of cooling.
        Although this subject is obscured by people being imprecise, I think the usual contention is that maximum solar activity means warming.–
        Yes.
        But maximum solar activity can mean greater variation- or more change
        in given amount of time.
        Though this point might be too much like global warming is same meaning as climate change- and so, be likewise regarded as invalid.
        But it is max activity not max heating.

      • It would plainly be better if Leif avoided playing the man, and attended to the argument. Christopher, as well.

  11. My adventures in climate science are more of the broad stroke type and I don’t go into the nut and bolt details. However, I detected an epiphany in your discussion of the ‘entire’ Bode diagram but am not sure what it portends. Am I to read the hyperbolic graph above a gain of 1 as abruptly dropping down to deep negative from high positive? I thought everything blew up in climate and electronics beyond “1”.

    • Mr Pearse has indeed spotted the significance of the singularity at a loop gain of unity in the Bode equation. At that point in an electronic circuit, the current transits from the positive to the negative rail: i.e., it goes round the circuit the other way about, so that the voltage that was doing its best to become infinitely positive tries its best to become infinitely negative.
      In the climate, however, no such reversal is physically possible. Wiser minds than mine are working on this real difficulty, and I am hoping that an expert paper on the subject that is now in peer review will make everything clear.
      It is of course obvious that the Bode graph as it stands does not really represent even an electronic circuit. There are obvious asymptotic bounds preventing an infinite positive (or, above unity, negative) voltage from being output by the circuit.
      Another reason why the Bode equation – at least in its unmodified form – seems inapplicable to the climate is that temperature change – the output – is the very instrument by which the climate system self-equilibrates. Bode simply does not model this self-regulation. The use of Bode, I believe, especially in combination with implausibly high net feedback sums, is the reason why the more complex models erroneously predict far more warming than has occurred or will occur as a consequence of Man’s sins of emission.

      • Mr Pearse has indeed spotted the significance of the singularity at a loop gain of unity in the Bode equation. At that point in an electronic circuit, the current transits from the positive to the negative rail: i.e., it goes round the circuit the other way about, so that the voltage that was doing its best to become infinitely positive tries its best to become infinitely negative.
        No, dammit! You are making the implied assumption that your input is positive to begin with! You’re just being sloppy. The reality of your model is that it inverts for gains greater than unity and you can have a system which is stable with gains greater than unity. You just have to be careful that you have adequate phase margin. Stop being so sloppy.
        In the climate, however, no such reversal is physically possible. Wiser minds than mine are working on this real difficulty, and I am hoping that an expert paper on the subject that is now in peer review will make everything clear.
        Yes, this is a good observation to make. It flies directly in the face of the catastrophists.
        It is of course obvious that the Bode graph as it stands does not really represent even an electronic circuit. There are obvious asymptotic bounds preventing an infinite positive (or, above unity, negative) voltage from being output by the circuit.
        Over the frequency and amplitude range of interest, it does. If your circuit is unstable (resonances in a completely undamped system or positive feedback), then you fail a basic criterion for frequency analysis and are in a different regime altogether.
        Another reason why the Bode equation – at least in its unmodified form – seems inapplicable to the climate is that temperature change – the output – is the very instrument by which the climate system self-equilibrates. Bode simply does not model this self-regulation.
        I don’t even know what this means. I’m not even sure what “The Bode Equation” is, since what anyone in control theory would call your model is a transfer function. Voltage (or position, or temperature, or pressure head, or…) is the very instrument by which a properly designed circuit self-equilibrates. It is both the input signal and the output. If it couldn’t do so, then there would be no notion of a stable feedback loop.

      • If the open-loop gain of a feedback system is a decreasing function of input level, the system will stabilize into periodic oscillation satisfying the Barkhausen criteria (unity gain, zero phase-shift). This quasi-equilibrium state is near the mid-point of the phase transition at the singularity in your Bode analysis. Observing the paleoclimate plots, one is struck by their similarity to a so called limit-cycle oscillation in which the required gain reduction comes from some hard limit in the system (e.g. an op-amp on its rail has zero small-signal gain). Such stably unstable systems, when forced with a periodic signal will under certain conditions phase-lock to the source, even if the forcing function is quite small (google “injection locked oscillators”). Perhaps the entire climate system is injection locked to the Milankovitch cycle which might explain how it’s small influence is able to exert such dramatic influence on temperature.

  12. I agree that adding GHGs (all else remaining equal) would raise the effective radiating height and that the effective radiating height would be the same temperature as before and not at a lower temperature as proposed by AGW theory.
    However, radiation from within the atmosphere direct to space would increase and so less energy returns to the surface in adiabatic descent than was taken up in adiabatic ascent. At any given moment half the atmosphere is rising and half is descending because everything that goes up must come down.
    That reduction in energy returning to the surface in adiabatic descent offsets any surface warming effect from the presence of GHGs in the atmosphere so that surface temperature does not change and nor does the effective radiating height
    Thus the effect of GHGs is simply to reapportion totalradiation to space between radiation to space from the surface and radiation to space from within the atmosphere.
    More GHGs means more radiation to space from within the atmosphere and less radiation to space from the surface and vice versa.
    A simple illustration:
    i) If the atmosphere had no radiative capability at all then ALL radiation to space would be from the surface.
    ii) If the atmosphere were 100% radiatively efficient then ALL radiation to space would be from within the atmosphere.
    In reality, no atmosphere is 100% radiatively efficient so in practice the proportion of radiation escaping to space is split between surface andatmosphere in proportion to the radiative efficiency of the atmospheric gases.
    It is convection involving adiabatic cooling on ascent and adiabatic warming on descent which varies as necessary to balance conduction between surface and atmosphere with radiation in from space and radiation out to space.
    That balancing process allows the atmosphere to remain suspended against gravity indefinitely whilst energy in from space and out to space remains the same.
    Climate changes are then induced by cloudiness variations caused by solar effects from above modulated by oceanic effects from below.

    • “Climate changes are then induced by cloudiness variations caused by solar effects from above modulated by oceanic effects from below.
      Yep, that makes sense. Now all “science” has to do is model “all the effects” of cloud formation and maybe, just maybe, in the next 200 years, we may have a “real climate model”. Who knows? If you get to that point, something out in the universe may throw a monkey wrench in the works.

    • Steven,
      one of your better comments.
      When you get to the next stage, understanding that tropospheric convective circulation in the Hadley, Ferrel and Polar cells would not accelerate but stall without radiative subsidence, then your model will be complete.
      Radiative gases are not neutral in our atmosphere. They are coolants.

      • They would not stall due to continuing uneven surface heating giving rise to density differentials in the horizontal plane.
        Radiative gases are neutral when one considers both their insulating effect AND their ability to radiate to space from within the atmosphere which causes less energy to be returned to the surface on descent than was taken up during ascent.

      • Radiative gases have a net cooling effect. Time to brush up on your radiative physics Stephen.
        Unless you understand that radiative gases cool the atmosphere you’re not in the league. “Neutral” is for losers. Currently you are little better than Momckton, a loser. I understand you are Australian. Therefore I am within my rights to demand better.

        • Konrad,
          Radiative gases both cool the atmosphere by radiating to space and warm the surface by slowing longwave radiation from the surface to space.
          The difference between kinetic energy taken up in convective ascent and kinetic energy returned to the surface in convective descent changes as necessary to adjust for the radiative characteristics of the atmosphere.
          The net thermal effect is zero but GHGs do reapportion radiation to space from within the atmosphere and radiation to space from the surface.
          That is all that they do.

  13. TS.6.2 Key Uncertainties in Drivers of Climate Change
    • Paleoclimate reconstructions and Earth System Models indicate
    that there is a positive feedback between climate and the carbon
    cycle, but confidence remains low in the strength of this feedback,
    particularly for the land. {6.4}
    “…remains low…” Since when? Fo-ever?
    IPCC AR5 acknowledges uncertainty about the magnitude of feedback.
    The plethora of uncertainties listed in TS.6 pretty much follows the uncertainties identified in the APS workshop findings.
    Read the homework assignment, folks.

  14. …and there will be some pathway, over time to equilibrium, by which the temperature response will increase (with net-positive feedbacks) or decrease (with net-negative feedbacks) compared with the instantaneous response.

    This again seems to underline a misunderstanding brought about by the inappropriate use of terms by IPCC.
    The pathway will *always* increase to equilibrium, even with the strongest -ve f/b. The difference is how quickly it reaches equilibrium and what the final offset is. There is no “instantaneous” response other than in dT/dt, it always takes time for temperature of a body to increase in response to a radiative change.
    I support this effort to clarify short-comings but there is a fundamental lack of understanding of feedbacks in much of this writing.

    • I am most grateful for the kind words of “wickedwenchfan”. What is striking about the discussion of our paper here at WUWT is how – with very few exceptions – those who are contributing are doing so in a genuine spirit of scientific enquiry. I welcome that very much, which is why I am grateful for Mr Born’s discussion of our paper, even if I do not agree with his conclusions.

  15. In response to “Mike”, the feedbacks and their influence and mutual amplification are well and clearly explained in our paper. One accepts that the word “instantaneous” is a term of art which incorrectly conveys the impression that a forcing brings about an immediate change in temperature, when in practice various homeostatic factors, notably the massive heat capacity of the ocean, damp the immediacy of the response.
    However, one should be clear that the action of net-negative feedbacks is to diminish, and not to augment, the instantaneous or (perhaps better expressed) zero-feedback response. And if there is a slowly-acting negative feedback, it may well be that the zero-feedback or Planck response will occur before the negative feedback has acted, in which event the path from zero feedback to equilibrium after all feedbacks have acted will be a negative path. For this reason, there is nothing in the equations that dictates “Mike’s” conclusion that “the pathway will ALWAYS increase to equilibrium”.

    • Lord Monckton,
      You said:
      “temperature change – the output – is the very instrument by which the climate system self-equilibrates”
      I don’t think that is right as per my post at 3.36pm.
      The instrument by which the climate system self-equilibriates is by way of variations in the balance between energy taken up in adiabatic ascent and energy brought down in adiabatic descent.
      The more GHGs are present the greater the difference because the more radiation that escapes to space from within the atmosphere the less can be brought down again.

    • “..the instantaneous or (perhaps better expressed) zero-feedback response. ” There terminology is a problem here. Planck f/b is not the “zero feeback” it is the most powerful feedback that ensures a workable climate. The others that everyone is arguing about just tweak it up or down a bit.
      There are probably no “slow acting” f/b on the time scales being discussed ( decadal to centennial ) , there may be a later cooling but this would be due to thermal intertia of the oceans. The negative f/b induced by surface warming can easily last longer than the initial warming disturbance. The opposite of this can be seen after Pinatubo when the warming feedback continued after the aerosols had subsided. ( This is the explanation of errors noted in Santer 2014, which to be fair he did document, even though he failed to realise his errors). But that’s probalby already stepping outside the bounds of the simplistic Bode model.
      Be careful how much of the IPCC elixir you drink, there is a lot less “polar amplification ” in Antarctica. That’s just part of the AGW spin. Antarctica is supposed to be warming too but the sea ice is growing. AGW does not produce the “solar see-saw” which is probably more of the reason that the Arctic was warming quicker.

      • No, the Planck “feedback” is not a feedback, and it is rightly not treated in the same way as the true temperature feedbacks in the central equations that determine climate sensitivity.
        And polar amplification is what one would expect – all other things being equal. The fact that the Arctic has been warming and the Antarctic cooling suggest that such little warming as has occurred is not yet global.

      • the Arctic has been warming and the Antarctic cooling suggest that
        =======
        there was a recent paper that showed the energy escaping from each N/S hemisphere was essentially equal to a fraction of a percent. As such, heat must flow from one hemisphere to the other to maintain this balance due to orbital mechanics and differences in land mass.
        this would explain the polar see-saw. heat flowing from one hemisphere to the other to maintain the radiative balance will alternately warm and cool the opposing poles.

  16. “…we then adopted assumptions that seemed to us to be less inappropriate, and ran the model to reach our own estimates of climate sensitivity: around 1 K per Co2 doubling.”
    I think that is a far closer estimation than IPCC, globally. It is much less in the tropics.

  17. I asked at Science of Doom if
    “Temperature at night drops rapidly and goes up during the day depending on the level of Greenhouse gases.
    The temperature that it rises to during the day must reflect the amount of GHG and the sub amount of CO2 present,
    To my mind this should mean there is no real lag time with respect to a GHG level dictating a temperature level.
    Secondly energy in equals energy out so the amount of energy present to heat the air doesn’t change.
    * Therefore is it possible to have a hot blanket of air and a colder land or sea temperature? in a warming [atmospheric] world?
    Does the earth and sea have to heat up over time or if the energy is in balance would it just be the air that gets a few degrees warmer and which would “go away at night”.
    Y”Precisely because the effective radiating temperature at the characteristic-emission layer is near-constant under an increase in the mean altitude of the characteristic-emission layer, and precisely because the lapse rate of atmospheric temperature with altitude is very nearly constant under that increase, it is the surface temperature, not the effective radiating temperature at the characteristic-emission altitude, that rises in response to that increase in altitude.”
    *The second question is why do you have to be so sure about GHG and water vapor only being an add on forcing. As you know there is a lot going on about clouds and balance of temperature by more clouds more albedo to the stage where such feedback might be negative.
    If there is more than one effect possible in a complex system you should not rule out other possibilities no matter how much you attempt to prove AGW.
    On this score you state
    “GCMs all come to the conclusion that more GHGs results in a hotter world (2-6ºC). the result is clear and indisputable.”
    This fails the science test with a range of 2.0 to 6.0 degrees.
    CO2 causes a known rise in temperature [GHG effect] which you could state independent of models.
    The fact that given said CO2 input GCM can range 4.0 degrees in their expected effect make them neither clear nor indisputable.
    Sorry for my intemperate attitude.
    pleased for any scientific feedback, particularly on the first question which is ignorant rather than evil.

  18. “Mike”, who kindly prefers our best estimate of climate sensitivity to that of the IPCC, is correct to point out that any warming will be less in the tropics than elsewhere, because the climate system advects the warmth poleward from the tropics, so that at the poles there will be about twice as much warming as the global average: this is known as “polar amplification”.

  19. Sorry for adding too much above
    I was wanting to say
    Your answer
    “Precisely because the effective radiating temperature at the characteristic-emission layer is near-constant under an increase in the mean altitude of the characteristic-emission layer, and precisely because the lapse rate of atmospheric temperature with altitude is very nearly constant under that increase, it is the surface temperature, not the effective radiating temperature at the characteristic-emission altitude, that rises in response to that increase in altitude.”
    seems to explain my question
    Rest of response was to SOD , not you.

  20. From a layman’s point of view, if feedbacks are >1 then oceans should already be at James Hansen’s (since withdrawn) boiling scenario. If CO2 caused water vapour to increase to a point where the water vapour caused more warming than the CO2 the warming from the water vapour would cause yet more increases in water vapour which must also have feedback loops greater than 1 (water vapour does after all have a greenhousyness six times greater than CO2 assigned to it) leading to a compounding self generating warming ad infinitum.

    • James Hansen’s claim that Venus’s surface temperature 225% the gray body temperature in its orbit is a risible falsehood the failure to universally repudiate of which is emblematic of the utter nonscience of 97% of those who label themselves climate scientists . No spectrum exhibits such an extreme heat gain with respect to the solar spectrum . See http://cosy.com/Science/HeartlandBasicBasics.html .

      • Oh, I am no James Hansen fan (I’m a Wicked Wench fan 🙂 ). In fact it his extreme past statements that were among the first things that had me questioning the CAGW assertions.
        My (I hope) common sense logic had me looking at the CO2 concentrations (96.5%) and mass of CO2 in comparison to Earth (92 times the mass by memory which equalled approx 230,000 times the number of CO2 molecules compared to Earth) of Venus and following the trajectory of the IPCC future temperature graphs. My conclusion was that according to the IPCC worst case projections (hockey stick) Earth’s temperature would surpass that of Venus before CO2 concentrations hit 1% of the atmosphere. That to me was absurd! Even the linear graphs had Earth surpassing Venus at 5% CO2 concentration (those showing 2C rise for 560ppm).
        I am still waiting for a rebuttal of any kind from any scientist about my observations. I would welcome one, to be honest, as my friends keep telling me I must be missing something and surely the scientists have an explanation. Maybe. Prove me stupid and simplistic, someone. Anyone!

      • Wick, how many doublings would be required to reach the Venus concentration?
        1% (10,000 PPM) of the atmosphere is about five plus doublings. This is about 5 C using the direct affect, and about 15 degrees C using approximate mean IPCC feedbacks.
        \
        The linearity of sensitivity based on doubling CO2 is certainly a legitimate subject. The CAGW Venus analogy has been quite thoroughly criticized with atmospheric density and proximity to the Sun being primary reasons for Venus T.

      • I often hear that the temp, relationship with CO2 is logarithmic, but the alarmist graphs do not reflect this. Follow the actual trajectory of the graphs they show and we do not see a doubling of CO2 for each 1C or 2C or whatever the scale proposed by those on here. What we see is a linear trend for the Luke warm projections or a hockey stick compounding trend for the alarmist trends. If the graph trajectories did in fact show the five doublings for give equal increases, all of us here could leave the augment up to academics to haggle over details as the fearful “C” in CAGW would cease to exist.
        The reason given for the linear graph or hockey stick graphs is water vapour feedbacks. My response: did the water feedback not exist between 1850 and today?
        Do you see my point? Regardless of what CO2 does to water, it is included in the mathematics behind the graph that explain 280ppm to 400ppm=+0.8C if the projection for 520ppm=+1.6C then it also follows that 1480ppm=+8C and 12280ppm (1.22%)=+80C!
        That is THEIR graph not mine, and that is for just a linear relationship. It is much worse in the hockey stick.
        The revaluation in these graphs is obscured because usually the temperature is not shown with CO2 concentrations but with years, 2C by 2100 or whatever. But in the text of the article showing the graph will be the date of the expect “doubling of pre industrial levels of CO2” as well. Simply place 560ppm on said date and you will discover the graphs trend is always linear or compounding, never logarithmic. Again, I call out the common sense rebuttal to the alarmists. If the trajectory of your graph shows seas boiling at CO2 concentrations that are approximately the same as my outward breath, isn’t that a sign that you are barking mad?

  21. Where Complex Models Go Wrong
    It’s not complex models that go wrong; it’s simpleton modelers that are the problem.
    Let’s assume that modelers have a hotline to Heaven, and by the grace of God are able to assemble a model that accounts for every little forcing function, feedback loop, and so on.
    All that model is going to be able to provide is a qualitative description of how climate might behave in the future.
    To believe that the model is going to give the modeler the power to actually forecast the climate is absolutely imbecilic.
    Oops … gotta go … the Lord’s on the Line …

    • Models are programmed on deterministic machines using deterministic code attempting a veneer of non-determinism by using pseudo-random number generators, which are so-called because the code generating them is necessarily deterministic.

      • Even a chaotic object is deterministic, but the solecism of the modellers is to assume, even in the absence of any data describing the sub-grid-scale processes without which the deterministic object that is the climate is not determinable, that they can predict the evolution of that object when on the evidence of the failure of their predictions to date it is plain that they cannot.

      • Chaotic objects are deterministic at infinity. Anything less and they are not. So, while one can theoretically predict future climate, for all practical purposes the prediction will show no more skill than a coin toss.
        However, the IPCC models show one fascinating trait. They universally predict too high. The odds of this happening by chance are astronomically small.
        I for one would like to see MOB or Briggs write an article on just how unlikely it is that 100+ climate models could all be wrong in the same direction.

  22. Monckton of Brenchley here is my take on how the climate may change.
    Here is what I have concluded. My explanation as to how the climate may change conforms to the historical climatic data record which has led me to this type of an explanation. It does not try to make the historical climatic record conform to my explanation. It is in two parts.
    PART ONE
    HOW THE CLIMATE MAY CHANGE
    Below are my thoughts about how the climatic system may work. It starts with interesting observations made by Don Easterbrook. I then reply and ask some intriguing questions at the end which I hope might generate some feedback responses. I then conclude with my own thoughts to the questions I pose.
    From Don Easterbrook – Aside from the statistical analyses, there are very serious problems with the Milankovitch theory. For example, (1) as John Mercer pointed out decades ago, the synchronicity of glaciations in both hemispheres is ‘’a fly in the Malankovitch soup,’ (2) glaciations typically end very abruptly, not slowly, (3) the Dansgaard-Oeschger events are so abrupt that they could not possibility be caused by Milankovitch changes (this is why the YD is so significant), and (4) since the magnitude of the Younger Dryas changes were from full non-glacial to full glacial temperatures for 1000+ years and back to full non-glacial temperatures (20+ degrees in a century), it is clear that something other than Milankovitch cycles can cause full Pleistocene glaciations. Until we more clearly understand abrupt climate changes that are simultaneous in both hemispheres we will not understand the cause of glaciations and climate changes.
    . My explanation:
    I agree that the data does give rise to the questions/thoughts Don Easterbrook, presents in the above. That data in turn leads me to believe along with the questions I pose at the end of this article, that a climatic variable force which changes often which is superimposed upon the climate trend has to be at play in the changing climatic scheme of things. The most likely candidate for that climatic variable force that comes to mind is solar variability (because I can think of no other force that can change or reverse in a different trend often enough, and quick enough to account for the historical climatic record) and the primary and secondary effects associated with this solar variability which I feel are a significant player in glacial/inter-glacial cycles, counter climatic trends when taken into consideration with these factors which are , land/ocean arrangements , mean land elevation ,mean magnetic field strength of the earth(magnetic excursions), the mean state of the climate (average global temperature gradient equator to pole), the initial state of the earth’s climate(how close to interglacial-glacial threshold condition it is/ average global temperature) the state of random terrestrial(violent volcanic eruption, or a random atmospheric circulation/oceanic pattern that feeds upon itself possibly) /extra terrestrial events (super-nova in vicinity of earth or a random impact) along with Milankovitch Cycles.
    What I think happens is land /ocean arrangements, mean land elevation, mean magnetic field strength of the earth, the mean state of the climate, the initial state of the climate, and Milankovitch Cycles, keep the climate of the earth moving in a general trend toward either cooling or warming on a very loose cyclic or semi cyclic beat but get consistently interrupted by solar variability and the associated primary and secondary effects associated with this solar variability, and on occasion from random terrestrial/extra terrestrial events, which brings about at times counter trends in the climate of the earth within the overall trend. While at other times when the factors I have mentioned setting the gradual background for the climate trend for either cooling or warming, those being land/ocean arrangements, mean land elevation, mean state of the climate, initial state of the climate, Milankovitch Cycles , then drive the climate of the earth gradually into a cooler/warmer trend(unless interrupted by a random terrestrial or extra terrestrial event in which case it would drive the climate to a different state much more rapidly even if the climate initially was far from the glacial /inter-glacial threshold, or whatever general trend it may have been in ) UNTIL it is near that inter- glacial/glacial threshold or climate intersection at which time allows any solar variability and the associated secondary effects no matter how SLIGHT at that point to be enough to not only promote a counter trend to the climate, but cascade the climate into an abrupt climatic change. The back ground for the abrupt climatic change being in the making all along until the threshold glacial/inter-glacial intersection for the climate is reached ,which then gives rise to the abrupt climatic changes that occur and possibly feed upon themselves while the climate is around that glacial/inter-glacial threshold resulting in dramatic semi cyclic constant swings in the climate from glacial to inter-glacial while factors allow such an occurrence to take place.
    The climatic back ground factors (those factors being previously mentioned) driving the climate gradually toward or away from the climate intersection or threshold of glacial versus interglacial, however when the climate is at the intersection the climate gets wild and abrupt, while once away from that intersection the climate is more stable. Although random terrestrial events and extra terrestrial events could be involved some times to account for some of the dramatic swings in the climatic history of the earth( perhaps to the tune of 10% ) at any time , while solar variability and the associated secondary effects are superimposed upon the otherwise gradual climatic trend, resulting in counter climatic trends, no matter where the initial state of the climate is although the further from the glacial/inter-glacial threshold the climate is the less dramatic the overall climatic change should be, all other items being equal.
    The climate is chaotic, random, and non linear, but in addition it is never in the same mean state or initial state which gives rise to given forcing to the climatic system always resulting in a different climatic out-come although the semi cyclic nature of the climate can still be derived to a degree amongst all the noise and counter trends within the main trend.
    QUESTIONS:
    Why is it when ever the climate changes the climate does not stray indefinitely from it’s mean in either a positive or negative direction? Why or rather what ALWAYS brings the climate back toward it’s mean value ? Why does the climate never go in the same direction once it heads in that direction?
    Along those lines ,why is it that when the ice sheets expand the higher albedo /lower temperature more ice expansion positive feedback cycle does not keep going on once it is set into motion? What causes it not only to stop but reverse?
    Vice Versa why is it when the Paleocene – Eocene Thermal Maximum once set into motion, that being an increase in CO2/higher temperature positive feedback cycle did not feed upon itself? Again it did not only stop but reversed?
    My conclusion is the climate system is always in a general gradual trend toward a warmer or cooler climate in a semi cyclic fashion which at times brings the climate system toward thresholds which make it subject to dramatic change with the slightest change of force superimposed upon the general trend and applied to it. While at other times the climate is subject to randomness being brought about from terrestrial /extra terrestrial events which can set up a rapid counter trend within the general slow moving climatic trend.
    .
    Despite this ,if enough time goes by (much time) the same factors that drive the climate toward a general gradual warming trend or cooling trend will prevail bringing the climate away from glacial/inter-glacial threshold conditions it had once brought the climate toward ending abrupt climatic change periods eventually, or reversing over time dramatic climate changes from randomness.
    NOTE 1- Thermohaline Circulation Changes are more likely in my opinion when the climate is near the glacial/ inter-glacial threshold probably due to greater sources of fresh water input into the North Atlantic.

  23. Lord Monckton,
    I have great appreciation for your work, and for your pachydermal ability to take the abuse hurled in your direction.
    You deserve a wee bit of respite.
    I would very much enjoy sharing a few of my cartoons with you, if the gentle readers of WUWT will permit my reposting of them for the occasion.
    http://www.maxphoton.com/ice-capades/
    http://www.maxphoton.com/linear-thinking-cyclical-world/
    http://www.maxphoton.com/cloud-over-humanity/
    http://www.maxphoton.com/what-a-waste/
    http://www.maxphoton.com/before-nuts/
    http://www.maxphoton.com/chicken-little/
    http://www.maxphoton.com/anthropogenic-climate-change/
    And lastly, although you are true gentleman, perhaps this might speak to you on occasion …
    http://www.maxphoton.com/digitization/
    Keep up the good fight!
    Your friend,
    Maxwell C. Photon

  24. Christopher Monckton,

    We assumed ad argumentum that all warming since 1850 was anthropogenic, ran our model and found that the variance between its predicted warming to 2014 and the observed outturn was nil, implying – as explicitly stated in the paper, that there is no committed but unrealized global warming in the pipeline.

    You refer us to Table 4. of MSLB (2015), wherein I find that the only tunable model parameters you hold constant are the CO2 fraction (qₜ), and the CO2 forcing change (ΔFₜ). The table supplies three different values for the transience fraction (rₜ) which is sensible since one would not expect such a massive system to respond immediately to a gradual change in external forcing on the order of 0.1 W/m^2 per decade. You propose that rₜ is a function of the feedback sum (f) over some time interval t, and Table 4 does indeed map rₜ to three different values for f, which I believe is also reasonable. [1]
    The third tunable parameter you vary in Table 4 is the equilibrium climate sensitivity parameter (λ∞). You discuss λ∞ only very briefly in the body of the paper, I quote the relevant section in full:
    4.6 The equilibrium climate-sensitivity parameter λ∞
    The equilibrium-sensitivity parameter λ∞, in K W -1 m 2 , is the product of the Planck parameter λ₀ = 3.2 -1 K W -1 m 2 and the system gain factor Gₜ. Climate sensitivity ΔT∞ is the product of λ∞ and a given forcing ΔF∞.

    By this, for there to be “no committed but unrealized global warming in the pipeline” — according to your model — means that present-day temperatures must represent ΔT∞ for the 1850-2014 interval, implying a value for rₜ as near to unity as not to make a difference, yet 0.6 is the value shown in Table 4 as the best fit to observation. As such, I do not believe that your conclusion follows from premises.

    [1] MSLB (2015) notes that the relationship between rₜ and f are derived from Ref. 38: Roe G (2009) Feedbacks, timescales, and seeing red. Ann Rev Earth Planet Sci 37:93–115, which I’ve not reviewed.

      • Christopher Monckton,
        MSLB (2015) Table 4 sets rₜ to 0.6.
        says about rₜ:
        4.8 The transience fraction rₜ
        Not all temperature feedbacks operate instantaneously. Instead, feedbacks act over varying timescales from decades to millennia. Some, such as water vapor or sea ice, are short- acting, and are thought to bring about approximately half of the equilibrium warming in response to a given forcing over a century. Thus, though approximately half of the equilibrium temperature response to be expected from a given forcing will typically manifest itself within 100 years of the forcing (Fig. 4), the equilibrium temperature response may not be attained for several millennia [38, 39]. In Eq. (1), the delay in the action of feedbacks and hence in surface temperature response to a given forcing is accounted for by the transience fraction rₜ. For instance, it has been suggested in recent years that the long and unpredicted hiatus in global warming may be caused by uptake of heat in the benthic strata of the global ocean (for a fuller discussion of the cause of the hiatus, see the supplementary matter). The construction of an appropriate response curve via variations over time in the value of the transience fraction rₜ allows delays of this kind in the emergence of global warming to be modeled at the user’s will.

        Emphasis added. That you have achieved a good fit from 1850-2014 using a transience fraction of 0.6 implies that four tenths of the expected ΔT∞ from the change in radiative forcing since 1850 has not yet been realized. That’s what the text above says, that’s what the model proposed in Eq. (1) says. The conclusion, ” … there is no committed but unrealized global warming in the pipeline …” appears incompatible with your model so long as rₜ is set to anything < 1 by the user, as you have done.
        If there is some other place in the paper which explains this apparent contradiction, I'd be pleased if you would provide a specific quote.

      • Mr apGates and I are labouring under distinct interpretations of the meaning of committed but unrealised warming. As it is used by the IPCC, it means warming that would have been realised not at equilibrium some 3000 years away but by now.
        There has been 0.9 K warming since 1750, 0.7 K of which has occurred since 1950, when we might have begun to influence global temperature. Now, as Roe’s graph in the head posting and our worked examples in the paper show, he and the IPCC would expect half of the equilibrium warming from the forcings since 1959 to occur within 100 years of that forcing: but, even on the assumption that the forcing since 1950 has been linear, the mean start date for the anthropogenic forcing is 1983, just a third of a century ago.
        The modellers, therefore, are saying the would have expected a further 0.6 K of warming to have occurred by now. For the reasons clearly set out in our paper, we disagree.

      • Christopher Monckton,

        Mr Gates and I are labouring under distinct interpretations of the meaning of committed but unrealised warming.

        I think the definition is rather simple: unrealized means warming which would occur if ΔF — any forcing — immediately stabilized at zero and remained unchanging long enough for the balance of the climate system to reach equilibrium. This is a conceptual construct only; such a thing could not conceivably occur in the system with or without any putative human influence. However, that is the concept MSLB (2015) discusses as the transience fraction, rₜ, with which I have no dispute.
        Again, what I do take issue with follows. Your Fig. 4 sets the value of that parameter as 0.6. Implicit on the assumptions of the model, that means that four tenths of the expected warming from increased forcings already experienced has not yet occurred. That is not consistent with the concept of “no unrealized warming” as I understand those terms in plain English.
        Kindly refrain from discussions of IPCC definitions or models, which I see as an unnecessary distraction, until you have answered to your own model, definitions and the apparently conflicting conclusion you have drawn from them.

      • Mr Gates should understand that when we considered the IPCC’S assertion that there was 0.6 K warming in the pipeline it was relevant to use the IPCC’S definition.
        The 2.3 W/m2 forcing from our sins of emission since 1750 will cause 2.3 X .9 = 2 K warming at quilibrium using the IPCC’S overblown climate sensitivity. Yet just 0.9 K has occurred to date, leaving 1.1 K to come, of which the IPCC says 0.6 K should have occurred by now. Our paper considered whether the latter figure was appropriate.

  25. It is of course obvious that the Bode graph as it stands does not really represent even an electronic circuit. There are obvious asymptotic bounds preventing an infinite positive

    Indeed, there are always overwhelming -ve feedbacks in any system that is long term stable. ( Climate seems to qualify there ).
    In the circuit analogy, the output is only linear within a certain range beyond which the output is clipped. In climate it is highly non-linear Planck feedback. Now GCMs do have T^4 equations for Planck and Paul_K posted a discussion over at Lucia’s Blackboard a couple of years back about the “curvilinear” response of models, so I don’t think they are producing Bode like output.
    Again the main question is which way the also-ran feedbacks tweak the Planck effect. This is what IPCC stupidly call “net-positive” or “net-negative”, in reality it is a case of ‘even more negative’ or ‘a bit less negative’.

    • The Planck “feedback” is not a feedback. It is a climate-sensitivity parameter. It is not, repeat not, treated like a true temperature feedback in the equations. Read our paper.
      And the GISS ModelE, to name but one, definitely uses the Bode system-gain equation. See Hansen (1984, 1988).

  26. “However, the equation actually used in the climate models (including ours) is, like it or not, the Bode system-gain equation.”
    There is no GAIN in the climate system, it is comprised of passive materials which are the electrical equivalent of resistors, capacitors and inductors. To create gain in an electronic circuit it requires an external source of energy. See how well the volume control knob on your stereo amplifier works when there is a power outage. NONE of the feedback equations apply.
    What the climate science community wrongly calls feedbacks are in fact just coupled interactions. Any energy that causes warming in one localized location HAD to come from someplace else. Ignoring this violates the law of conservation of energy.
    However, you do get points for barking way up a different branch of the same old wrong tree.
    Cheers, KevinK

    • KevinK raises an interesting matter of definition. What is “Gain”?
      In a system influenced by feedbacks, there are two gain factors: the closed-loop gain (which, in the climate is the product of the Planck sensitivity parameter and the feedback sum) and the open-loop or system gain, which (by the Bode system-gain equation) is the reciprocal of (1 minus the closed-loop gain).
      Now, if I add CO2 to the atmosphere and the atmosphere warms, it can carry near-exponentially more water vapor, a greenhouse gas. If it does carry the extra that it can carry (and the data to date are divided on whether and to what extent it does), then that is a temperature feedback. If the ocean warms (as it is, a little bit), then it outgasses CO2, a greenhouse gas, and that is another temperature feedback. Tot up all these feedbacks and multiply by the Planck parameter, and you get the closed-loop gain. So, contrary to KevinK’s suggestion, it is not appropriate to say there is no gain in the climate system.

      • Sir, with respect; “If it does carry the extra that it can carry “, where does the “extra” come from ????
        In your stereo amplifier all those extra electrons come in from the wire you plugged into the wall outlet (if you followed the carefully translated Chinese instructions). Without that wire there is no source of any “extra” anything.
        There is no “gain” (as understood by the electrical engineering profession, those that created these equations you are misapplying) in the climate.
        Cheers, KevinK.

      • KevinK asks where the additional water vapor in a warming atmosphere might come from. The major source would, of course, be the ocean.
        While one agrees that “gain” in the climate is not the same thing as “gain” in an electronic circuit, there are such things as temperature feedbacks in the climate, but, for the reasons spelt out in our paper and further considered in the head posting here, their mutual amplification to obtain the system gain factor using the Bode equation seems improper and likely to be responsible for the wild exaggerations of climate sensitivity in the models that are becoming more evident with each passing month.

      • Alex asks what is meant by the atmosphere carrying more water vapor. One of the few proven results in the slippery subject that is climatology is the Clausius-Clapeyron relation, which says that, subject only to a weak dependence on temperature in the denominator, the propensity of the space occupied by the atmosphere to hold water vapor – known as its carrying capacity for water vapor – increases exponentially as that space warms.
        However, as the head posting demonstrates, not all datasets show the column water vapor increasing. The differences between the datasets are considerable because water vapor, unlike CO2, is not well mixed in the atmosphere.
        And, though some modellers do not seem to realise this, merely because the warmer atmosphere can carry more water vapor there is no requirement that it must.

    • Kevin,
      Your ruminations on the defects of the electrical gain analogy, led me to wonder about other types of positive feedbacks in nature that might provide a superior analogy for the catastrophic global warming model. I came up with these:
      – Avalanches
      – Growth of bacteria colonies on an agar plate.
      – Development of silver halide crystals in a darkroom
      – Bursting of a levee, or a dike by floodwaters.
      – Cutting of alluvial river bends by a current.
      – clogging of the downspout of a rain gutter.
      Of those six, the one I like the best as an analogy to the proposed runaway global warming is clogging of the downspout of a rain gutter. That actually seems a fairly decent analogy to the catastrophic model that is argued. The idea is that the flow through the downspout is similar to the IR radiated back into space, and the rainfall is analogous the the visible light that penetrates to the earth’s surface. Dirt and leaves are the AGW gases. More dirt and leaves causes increased clogging, which slows the flow, which causes even more clogging. If the gutter gets clogged, a catastrophic build-up occurs.
      The problem of course is that all positive feedback mechanisms have some limit. In the case of the climate model, the obvious limit is the increase in cloud cover that would result from more water evaporation. The high albedo of the clouds reduces the incoming visible radiation, and a feedback limit is reached.
      Simply sitting here noodling, it has always seemed more likely that the feedback is actually negative, and therefore stabilizing. Increased evaporation would seem likely to have greater effect by reducing incoming radiation due to higher cloud albedo, more than it would to produce a global warming effect by reflecting IR back to the ground.

  27. In fig. 5 of the paper, the horizontal axis refers to closed loop gain from -1 to +2.
    Can we have a minus gain? and what does it mean?
    I can understand op-amps with a gain of -2 etc, but that means a gain of 2 with a signal inversion.
    Gain is a unit-less ratio: output / input.

    • Mr Richards asks whether one can have a negative loop gain. Yes, one can. The concept of negative feedback (and hence of negative loop gain) was first posited on the back of a newspaper by R.S. Black at Bell Labs (if I remember aright), while he was traveling on the Lackawanna Ferry. The labs still preserve the cutting. See Roe (2009) for the historical account.
      In the climate, if the sum of the individual feedbacks is negative, then the loop gain must also be negative, because it is the product of the feedbacks and the Planck parameter.
      Gain is indeed a unitless ratio. In the climate, the feedbacks are measured in Watts per square meter per Kelvin and the Planck parameter (properly expressed) is in Kelvin per Watt per square meter. The product of the two is, therefore, unitless, as shown in Fig. 5.

  28. What an awesome response. Kudos to Mr. Born for having the cajones to post the original question and giving us the opportunity to behold the answer.

  29. @KevinK March 16, 2015 at 4:39 pm
    I see the power source for our planet rise every morning!
    To say that the earth’s climate does not respond similar to a proportionally controlled system is, in my opinion, ignoring obvious data. Plots of long term temperature records show many, many cases of damped oscillations that give the appearance of a system of feedback that returns the temperature to a long term average value.

    • Steven, GAIN as seen in an electronic circuit requires the application of an external energy source ABOVE and BEYOND the signal being amplified. Amplifiers require energy to operate, resistors do not require energy to operate.
      Trying to apply feedback equations from electronic circuits to the climate is wrong.
      The energy arrives from the SUN, it warms things up, the warm things cool back down. There is nothing in the climate that amplifies the amount of heat.
      Cheers, KevinK.

      • Kevin actually makes a very good point here, for example you need…say + and – 12 volts to power the amp and then you need to apply the signal, a signal which is amplified through the biasing of transistors etc from the 12 volts. To stop the output signal rising too high the out put is then feed back to the input (inverted) to reduce the out put.
        The first stage is an amp to make things bigger then you have the feed back to make things smaller (negative) if the output gets too small then the feed back will make it bigger (positive).
        In this case is the sun the equivilant of 12 volts or is it the input signal, whichever it is it cannot be both.
        Cheers

      • What about resistance? Anything that increases the residence time of energy in the system (Land Ocean / Atmosphere) while input (TSI in this case considered for the purposes of this paper to be steady) remains the same, adds energy or heat to the system.

    • “Plots of long term temperature records show many, many cases of damped oscillations that give the appearance of a system of feedback that returns the temperature to a long term average value.”
      Steven, you are mistaking a resonance condition for a feedback situation.
      A plain old tuning fork exhibits resonance (it vibrates at one frequency much more easily than other frequencies). A tuning fork when struck (an input of energy with many frequencies) will “ring” at one frequency. It converts all of the energy coming in at all frequencies to one selective output frequency. There is no gain involved, the energy out (the tone) is less then the energy in (striking it).
      NO GAIN WITHOUT EXTERNAL ENERGY.
      Cheers, KevinK.

      • Kevin, warming of the surface of the earth is our subject. If we directly warm it with the sun, and the radiated heat from the surface is intercepted by carbon and water vapor molecules and partly radiated back to the surface, it is somewhat like a leaky blanket keeping more of the heat at the surface than would be there if it were simply radiated from the surface to outer space. This results in more water vapor being evaporated and even some more CO2 exsolving from the seawater. There is a simple warming (modulated to be sure at certain states of the warming by convective cooling and a host of other complications). Meanwhile this activity results in a cooling of the stratosphere that is robbed of its hit by interception near the surface. What we end up with in the net is that the radiation energy entering the system, basically equals the energy leaving at equilibrium with heating and cooling above and below the supplied energy but averaging equality.
        To be clear, what is being discussed here is a wiggly surface temperature trace at the bottom of the atmosphere that, even though it has been egregiously tortured by warmist impatience to get it to a crisis, is the warming that a steady sun can effect with help from CO2 and H2O vapor. The effect, as mentioned, sets up negative feedbacks at a certain point that limit, halt or reverse warming for varying periods. Definitely, the electronic circuit doesn’t have these other specific side effects and maybe Bode is the wrong analogy, partly because the amplifier is the whole system, whereas the climate is just a part of the system.

  30. Having posted previously both criticism and praise of this paper over at Judith Curry’s, plus having received the honor of a direct response there from Lord Monckton, i choose to refrain from further debate–
    Except for one point that Judiths inability post the rearranged math mostly missed. The Monckton term 1/(1-lambda0 *gt) is mathematicaly equivalent ( using their own paper definitions) to Bode (1/[1-f]). That means their equation reduces to the Bode equation they criticize, but within the ‘well behaved’ parmeter regime) times a different way to calculate the ~1.2 Planck constant that Lindzen uses (deltaT = 1.2*(1/[1-f]). Now, the Monckton equation is equally/more useful, especially when ‘better’ estimates of the transience fraction rsubt and f ( lambda0 times gsubt) are plugged in. I remain a fan of the paper despite such quibbles. Because with observational parameterization, it agrees with the newer observational ECS.
    And, the paper’s alternative derivation of lamda0 = 0.31 is wonderful, precise, and IMO correct. Plus quite instructive about how the GHG effect actually works, Skydragons.

    • Most grateful to Mr Istvan for his – as always – interesting comment. Yes, indeed, we have used the Bode equation in our model, but we have also expressed concerns about its applicability to the climate, particularly in the IPCC’s posited regime of strongly net-positive feedbacks. For if the equation requires modification (and we think it does), then it is at the singularity in the region of a closed-loop gain of unity that some asymptotic bounds should be imposed on the temperature output. We are still meditating on how to obtain credible empirical values and theoretical justification for such bounds. in the meantime, the equation works well enough for negative or weakly net-positive feedback sums.
      I am glad Mr Istvan finds our model helpful. And I am particularly glad he welcomes our method of deriving the Planck parameter lambda-zero (we find the IPCC correct in its value for lambda-zero). For it took me many years to track down how this parameter ought to be derived: virtually everyone who used it actually had no idea.

      • Bode only applies to small perturbations in linear time-invariant single-variable systems. Whereas, Perkins and Cruz have provided a generalized sensitivity operator applicable to arbitrary parameter changes in multivariate nonlinear time-varying systems.
        Cruz, J. B., Jr. “Feedback Systems,” 1972.
        Cheers

  31. I posted this on another thread today and it is the way I look at this.
    —————-
    The new paper by Stephens et al 2014 on Earth’s Albedo as measured by satellites is a very significant paper.
    http://webster.eas.gatech.edu/Papers/albedo2015.pdf
    The NH and the SH Albedo is almost identical despite there being more high Albedo land surface in the NH.
    Throughout the year, the Earth’s Albedo hardly varies at all despite a large difference in the total solar irradiance received by the Earth through that year and a larger temperature difference in the NH summer versus the SH summer.
    Clouds appear to be the main stabilization mechanism (although why that would be is missing in my opinion).
    A comment a JudithCurry’s website caught my eye. That climate sensitivity should only be considered the CO2/GHG value only before any feedbacks until someone proves that the feedbacks are operating as surmised.
    Climate science has the cloud feedback at a semi-large positive value (0.7 W/m2/K) that add’s roughly 1.0C to the 3.0C per doubling by itself. Here is how all the feedbacks multiply on top of each other calculated in the proper way using the Stephan Boltzmann equations at every single step to arrive at the 3.0C per doubling.
    http://s10.postimg.org/i9q1gnjfd/Global_Theory_and_Feedbacks_3_0_C.png
    It is now clear that the cloud feedback should definitely be set at Zero given the new Stephans paper. Nobody has been able to find a positive cloud feedback or at least there is both positive and negative feedbacks seen. Set to Zero.
    Ice-Albedo feedback seem clear enough. When it is warmer, ice melts, less reflection of sunlight. But doubled CO2 also produces a large vegetation response and just 1 degree of added greening in the low-mid-latitudes where all the deserts currently form would more than offset any melting at 75N or 75S. This new paper says that Albedo is more stable than that anyway. Set ice-Albedo back to Zero. Another 0.2C of the 3.0C per doubling is gone.
    The Lapse Rate feedback at about -0.9 W/m2/K appears to be completely opposite. The Tropopause is increasing in temperature far lower than the surface meaning that the lapse rate feedback is a positive value not a negative. This essentially means we should be less focussed on the tropopause and move all the measurements back to the surface and forget about lapse rates all together. Lapse Rate feedback Zeroed out (it was negative so this adds-back some to the warming).
    Water Vapor feedback is the biggest positive feedback at about +2.3 W/m2/K in the theory. I have been tracking water vapor numbers for a long time and although there is the Clausius Clapeyron relation which appears to be solid theory, water vapor is only increasing at something like 50% of that predicted in the theory. Set that back to 1.225 W/m2/K.
    Put all that together and we get just 1.65C per doubling.
    Or as the commenter at Judith Curry’s website says, maybe we should just consider the warming from CO2 alone (and I am now saying not for the Tropopause anymore but the Surface only) as the true climate sensitivity which is just 0.78C per doubling or 1.0C per doubling if one allows the positive water vapor feedback which appears to be showing up).
    Again calculated properly using the Stefan Boltzmann equation all the way.
    http://s4.postimg.org/gff2bl4wt/Empirical_Results_Feedbacks_1_0_C.png

    • Bill, on my comment to Monckton’s equation over at Judith’s, I gave physical reasons that (1) cloud feedback is about zero, and (2) water vapor feedback should be halved (from AR5 ~0.5). See detailed arguments in my ebook Blowing Smoke. Plug those in to a reasonable observational transcience parameter, and out pops Callendar’s 1938 ECS, or Lewis and Curry’s 2014 ECS. That is magical, in the sense of wildly dispararete times and calculation methods all agreeing. My own guess is 1.7-1.8 rather than 1.65. Good enough for government work!
      See also my reply to Lord Monckton upthread.

      • And one should not ignore the evidence for net-negative feedback. The near-perfect thermostasis of surface temperature for the past 810,000 years suggests either a giant feedback response to minuscule forcings (the official guess) or a minuscule feedback response to larger forcings.

    • Interesting that long term ocean feedbacks are not considered in the above, just as long term flux, positive or negative, in SW radiation reaching the SW selective oceans are apparently not considered?
      The earth atmosphere actually cools in the SH summer, despite an IMMENSE increase of some 90 watts per M sq. What does the earth’s albedo do in the SH summer? (More NH albedo yes, more SH cloud albedo?) How much SH summer energy is lost to the atmosphere via solar insolation SW entering the oceans?
      How much does an increase in atmospheric T and W/V reduce surface insolation and long term energy entering the oceans?
      I have only seen poster Konrad address some of these questions, and I have seen no one address the disparate residence time of different wave length SW radiation penetrating the ocean surface to up to 800′ depth.
      If we do not know the residence time of S/W radiation entering the oceans, we do not know how much energy a change in S/W ocean surface flux (positive or negative) can make to the earth’s energy budget.

      • Using my name (aka “Legion”) can get you censored at WUWT….
        But really, I’m just the dark haired boy who played the Tennessee flat top box (HP Elite Book Workstation) –

        But ride with me, fair warning, you better know you’re riding the Walbash cannonball –

  32. http://www.eoearth.org/files/115701_115800/115741/620px-Radiation_balance.jpg
    http://www.eoearth.org/view/article/152458/
    As the earth is a sphere TSI changes and greenhouse gas forcing changes should have the greatest effect in the tropical region. The warming in the last 30 years is the same pattern of warming (high latitude warming) that occurs in the paleo record cyclically. We know of course the cyclic warming in the paleo record was not caused by changes to atmospheric CO2. The obvious questions is what caused the past cyclic warming and cooling of the earth. (Hint solar magnetic cycle changes correlate with the past warming and cooling cycles.)
    The majority of the warming in the last 30 years has been in high latitude regions, which supports the assertion that the majority of the warming in the last 30 years was not caused by increases in atmospheric CO2 and was not caused by TSI changes.
    The majority of the warming in the last 30 years has caused by cloud modulation effects of solar wind bursts, primarily from coronal holes. What causes coronal holes to appear on the sun, at what latitude on the sun coronal holes appear at, and when in the solar cycle the coronal holes appear at is not known.
    Galactic cosmic rays (GCR) creates ions in the atmosphere. The amount of ions in the atmosphere changes cloud properties and cloud duration. The complication is solar wind bursts (primarily from coronal) holes create a space charge differential in the ionosphere which removes ions for 5 to 10 days which causes a reduction in cloud cover in high latitude regions and change in cloud properties in the tropical region. Solar wind bursts can inhibit the effect of high GCR.
    As this paper notes changes planetary temperature correlate to the number and interval between solar wind bursts. For some reason there are people who are fixated with the number of sunspots on the surface of the sun rather than direct measurement of the variables that modulate planetary clouds. There are some people how appear to try to block the resolution how does solar changes modulate planetary climate. Hint: Changes to clouds (extent, cloud properties, and cloud duration) and changes to wind speed.
    http://sait.oat.ts.astro.it/MmSAI/76/PDF/969.pdf

    Once again about global warming and solar activity
    Solar activity, together with human activity, is considered a possible factor for the global warming observed in the last century. However, in the last decades solar activity has remained more or less constant while surface air temperature has continued to increase, which is interpreted as an evidence that in this period human activity is the main factor for global warming. We show that the index commonly used for quantifying long-term changes in solar activity, the sunspot number, accounts for only one part of solar activity (William: Closed magnetic field) and using this index leads to the underestimation of the role of solar activity in the global warming in the recent decades. A more suitable index is the geomagnetic activity (William: Short term abrupt changes to the geomagnetic field caused by solar wind bursts, which are measured by the short term geomagnetic field change parameter Ak. Note the parameter is Ak rather than the month average with Leif provides a graph for. The effect is determined by the number of short term wind bursts. A single very large event has less affect than a number of events. As Coronal holes can persist for months and years and as the solar wind burst affect lasts for roughly week, a coronal hole has a significant effect on planetary temperature) which reflects all solar activity, and it is highly correlated to global temperature variations in the whole period for which we have data. ….
    …The geomagnetic activity reflects the impact of solar activity originating from both closed and open magnetic field regions, so it is a better indicator of solar activity than the sunspot number which is related to only closed magnetic field regions. It has been noted that in the last century the correlation between sunspot number and geomagnetic activity has been steadily decreasing from – 0.76 in the period 1868- 1890, to 0.35 in the period 1960-1982, while the lag has increased from 0 to 3 years (Vieira
    et al. 2001).
    …In Figure 6 the long-term variations in global temperature are compared to the long-term variations in geomagnetic activity as expressed by the ak-index (Nevanlinna and Kataja 2003). The correlation between the two quantities is 0.85 with p<0.01 for the whole period studied. It could therefore be concluded that both the decreasing correlation between sunspot number and geomagnetic activity, and the deviation of the global temperature long-term trend from solar activity as expressed by sunspot index are due to the increased number of high-speed streams of solar wind on the declining phase and in the minimum of sunspot cycle in the last decades.

    • @William Astley,
      It might be easier reading if your comments in quotes were set off with square brackets–[ ]–which is the norm. 😉

  33. Dear Lord Monckton;
    “While one agrees that “gain” in the climate is not the same thing as “gain” in an electronic circuit”
    Thank you for that admission.
    Will the climate science community now stop pretending to be electrical engineers….
    You’re making us real electrical engineers (this one degreed with decades of experience) look bad, all we admit to is the ability to keep the lights on (most of the time). We do not have the extraordinary amount of HUBRIS necessary to try and predict the weather at the end of this century. Of course maybe if we were less careful back in college and shocked ourselves a few more times with that old 220 Vac we might actually believe we could….
    Cheers, KevinK

  34. So where does water vapor, clouds, precip, evaporation/condensation, etc. fit into all of this? A greenhouse without water is a huge unstable hot box!
    TS.6.1 Key Uncertainties in Observation of Changes in
    the Climate System
    • There is only medium to low confidence in the rate of change of
    tropospheric warming and its vertical structure. Estimates of tropospheric
    warming rates encompass surface temperature warming
    rate estimates. There is low confidence in the rate and vertical
    structure of the stratospheric cooling. {2.4.4}
    • Confidence in global precipitation change over land is low prior
    to 1951 and medium afterwards because of data incompleteness.
    {2.5.1}
    • Substantial ambiguity and therefore low confidence remains in the
    observations of global-scale cloud variability and trends. {2.5.6}
    • There is low confidence in an observed global-scale trend in
    drought or dryness (lack of rainfall), due to lack of direct observations,
    methodological uncertainties and choice and geographical
    inconsistencies in the trends. {2.6.2}
    • There is low confidence that any reported long-term (centennial)
    changes in tropical cyclone characteristics are robust, after
    accounting for past changes in observing capabilities. {2.6.3}
    • Robust conclusions on long-term changes in large-scale atmospheric
    circulation are presently not possible because of large variability
    on interannual to decadal time scales and remaining differences
    between data sets. {2.7}
    IPCC doesn’t know.
    http://www.writerbeat.com/articles/3713-CO2-Feedback-Loop
    Barring some serious flaw in science or method, Miatello’s paper should serve as the death certificate for AGW/CCC.
    http://principia-scientific.org/publications/PSI_Miatello_Refutation_GHE.pdf
    The Greenhouse Effect and the Infrared Radiative Structure of the Earth’s Atmosphere
    Ferenc Mark Miskolczi
    Geodetic and Geophysical Institute, Hungarian Academy of Sciences, Csatkai Endre u. 6-8, 9400 Sopron, Hungary
    fmiskolczi@cox.net
    How much more does this ground have to be plowed? How much longer must we beat this most certainly dead horse? As long as the money wheel goes around and around?

    • Nick, we are beating a dead unicorn, except some folks are desperately looking for signs of life out of said unicorn, WAIT ,WHAT’S THAT I HEAR, did that unicorn just exhale one little tiny breath, WHY YES IT DID, It’s right there in my peer reviewed computer model…..
      It is fun, a little diversion from real world tasks, engage the unicorn beaters for an hour or so once in a while. Surely there is one last breath left in that unicorn….
      Heck, we have peer reviewed science based on electrical engineering principles whose authors admit “well, it’s not really like an electrical circuit”…… OH KAY, whatever….
      Cheers, KevinK

  35. Crakar24 wrote;
    “In this case is the sun the equivilant of 12 volts or is it the input signal, whichever it is it cannot be both.”
    The Sun is the signal, and there ain’t no stinking +/- 12 volt power supply to drive the amplifier……
    Cheers, KevinK.

  36. The characteristic-emission layer – the “altitude” from which the Earth appears to radiate spaceward, and at which, uniquely in the climate system, the fundamental equation of radiative transfer applies – is the locus of all points at or above the Earth’s surface at which incoming and outgoing radiation are equal.

    I think that’s an excellent statement of the locus of radiative balance except that is is collapsed across spectrum . As you imply the altitude varies all the way from the surface for much of the visible spectrum to high in the atmosphere for wavelengths outside that interval .
    An important aspect of that boundary is that within it , the divergence theorem implies the same mean temperature as that calculated for that boundary .
    This could take a good half dozen lines of an APL to properly express in executable form for a spectral voxel map of the planet not counting those necessary to put the data in convenient form ..

    • It is the intellectual stupidos like Al Gore and bell-wethers of that ilk who prefer abundant control to human well-being. And sheeple follow w/o thinking as they always did far too often in history: “Führer befiehl, wir folgen Dir!”.

    • tabnumlock

      Why don’t we want nicer weather and more abundant crops, again?

      And what should “we” do to get nicer weather and more abundant crops?
      (Hint: More Co2 in the air => More crops. Everything is now 12% to 27% faster, stronger, greener, with more fruits, food, fuel, and fodder for all.)

  37. Gary Pearse;
    “Kevin, warming of the surface of the earth is our subject. If we directly warm it with the sun, and the radiated heat from the surface is intercepted by carbon and water vapor molecules and partly radiated back to the surface, it is somewhat like a leaky blanket keeping more of the heat at the surface than would be there if it were simply radiated from the surface to outer space.”
    Gary, you really should read a bit about how optical integrating spheres work. They have been around for a very long time and are well understood. An integrating sphere works like a perfect radiative “blanket” as described by the climate science community. Except that the “backradiation” reflected off the interior surface of the sphere does not ADD to the flux leaving the light bulb inside the sphere, It acts as a “virtual light source” and does not act as a blanket.
    I do understand the “greenhouse hypothesis” quite well, except it is incorrect, and always has been incorrect. But thanks for yet another explanation of a hypothesis that has never been observed. LOOK A UNICORN, RIGHT THERE NEXT TO THE SQUIRREL…..
    The energy that is “partly radiated” back to the surface simply delays the flow of energy through the system, since radiation travels at the speed of light this simply delays the flow of energy through the system. This is why optical engineers never use gaseous blankets to raise the temperature of a passive heat source (like a rock, or the surface of the Earth).
    When you put a blanket over a rock (or a deceased human being) the “response time” of the temperature change simply lengthens. A dead body does not get warmer than room temperature with or without a blanket.
    Thanks for yet another tired explanation of a failed hypothesis.
    Cheers, KevinK

    • A dead body does not get warmer than room temperature with or without a blanket.
      Obviously a live body doesn’t get any warmer either, right?
      This is just a stunningly bad understanding of basic heat transfer.

      • Tsk Tsk,
        Actually, after my dear departed mother “crossed her last bridge” I gave her a farewell “peck on the cheek” before we interred her remains in an “eternal resting spot”.
        She was room temperature, I was not. I do not think that adding a blanket to her “remains” would have changed that simple FACT.
        Also, I have done lots of detailed engineering work regarding basic heat transfer, if I had a “stunningly bad understanding of basic heat transfer” why am I still employed as a senior engineer (three decades plus) ???
        Cheers, KevinK.

  38. While clearly there is natural variability countering, easily, the tiny addition in CO2 parts per million added to the atmosphere anthropogenically (never mind any proposed amplification related to increasing water vapor cuz there ain’t any), this paper turns South with its outdated use of clearly discalibrated Solar data.
    Solar scientists have acquiesced to the excellent research Leif and others have burned the midnight oil over regarding the various means by which sunspot numbers have been counted in the past. That the above paper fails to use this most excellent research, speaks.
    For me, it speaks loudly and encourages me to take the rest of the paper with a grain of salt. Why? The discalibrated Solar data is a no-brainer. It is research that is clear and well-founded. Not to use it means that authors are willing to disregard gold standard research. Again, that decision speaks. Clearly.
    If you want to make a reasoned main point, every subpoint you make must also be well-reasoned. Fix it. Add a corrigendum.

    • Ms Gray has not demonstrated tha our paper relied on solar activity data at all. In fact, it did not do so. She should perhaps have read it before rishing to judgment.
      Mr Svalgaard has not yet explained why the weather was so cold during the Maunder Minimum if it did not occur.

      • Sorry Dr. S,
        If you don’t understand how the sun heats the oceans, you can’t understand how component TSI effects climate. You can’t understand the true effect of cloud cover variation. You don’t understand how the sun heats the oceans. You have demonstrated this many times. Your comment is without value.
        But hey, Viscount Monckton doesn’t either. you could join his club!

      • “Explanation is simple: solar activity has very little to do with the climate.”
        Ridiculous statement for someone who has spent their time on solar activity. Halve output: huge influence. Remove all output: huge influence. Vary output slightly up or down?
        Perhaps a temporary change in the equilibrium, but the atmosphere is self-correcting to a point. At what point is it not? You don’t know. I don’t know.
        Your assumption that solar activity has little to do with climate is based on your assumptions about how much solar activity has varied (your models), and what effect it has had on temperatures (proxy reconstructions).
        You can answer neither variable with any degree of certainty, therefore your opinion should be taken with a mountain of salt, regardless of your personal hubris on the subject.

      • Mr Svalgaard asks whether our model explains the Little Ice Age. No. The model is designed to study the influence of changes in CO2 and other greenhouse-gas concentrations on the climate.

      • Mr Svalgaard first says solar activity has no effect on climate and then asks why my model takes no account of solar activity.
        If he would do us the kindness of reading our paper at scibull.com,he will find that it is designed to study the anthropogenic contribution to global warming.

        • It is not what I think that is important here. You believe [or at least claim so as per the graph you showed] that solar activity is very important, yet you ignore it in your model. That is the disconnect.

      • Monckton of Brenchley March 17, 2015 at 9:18 am
        ”Konrad has descended to yah-boo. That is not helpful.”
        No, I descended to Johnny Cash, an entirely different matter.
        Get over yourself Monckton old boy. I gave you a serve on a previous thread against your stupid “yah-boo” accusation. I’m calling you out. Oceans a near blackbody or an extreme SW selective surface? Wanna run back to your Effective Radiating Level or whatever the heck warmulonians are calling it this week?
        I so totally own you.
        “yah-boo”? Or for Fu@Ks sake! Why not just screech “slayer” or “sky dragon” like a typical panicked warmulonian? Worthless little mathematician. Empiricist is just as little above your pay grade isn’t it?
        Just fold Christopher. I know what you did last summer. You cannot win. You still gave to pay for what you did.
        Seriously, you supported the idea that adding radiative gases to the atmosphere would reduce the atmospheres radiative cooling ability. I said that the net effect of our radiatively cooled atmosphere was cooling of the oceans. Black or white. Right or wrong. There is no middle ground. I own you because you were stupid enough to put “realpolitik” ahead of science. This is the age of the Internet. Therefore you wear this forever. As I said. Stupid.

    • Incidentally, Pamela, are you for a monetary gold standard?
      While I most certainly am — (the unadulterated gold standard cum gold bills … not Rothbard’s American libertarian version …), most people around these parts fall for the Gold War propaganda that gold is a “barbarous relic”, that its value is subjective, that it has no utility, and other claptrap. (Gold is still the central pillar of the world’s monetary system, its value is objective, and it has constant marginal utility.)
      May I suggest that you not use the phrase “gold standard research” unless you yourself believe that the gold standard is the gold standard. Otherwise, you contradict your own point … loudly.

      • You have lost me. Gold standard research is a common term amongst researchers. I have published research so am quite familiar with its meaning. You post makes no sense.

    • I’ll agree w/Pamela that the solar-theory doesn’t hold water. But I don’t think that shoots a hole thru Monckton’s analysis — it just means variations like the Medieval & Roman warm periods, and the LIA are internally-generated. Shouldn’t be a surprise — look at the much more drastic D/O and Heinrich events during the glacial periods. Certainly those aren’t solar-caused, or our sun is hiding some kind of extreme behavior that we have no proxy evidence or theory for support.
      One point — assuming ALL the warming since ~1850 is GHG is a stretch — how can a natural temp cycle like the previous ones be disregarded? OK, for the sake of analysis to get a worst-case, but how much is it really? 90%? 50%? 10%? Models can’t do such natural-cycles, they just show linear changes in temperatures proportional to GHGs.

  39. Lord Monckton, Mr Born,
    thanks for your — at least to me — intellectually challenging exchange of scientific facts and opinions.
    Live and learn…

  40. The GHE might be a simplistic and imperfect analogy, but it really fails when it ignores water vapor. Walk into a greenhouse and what do you notice? 1) it’s hot, 2) it’s humid.
    Picture an empty glass box in Arizona. Picture another glass box with a hot tub set at 55F, jets to bubble the surface like waves, fans to move the air as wind. Record temperatures and humidity.
    It’s the latent heat of water vapor, clouds, precip, albedo, condensing and evaporating, absorbing and releasing heat at a constant temp, that moderates and modulates the atmosphere. Nothing new. And that demonstration/explanation above doesn’t need pages of calculus.
    Visit your local power plant with a wet cooling tower. What’s happening inside that tower, described by moist air psychometrics, explains it all.

  41. Mr Born is correct that if the CO2 suddenly increased in the atmosphere (a not realistic case), the average altitude of radiation to space would increase, and the radiation out would drop due to the lower temperature at the higher altitude. The unbalance would cause excess energy to accumulate and heat the atmosphere until the radiation balance to and from space matched again, so the final average temperature at the higher altitude was the same as the previous temperature at the lower average altitude. However, Lord Monckton is correct that at equilibrium, the temperatures would be the same. Since CO2 concentration changes slowly, the atmosphere is never far from effective equilibrium, and Lord Monckton’s point is more realistic to the real world. If Me Born thinks that the unbalance still holds at equilibrium, and this is the cause of increased temperature, he is wrong. Otherwise you are talking past each other on transient vs equilibrium processes.

    • “Mr Born is correct that if the CO2 suddenly increased in the atmosphere (a not realistic case), the average altitude of radiation to space would increase”
      Really? You know this, how? By how much are you suggesting? Twice? Fifty times? On what basis do you suggest that, say, a doubling or tripling of CO2 would have the slightest effect on other than a short-term rebalancing of the equilibrium?
      You have no emperical evidence that this would be the case. This is just blind speculation!

    • Just to complete the thought: No, I don’t think the unbalance still holds at equilibrium. As a definitional matter, though, I think we need to consider the forcing to remain even after balance is restored, so long as the CO2 concentration remains elevated; otherwise, the surface temperature would relax back to its pre-disturbance value.

      • Joe, The only forcing that remains is that the new average altitude of radiation to space has increased and remains increased for the increase in CO2. The lapse rate does the rest. There is no mechanism that changes unless the albedo or lapse rate changes. If there are feedbacks, the comments are for the final average equilibrium state, not just the CO2 alone.

  42. There is another thing which changes with “an increase in the mean altitude of the characteristic-emission layer”, because the area increases. It probably does not change evenly, but even so it probably is not significant because the radius is from the center of the Earth. The baseline at the surface is over 6,000 km.
    Also, a larger area at a higher altitude also means that the radiation from the surface is spread over a larger area. Perhaps not to a significant extent, but the greater area would have some cooling effect at the layer.

  43. I get so tired of cryptic sarcastic responses from certain “authoritarian” people.
    If the earths atmosphere wasn’t self-correcting, the planet would have burned out long ago, or have been completely frozen, take your pick.
    We are still here after billions of years of change.
    Unless Al Gore runs for president in 2016. Heard that today on the Michael Medveyd show, people 3 cars away on the highway doing 60 MPH could hear me screaming!

    • And that’s exactly why CAGW theory is a crock, for if – put simply – the theory of a modest rise in temperature automatically leading to a series of further large increases was true, we would not be here to discuss it. The Earth has its own imperfect thermostat and we have little idea how it really works.
      One thing which always puzzles me is this: if temperature rises, then obviously there should be more water vapour in the atmosphere, but why does the IPCC state that this would mean less clouds?

      • In response to Mr Miller, actually we have a very good idea of the processes by which the Earth’s thermostasis is mantained within an interval little greater than that programmed into a domestic thermostat. The atmosphere, after all, is sandwiched between two near-infinite heat-sinks: the oceans and outer space. The heat capacity of the oceans is so large that even the billions of “Hiroshima bombs” of energy that the climate-extremists talk of do not much alter ocean temperature. Then there are the processes of evaporation and convection that take heat away from the surface. And so on.
        All these processes and properties of the climate ensure that, under modern conditions, the Earth’s thermostat is near-perfect. For the past 810,000 years, global mean surface temperature as reconstructed on the basis of ice-core samples has varied by little more than 3 Kelvin either side of the long-run mean, and that is not much more than 1% in absolute terms.

      • Mr. Monckton, thank you for willingness to actually respond to so many questions and critiques.
        Regarding this portion of Mr. Millers question, I would appreciate your response, or any response from anyone who knows.
        “One thing which always puzzles me is this: if temperature rises, then obviously there should be more water vapour in the atmosphere, but why does the IPCC state that this would mean less clouds?

      • Lord Monckton wrote:

        … actually we have a very good idea of the processes by which the Earth’s thermostasis is maintained within an interval little greater than that programmed into a domestic thermostat. The atmosphere, after all, is sandwiched between two near-infinite heat-sinks: the oceans and outer space. The heat capacity of the oceans is so large that even the billions of “Hiroshima bombs” of energy that the climate-extremists talk of do not much alter ocean temperature. Then there are the processes of evaporation and convection that take heat away from the surface. And so on.
        All these processes and properties of the climate ensure that, under modern conditions, the Earth’s thermostat is near-perfect. For the past 810,000 years, global mean surface temperature as reconstructed on the basis of ice-core samples has varied by little more than 3 Kelvin either side of the long-run mean, and that is not much more than 1% in absolute terms.

        And isn’t that remarkably beautiful! Siddhartha, after spending a lifetime torturing himself looking for Nirvana finally came to the realization that one does not need to fast, or do yoga, or mediate, or whatever, to reach Nirvana. We are already here! There is nothing to do but see it in front of us: we need fresh water, and rain miraculously falls from the sky; we need coffee in the morning, and the most incredible network of people and technology all conspire, as if by magic, to fill our cup; we need a narrow temperature range to flourish, and as if adjusted by the hand of some great benevolent being, our thermostat stays set at nice and comfy.
        This is it. This is your life. This is Nirvana.
        Incidentally, that San Francisco is surrounded by a near-infinite heat sink explains its remarkably even temperature year-round.
        Cheers Lord Monckton. You’re the Buddha of the Brenchley.

  44. One more comment:
    Heard a radio ad today about the “warm winter” we had in the US Pacific NW, and therefore the coming summer was going to be a scorcher.
    Their solution??? Install residential AC to combat global warming!!!😱😱😱
    Yes, let’s use more energy to keep ourselves cooler.
    And this from a company who regularly promotes energy conservation in commercial buildings to “prevent” global warming.
    My head hurts…

    • “Their solution??? Install residential AC to combat global warming!!!😱😱😱”
      Sounds like somebody wants more CO2 “credits” or an increase solar/wind electric generating rates.

  45. Unfortunately, there is likely to be something of a delay before I can respond completely. In fact, I can’t get to the most-central issue right now. But let me make a down payment before I turn in.
    Lord Monckton says that “Mr Born’s essay is predicated on a fundamental assumption that is flat wrong. . . . His fundamental error lies in his assertion that the increase in the Earth’s characteristic-emission altitude reduces the effective temperature at that altitude, ‘so less heat escapes, and the Earth warms’.” Lord Monckton’s characterization is that “the Earth’s effective radiating temperature is unaffected by a mere change in the mean altitude of that layer.”
    I say potato, he says potahto.
    My understanding is that the earth warms—the surface temperature increases—to raise the temperature of the new, higher emission altitude to what the previous, lower emission altitude’s temperature was. If carbon-dioxide concentration suddenly exhibited an increase, the effective radiation altitude would suddenly increase, but the surface’s heat capacity would prevent its temperature from responding instantaneously. So initially the effective emission altitude would be cooler than the previous emission altitude was, and the surface temperature would need to increase so that a constant lapse rate would cause the new effective emission altitude’s temperature to rise in tandem with the surface and thereby redress the erstwhile radiation imbalance. When it has done so, then, yes, the Earth’s effective radiating temperature is ultimately unaffected by the change.
    The surface temperature rises fast, but that rise is not instantaneous. And it rises because less heat was escaping. Why was less escaping? Because, until the surface could warm, the effective radiation temperature was lower at the higher altitude. That’s why I employed my Fig.3’s 1/\lambda_0 block; there is necessarily a lag—of what magnitude I’ll admit I don’t know—between the optical-density stimulus and the temperature response, even before any knock-on effects.
    Now, it is entirely possible—indeed, likely—that my understanding of how forcing results from CO2-concentration increase is in some respects faulty. But Lord Monckton has not made a very compelling case for that proposition. More important, though, he has not identified how the transience-fraction issues to which my post was directed depend on the radiation-altitude issue; he does not explain how “Many of the subsequent errors in Mr Born’s understanding appear to flow from this one.” The issues I raised have nothing to do with how the forcing arose; they deal with the model’s treatment of the response to that forcing.
    So in my view the radiation-altitude issue is really a bit of a red herring. As is Lord Monckton’s statement that “Mr Born says that he is not sure he should take on trust our assertion that the Planck or instantaneous climate-sensitivity parameter is about 0.31 Kelvin per Watt per square meter.” Actually, I wasn’t aware I’d made an issue of that; as far as I recall, I merely admitted that I had accepted it blindly when Bill Illis questioned my having done so. What does it matter whether I accepted it on faith? I didn’t criticize the paper because of the value the authors adopted for that parameter.
    I need to put off the more-substantive issues for a bit, but before I go, I’ll mention two very specific issues that anyone can check for himself.
    In Monckton et al.’s §7 they refer to their Table 4, which compares their model output with the observed temperature increase, and they conclude from it that

    Assuming that all global warming since 1850 was anthropogenic, the model fairly reproduces the change in global temperature since then, suggesting that the 0.6 K committed but unrealized warming mentioned in AR4, AR5 is non-existent.”

    Now, Table 4 compares the temperature increase they refer to as “\Delta T_{2x} (Model)” with the observed value they called “\Delta T_{2x} (Obs.) HadCRUT4,” showing that the central value of the former equaled sole value of the latter, namely, 0.8 K. The 2x subscript might suggest that those values are temperature results of doubling CO2, but the §7 text identifies the latter value as the advance in temperature between January 1850 and April 2014, while Table 4 shows how Monckton et al. arrived at the former, modeled value: the formula q_t^{-1}r_t\lambda_\infty\Delta F_t, where that \Delta F_t value corresponds to the measured CO2 increase for that time interval. The resultant computation was (1.27)(0.6)(0.588)(1.72) \approx 0.8, the value in their table. Since the r_t=0.6 value used in that computation is the ratio of the time-t temperature change to the equilibrium value, it is hard not to infer from their model that there’s (1 – 0.6) * 0.8 K / 0.6 = 0.5 K left in the pipleline.
    So how did they conclude that committed but unrealized warming was non-existent?
    One last observation for now. You’ll find that the Table 2 r_t values for f < 0 are questionable if you plot the implied step response by running the following R code:

    r_tbl2 = rbind(rep(1, 12),
    c(0.65, 0.70, 0.74, 0.77, 0.79, 0.80, 0.81, 0.82, 0.83, 0.84, 0.85, 0.85),
    c(0.55, 0.63, 0.65, 0.68, 0.70, 0.71, 0.72, 0.73, 0.74, 0.75, 0.75, 0.76),
    c(0.40, 0.49, 0.53, 0.56, 0.57, 0.59, 0.60, 0.61, 0.62, 0.63, 0.64, 0.64),
    c(0.15, 0.19, 0.22, 0.23, 0.25, 0.26, 0.27, 0.28, 0.29, 0.30, 0.30, 0.30));
    r_tbl2_padded = cbind(rep(0, 5), r_tbl2)
    f_tbl2 = c(0, 0.5, 1.3, 2.1, 2.9);
    t_tbl2 = (0:12) * 25;
    L_0 = 0.3125
    L_inf = L_0 / (1 - L_0 * f_tbl2);
    u_tbl2 = L_inf * r_tbl2_padded;
    plot(NA, xlim = c(0, 300), ylim = range(0, u_tbl2), xlab = "Time in Years", ylab = "Step Response");
    for(i in 1:length(f_tbl2)){
    lines(t_tbl2, u_tbl2[i, ], col = i);
    }
    legend("bottomright", legend = paste("f =", f_tbl2), lty = 1, col = 1:5, bty = "n");

    Doesn’t it seem odd that the f = 0 curve intersects the f = 0.5 and f = 1.3 curves?

    • Joe Born,

      Since the rₜ=0.6 value used in that computation is the ratio of the time-t temperature change to the equilibrium value, it is hard not to infer from their model that there’s (1 – 0.6) * 0.8 K / 0.6 = 0.5 K left in the pipleline.

      Yup.

      So how did they conclude that committed but unrealized warming was non-existent?

      They didn’t.

  46. Mr Born May find it profitable to study the altitudinal profile of temperature change. He will discover that the temperature at the characteristic emission layer does not change, precisely as the fundamental equation of radiative transfer dictates. His posting incorrectly said it would change.
    He has also not appreciated that the IPCCs definition of committed but unrealised warming is warming that should have happened by now, not at equilibrium.
    As to the values of the transience fraction over time, Mr Born is free to adopt any values he wishes.

    • Christopher Monckton,

      As to the values of the transience fraction over time, Mr Born is free to adopt any values he wishes.

      As your colleague Dr. Briggs would be the first to tell you, varying a parameter does not change reality. You have made claims about reality based on an rₜ value of 0.6 in your own model, and published results in peer-reviewed literature which are apparently inconsistent. Your calculations and communicated conclusions are at issue here, not IPCC definitions.

      • Asked and answered, twice. The definition of “committed but unrealized warming” that the IPCC has in mind is not the warming to equilibrium that has not yet occurred as a result of our past sins of emission, but the warming that it considers ought to have occurred to date.
        Of course varying the value of a parameter will alter the output of our model, or of any model. That is precisely my point. If Mr Born does not like the values we have derived from Dr Roe’s paper of 2009, as we carefully explained them in the text of the paper, he is free – as any user of a model is – to adopt his own preferred values.
        Our choice of values – if you or Mr Born do not like it – does not invalidate the model. Don’t whine. Just choose your own values and make your own determination of climate sensitivity. But our best estimate is that it will be around 1 K at equilibrium – and, at equilibrium, there is no argument about the value of the transience fraction. It is by definition unity. Let us not, therefore, quibble about how many angels live and move and have their being on the head of a pin.

      • Christopher Monckton,

        But our best estimate is that it will be around 1 K at equilibrium

        Finally. Mr Born has already computed the same answer I have: Since the rₜ=0.6 value used in that computation [Table 4] is the ratio of the time-t temperature change to the equilibrium value, it is hard not to infer from their model that there’s (1 – 0.6) * 0.8 K / 0.6 = 0.5 K left in the pipleline.
        And then he asks the same question I have been: So how did they conclude that committed but unrealized warming was non-existent?
        Anyone with basic algebra and the barest understanding of the meaning of equilibrium can see the clear implication of your model output using parameters derived from Table 4:
        1) 0.8 K + 0.5 K = 1.3 K
        2) 0.5 K ≠ 0.0 K
        The only possible, and therefore only proper, conclusion is that the system is NOT at equilibrium and 0.5 K additional warming is “in the pipeline” even if all net forcing change went to zero from now until equilibrium has been realized. Yet we read at the bottom right of p. 130 in MSLB (2015):
        8.4 How much post-1850 global warming was anthropogenic?
        Assuming 285 ppmv CO₂ in 1850 and 400 ppmv in 2014, and applying the observationally derived values of fₜ, holding rₜ at unity, and taking qₜ⁻¹ = 2.29/1.813 = 1.263 to allow for the greater fraction of past warming attributable to CH₄, the simple model determines the approximate fraction of the 0.8 K observed global warming since 1850 that was anthropogenic as 78% [62%, 104%].
        If it is assumed that gₜ < +0.1, warming is already at equilibrium, since rₜ → 1 for the implicit values
        fₜ ≤ 0.3 W m⁻² K⁻¹, on this scenario there is probably no committed but unrealized global warming. If AR4 is correct in its estimate that 0.6 K warming is in the pipeline, then < 0.2 K anthropogenic warming has occurred since 1850, indicating that warming realized since then is substantially natural.
        Again, I refer you to your own paper, Table 4, and note that rₜ is NOT set to unity, but 0.6. The conclusions of your text above do not follow from that premise. At best there is some unresolved ambiguity in your argument which you’ve yet to articulate or I’ve yet to comprehend. In the middle, we have an honest, but serious, error which was missed by peer-review and could (should) be rectified by publishing a correction. At worst, you are saying two different things as if they were one and hoping nobody will notice.
        The more you appeal to non-relevant IPCC definitions by way of defense of this paper, the more it looks like the latter, worst case, is the operative one.

        … at equilibrium, there is no argument about the value of the transience fraction.

        Granted, but this is another irrelevancy. As I have previously stipulated, I am not quibbling here about what I think the “true” value of rₜ should be. The issue at hand is that MSLB (2015) is ambiguous as to whether the system is at equilibrium or not. You would do well to address that issue directly, without further diversions, as the balance of your main conclusions flow from it.

      • Do the math. After 2.3 W/m2 of forcing, IPCC would expect 2 K of warming at equilibrium, of which just 0.9 K has occurred to date. That leaves 1.1 K to come, of which IPCC reckons about half, or 0.6 K, should have occurred by now. It is that 0.6 K that is committed but not yet realized.

    • I confess to having been unaware of that, to me, at least, incomprehensible definition of committed but unrealized warming. It “should have” happened by now? I struggle to put a meaning to that expression. Do you have a link to that definition?

      • See my comment about the math. IPCC would expect 1.1 K warming from now to equilibrium on the basis of our past sins of emission, but it would expect only 0.6 K of that to have occurred by now.

  47. Joe and Christopher,
    You both seem to agree that the higher effective emissions location will be the same temperature as before and you both assume that as a consequence the surface temperature must rise in order to support the increased length of lapse rate slope at the new height and temperature.
    That differs from AGW theory which says that the new effective emissions height is at a lower temperature and so less energy flows to space and the surface tempetrature must rise.
    However, Christopher has pointed out just how stable the surface temperature has been despite vast changes over vast time scales apart from during ice age / interglacial epochs which appear to be driven substantially by variations in the distribution and amount of insolation via the Milankovitch cycles.
    The reason for that stability is that you are all wrong about the surface temperature and the effective emissions height needing to rise.
    I explained why above but no one has picked up on the point.
    The reason is the behaviour of gases when they move up or down within a gravitational field.
    Unlike solids and liquids the molecules of gases move apart when lifted upward within a gravitational field because there is then less weight bearing down from above to force them closer together.
    As they move apart during upward movement their kinetic energy changes to potential energy and they cool as per the Gas Laws.
    As they move closer together during downward movement their potential energy changes to kinetic energy and they warm as per the Gas Laws.
    It is that process which creates the lapse rate slope and convection up and down would still be present even without GHGs because of uneven surface heating causing density differentials in the horizontal plane. The atmosphere could never become isothermal as proposed by many.
    In the absence of radiative gases all radiation to space must be from the surface and so all potential energy created from kinetic energy during uplift must be returned to the surface as kinetic energy during descent before it can be radiated to space. In that case the amount of kinetic energy removed from the surface during uplift is exactly the same as the kinetic energy returned to the surface duriong descent.
    In the presence of radiative gases it becomes possible for radiation to escape to space from within the atmosphere which short circuits the convective process.
    However, if that happens then a differential develops between kinetic energy removed from the surface on ascent and kinetic energy returned to the surface on descent.
    It is that reduction of kinetic energy returning to the surface on the descent which offsets the potential surface warming effect of radiative gases so the surface temperature and the effective radiating height both remain the same.
    That is how one must reconcile the Gas Laws with the radiative theory of atmospheric gasers whilst accounting for the remarkable thermal stability of planets with atmospheres.

    • Mr Wilde is not correct to say that my understanding of the unchanging temperature of the characteristic-emission layer is not standard theory. In the head posting I have carefully explained that the near-constant temperature of the characteristic-emission layer is a direct consequence of the fundamental equation of radiative transfer, which is not up for repeal anytime soon, being one of the few results in climatology that has not only been derived empirically but also demonstrated theoretically.
      It is trivial that, all other things being equal, a higher altitude within the troposphere will be cooler than a lower altitude. However, a radiative perturbation means there is a warming of the entire atmosphere, so that the new altitude at which emission is “seen” by satellites to occur becomes warmer than that altitude was before. But it is at the same temperature as the lower altitude at which emissions were previously “seen” was before the perturbation.

      • Lord Monckton clarifies his position relative to the standard theory so perhaps I misunderstood the standard theory. I am sure someone has explained that theory as the higher level being cooler and thus emitting less energy to space but perhaps they were wrong.
        As I said previously I agree that if GHGs have a net warming effect then all else being equal the effective emission height would be higher but at the same temperature as the previous lower emission height.
        However, one still needs to address my fundamental point that in reality all else is not equal and the effective emission height and surface temperature need not change at all because in the presence of radiative gases radiating direct to space from within the atmosphere less kinetic energy can be returned to the surface in convective descent that was taken up from the surface in convective ascent.
        That reduced energy returning to the surface offsets the potential surface warming effect of GHGs so that no change in surface temperature or effective emission height is required.

      • “As I said previously I agree that if GHGs have a net warming effect then all else being equal the effective emission height would be higher but at the same temperature as the previous lower emission height.”
        Stephen:
        I take the theory to be that the path-length of terrestrial IR to space is increased, as in more CO2 molecules and with the column lengthened vertically – therefore at a lower temp at the top. GHG’s have raided the Earth’s BB temp by 33C with -18C now around 7km up. Without them it would be -18C on the deck. That process proceeds in parallel. Unfortunately.

  48. @KevinK March 16, 2015 at 5:10 pm
    I see the sun as the ‘power source’ for our climate.
    I see external influences as the signal. (Set Point, if you wish) These influences could include cosmic particles (creating clouds etc).
    I see a multitude of feedback loops: air holds varying amounts of water depending upon temperature.
    Clouds form (become visible H2O) with only small changes in temperature.
    Wind is created due to small changes in temperature.
    I see the differential between land and sea heating causing wind (the midday sea breeze).
    There is a host of interactions caused by the variations in air temperature and its impact on its water holding ability.
    The amount of water evaporated from the oceans and land, then dropped as rain is huge, a lot of ‘work’ is going on in our climate system.
    Do you still persist in the view that none of the above could be analogous to a variable amount of ‘damping’ causing the ‘Measured Value’ (MV) to remain close to a long term value?

    • Steven;
      “Do you still persist in the view that none of the above could be analogous to a variable amount of ‘damping’ causing the ‘Measured Value’ (MV) to remain close to a long term value?”
      Yes, a variable amount of damping that causes the “MV” to remain close to a long term value (as determined by the massive thermal capacity of the Oceans) is probably the correct long term value.
      As an engineer the first thing I look at when “figuring out” the room temperature inside my house is THE FURNACE. It is providing all of the thermal energy inside my house, the tee tiny little bit of “back-radiation” (not an additional energy source) from the ceiling has no effect on the “room temperature”….
      The only “furnace” determining the temperatures inside my house is the furnace, outside of my house it is the SUN (big yellow ball that rises and falls every day).
      Cheers, KevinK

  49. Christopher Monckton, if you have a chance could you respond to my question in this post here…
    http://wattsupwiththat.com/2015/03/16/where-the-complex-climate-models-go-wrong/#comment-1885248
    ======================================================
    BTW, thirty years ago who could of guessed that such scientific discourse and debate could be carried out in such a public accessible and open manner. It is remarkable. I wish all lobby efforts were legally and severely restricted to such open scrutiny.

  50. Using MODTRAN and doubling the amount of CO2 from 400 to 800 ppm produces an increase of IR radiation reaching the surface by about 2-3 Wm-2. Putting this into Stephan Boltzmans equation and solving for T gives and increase of about 0.1 to 0.2 K.
    As there is no evidence for positive feedback in the historical record then what’s the problem.

    • The problem would be that Modtran does not give the amount of IR reaching the surface.
      In the non-feedback case doubling CO2 will give a surface temperature increase of about 1.2 degrees Celsius . As you say, that in itself is not a problem.

      • MikeB “The problem would be that Modtran does not give the amount of IR reaching the surface.”
        Then why if the model is given the following inputs:
        CO2 = 400ppm
        Locality = Mid Latitude Summer
        Altitude = 0 , looking UP
        No Clouds or rain
        does it give as MODEL OUTPUT
        Downward IR Heat Flux = 310.106 W/m2
        Changing CO2 to 400ppm yields
        Downward IR Heat Flux 312.21 W/m2

  51. Up welling, down welling, SWIR, LWIR, S-B constant, pages full of calculus are well & good between us girls, but it all leaves the public and the media cold, thinking only “climate $cienti$t experts” understand it.
    We need something simple, easy to understand to lay before the public and media that illustrates how powerful the water cycle is and how insignificant in comparison is CO2.
    Drawing on my own experience (don’t we all) for every kWh (3,412 Btu) that leaves a typical Rankine cycle steam power plant as electricity, 50/35 or 143% that much energy passes through that cooling tower handled by the evaporation of water. Try doing the same with air.
    Because of real or politically imagined shortages of water, air cooled condensers have become a popular option to the wet tower. Contrast the size of the equipment and energy required to handle the same heat load using air (CO2).
    We have to find the wooden stake or silver bullet that puts an end to this nonsense.

  52. Let me touch on isolated issues as time permits.
    For now, let’s consider the following: “Next Mr Born says we have incorrectly assumed a steep initial increase in temperature response.” That’s misleading; I objected to the response not because of what it was but because of the way it was arrived at. As we shall see, though, Lord Monckton actually did get around to giving a straight answer to my real objection. So let’s recall what that objection was.
    The values in Gerard Roe’s paper for time t were based on the stimulus’s having assumed its current (in that case, 4 W/m^2) value t years before. But Monckton et al compared the resultant output with that of a system whose stimulus rose gradually. Note the distinction between stimulus and response. I wasn’t objecting because Roe’s response rose gradually, I was objecting to the fact that apples were being compared with oranges. Essentially, this is what Monckton et al. were saying: Since the response of the model Roe relied on had a given value y at a time t years after its stimulus assumed a certain value x, we’re going to take y as our model’s output whenever the current stimulus is x after having increased for t years.
    In any but the most trivial of systems, the current output depends not merely on the current stimulus value but also (and, typically, principally) on its history. Now, if the radiative forcing had been a step function, then taking the Roe value for t years after the step occurred would have been proper. For any other stimulus, though, that approach is improper. For any other stimulus, you have to convolve that stimulus’s rate of change with the step response; you can’t just pick a step-response value. So, even if we assume that Roe’s model was correct, and even if we assume that Monckton et al. correctly copied the corresponding r_t value into their Table 2—Monckton et al.’s used Table 2 improperly.
    But then Lord Monckton actually gave the authors’ rationale for the approach they took. He had inferred from his epidemiological work that assuming a stimulus step rather than the actual, gradual stimulus change makes little difference. He said of that experience that “assuming a single stimulus all at once produced very little difference compared with the time-smeared stimulus, merely displacing the response by a few years. Similar considerations apply to the climate.”
    Of course using the step response for just any stimulus does not in general produce acceptable results, but it is at least plausible that in the case of the climate’s response to a ramp stimulus Lord Monckton’s rationale holds up. So I thank Lord Monckton for addressing an issue I actually raised.
    Moreover, his answer is reasonably consistent with his Table 2 r_t values. For the 75-year ramp used in transient-climate-response discussions, for example, the response is between 68% and 78%—or even 84% if you accept that table’s first-row values—of the step-response value.
    Unfortunately, such calculations are so sensitive that such a difference can be significant. Since the fifth row’s ramp response at 75 year equals the fourth row’s step response for that time, for example, one could infer an equilibrium response that’s over three times too high by failing to take the type of stimulus into account. Still, that sensitivity is a problem that afflicts such determinations generally; it is not a particular shortcoming of Monckton et al.’s model.

  53. and, sure enough, Central England temperature also showed increases, no doubt enhanced somewhat by CO2 emissions in the late 20th century.

    In that there is no empirical evidence ever presented that proves atmospheric CO2 up to 400 ppm has any measurable effect on near surface air temperatures ….. then why do so many learned individuals continue to infer or suggest that ….. “increases in CO2 caused/causes increases in near surface temperatures”?
    Do said learned individuals require the aforesaid “unknown CO2 fudge-factor” simply to bolster theirs or other’s claims about near surface air temperatures?

  54. One of the points I am trying to bring out is the following:
    The problem with so many in climate science is that the scientist(which is a stretch) in this field try to prove their points as to what may or may not effect the climate with specific items, as if they are in ISOLATION, rather then in the context of the entire climatic picture.
    Again a given force and magnitude changes of that force which may impact the climate has to be taken into consideration with the entire spectrum of items that are exerting an influence on the climate at that given time ,along with the state of the climate at that given time in order to get a sense of what impact that specific force may or may not exert on the climate.
    This is why it is so hard to prove and show a simple cause and effect relationship between the climate and items exerting a force upon the climate even though it does exist.
    Along those lines many data sources show convincingly that the temperature response from the Holocene Optimum to Present Day has been governed by Milankovitch Cycles which have been in an ever so slight cooling pattern post 8000 BC – present with solar variability superimposed upon this pattern which can explain the warmer periods in global temperatures within this very slow gradual cooling trend. Those warmer periods being the Minoan ,Roman ,Medieval, and recent Modern Warm Period.
    To refine the global temperature record further data on the PDO,AMO ,ENSO and VOLCANIC ACTIVITY ,have to be further superimposed upon the data provided by Solar Variability, and Milankovitch Cycles.
    This data when evaluated against the existing global temperature record (especially post Holocene Optimum – Present Day) gives the best explanation for the existing global temperature record.
    Some will argue that this is not so, and they are in denial and want the data to conform to the way they think rather then trying to conform the way they think to what the data shows.
    AGW enthusiast are the perfect example of this, who ignore the data which does not correlate with their absurd theory. If this were not so they would have abandoned this theory a long time ago.

  55. What a pleasure to read Lord Monckton! I love his style, and I am so glad that he has brought some sense to the silliness of AGW. Seems they got lost in their equations, but they didn’t include all the relevant factors.

  56. That chart can be found on the web-site talkblokestalkshop.
    In addition to the argument I just presented ,data further shows that CO2 concentrations are in response to the climate, forestation and biological processes and this is why CO2 always follows the temperature and never leads it.
    AGW theory does not conform to what the data is presenting.
    Here is the data ,now you need to reconcile your theory with the data.
    http://www.c3headlines.com/are-todays-temperatures-unusual/

  57. Christopher Monckton – Thank you for bringing us this most excellent debate and your vigorous defense of your paper. You are an shining example of a true skeptical observer.
    Leif lsvalgaard – You are a much respected scientist and we are lucky to have you participate on this blog. You keep us well grounded here. However, over the last couple years you seem to harden into a more dogmatic scientist, incapable of giving credit, where some credit is deserved. The fat lady has not sung her song on climate change nor has Sol revealed all of her secrets yet. Allow some room (respect) for other peoples work and especially their data. It will make you an even greater scientist. EOS (end of sermon) GK

      • “You are a much respected scientist and we are lucky to have you participate on this blog. You keep us well grounded here. However, over the last couple years you seem to harden…”
        I’ve wanted to comment on this for quite some time, as I’ve watched the change over the years.
        I’m often disappointed in how Dr. Svalgaard is treated by many commenting. He has shown a willingness to engage and his input is much too valuable for him to be treated poorly. As a long time reader, my two cents is that he has been attacked so often and that has brought out “tone”.
        We could argue which came first, but at this point it is irrelevant. Dr. Svalgaard’s contribution is huge and it seems to me he’s earned being treated respectfully by everyone.

  58. Another installment.
    The problem I have with using the Roe plot is that Monckton et al. don’t tell how they got from the plot to their table. How, for instance, did they identify the point in that plot’s blue area that represents feedback of 2.1 W/m^2/K at 75 years? Also, did the source of that model establish how well it matched the climate system, or was he just taking arbitrary values (as I did in my post) to illustrate a point? I still don’t know the answer. Yes, I get it that we can roll our own r_t’s but a reader is justified in wondering how the authors got theirs.
    As to the circuit, Lord Monckton mentions many eminent but unnamed luminaries who say I’m wrong. Well, I gave actual specifics of how a circuit works. I left no ambiguity. I presented a clear target. If they can identify any point at which I erred, I’m happy to hear it. But vague statements about my providing a “modification of a circuit to prevent its output from behaving as it would otherwise do” don’t cut it.
    Note that Lord Monckton does not identify what that modification is or how it prevents what the circuit would otherwise do. The only departure of that circuit from straight positive feedback is that the amplifier has a limit—as they all do. Without that limit, the output would have kept growing positively without bound—and without the “transit to the negative rail.” If I am wrong about that behavior, it should be a simple matter for Lord Monckton’s vaunted experts to point it out.
    Look, I may be just a retired lawyer, but I, too, have dealt with experts. In fact, I fixed radar sets myself during the Vietnam War; I heard of Bode when Lord Monckton was still an adolescent, and I know how tricky it is to characterize the math properly. I have no doubt that there’s some way the g>1 regime can be characterized as reversing voltage; in the AC analysis, there’s certainly a phase change at g=1.
    But I showed that Lord Monckton’s “transit to the negative rail” is an inapposite description of circuit behavior, at least in the context of establishing that math that works for circuit feedback doesn’t work for the climate. Again, my description left little to the imagination; if there was something incorrect about the behavior I described, it should be a simple matter for Lord Monckton’s brain trust to identify it.

    • The Bode relation shows a singularity at loop gain 1 that is not applicable to the climate. Furthermore, Bode does not model dynamical systems whose output is the agent of their self – equilibration.

  59. Monckton of Brenchley, a very misleading statement – temperature has varied by little more than 3 Kelvin either side of the long-run mean, and that is not much more than 1% in absolute terms.
    Data has shown it has been more like 5 Kelvin ,but that aside what is much more meaningful is that although the climate in absolute terms of temperature variation is relatively stable the climate is unstable when it comes to being in a glacial state versus an inter-glacial state. In addition the places where the earth changes from inter-glacial to glacial conditions experience a temperature change far greater then 5k. The 5k change or 3k change in temperature you suggest only valid due to the fact the global temperatures in the tropical areas of the globe show very little temperature change during glacial versus inter- glacial global conditions.

    • Let us begin by agreeing the facts. After halving the Antarctic temperature changes indicated by the ice cores to allow for polar amplification in the usual fashion, the variations in global temperature either side of the 810,000-year mean are about 3.5 K, or little more than 1% in absolute terms. These small variations are sufficient to cause ice ages at the lower bound and interglacial warm periods toward the upper bound: but, as should surely be obvious, adding CO2 to the atmosphere does not menace us with an ice age: it merely serves to prolong the interglacial.
      The paleoclimate record tells us that at present we are about 4.5 K above the glacial minimum temperature, and 2.5 K below the peak mean global temperature achieved during the previous interglacial about 100,000 years ago. That is quite a comfortable place to be. In the unlikely event that global temperature rose by a further 2 K, we should still be below the previous interglacial.
      But the central point is that, given the very large forcings first one way and then the other caused by the Milankovich/Croll cycles, the eruption of supervolcanoes, etc. the final variance in temperature has been altogether too small for us to be able to posit the existence of strongly net-positive temperature feedbacks in today’s conditions.
      Take away the over-positivity of the IPCC’s feedback sum (and it has taken a major step towards our position in its 2013 report), and then take away the unsatisfactory Bode system-gain equation (or modify it to remove its defects), and climate sensitivity falls to not more than a third to a half of what the IPCC predicts. And that means we have no climate crisis.

  60. As a nominally-educated layman (just a simple Bachelor of Science), I wonder, isn’t the entire issue of a single forcing a bit of a red-herring? My impression is that the skeptic camp is under a bit of pressure to – not just discredit – but provide a counter-argument to the concept that C02 (and particularly that sticky HUMAN C02) is the main driver. In as complex a system as climate – which involves everything from greenhouse gases, to solar energy (which itself is subject to orbital variance), tides, tectonic activity, and any number of other factors, it seems unlikely that any one aspect is, by itself, a driver or predictor of future climates – certainly nothing within the capacity to predictably regulate.

  61. …In as complex a system as climate – which involves everything from greenhouse gases, to solar energy (which itself is subject to orbital variance), tides, tectonic activity, and any number of other factors, it seems unlikely that any one aspect is, by itself, a driver or predictor of future climates – certainly nothing within the capacity to predictably regulate….
    More likely, any of the above, considered on their own, COULD be drivers, but the result of the complex interactions (which we can neither predict nor regulate) is likely to be as near zero as makes no difference – since we see from history that the climate is a fairly stable phenomenon…
    However, I don’t think the complex climate models have gone wrong. The activists needed heat prediction – the models provided it – the grants kept coming in. As Willis often says: “What’s not to like?”…

  62. My thanks to all here for a most informative and thought-provoking thread, conducted for the most part in the greatest good humour by Lord Monckton and also by some of his critics. Thanks also that the usual football crowd have stayed away, perhaps recognising the high standard of the debate.
    Some of you may not know that Christopher Monckton is not himself a science major, but has taken much time and trouble to study (and, prima facie, master) the necessary disciplines in order to be a part of these massively important investigations. Some will count that against him, but I think we all – alarmists and sceptics alike- owe him a considerable debt. Even if he is not right.
    It is rather unfortunate for us that Lord Monckton is – solely by virtue of the welcome longevity of his father -not enfranchised to speak and vote in the UK House of Lords. That time-honoured institution is sorely lacking in free thinkers of his calibre; increasingly so now that it is moving inexorably towards an appointed/elected assembly which will be merely an echo-chamber for the petty politicos of the Commons.
    Keep at it, Christopher

    • Mothcatcher is very kind. I shall do my best to keep at it, as he suggests. Our paper provides some good reasons why the models are exaggerating climate sensitivity. So far, there has been no really strong scientific challenge to our analysis. We are looking forward to seeing whether any of the usual suspects submits a paper to the Science Bulletin in attempted refutation of what we have said. And we have asked the editors to extend the usual academic courtesy to us, if that should happen, and allow us to reply to any attempted rebuttal in the same issue of the journal.
      I have now learned that my more detailed paper on the problems presented by the incautious application of the Bode system-gain equation in the models will appear next month,

  63. I am happy to see this point discussed as it struck me as an odd statement, as I noted in a comment on Mr Born’s article:
    Mr Born:
    >>“and, lapse rate being what it is, reduces the effective temperature from which the Earth radiates into space, so less heat escapes, and the Earth warms”.
    I objected to that statement about less heat escaping.
    Lord M:
    >”No. The characteristic-emission layer – the “altitude” from which the Earth appears to radiate spaceward, and at which, uniquely in the climate system, the fundamental equation of radiative transfer applies – is the locus of all points at or above the Earth’s surface at which incoming and outgoing radiation are equal. In general, the mean altitude of the locus of these balance-points rises as a greenhouse gas is added to the atmosphere. Thus far, Mr Born is correct.”
    That provides a good definition and I also agree.
    Lord M.
    >”His fundamental error lies in his assertion that the increase in the Earth’s characteristic-emission altitude reduces the effective temperature at that altitude, “so less heat escapes, and the Earth warms”.
    Agreed, about the part that says it loses less heat and is thus responsible for the increase in the surface temperature.
    Lord M.
    >”The truth, which follows from the definition of the characteristic-emission layer and from the fundamental equation of radiative transfer that applies uniquely at that layer, is that the Earth’s effective radiating temperature is unaffected by a mere change in the mean altitude of that layer.”
    I do not agree that the mere change in mean altitude does not affect the radiating temperature. The need for an increase in altitude was, remember, caused by an increase in the number of radiating molecules of GHG’s. This change has not been considered in the analysis. Doubling the amount of CO2 makes for a more radiative atmosphere.
    It is true that increasing the temperature of the atmosphere means the altitude of characteristic-emissions layer will rise but neither Mr Born’s nor Lord M’s description is correct with respect to the temperature of that theoretical radiating layer.
    I hope I have read and understood this correctly. Mr Born’s position is that the altitude increase will cause an adiabatic temperature drop and less total heat will be lost into space ‘at a lower temperature’. The ‘less heat’ thing we already addressed. It is not less heat. Mr Born is confusing heat energy with temperature. OK, we are over it.
    There are two ways to increase temperature of the system: put in more heat, or insulate the Earth with GHG’s. Putting in more heat means more heat has to be lost. More GHG’s requires an increase in the temperature at which the increased number of GHG molecules radiate, or an increase in the radiating surface (which an altitude change accomplishes to a slight extent).
    Do you see where I am going with this? The input about output heat are assumed to be constant with chemical conversion on the ground (plants) being the only subtraction and we are talking about an increase in GHG’s only. If there are more GHG molecules, there are more radiators at altitude, just as everywhere else. Increasing the surface temperature by increasing GHG concentrations raises the effective altitude from which that heat must be radiated – that is agreed. However the average temperature of those radiating molecules is not as high as it used to be because now there are more of them radiating at that altitude. The albedo has changed.
    It is the same as darkening a pot. If heat input to a pot is constant and low, the temperature of the pot surface will stabilise at some temperature. Increasing the heat transfer efficiency to the pot will raise the temperature of the radiating surface until it is in balance again, at a higher temperature. But if the pot was darkened it will radiate more effectively and the temperature of the surface will drop, whether the heat coming in was increased, constant or decreased. If it was in equilibrium, and the pot surface colour changes (akin to changing the GHG concentration) the temperature will change.
    Adding GHG’s to the atmosphere raises the surface temperature. It also raises the effective radiating altitude, but simultaneously, the equation that ‘sets the temperature’ allows that the effective radiating temperature will drop because the atmosphere has become more efficient at radiating heat.
    Conclusion: An increase in GHG’s will raise the effective altitude of radiation into space, provided that the increased efficiency of radiation caused by that increase in GHG concentration is not larger than the need to increase the altitude (which holds open the possibility that the altitude might decrease).
    A linear increase in GHG concentration causes a non-linear change in the altitude from which the heat will radiate. Because an increase in altitude will decrease the temperature at which the radiation takes place, the temperature cannot drop and still maintain the same total energy loss unless there is an increase in the number of ‘forward radiating’ molecules, which by definition, there is. That, I believe, is where both authors erred.
    Double the GHG concentration, double the radiating capacity at any given temperature. As it is not necessary to double the amount of heat lost, only to maintain the rate, the radiating temperature will definitely be lower than it was and further, the effective altitude will definitely be higher (because that is where it is colder). These conditions will prevail if the cause of the altitude increase was an increase in GHG concentration. In the end the total energy lost will be equal to the input, as before, sent out at a lower temperature by a greater number of radiating molecules.

    • Crispin in Waterloo,

      Conclusion: An increase in GHG’s will raise the effective altitude of radiation into space, provided that the increased efficiency of radiation caused by that increase in GHG concentration is not larger than the need to increase the altitude (which holds open the possibility that the altitude might decrease).

      Almost. This is an equilibrium problem as you correctly identify. The theory to invoke is that the effective radiation altitude is a response of the system attempting to reach equilibrium, not the cause of it being out of equilibrium to begin with. Radiative transfer codes don’t rely on it as a parameter, but it is something that emerges from them. Even so, my understanding is that it’s generally considered a curiosity value. Nobody writing serious literature is attempting to pin it down because it’s not directly observable and doesn’t have any use further down the line for other calculations. I think ScienceOfDoom argues these points rather well …
      http://scienceofdoom.com/2013/01/08/visualizing-atmospheric-radiation-part-three-average-height-of-emission/
      … which rather obviously influences my understanding of the concept. It checks out with everything I’ve read in literature, so I trust it. YMMV.

      • Brandon I am not sure you got the point of that paragraph compared with the conclusion. If an especially effective GHG was introduced to the atmosphere, it ‘might’ radiate so effectively at a lower temperature that the effective altitude actually dropped with an increase in the GHG concentration, and with a rise in surface temperature. I am just describing the possibility, not that I have a working example.
        “The theory to invoke is that the effective radiation altitude is a response of the system attempting to reach equilibrium, not the cause of it being out of equilibrium to begin with. ”
        I didn’t suggest that it was. The ’cause’ of the surface temp rise is an increase in GHG’s. Whether there are thunderstorms bring that heat up to altitude or not, or it is a peaceful planet below, makes difference to the effective altitude of radiative cooling. But we can’t have a claim for needing an increase in altitude because of the higher temperature at the surface without also including in the mental model an increase in the ability of that same atmosphere to radiate more effectively at a lower temperature because of the increase in the GHG concentration.
        In brief, it will stabilise at an altitude and temperature lower than ‘one might expect’.
        Suppose the concentration rose so high that the effective radiating altitude was below the average cloud height? Would Guam tip over?

      • Crispin in Waterloo,

        Brandon I am not sure you got the point of that paragraph compared with the conclusion. If an especially effective GHG was introduced to the atmosphere, it ‘might’ radiate so effectively at a lower temperature that the effective altitude actually dropped with an increase in the GHG concentration, and with a rise in surface temperature. I am just describing the possibility, not that I have a working example.

        You’re right, I don’t get the point because to me it makes no physical sense. By Kirchoff, an effective emitter is an equally effective absorber. Emissivity/absorptivity is wavelength sensitive, which is why doing any serious radiative transfer work requires (spectral) line-by-line codes to get reasonably accurate answers. Your instinct that an effective emitter will tend to cool things is correct, but only in part — it’s only going to be able to do that when more than half of its radiating energy is free to escape the system entirely. That’s not true at the surface.

        I didn’t suggest that it was. The ’cause’ of the surface temp rise is an increase in GHG’s.

        Yes I know. I should have made it more clear that my comment there was directed at the many others here who have described the effect in those terms. The cause of the warming due to GHGs at the surface is because increasing those gasses increases the optical thickness of the atmosphere in wavelengths the planet is “trying to use” to shed absorbed solar energy. The 15 micron band is particularly important because not only is that in the fat part of the S-B curve for the surface, it’s the sweet-spot for CO2 absorptivity/emissivity as well:
        http://acd.ucar.edu/textbook/ch15/fig3.jpg
        That’s a really elegant plot in a lot of ways, not least because taking the shot over the Sahara minimizes the “interference” from water vapor and better isolates CO2’s role. Note that the S-B predicted temperature in the atmospheric “window” portion of the plot is 320 K, implying a surface temperature of 47°C. However, in the 15 micron CO2 band, the predicted S-B temperature is only 220 K, so …
        http://mintaka.sdsu.edu/GF/explain/thermal/figs/stdatm.gif
        … a rough guess is that those photons were emitted at an average altitude somewhere around 10 km.

        Whether there are thunderstorms bring that heat up to altitude or not, or it is a peaceful planet below, makes difference to the effective altitude of radiative cooling.

        Absolutely yes, it does make a difference. I believe that’s one reason why literature doesn’t attempt to put a value on it. It would be fiendishly difficult to figure out from observation, and not much use.

        But we can’t have a claim for needing an increase in altitude because of the higher temperature at the surface without also including in the mental model an increase in the ability of that same atmosphere to radiate more effectively at a lower temperature because of the increase in the GHG concentration.

        I don’t like that rebuttal to the claim any more than the claim itself. The atmosphere is an infinite number of layers of gas encompassing an essentially solid sphere. The only hard boundary is the surface. The whole reason for the Beer-Lambert law is that the attenuation of light through a fluid is a completely different process from sensible heat diffusing through a solid material to a well-defined surface and thence radiating away.
        You MUST keep in mind that good emitters at a given wavelength area ALSO good ABSORBERS at the same wavelength.
        Which brings us to …

        In brief, it will stabilise at an altitude and temperature lower than ‘one might expect’.

        If one is thinking of this only in terms of radiative cooling and surface area, none of this is going to work like ‘one might expect’.

        Suppose the concentration rose so high that the effective radiating altitude was below the average cloud height? Would Guam tip over?

        No, but I’m going to go tip back a beer because I’m temporarily weary of trying to explain energy balance and equilibrium problems to folk who only look at one half of the relevant fluxes. If we must use the surface area argument — and I’d really rather we didn’t since it’s not the most relevant physics — ponder the notion that the inner portion of that surface is radiating back down at the same time.

    • It is always wise to start with the appropriate equation. The equation that governs the relation between temperature and radiation at the characteristic emission layer is the fundamental equation of radiative transfer. Under the assumptions that total incoming solar irradiance is constant over time, that albedo does not change, that emissivity is constant at close to unity, it necessarily and ineluctably follows that the temperature of the characteristic-emission layer is constant.

      • Lord M
        Well I can’t fault this as a whole: “Under the assumptions that total incoming solar irradiance is constant over time, that albedo does not change, that emissivity is constant at close to unity, it necessarily and ineluctably follows that the temperature of the characteristic-emission layer is constant.”
        But the albedo of the atmosphere does change because the concentration of radiating gases has changed. That is my point. Your sentence is correct, but doesn’t apply to an altered system but has one assumption too many.
        Here is my version:
        Under the assumptions that total incoming solar irradiance is constant over time, that the albedo of the atmosphere changes with the concentration of CO2, that emissivity of the surface is constant at close to unity, it necessarily and ineluctably follows that the temperature of the characteristic-emission layer will drop, otherwise it would over-cool the atmosphere, completely undoing the GH effect.
        Either the emitting layer is cooler, or CO2 has no net effect on temperature. One of the two.
        Coming at it from the other side, if the ‘exit temperature’ were constant, and knowing that the emissivity and irradiance are also constant, it would follow that there had been no change in the concentration of radiating gases. We are running this thought experiment because the concentration has changed, therefore the absorption and radiation is more effective, both up and down, ergo the albedo has changed. Not the albedo of the surface, the albedo of the effective radiating layer of the atmosphere. The surface remains at unity.
        If I printed small black dots on the outside surface of a polished silver pot, it would settle on a temperature for any given constant input of heat. If I (only) print more dots on the surface, the surface temperature will drop if the input of heat remains constant because I have changed the albedo. CO2 molecules are like radiating black dots.
        An irreducibly simple climate model must consider the change in atmospheric albedo because the GH effect is directly caused by a change in the albedo of the atmosphere catching IR more efficiently on the way up. It is the atmosphere that is radiating into space, not the surface. Increasing the concentration of CO2 increases the outward radiating efficiency, same as with the silver pot.

      • The only reason why one hypothesizes about an ‘effective radiating level’ (ERL) being all of a sudden too cool and hence being out of balance with the incoming from the Sun, leading to warming below, is that one tends to postulate an instantaneous doubling of atmospheric CO2 concentration in the various climate sensitivity scenarios. In reality, Monckton is right; such a cooling of the ERL would never actually measurably occur, because the rise in CO2 is far too slow and gradual and the system would thus have no problem adjusting practically in phase.

      • Kristian
        “The only reason why one hypothesizes about an ‘effective radiating level’ (ERL) being all of a sudden too cool and hence being out of balance with the incoming from the Sun, leading to warming below, is that one tends to postulate an instantaneous doubling of atmospheric CO2 concentration in the various climate sensitivity scenarios. ”
        That is simply not going to happen – it was poorly thought out guess. It is not the reason why ‘it warms below’. Far from it.
        Whether or not the increase were sudden or slow, the fact is that adding CO2 to the water vapour and other CO2 is going to increase the effectiveness of the radiating medium – the air. That means to be in balance, the emitting layer will be cooler than it was before the CO2 was added. This is straightforward and can be determined from the concentration and radiating characteristics of water vapour and CO2 (as the most important direct transmitters of heat into space). As soon as the calculation is done for two different gas mixes, the characteristic radiating temperature is known, and the answers are not the same. Higher CO2 means it radiates more ‘efficiently’ and can leak the heat, so to speak, at a lower temperature, which implies that it will be at a higher altitude, or if at the same altitude, it is cooler (cooled by radiation).
        For a postulated doubling of CO2, the effect should easily be measured. Suppose the effective elevation is 16 km. What is the temperature? Double the efficiency of the CO2 portion of the atmosphere (by increasing its concentration). Three things could happen:
        The air dries out (which has been measured and is happening)
        The temperature drops (ditto)
        The altitude of the effective elevation rises (don’t know).
        Other things being equal, only CO2 rising, the average temperature of the emitting layer will drop. Maybe a combination. If the temperature remains the same, then the water vapour concentration must drop to compensate for it or the altitude must drop. For constant T, the equation requires one or both. It has to balance.

  64. “and provided that the Earth’s albedo does not change much (it doesn’t).”
    Is this really established? Phillip Goode, etal. from Big Bear Solar Observatory are claiming that changes in albedo that have been measured at Big Bear over the last decades translate to a six watts per square meter variation.

      • Yes, this is my understanding, they cancel over time – meaning times greater than a year (like the oceans). Also, I believe, after glancing at the Big Bear graphs, meaning times greater than a decade. This “cancel over time” notion brings to mind the lesson of the playa lakes: Great Salt Lake, Lago Enriquillo, Devils Lake of North Dakota, and Laguna Epecuen. That is to say, that appropriate averages in the context of climate can mean averages over a time far greater than a year because even though Devils Lake in North Dakota has an average annual rainfall of twenty inches doesn’t mean that over the decades the lake level won’t vary by as much as fifty feet. Hence, if climate models take albedo or conversely emmisivity as a factor ( or parameter, I’m not sure which term is more appropriate), then they are taking on something with a good amount of uncertainty – over time.

  65. ANTHROPOGENIC Global Warming (AGW) theory claims the earth is warming because rising CO2 is like a blanket, reducing Earth’s energy loss to space. However, data from the US National Oceanic and Atmospheric Administration (NOAA) shows that at least for the last 30 years, Earth’s energy loss to space has been rising.
    From the article.

    • The blanket analogy troubles me. Would not increasing CO2 in the upper atmosphere also act as a reflective shield? If shortwave radiation strikes CO2 in the upper atmosphere it seems as likely to radiate long wave radiation back into space as it would to radiate towards earth? Would this not cause less Albedo effect at the surface?

  66. Monckton of Brenchley

    The Planck “feedback” is not a feedback. It is a climate-sensitivity parameter. It is not, repeat not, treated like a true temperature feedback in the equations. Read our paper.
    And the GISS ModelE, to name but one, definitely uses the Bode system-gain equation. See Hansen (1984, 1988).

    Your very first equation presents &lambda0 as the constant of δT vs δF, this is effectively a classic first order linear ODE, of the simplest kind. It describes a linear feedback and &lambda0 “sensitivity parameter” is that feedback.
    The ODE would normally have a negative sign which defines the feedback as negative but this is simply a case of the convention of which direction is considered positive heat flux in climate. In engineering the greater heat flux opposes the increased temperature so it would be negative.
    This is mainly a problem of adopting the rather unscientific language of IPCC: talking of “net positive ” feedbacks when they really mean “less negative” feedback, but it is important if you are writing scientific papers to clear about the terms and what they represent physically.
    This term represents how “sensitive” climate is, because it is a feedback.
    &lambda0 “sensitivity parameter”: the Plack feedback is indeed a feedback. It is the main feedback. which stabilises the climate system and that is why all other feedbacks are considered relative to the Planck feedback.
    All your other feedbacks are stated as a proportion of Planck sensitivity: &lambda0 ft
    This purely linear approximation to T^4 is fine for deviations of the order of 0.1K, in equilibrium temperature. The guts of the models will be using T^4 for actual spot temperature physics.
    However, if they start to discuss 2K deviations or some of the more fanciful figures like 4-6 kelvin of warming then the non linear form will be required. A supposedly linear sensitivity will start to reduce if such a significant warming is produced. This was found to be the case by Paul_K whose article I linked above. Models do not display fixed linear sensitivities at higher dT.
    This is where the asymptotic rise to infinity falls apart. Like in the electronic amplifier, the continued rise is irrelevant because it is physically meaningless and will not happen. Any discussion of going over the top *through infinity* to re-emerge the other side and flipping sign is nonsense.
    Whatever any particular electronic circuit does when you try to drive it like that is entirely determined by the undocumented, NON-linear behaviour it exhibits when driven beyond its design parameters. Whether it latches up, burns out or oscillates, tells us nothing about climate nor the linear system it follows under normal operation. Your electronics experts should have explained that to you.

    • The Planck “feedback” is not a feedback. It is not treated as such in the standard equations of climate sensitivity. It is better regarded as a zero-feedback climate-sensitivity parameter, by which a direct forcing is multiplied to obtain the temperature change caused by that forcing in the absence of any feedbacks. The product of the feedback-sum and the Planck parameter is then the loop gain in the system.
      When sufficient feedback occurs in an electronic circuit to drive the loop gain above unity, the current goes around the circuit the other way, so that the output voltage that had been positive suddenly becomes negative. I have seen this explicitly mentioned in the specialist literature, and it was confirmed by the eminent process engineer whom I consulted in detail. Also, my paper providing a more detailed consideration of this question has passed peer review at the hands of another even more eminent specialist and will be published next month.
      The climate, in various fundamental respects, does not behave like an electronic circuit. See the head posting. The Bode equation, therefore, is the wrong equation and requires to be modified or replaced to remove the absurd exaggerations of climate sensitivity to which its use gives rise.

      • Thanks for your reply but I think you have a misunderstanding here.
        Climate sensitivity, as defined in the simple linear equation is a diagnostic of model ( or climate ) behaviour. Climate models at the detailed physics level of thier calculations at each grid point use T^4 S-B derviced equations. It is in analysing the model output that attempts are made to characterise its behaviour in terms of a simplified constant linear parameter.
        Thus climate sensitivity is an emergent property, not one that is programmed in.
        You suggested the GISS model does this, can you provide a direct link to the Hansen papers from which you say you got this conclusion?
        ” It is better regarded as a zero-feedback climate-sensitivity parameter”
        That is self contradictory. with zero feedback there would be no “sensitivity”. The slightest δF would cause continual warming and the system would be unstable. It is better to call it what it is : the greatest f/b which ensures the system is stable.
        Again you are falling for IPCC linguistic games. Like perfectly normal temperature deviations are called “anomalies” in order to imply from the outset that any change is “abnormal”, the idea of “net positive” feedbacks implies instability, when in fact it is just a misrepresentation of “less negative” feedback, or *slightly* less stable.
        This leads to the idea of “tipping points” which is non-sense. Nothing is going to overpower a T^4 neg. f/b. You should challenge this language not adopt it.
        Planck IS a feedback and it is the sole reason we are here to have the this discussion.
        “When sufficient feedback occurs in an electronic circuit to drive the loop gain above unity, the current goes around the circuit the other way ….”
        As I explained in detail above, this kind of talk is meaningless. It depends totally upon how a particular circuit design FAILS to remain linear when run outside it’s design parameters. It tells you nothing about linear systems because it is no longer linear. This is akin to speculating what happens on the other side of the mathematical singularity at a blackhole ( should such a thing exist ).
        A nuclear fission explosion is probably the most dramatic illustration of a positive feedback and even that eventually is constrained by negative feedbacks. The explosion is localised. The whole world does not explode and we don’t pop out of the other side with energy flowing in the other direction !
        I suggest you limit yourself to pointing out there are limits as to how far linearity can be used as a reasonable approximation. You are going well beyond what you understand here and risk destroying any credibility that you may have accrued by your efforts.
        The paper is apparently stirring a few thoughts among simplistic climatologists and is probably a useful explanation of the use of the linear model. Try not to undo that.
        What you are calling the Bode equation is not specific to electronics. It can be applied, simplistically to many physical systems. Knowing when it fails to apply, either in electronics or any other application is essential to proper use. It is not more or less applicable to climate because it is used in electronics.
        This is another logical error that you have been promulgating for some time.
        Best regards.

      • Mr Goodman is misunderstanding various matters. First, the equation for climate sensitivity is non-linear in that the fundamental equation of radiative transfer is a fourth-power relation, and again non-linear in that the CO2 forcing function is logarithmic; and again non-linear in that most feedbacks are non-linear (see the appendix to our paper for this), and again non-linear in that response times are non-linear, and again non-linear in that the object under discussion behaves as a chaotic object.
        Next, climate sensitivity may be an input to or an output from the model, depending upon its design. In our model, climate sensitivity is an output.
        Next, it is incorrect to say that in the absence of feedbacks there would be no climate sensitivity, and additionally incorrect to say that without feedbacks the object must be unstable. The mean value of the Planck or zero-feedback sensitivity parameter is about 0.3125 Kelvin per Watt per square meter of direct radiative forcing. Multiply that parameter by the forcing and the climate sensitivity in the absence of temperature feedbacks emerges: thus, where the forcing in response to doubled CO2 concentration is 5.35 times the logarithm of 2, or 0.69 Watts per square meter, the zero-feedback climate sensitivity is about 1.16 K – not exactly an unstable result.
        It is where the feedbacks are imagined to be strongly net-positive that the instability arises, as the plot of the singularity in the Bode equation makes clear.
        The Bode equation also shows what happens to the output voltage in an amplifier where the closed-loop gain exceeds unity. What was a drive towards positive infinity becomes a drive towards negative infinity in the voltage. Circuits can thus be made to oscillate by driving the loop gain above unity and then relaxing it back below unity again. There is plenty of literature on this. Try search for “from the positive rail to the negative rail”, for instance, or study “feedback-induced oscillation”. Or build a robust circuit and try it out.
        However, in the climate a loop gain of more than 1 would not produce a plunge in temperature. In this and in other respects (see my forthcoming paper), the Bode equation does not – whether you or I like it or not – satisfactorily model the climate. We are not the first to have pointed this out in the literature, though we have been more explicit than anyone to date in expressing our concerns.
        The Bode equation requires modification or replacement before it can be legitimately applied to the climate object. If peer review of a paper by an eminent professor who specializes in this field is successful, the extent to which Bode does not apply to the climate will become clear to all.
        I am well aware that the Bode equation applies not only to electronic circuits but also to a class of dynamical systems. The climate is not, repeat not, in that class.

      • Monckton of Brenchley March 18, 2015 at 9:47 am
        Mr Goodman is misunderstanding various matters. First, the equation for climate sensitivity is non-linear in that the fundamental equation of radiative transfer is a fourth-power relation, and again non-linear in that the CO2 forcing function is logarithmic; and again non-linear in that most feedbacks are non-linear (see the appendix to our paper for this), and again non-linear in that response times are non-linear, and again non-linear in that the object under discussion behaves as a chaotic object.

        As you admitted in an earlier conversation that Appendix doesn’t exist, perhaps you can make it available here?

      • The Bode equation also shows what happens to the output voltage in an amplifier where the closed-loop gain exceeds unity. What was a drive towards positive infinity becomes a drive towards negative infinity in the voltage. Circuits can thus be made to oscillate by driving the loop gain above unity and then relaxing it back below unity again.
        No, the loop gain does not change, the nature of the stationary point changes to an unstable focus and follows an oscillatory path to a stable limit cycle. See the Wien bridge oscillator for an example, gain of 0.99 = stable operation, 1.01 = oscillation (sine wave), 1.50 = distorted oscillation.

  67. There’s actually nothing wrong with using the electronic analogy since the linear description of such circuits is a simplified model as is that of climate. The same degree of understanding of the limits of the linear approximation are required but within that limit there is no reason to suggest it is not proper because it only applies to electronics. This is not the case. Many other systems are modelled and analysed as linear simplifications.
    What you need to model is an operational amplifier ( op-amp ) with strong negative feedback. The discussion of climate sensitivity is then adding a little more neg. f/b or a little +/ve f/b. This can be done in couple of minutes with a 741 on a bit “breadboard” or on paper. It’s first year electronics.
    The deviations of the output voltage caused by a predefined disturbance at the input can be studied. In the case where some +ve f/b is added the output voltage will vary more than the untampered “Planck” amplifier: it more “sensitive”. Conversely, with more negative f/b the amp output will change less: it is less “sensitive”.
    One could then add some RC networks into the circuit and make an analogue computer model for the climate system, with single slab, or multiple slab ocean heat capacities. Three such amps could be set up with different sensitivities, one for the tropics an one each for NH SH extra-tropical zones. Suitable linkage between the outputs to reflect inter-zone heat transfer.
    Add a resistor chain and an push button to simulate volcanoes. You can take the analogy as far as you like.
    Just realise what the Planck term is before you start. 😉

  68. What a fantastic thread!
    Slightly off topic, but I cannot help myself:
    Where are the trolls?
    In thread after thread we are inundated with trolls explaining to us how stupid we are, most quote the much worn out 97% consensus meme or similar appeal to authority, some claim to be “teachers” of climate science, but wilt when asked to discuss the actual science. So where are they? Here the science is being debated at its most raw level, with heavy weights, light weights, and interested observers arguing, supporting, refining, discussing the science.
    But from the trolls, not a peep. You’d think with their vaunted superiority they’d be thick as thieves in this thread, explaining the facts to us. Seems when actual science is on the table… they scurry away in fear of making fools of themselves by entering the fray.

    • Mr Hoffer is right. This thread has been a real pleasure because on all sides there has been a willingness to discuss the science. Indeed, the object of our paper was to make climate – sensitivity math widely accessible without excessive simplification.

  69. Isn’t gain in electronics the same as infinite series in mathematics?
    for example:
    1/2+1/4+1/8+1/16…..
    this infinite series has a finite answer.
    while a series like:
    1/1+1/2+1/3+1/4+1/5 …
    does not.
    and a series like
    1+3+9+27….
    most definitely does not!
    So for feedback to be stable, it seems it must at the limit be an infinite series with a result that is less than infinity.

    • Exactly.
      The particular series that’s analogous here is a power series like your first and last, which take the form 1 + r + r^2 + r^3 + . . . .
      Lord Monckton’s theory is analogous to saying that the sum is negative if r > 0; your last series 1 + 3 + 9 + . . . sums to a negative value according to Lord Monckton’s way of looking at things.
      Why? Well, if S = 1 + r + r^2 + r^3 + . , then rS = r + r^2 + . . ., so S – rS = (1 – r) S = 1, so S = 1 / (1 – r), which is negative for r > 1.
      Math is tricky, especially when you work with infinities.

  70. My final say on this thread. We have directly measured the potential affects of TSI on global warming. This is not a model. This is a measurement from satellites. The change in watts per meter squared of incoming solar radiation from a busy Sun to a quiet Sun is known. Physics then tells us the possible change in temperature in Celsius and Fahrenheit the change in watts/m2 can possibly have on our temperatures here on Earth.
    The above various proponents of Solar-driven reasons for the recent warming know this so they instead depend on a variety of unobserved amplification mechanisms. It smacks of the CO2 water vapor amplification mechanism proffered from the other camp. Which is also unobserved.
    http://phys.org/pdf129483836.pdf
    So to both I say, you are ignoring an incredibly variable and complex planet. One that can strike out incoming solar irradiance change to its knees and home-run the change up pitch of CO2 over the fence. Earth wins the game. Not CO2 and not Solar variation.

  71. Pamela Gray wrote, “My final say on this thread. We have directly measured the potential affects of TSI on global warming. This is not a model. This is a measurement from satellites. The change in watts per meter squared of incoming solar radiation from a busy Sun to a quiet Sun is known.”
    Your statement is not actually correct. TSI has been measured from what was deemed an active sun and what was deemed a quite sun. TSI HAS NOT been measured when the sun was in grand minimum with no sun spots most years. Perhaps TSI does drop predictably as the number of sun spots declines. But how much does it drop when sun spots hit zero for a time?
    No one knows how low the solar emissions are in a grand minimum. Some solar physicists think that the sun probably is not very variable and put an estimate to the variation that they think is possible and most have used that kind of estimate. But the problem is that stars that are deemed by astronomers to be very similar to ours have shown quite a bit more variation than the solar physicists are deeming possible for our sun.
    A grand minimum could have TSI dropping quite a bit more than has ever been measured in modern times.

      • lsvalgaard wrote, “And there are other ways of getting at this, e.g. http://climateaudit.org/2007/11/30/svalgaard-solar-theory/
        I studied the information in the link. From a scale of 1 to 10 where 10 is a fairly strong scientific conclusion, I would rate it as a 1 only because there is no lower number. On the other hand, your solar sunspot number reconstruction – I would rate it at a 10.
        From the link to Svalgaard Solar Theory “The existence of “floors” in IMF and FUV over ~1.6 centuries argues for a lack of secular variations of these parameters on that time scale. . The five lines of evidence discussed above suggest that the lack of such secular variation undermines the circumstantial evidence for a “hidden” source of irradiance variability and that there therefore also might be a floor in TSI, such that TSI during Grand Minima would simply be that observed at current solar minima.”
        No it doesn’t! You have one very short sample time period in the “life” of the sun. It is not significant. Especially when solar physics models of the sun are not able to determine yet how variable the sun is or what the changes in TSI will be based on variability.
        To form meaningful lines of evidence in the way you tried, the theoretical background needs to be much more settled.

        • Especially when solar physics models of the sun are not able to determine yet how variable the sun is or what the changes in TSI will be based on variability
          On what do you base that? We measure how variable the Sun is on time scales of interest [centuries].

        • Well, you may have studied the link, but you failed to appreciate the information given. The radiative output [TSI] is observed to have two component: (1) that comes from the core of the Sun and (2) one that due to the magnetic field at the surface. Some spectral lines are very temperature sensitive. Such lines have been carefully monitored for many decades in areas where there were no sunspots and no observable magnetic fields. The results show that there is no solar cycle variation of this ‘basal’ temperature, it is indeed constant, so would not be expected to be any different during a grand minimum. If you disagree, then you have to produce evidence that there would a difference. The magnetic component of TSI has also been carefully monitored for decades and show that it is accounted for by the observed magnetic field and that there is no mystery about this.

      • lsvalgaard wrote, “On what do you base that? We measure how variable the Sun is on time scales of interest [centuries].”
        The time period “of interest” that has been observed still does not include a grand solar minimum similar to the Maunder Minimum. In fact, without having a robust theoretical understanding of solar variability, it is not scientifically robust to simply pick a time period and from that time period, be able to make robust determinations of what may happen in longer time period given the current knowledge of solar physics.
        lsvalgaard wrote, “Well, you may have studied the link, but you failed to appreciate the information given. The radiative output [TSI] is observed to have two component: (1) that comes from the core of the Sun and (2) one that due to the magnetic field at the surface. ”
        The information suffers from the same problem as above. You really can’t determine how much time you must observe the sun in order to determine if you have a good sample of it’s variability.
        lsvalgaard wrote, “The results show that there is no solar cycle variation of this ‘basal’ temperature, it is indeed constant, so would not be expected to be any different during a grand minimum.”
        That it would be no different in a grand minimum is an untested hypothesis based on very little.
        lsvalgaard wrote, “If you disagree, then you have to produce evidence that there would a difference.”
        No, it is your hypothesis. You need to find a better way to test it. Although the next couple solar cycles might help with that if there is a long period with no sun spots.
        I am pointing out that your hypothesis is based on insufficient data and lacks a firm theoretical (solar physics) foundation. In my opinion, it is more conjecture than hypothesis.

        • Well, I think we have a good understanding of how this works. I spelled it out for you, but to no avail. The null hypothesis must be that there are no unknowns lurking about. All the data we have say that the basal temperature [and thus base TSI] does not change, and that the additional irradiance is simply that due to magnetic activity.

        • That it would be no different in a grand minimum is an untested hypothesis based on very little.
          The untested hypothesis is that it would be different. On what do you base that?

        • lacks a firm theoretical (solar physics) foundation
          I explained to you what the firm theoretical foundation is. Here it is again: TSI has two components: one that comes from the energy producing core taking hundreds of thousands of years to make it to the surface and therefore must be constant on time scales of centuries, and one [a very small part: 1/1000 of the base] that is driven by the magnetic field which varies in the well-known sunspot cycle. Taking away the latter at most changes TSI by 1/1000th as we saw it in 2008-2009.

      • Yet another example I fear of folks who talk Solar, but who have not availed themselves of a basic current education in solar mechanics and physics. And I do mean from a proper textbook, not the internet.

      • lsvalgaard, “Well, I think we have a good understanding of how this works. I spelled it out for you, but to no avail. The null hypothesis must be that there are no unknowns lurking about. All the data we have say that the basal temperature [and thus base TSI] does not change, and that the additional irradiance is simply that due to magnetic activity.”
        Being interested in the topic, I follow astronomical papers on what has been found with respect to changes in TSI and irradiance in similar stars to our own. I also would note that I’ve read a large number of papers and many have stated explicitly that it is unknown if TSI varies enough to explain the temperature changes seen in the Maunder Minimum.
        Example paragraph 1, page 29 of a PHd dissertation by William T. Ball:
        ” In Fig. 1.2, taken from Hall and Lockwood (2004),
        the S-index from 3709 observations of 57 Sun-like stars are plotted as the black histogram.
        Measurements of the Sun are plotted as the white histogram outline, with the
        y-scale reduced by a factor of 3; the grey histogram are a subset of stars with essentially
        flat time series, as discussed in Hall and Lockwood (2004). The implication from this plot
        is that the Sun may vary more than current observations suggest, as the S-index from the
        stars in this plot lie outside the Sun’s observed range approximately a third of the time
        (Haigh et al., 2005). Since magnetic activity is related to changes in luminosity, this has
        implications for the amount of energy received from the Sun at Earth. Therefore, solar
        analogs and their properties need to be accurately determined over long periods of time
        to precisely place the Sun among them. The conclusion from solar analog studies is that
        the range of possible fluctuations in the Sun may be very much greater than that currently
        observed. However, cosmogenic isotopes suggest that the Sun has been unusually active
        in recent decades (Solanki et al., 2004; Steinhilber et al., 2008). These results lead to the
        question, how significant an effect on terrestrial climate can the Sun have, and over what
        time scales?”
        http://wwwf.imperial.ac.uk/~wtb08/files/phd_will_ball_2012.pdf
        It is a recent dissertation which is why I picked it as the author has recently looked over the available research.
        The dissertation also happens to discuss at length the pros and cons of your position – that base TSI varies little and discusses most of your “evidence”.
        I could post various papers supporting the same points. There supporting evidence is that the earth does cool more than would be expected during periods like the Maunder Minimum if TSI varies little below the base value. And the fact that other similar stars to ours are more variable also is more circumstantial evidence. The fact that other stars are less variable may simply be due to the the fact that the period over which stars vary could be greater than the few decades of time astronomers had instruments capable of doing this type of study.
        To restate my viewpoint. I’m a skeptic about this. I don’t know if TSI varies much below the “base” case that has currently been established. The evidence you present is unconvincing and circumstantial. Especially given there is no direct measurements of TSI or irradiance during a Maunder minimum type period and the fact that there is direct evidence that the temperature of the earth tends to be colder than normal in grand minumum type periods and the direct evidence that other similar stars to ours have been observed to vary more than our own sun – I think the matter is still undecided.

        • There are VERY few really sun-like stars that are well observed. The general consensus is that the stars in question are later in their evolution than the Sun.
          I think the matter is still undecided
          Indeed, some people have a hard time giving up cherished views.
          However, cosmogenic isotopes suggest that the Sun has been unusually active in recent decades
          The cosmogenic proxies are hard to calibrate and are influenced much by climate and are different at different locations, e.g. http://arxiv.org/ftp/arxiv/papers/1004/1004.2675.pdf and http://arxiv.org/ftp/arxiv/papers/1003/1003.4989.pdf
          From direct solar observations it is now clear that there was no such Grand Modern Maximum. Even the Steinhilber paper you cite in support of this shows that, e.g. Slide 20 of http://www.leif.org/research/Does%20The%20Sun%20Vary%20Enough.pdf
          As Ball points out:
          “all variations in solar irradiance are caused by changes in surface magnetic flux emergence”
          which is an observed quantity and cannot go below zero implying a floor or basal value.

      • The Ball paper compares the [heavily tweaked] SATIRE model with observations of TSI and concludes: “The most important result is that the model recreates the change in TSI between the solar cycle minima of 1996 and 2008, in agreement with the change estimated by the PMOD composite”
        However it is now clear that the PMOD composite is wrong in asserting such a decrease, there is uncompensated degradation in the PMOD instruments as first pointed out by me here http://www.leif.org/research/PMOD%20TSI-SOHO%20keyhole%20effect-degradation%20over%20time.pdf and continuing to this day. This degradation was eventually admitted to by the experimenters, e.g. Slide 29 of http://www.leif.org/research/The%20long-term%20variation%20of%20solar%20activity.pdf [Schmutz, 2011]. Bottom line: TSI at the recent minimum was not lower than at previous minima, in addition a good proxy for EUV [and thus the magnetic flux] shows that all the way back to the 1830s the flux at every minimum has been constant, see http://www.leif.org/research/Reconstruction-Solar-EUV-Flux.pdf
        so it seems that people will go to great length to try to conform with current dogma.
        Now, it is possible that solar magnetic activity as observed is larger on average than on most solar-like stars, but that does not mean that the basal value of TSI follows suit. Different Chemical composition and evolutionary history including formation of planetary systems are likely to cause differences in the level of TSI, but since on century [or even millions of years] timescales those parameters don’t change for the Sun we don’t need to worry about them.

      • BobG March 18, 2015 at 6:46 pm
        I also would note that I’ve read a large number of papers and many have stated explicitly that it is unknown if TSI varies enough to explain the temperature changes seen in the Maunder Minimum.
        And yet, you use such a relationship as support for your large variation of TSI. In spite of the difficulty of finding solar analogs [same age, composition, planetary systems, etc.] progress has been made. This paper http://arxiv.org/pdf/1207.0176v1.pdf is a good review of the current state of the art. They conclude “This consequence exclude the possibility for the existence of a considerable fraction (e.g., ∼ 1/3) of “Maunder-minimum stars” such that having activities significantly lower than the current solar-minimum level as once suggested by Baliunas and Jastrow (1990).” and “This excludes the once-suggested possibility for the high frequency of Maunder-minimum stars showing appreciably lower activities than the minimum-Sun”. and “our Sun belongs to the group of manifestly low activity level among solar analogs, the fraction of stars below which is essentially insignificant”. Thus, the Sun does not vary a lot more than commonly thought, it already belongs to a class of low-activity stars.

      • lsvalgaard wrote, “The difference between us is that you think that because something is undecided it is legitimate to assume that it is true.”
        What I believe is that if there is not enough evidence, there is not enough evidence. Generally speaking, most new hypothesis and ideas people come up with can be ruled out with logic and science. I look at any new hypothesis or scientific view from the point of view of can I disprove it or rule it out?
        lsvalgaard wrote, ” Al Gore, it is rumored, once said “if you don’t know anything, everything is possible”. ”
        Well, if you told Al Gore your hypothesis, then I’m sure he would think it is true.
        lsvalgaard wrote, “The physical basis of SATIRE-S is that all variations in solar irradiance are caused by changes in surface magnetic flux emergence
        which means that given [we see that observationally] that all variations are caused by changes in surface magnetic flux emergence that is a good basis for the model. Your accusation of ‘out of context’ is thus misplaced. I’ll assume that was just based on ignorance without further intentions.”
        You obviously didn’t read his entire thesis. The point of view of the view of the author is that SATIRE-S was a model which quite possibly is wrong.
        lsvalgaard wrote, “”You should read the paper I directed you to. http://arxiv.org/pdf/1207.0176v1.pdf that concludes that “our Sun belongs to the group of manifestly low activity level among solar analogs, the fraction of stars below which is essentially insignificant”. ”
        I had read it. And this is one of my points. The sun AT THIS TIME seems to be a star that has low activity among solar analogs. Is this observational bias (due to when the observations have been made)? That is a common possibility listed in similar papers. My point is that the fact that there are many stars that are more active and about 10% or so (from the same paper you cited) seem to have lower activity fits right in with what would be expected if periods of low activity where the solar cycle is low happens periodically. Which means that we may not have seen our sun in a period of lower activity.
        I do think this question though will be answered in the next 20 years to my satisfaction with more stars that are observationally similar to ours being observed for longer periods. Also, if the next two solar cycles are small and with low numbers of sun spots, we will see evidence if TSI trends below the “base” or not.

        • The point of view of the view of the author is that SATIRE-S was a model which quite possibly is wrong.
          He certainly hides that well when he says that the model “provides an unbiased comparison of the composites of direct radiometric observations of total solar irradiance (TSI), which began in 1978. The excellent agreement with, in particular, the PMOD composite supports the simple model assumptions.”
          The point of the stellar connection paper was that “our Sun belongs to the group of manifestly low activity level among solar analogs, the fraction of stars below which is essentially insignificant”. So the chance that the Sun would jump down to become part of that ‘insignificant’ fraction would be insignificant. The Sun is essentially as low as it can go at sunspot minimum. This is also the finding [from helioseismology] of the Goode & Dziembowski paper [confirmed observationally by Berger et al. 2007] concluding that the Sun cannot have been any dimmer than it is now at activity minimum, and the Schrijver et al. paper (2011) that “therefore, the best estimate of magnetic activity, and presumably TSI, for the least‐active Maunder Minimum phases appears to be provided by direct measurement in 2008–2009.”
          Now, I realize that probably no amount of argument [or data] can move you off your position, but I think I have demonstrated that a score of ‘1’ that you opened with is a bit unjustified. The observations have moved me to my present view, much to my chagrin.

    • lsvalgaard wrote, “There are VERY few really sun-like stars that are well observed. The general consensus is that the stars in question are later in their evolution than the Sun.
      I think the matter is still undecided
      Indeed, some people have a hard time giving up cherished views.”
      When I read that last sentence of yours, I had to laugh because I was thinking the same thing about you.
      I disagree with you about the general consensus. I think the general consensus is that this point is undecided. Also, the evidence I’ve read indicates at least a couple of the very few stars studied that are more variable are not farther in their evolution than the sun. Should this be further substantiated, it only takes one counterexample to destroy the most finely wrought hypothesis. Of course, a more robust understanding of the physics involved which might be determined in the future would be a good way to settle it also.
      Lastly, you wrote – perhaps somewhat wickedly to see if it would be noticed, “As Ball points out:
      “all variations in solar irradiance are caused by changes in surface magnetic flux emergence””
      This statement is out of the correct context – as I’m sure you knew. He is talking about the model. Putting it in the correct context, he wrote, “The physical basis of SATIRE-S is that all variations in solar irradiance are
      caused by changes in surface magnetic flux emergence.”

  72. It is difficult to sort out the issues in a discussion of a particular (mathematical) feedback equation which is clear, and the performance of a particular electronic circuit which only feels “obliged” to obey that equation within a certain realm. This is why we do EXPERIMENTS (easy in electronics!); to find the truth.
    Back in November of 2013 (motivated by some feedback issue – probably here) I set out to write up a “few pages” and post them on my Electronotes site. It did get out of hand, 24 pages, but NOT lost in technical details (in my opinion). I think it is quite readable. It is here:
    http://electronotes.netfirms.com/EN219.pdf
    Calling attention to Fig. 12, a positive feedback of +2, I have a test circuit (similar to others there). This one has what looks like a correct analysis, suggesting a resulting gain of -1, CROSSED OUT with orange lines! The analysis was BOGUS (see green measured numbers) because the first op-amp failed as a “virtual ground” because the NEGATIVE feedback (on which the op-amp summer is based) failed.
    Just a warning note from the test bench – nothing more.

    • Thank you for the link.
      I haven’t read it yet, but a quick scan confirms–as if confirmation had been needed–that I wasn’t breaking new ground by discussion a loop gain g > 1 circuit.
      Incidentally, although I responded to your previous question by saying that because frequency analysis wasn’t germane I hadn’t looked at it much, that question made me think about what it was his consultants told Lord Monckton that made him take away the circuit misapprehension from which none of us has been able to budge him. As often happens, I got distracted before I really completed the math, but I think I would have found found that the result isn’t too surprising.
      For non-zero frequencies, I believe, the overall gain remains finite through g = 1 but undergoes a phase reversal there. And, of course, the homogeneous solution blows up beyond g = 1. That’s probably what Lord Monckton heard, and he conflated the two concepts: there’s a phase reversal at g = 1, and the non-driven response component causes the amplifier to get pinned to the supply rail.
      What I think I’d also find is that theoretically the sign of the homogeneous solution–i.e., the rail the amplifier gets pinned to–depends on the phase at which the sinusoidal stimulus starts, with one particular phase resulting, only theoretically, of course, in no homogeneous component at all. (In practice, of course, the stimulus is never precisely what we think, and the circuit isn’t either, so which rail it gets pinned to in practice is probably unpredictable.)

      • Joe – thanks for all you write.
        I did see your response comments on your original circuit. You were (too?) quick to note that I got the zero position right. This was a surprise to me because I had just concluded that I got it wrong! I think it depends on A, so that’s why we both see different answers. Anyway, your original circuit has that capacitor so it does have a pole and a first-order low-pass filter in the feedback loop. [The DC “gain” is the resistive voltage divider and the “RC time constant” is the parallel combination of the two R’s, times C. Thevenin equivalent. Thus the magnitude of the feedback rolls off below the attenuation of the voltage-divider, and phase approaches 90 degrees so that the feedback is no longer purely positive. I need to work this out and verify experimentally. ] As you noted, we are probably not particularly interested in frequency response. Step response is more revealing here. Yours seems a good way to represent a delay.
        None of my ANALOG circuits has a capacitor so no frequency dependence. Just gain changes. The discrete-time networks DO have a frequency dependence (a pole) because they have a delay, and the delay is a “phase shift” according to frequency.
        Still more to learn. Email me (Google my name or Electronotes) if you want to know if I am posting anything. I guess the main lesson is to be careful.
        Bernie

  73. Someone still needs to address my fundamental point that the effective emission height and surface temperature need not change at all in the presence of radiative gases radiating direct to space from within the atmosphere because less kinetic energy must then be returned to the surface in convective descent than was taken up from the surface in convective ascent.
    That reduced kinetic energy returning to the surface in adiabatic descent offsets the potential surface warming effect of GHGs so that no change in surface temperature or effective emission height is required
    Anyone?

    • The line in the sand you draw is an imaginary one, one in which the theoretical EEH is where its temperature matches that of Earth’s surface. Your conjecture is based on something that cannot be measured.

      • Pamela,
        I don’t follow that at all.
        The surface at 288K is obviously higher than the temperature that radiates to space (255K) and the lapse rate slope separates the two and then continues on to the cold of space.
        That ‘extra’ surface 33K is constantly cycled up and down adiabatically and retained within the mass of the atmosphere in the form of potential energy in the less dense gases above the surface layer.

      • Stephen,
        There is no ‘Earth temperature’ radiating to space at all. There is only an average final/total radiative flux from the system as a whole of 239 W/m2. This flux is what it is, not because of the physical temperature of some 2D layer somewhere inside the 3D volume of the radiating system, but because the system in question happens to absorb an average flux coming in from the Sun. Heat out simply balances heat in. On average.
        A 239 W/m2 emissive flux density is simply mathematically related to a blackbody surface temperature (through the Stefan-Boltzmann equation) at 255K. IF the Earth radiated its entire emission flux to space from ONE specific 2D blackbody surface, then this surface would have to be at 255K.
        But the Earth doesn’t radiate its entire emission flux to space from one such BB surface. It radiates from its entire 3D volume, from solid/liquid surface to the ToA, and from all gassy layers in between. Only the final, accumulated flux, the one moving out through the ToA to space, amounts to 239 W/m2. Everywhere below, it’s less, starting out as ~53 W/m2 escaping the actual surface, but also, up through the tropospheric column, turning the energy brought from the surface into the atmosphere by way of conduction and evaporation (24+88= 112 W/m2) into radiative heat to space and finally the solar heat absorbed by the atmosphere on its way down (75 W/m2). Everything is safely radiated back out to space after having done its heating job. To balance the incoming. All that enters also exits. There is nothing of the incoming from the Sun brought back to the surface to do more heating, to somehow raise temperatures ‘further’, neither by “back radiation” nor by “adiabatic descent”.

        • Kristian said:
          “Heat out simply balances heat in. On average.”
          That is correct but additonally one has an energy exchange between the mass of the surface and the mass of the atmosphere. The energy content of that exchange (KE low down and PE high up) remains in place for as long as the mass of the atmosphere is suspended off the surface.
          To find actual surface temperature as opposed to the S-B radiative calculation one has to add the kinetic energy being exchanged between surface and atmosphere at the surface to the kinetic energy at the surface derived from the S-B equation.
          For Earth that results in a surface temperature elevated above S-B by 33K.

    • The fundamental equation of radiative transfer specifies the relation between radiation at the characteristic emitting surface of a planetary body and the effective radiating temperature of that body. If the atmosphere warms, for whatever reason, the mean altitude of the characteristic emission surface must rise as long as the cause of the warming does not materially alter the lapse rate.

      • Lord Monckton,
        I gave you a reason why the atmosphere and surface does not warm and so the radiative equation shows no change.
        Please consider that reason for the atmosphere not warming.
        The reduction of kinetic energy returning towards the surface in adiabatic descent negates the warming effect of GHGs that would otherwise have occurred.

        • The reason for the atmosphere not warming applies to the radiative characteristics of the atmosphere.
          The warming that did occur was caused by a solar induced albedo (cloudiness) change which mimics the effect of a change in TOA insolation and so that can cause the temperature of the atmosphere to change.

      • Lord M
        From you: “The fundamental equation of radiative transfer specifies the relation between radiation at the characteristic emitting surface of a planetary body and the effective radiating temperature of that body.”
        From Mickey H Corbett at http://www.bishop-hill.net/blog/2015/3/20/the-ipcc-versus-stevens.html
        “Nicol argues that if you look at relaxation rates alone, adding more Co2 won’t affect this initial absorbtion . It will only effect the secondary bulk emission of IR radiation from the Co2 column to space”
        I think we need to settle something important. What is the radiating surface – the surface of the earth, or the effective radiating layer of the atmosphere – a mathematical construct that presents the radiating atmosphere as the source of emissions to space? Above I feel you dodged my main point. Mickey H Corbett provides support for my contention that the effective emitting surface is not the Earth, but is the atmosphere.
        That established, the albedo of the Earth is not directly relevant to the discussion (an in any case it doesn’t change), but the albedo of the atmosphere itself is. The radiating capacity, the ‘secondary bulk emission of IR radiation from the CO2 column to space’ is altered by adding CO2 to the atmosphere. I agree with Mickey. Because the albedo of the atmosphere is altered by the addition of CO2, the temperature of a balanced system, energy in/energy out requires that the emission from the emitting ‘layer’ be at a lower temperature than before the addition of CO2 because its efficiency has risen.
        This requires a change in your equation which is using the emissivity of the surface of the Earth as the emissivity of the emitting layer of the atmosphere. It cannot be assumed to be constant then the motivating change, the disturbance, adding CO2, changes the emissivity of the radiating layer. While the total amount of energy emitted will be the same, net, the albedo of the ‘layer’ increases and thus to achieve equilibrium, the temperature reduces. Not by as much as our fellow contributor far above this comment says, but it reduces nonetheless.

  74. That’s it, melord. Top-down. Include all factors, not jut the ones you can calculate closely. Drop ’em in as they arise. Modify or drill them down them as needed. Be that top-down puppeteer. You don’ need no stinkin’ billion-dollar baby; a desktop will do just fine — with your parameters laid out in beer on a used cocktail napkin. Game theory at its practical finest.
    You may or may not get all of your inputs right (one never does, of course), but you can plug-and-play with them in a bottom-line way that no abstruse, obtuse bottoms-up still-wet model designer can get close to. Keep up the excellent work, Lord C.!

    • Mr Jones appears uncomfortable with the idea of using a simple model to illuminate the shortcomings of more complex models. He should not imagine that “simple” means “naive”. Nor should he imagine that a complex model must necessarily outperform a simple model in determining climate sensitivity. There is much that a simple model cannot do, but the complex models are also constrained by the fact that the climate behaves as a chaotic object. See IPCC (2001, para. 14.2.2.2).

  75. Much as I would love to participate in the usual slugfest regarding solar activity and climate (an issue that I think nature will settle for us fairly soon if in fact the next two or three solar cycles are comparatively low as “expected” by at least some) I instead would like to point out a seriously neglected theorem that may be relevant to Mr. Monckton’s thesis.
    http://en.wikipedia.org/wiki/Fluctuation-dissipation_theorem
    This is a classic and quite general theorem associated with open systems that obey detailed balance. The Earth’s climate system is precisely such a system — it is an open system with inputs (e.g. solar energy, limited input from tidal and geothermal/nuclear energy) and output (overwhelmingly radiation, but with a small component from outgassing from the atmosphere).
    The point of the FDT is that it relates the spectrum of the response function to the modes through which the input energy dissipates in a very general way. In particular, if one makes a “sudden” change in the drivers of an open system, one learns a lot about the way it dissipates energy from the way it relaxes to a new equilibrium (in particular, from the spectrum of that relaxation). However, even at dynamical equilibrium, a chaotic system generates its own fluctuations — they need not be a substantial external forcing. The way the system fluctuates around its stable mean behavior contains a wealth of information about its dissipative modes.
    This is why nobody should take (most of) the climate models at all seriously, and should categorically reject the assertion put forth by the IPCC that if one takes the chaotic trajectories from 36 models and forms an envelope from them, that envelope is a reasonable picture of the probability distribution of future Earth trajectories within the chaotic regime.
    If one takes any one of those model trajectories (and here’s the point and the reason I bring it up here) and look at its fluctuations, one can easily generate its power spectrum. That spectrum is basically a fingerprint of the dissipative dynamics implicit in the model. One can then compare the spectrum to the spectrum of the actual climate and determine whether or not the model does, in fact, realize the correct dissipative dynamics, which in the case of a chaotic turbulent nonlinear highly multivariate open system in detailed balance like the Earth, means whether or not the model establishes the correct self-organized quasiparticle structures that act as dissipative modes. If the fingerprints do not match, at least within some reasonable bounds, the game is over for that particular model. It cannot be said to correctly incorporate the physics that describes the actual climate.
    A mere glance at the trajectories produced by many of the climate models is sufficient to instantly reject them on this basis. They exhibit too much positive feedback (there, finally, the point) and the fluctuations in the model consequently are much too large — causing the Earth’s model temperature to rocket up and down in an entirely nonphysical way. They also have the wrong small time-scale spectrum with broad oscillations with little small scale structure, unlike the actual climate. One imagines that they have the wrong spectrum at longer times as well, but with only 165 years of signficantly tampered data to work with, it will be hard to tell.
    rgb

    • In climate science, they don’t match detail. They match low ordered polynomial behavior over finite intervals and declare victory. Then, when the behavior fails to track beyond the interval, they insist it will rebound to it any day now, and call you nasty names.

      • Yeah, that’s about it. Briggs’ website has a whole thread of articles on the evils of fitting timeseries of non-stationary processes with low order polynomials (including but not limited to straight lines). And there are a few bright lights on this list (HenryP for example) who fit a quadratic and consider it to be predictive.
        It’s as if the last fifty or hundred years of mathematical progress never happened.
        Sigh.
        rgb

  76. What one has to keep pounding away at is the data and the data does not support not support AGW theory but it does support a solar /climate connection.
    Bob G- I am in agreement with what you expressed in your recent post.

  77. Bob G- You may find this of interest.
    PART TWO
    HOW THE CLIMATE MAY CHANGE
    Below I list my low average solar parameters criteria which I think will result in secondary effects being exerted upon the climatic system.
    My biggest hurdle I think is not if these low average solar parameters would exert an influence upon the climate but rather will they be reached and if reached for how long a period of time?
    I think each of the items I list , both primary and secondary effects due to solar variability if reached are more then enough to bring the global temperatures down by at least .5c in the coming years.
    Even a .15 % decrease from just solar irradiance alone is going to bring the average global temperature down by .2c or so all other things being equal. That is 40% of the .5c drop I think can be attained. Never mind the contribution from everything else that is mentioned.
    What I am going to do is look into research on sun like stars to try to get some sort of a gage as to how much possible variation might be inherent with the total solar irradiance of the sun. That said we know EUV light varies by much greater amounts, and within the spectrum of total solar irradiance some of it is in anti phase which mask total variability within the spectrum. It makes the total irradiance variation seem less then it is.
    I also think the .1% variation that is so acceptable for TSI is on flimsy ground in that measurements for this item are not consistent and the history of measuring this item with instrumentation is just to short to draw these conclusions not to mention I know some sun like stars (which I am going to look into more) have much greater variability of .1%.
    I think Milankovich Cycles, the Initial State of the Climate or Mean State of the Climate , State of Earth’s Magnetic Field set the background for long run climate change and how effective given solar variability will be when it changes when combined with those items. Nevertheless I think solar variability within itself will always be able to exert some kind of an influence on the climate regardless if , and that is my hurdle IF the solar variability is great enough in magnitude and duration of time. Sometimes solar variability acting in concert with factors setting the long term climatic trend while at other times acting in opposition.
    THE CRITERIA
    Solar Flux avg. sub 90
    Solar Wind avg. sub 350 km/sec
    AP index avg. sub 5.0
    Cosmic ray counts north of 6500 counts per minute
    Total Solar Irradiance off .15% or more
    EUV light average 0-105 nm sub 100 units (or off 100% or more) and longer UV light emissions around 300 nm off by several percent.
    IMF around 4.0 nt or lower.
    The above solar parameter averages following several years of sub solar activity in general which commenced in year 2005.
    If , these average solar parameters are the rule going forward for the remainder of this decade expect global average temperatures to fall by -.5C, with the largest global temperature declines occurring over the high latitudes of N.H. land areas.
    The decline in temperatures should begin to take place within six months after the ending of the maximum of solar cycle 24.
    Secondary Effects With Prolonged Minimum Solar Activity. A Brief Overview.
    A Greater Meridional Atmospheric Circulation- due to less UV Light Lower Ozone in Lower Stratosphere.
    Increase In Low Clouds- due to an increase in Galactic Cosmic Rays.
    Greater Snow-Ice Cover- associated with a Meridional Atmospheric Circulation/an Increase In Clouds.
    Greater Snow-Ice Cover probably resulting over time to a more Zonal Atmospheric Circulation. This Circulation increasing the Aridity over the Ice Sheets eventually. Dust probably increasing into the atmosphere over time.
    Increase in Volcanic Activity – Since 1600 AD, data shows 85 % approximately of all major Volcanic eruptions have been associated with Prolonged Solar Minimum Conditions. Data from the Space and Science Center headed by Dr. Casey.
    Volcanic Activity -acting as a cooling agent for the climate,(SO2) and enhancing Aerosols possibly aiding in greater Cloud formation.
    Decrease In Ocean Heat Content/Sea Surface Temperature -due to a decline in Visible Light and Near UV light.
    This in turn should diminish the Greenhouse Gas Effect over time, while promoting a slow drying out of the atmosphere over time. This may be part of the reason why Aridity is very common with glacial periods.
    In addition sea surface temperature distribution changes should come about ,which probably results in different oceanic current patterns.

  78. Seems to me the theme of this thread is how, how much, and how do we know GHGs warm what parts of the earth/atmosphere. I’m going to take a road apparently less traveled.
    According to IPCC AR5 Figure SPM.5 the incremental RF due to anthropogenic causes between year 1750 and year 2011 (261 years, 26.1 decades) is: CO2, 1.68 W/m^2; GHGs, 2.29 W/m^2. Decadal equivalent: 0.0644 W/m^2; 0.0877 W/m^2. A paper posted earlier on WUWT determined CO2 RF as 0.20 W/m^2 decadal.
    I searched through IPCC AR5 trying to find a comparable RF for natural water vapor. As we all know, it isn’t there because: 1) it’s not anthropogenic and 2) it can’t be blamed on coal fired power plants. So I looked around. Ok, so it’s Wiki.
    http://en.wikipedia.org/wiki/Cloud_forcing
    Clouds increase the global reflection of solar radiation from 15% to 30%, reducing the amount of solar radiation absorbed by the Earth by about 44 W/m². This cooling is offset somewhat by the greenhouse effect of clouds which reduces the outgoing longwave radiation by about 31 W/m². Thus the net cloud forcing of the radiation budget is a loss of about 13 W/m².[1] If the clouds were removed with all else remaining the same, the Earth would gain this last amount in net radiation and begin to warm up.
    Per Wiki the net cloud RF is 13 W/m^2. The time frame is not listed, however after comparison to a couple of popular annual global heat balances, from the magnitude I take it to be annual. 130 W/m^2 decadal.
    0.0644/130 = 0.050%; 0.0877/130 = 0.0675%
    So the net water vapor cycle RF could fluctuate .1% and the RF of the GHGs would simply vanish.
    So what’s the problem again?

    • The global net CRE according to CERES (2000-2014) is -21 W/m2 (LW effect +26 W/m2, SW effect -47 W/m2). This is also realised directly at the surface.

      • CRE means ‘cloud radiative effect’. The ‘net’ CRE is the sum of the ‘cloud LW effect’ (what the climate establishment calls their ‘greenhouse effect’) and the ‘cloud SW effect’ (what the climate establishment calls their ‘albedo effect’).
        http://ceres-tool.larc.nasa.gov/ord-tool/jsp/EBAFSelection.jsp?
        The ‘albedo effect’ of clouds is substantially larger than their ‘greenhouse effect’, globally by about 21 W/m^2. Still the IPCC and their followers claim that clouds make up about 25% of the total GHE, considerably more than CO2. Which means that, even though freely admitting that clouds in radiative terms exert an overall cooling influence on Earth’s climate, one still manages to argue that one fourth of the 33K extra warming of the global surface due to the radiative GHE – that’s about 8-8.5K – is caused directly and specifically by the atmospheric presence of clouds.
        How is this possible? How can something that clearly cools still end up warming? In reality, of course, it can’t. But in the ideal model world constructed by the climate establishment, it can.
        One simply needs to get hypothetically rid of the largest part of the ‘net effect’, that is, the ‘cloud albedo effect’ (the ‘cooling’ one). What is postulated is that if you remove the clouds from the atmosphere, then global cloud cover drops from 60 to 0%, but global albedo somehow stays exactly the same. If you put the clouds back in, you will then naturally introduce their ‘greenhouse (LW) effect’, but not their countering ‘albedo (SW) effect’. That’s how they get their 255K surface temp with a non-reflecting, non-absorbing atmosphere; 239 solar W/m^2 in through the ToA, 239 W/m^2 in to the surface.
        Clever, isn’t it? Completely detached from reality, of course. But still pretty clever …
        https://okulaer.wordpress.com/2014/11/10/the-greenhouse-effect-that-wasnt-part-1/

  79. All too often I see W/m^2 referred to as energy.
    That is incorrect.
    A watt is a power unit: Btu per English hour or kJ per metric hour.
    A generating station operating at a POWER level of 500 MW for one HOUR generates 500 MWH of ENERGY. In fact (500,000 kWh*3,412 Btu/kWh) = 1,706 E6 Btu.
    A watt without a specified time frame is useless.

    • A ‘watt’ [W] is equal to a ‘joule’ per second [J/s], that is, energy output per unit time. So the time frame is already an integral part of the power concept.
      W/m^2 is simply energy per time per area, normally called ‘power density’ or ‘energy flux density’.
      There is no inherent problem in working with flux densities when analysing an energy budget. As long as you know the time frame and the size of the study area, then it’s quite easy to translate measured flux values into absolute energy values.

  80. Lord Monckton has repeatedly referred to his consultants who disagree with me and others with regard to the circuit issues my post raised. I’m just a retired lawyer, so the reader has no reason to take my word for this over those of “a process engineer with three doctorates, who also consulted the literature; a doctor of climatology specializing in feedback analysis as applied to the Earth’s climate; and a Professor ditto (the last two being among the top six worldwide in this highly specialist field).” Frankly, though, I doubt that Lord Monckton actually consulted such eminences on the specific issues that I (as well as many others before me) raised. If he had, he would have been able to mount a more creditable defense of his thesis.
    Be that as it may, I have been spurred by Bernie Hutchins’ comments to look at the response of my post’s amplifier to sinusoidal signals and thereby have perhaps put my finger on how Lord Monckton has arrived at his erroneous view of circuit analysis. In any event, I will use this comment to memorialize the results and perhaps give Lord Monckton something to refer to in case he actually does consult experts on the specific objections that I and many others have raised.
    Although I showed a differential amplifier, i.e., one that has an inverting input port, nothing depends on that feature, and it probably avoids confusion to apply a positive signal to a non-inverting port rather than a negative signal to an inverting port. Assuming such a simplification, the resultant circuit’s equations are exactly the same as Monckton et al.’s model with \lambda_0 = A and Monckton et al.’s Table 2 values for (f, t) equal to 1-e^{(\lambda_0f-1)t/\tau}. Just as the circuit’s is, the model’s response to a sinusoidal stimulus \Delta F_t / q_t=\sin(\omega t+\phi) is simply B\sin(\omega t)+C\cos(\omega t), where B=-\omega\,\textrm{Im}(D), C=\textrm{Re}(D), D=\frac{(1/\tau+i\omega)[\sin(\phi)-i\cos(\phi)]}{(1-\lambda_0f)/\tau+i\omega}\lambda_0, and i=\sqrt{-1}. This is true independently of whether the loop gain g\equiv \lambda_0 f exceeds unity.
    In theory, that is, even with g>1 the response to a sinusoid stimulus is itself a finite-amplitude sinusoid. This is true both for the circuit and for Monckton et al.’s model. In particular, the response for g=1, where Monckton et al.’s Fig. 5 plot goes infinite, is a sinusoid whose magnitude when \omega\tau=1 is only \lambda_0\sqrt{2} times the stimulus’s and lags it in phase by 45 degrees.
    So, what does that plot’s infinity mean? Rather less than it seems to. True, as the stimulus sinusoid’s frequency approaches zero for g=1 the response sinusoid’s magnitude approaches infinity. Moreover, the stimulus and response polarities are the same just below g=1 but opposite just above it. This is no doubt where Lord Monckton got his impression that “voltage that was doing its best to become infinitely positive tries its best to become infinitely negative.”
    To the extent that this is true of the circuit, though, it is also true of the climate model; the same equations govern, so the same outputs must result. Barring some difference in the equations that Lord Monckton has studiously avoided identifying (and his insisting on characterizing the \lambda_0 parameter as not part of the feedback makes a distinction without a difference to the equations), it is not true that “In the climate, however, no such reversal is physically possible.” In the real climate, of course, the departure \Delta T from some reference temperature won’t become infinite, but neither will the circuit’s response voltage; in both cases the parameters that would dictate such results will in real life so change as no longer to require them.
    Despite what Lord Monckton imagines, the reason for not following “the Bode equation” blindly doesn’t lie in the distinction between circuits and climate. It lies in a factor common to both of them: there are limits. In the case of the amplifier circuit, the limit is the amplifier’s limited output range. In the case of the climate, it’s probably that the feedback becomes more negative as temperature rises. So long as the systems operate within regimes where the model equations apply, though, the climate model will indeed for g>1 exhibit a reversal of the temperature-departure response \Delta T with respect to the radiative stimulus, a reversal exactly analogous to the circuit output voltage’s reversal with respect to its input voltage.
    Even the low-frequency behavior just mentioned, moreover, does not mean what some may think. As was just observed, the output at low frequency does indeed switch from in phase to 180 degrees out of phase as the loop gain g crosses unity. So one might think this tells us something about the response to a step stimulus, which some would characterize as a zero-frequency stimulus. But that would be incorrect, as my post demonstrated.
    The problem, both for the circuit and for the climate, is that the foregoing analysis holds only when the stimulus is a perfect sinusoid. Even if it were the same as a perfect sinusoid from some time zero onward but had been equal to zero at all times before, the response would differ from the perfect-sinusoid case in that it would include not only the sinusoidal component set forth above but also a “homogeneous” component equal to \frac{\lambda_0\omega\cos(\phi)-(1-\lambda_0f)\sin(\phi)}{[(1-\lambda_0f)\omega]^2/\tau}\lambda_0e^{(\lambda_0f-1)t/\tau}: the homogeneous component is an exponential that dies out for g\equiv \lambda_0 f1.
    No matter how closely g approaches unity from the left, that exponential eventually dies out. And, on the right, the direction in which it grows without bound is not indicated by Monckton et al.’s Fig. 5 plot but rather dictated by the phase of the sinusoid that starts at time zero.
    In short, the mathematics requires considerable interpretation, and care must therefore be taken in drawing inferences from it. Now, circuits are more likely to be fairly linear in the region of interest than the climate is, so there are indeed good reasons to be particularly careful in applying linear-systems techniques to the climate. But distinctions such as failure to “transit to the negative rail” are not among them.

    • Although I don’t know Lord Monckton, I’ve followed the debate for years. Lord Monckton is one of the most colorful, interesting, knowledgeable and well spoken commentator for the skeptic position. I have not always agreed with everything he says or writes, but I do respect him and admire him. One thing I do believe to be true about Lord Monckton is that he is honest. If he wrote he consulted certain experts, I believe that he did. You have written that you doubt this – which to me is falling back on skills you learned as a lawyer. It is a great court room tactic to begin by denigrating the opposing sides honesty before talking about specifics.
      I can’t imagine Lord Monckton “outing” people who have helped him or agree with him on some fact without them agreeing to this and them also actually wanting to enter the “fray”. Because if he identifies them, it is possible that they would be harassed and attacked depending on where they work or even denied promotions. There is the movement from liberals and progressives to find ways of “punishing” skeptics. And skeptics have suffered in various ways due simply to not sharing a viewpoint.

      • A little exert from Professor Lockwood’s recent conclusions
        from the activity minima in the MM, the (unsigned) OSF falls
        to about 1014 Wb, which should be compared to values around
        1015 Wb at the peaks of recent solar cycles. Thus the Earth’s
        residence times in fast or intermediate flows would be an order
        of magnitude shorter in the MM than during recent solar cycles
        and enhancements in mean solar wind speeds would therefore
        be of order a tenth that in recent cycles, i.e. of order 25 km s−1, if
        fast and slow solar wind speeds remained the same and changes
        are all caused by variations in Earth’s residence times in such
        flow regimes. Therefore we conclude that solar wind speeds
        would be relatively uniform in theMM(between about 250 and
        275 km s−1, i.e. roughly half the average seen in modern times).
        The authors are grateful to many scientists for

      • Oh, I don’t doubt that he’s consulted experts at some point; indeed, I suspect I know who one of them is. I just don’t think he got input from them regarding the specifics of my post or understood them if he did. If he had gotten that input and understood it, his response would have been better.

        • Your second claim is most unusual. I know of no reputable journal that practices that, and the website of the Chinese journal you submitted to does not mention [or as far as I can see] support that the reviewer does not know the authors. You may wish to restate your ‘misspoken’ [I think that is the current euphemism] comment.

      • BobG is very kind. One of those with whom I have discussed the Bode problem has indeed asked to be kept anonymous, because he wants his paper to be peer reviewed and published before anyone plays politics with his scientific research. I am content to wait till that important paper appears. It could be the silver bullet that slays the bloodsucking global-warming vampire.

    • Joe is quite correct in that his original circuit did not have to be a differential amplifier. It would have been much better if he avoided the (-) input. It does however offer me an opening to make the point that feedback is neither positive or negative according to whether a non-inverting (+) or an inverting (-) terminal is used for the feedback. Instead, everything that happens around the loop (gains, phase shifts) matters. My write-up from Nov. 2013 has several relevant examples of multiple inversions leading to positive feedback (the concept is VERY well understood):
      http://electronotes.netfirms.com/EN219.pdf
      As for a frequency-dependent feedback loop, if you start out with what you believe is pure positive feedback, any amplitude attenuation in the loop (or course) reduces the degree of positive feedback. Any phase shift will, initially, also reduce positive feedback. ENOUGH phase shift will make the feedback negative. (Joe’s low-pass feedback will have a max phase shift of 90 degrees however).
      More alarming for EE’s is the case where (intentionally implemented) pure negative feedback starts to become less negative because of unintended phase shift. This can cause oscillations. Often such oscillations ARE in fact rail-to-rail ugly trapezoids (non-linear effects). And it matters not if you intended to input such frequencies or not, and you can’t just ignore them. Noise will always set them off.
      On the other hand, this sort of oscillation need NOT be rail-to-rail (power supply limits may not matter). For example, if you hang a scope cable (a capacitor) on the output of a unity-gain op-amp “follower” it can set off oscillations because of the phase shift due to the probe capacitance (perhaps 100 pF) and the output resistance (perhaps 100 ohms) of the real op-amp. This can be up around, say, 3 MHz, and is a small superposition on the desired waveform. The waveform looks very “fuzzy”. The oscillation is small and does not get to the rails because the op-amp output can’t “slew” anywhere near fast enough (limited by dV/dt for a particular op-amp type).
      Analog electronics is complicated in itself. At least it sits neatly on a lab bench!

    • Here are the frequency response (magnitudes) and the step responses for Joe’s circuit.
      http://electronotes.netfirms.com/JB.jpg
      I did make the input non-inverting, and set the two resistors equal (just to make an example). Thus the feedback gain from the resistors is 1/2 (for DC frequency, and for long time) so the response at these points is A/(1-A/2). The critical gain A for sign change is thus A=2.
      In the figure, the top two panels are for A=1 so the DC and long-time gains are 2, 1 on the opposite ends. The middle two panels are for A=1.9 (still stable), and is similar except for much larger gains with feedback. If we try A=2.1, the gain should be -42. This is the frequency response MAGNITUDE (bottom left panel). But not the exponentially ramping step response!
      Usually the freq. resp. is calculated as the product of all distances, from a frequency point on the j-omega axis, to each zero, divided by the corresponding product of distances to the poles. Thus unstable right-half-plane poles do not show – unless someone codes in an alarm. But the step response ramps up to warn us.
      What happens at A=2 where 1-(1/2)*2 = 0? The first freq. resp. point (DC) gives a divide-by-zero error. The step response is a LINEAR ramp.
      All makes sense.

  81. Mr Born’s continuing failure to grasp the very simple point I am making about the inapplicability of the Bode system-gain equation to the climate seems to arise from one error and one misinterpretation on his part. The error was his assumption that a change in the altitude of the characteristic-emission surface consequent upon a radiative forcing would cause the temperature of that surface to change. No. As previously explained, under the assumption that insolation, emissivity and albedo are near-constant, so will the temperature of the characteristic-emission surface be constant.
    The misinterpretation – commonplace, but wrong – is in his assumption that the Planck parameter is a feedback just like all the others. No. In fact, it plays a special role in the determination of climate sensitivity, is not summed with the true feedbacks but is, uniquely, instead multiplied by their sum, is separately multiplied by the initial forcing to determine zero-feedback warming, again unlike any of the true feedbacks, and is better expressed in Kelvin per Watt per square meter of forcing as part of the reference frame for the determination of climate sensitivity (see Roe, 2009, for a discussion).
    So to his criticisms of those of us who question the applicability of the Bode system-gain equation, which he seems to believe is of universal applicability in dynamical systems. No. It was not designed for systems – such as the climate – in which the output (temperature change, in the climate) is the instrument by which the system self-equilibrates. Nor is it applicable to systems, such as the climate, in which the feedbacks do not cause a reversal in the direction of the output at a loop gain of unity. In an electronic circuit, the singularity in the Bode equation has a physical meaning, though even there it should be treated with caution. In the climate the singularity does not represent physical reality.
    The matter is actually very simple. The Bode equation appears to suggest that at loop gains much above the process engineers’ rule-of-thumb design limit of 0.1 a very rapid amplification of the original perturbation occurs. In electronic circuits, that is indeed what happens, unless they have been specifically designed to act homeostatically and to resist feedback amplification.
    The climate, on the other hand, is pronouncedly thermostatic, so that no curve remotely resembling the Bode equation at or near the singularity can apply. Yet in the models (see e.g. Hansen, 1988 for some worked examples) the equation is applied strictly, and without even making the obvious allowance for the fact that asymptotic upper and lower bounds on temperature change must apply, just as they must apply to an electronic circuit, in which generating an infinite voltage is not possible.
    It is all very well for Mr Born to say airily that the input parameters would change to prevent climate sensitivities approaching infinity, but the modelers do not sufficiently change the parameters in their models to reflect the homeostatic real world.
    Those worked examples, incidentally, demonstrate that the modelers apply the Bode equation naively to the direct warming to obtain the amplified warming. As so often, Mr Born should really be taking issue with them and not with me. They are applying the Bode equation in a fashion in which it cannot legitimately be applied. Mr Born has so far been silent on how they actually use the equation: it is in their manner of using it that climate sensitivity ends up being prodigiously exaggerated.
    And, though Fourier analysis in the frequency domain is sometimes useful, in the present instance it is not really helpful.
    Absurd papers such as Murphy (2009) claim that climate sensitivities of 10+ K are possible: but the sole reason for that conclusion is their misapplication of the Bode equation to an object to which – in its unmodified form – it simply does not apply.
    Interestingly, on seeing our paper the climate extremists did not even attempt to suggest that there is nothing wrong with a strict application of the Bode system-gain equation to the climate. As soon as they saw the output curve, they realized that that curve does not apply to the climate. So, instead, one of them tried to deny that the equation is used in the models. He said, “I’m a GISS modeller: I know the equation is not used in our model.” But it is used in his model, though he had not realized this. And it is used in a fashion that is calculated to generate the absurdly high climate sensitivities that the output curve as it approaches the singularity would seem to suggest.
    Another commenter – at the World Federation of Scientists’ annual conference two years ago – said that the equation works well enough up to a loop gain of 0.8 – which, conveniently, is the IPCC’s implicit upper bound on its central climate-sensitivity interval. However, it is likely that in the real world all values >>0.1 there should be a toning-down of the equation’s output.
    Mr Born is entitled to his opinion that the voltage in an electronic circuit does not change direction at the singularity in the Bode equation: but, if he will put “feedback-induced oscillation” or “from the positive to the negative rail” into a search engine he may learn otherwise.
    However, the central point is that the models do not at present adjust the Bode equation even to the extent of attempting to model the effect of the necessary asymptotes on the output of the equation not only at the singularity but also across quite a substantial interval either side of it. For this reason, among many others, they are prone to exaggerate climate sensitivity. Any reasonable correction of the Bode equation would cause climate sensitivity to fall by two-thirds to four-fifths.
    That is why researchers far more versed in these matters than Mr Born or me have realized that the problem I have drawn to their attention is serious and requires attention. And, whether Mr Born likes it or not, they will now address the real problem that the Bode equation represents, a problem that has appeared previously in the literature, and – if current indications are confirmed – they will find climate sensitivity considerably lower than the overheated values currently in vogue.

    • Lord Monckton –
      You wrote: ” but, if he will put “feedback-induced oscillation” or “from the positive to the negative rail” into a search engine he may learn otherwise.”
      I tried both these on Google. Found nothing relevant – or so it seemed to me. Can you give actual links?

    • Lord Monckton. Addendum. The problem remains your saying:
      “ Mr Born is entitled to his opinion that the voltage in an electronic circuit does not change direction at the singularity in the Bode equation: but, if he will put “feedback-induced oscillation” or “from the positive to the negative rail” into a search engine he may learn otherwise. ”
      Searching with these terms leads mainly to OSCILLATORS. No one is suggesting that oscillators do not go negative (or at least become less positive), over and over in a cycle. That’s what an oscillator is all about. There are many MECHANISMS of achieving electrical oscillations going back more than 100 years.
      Sitting exactly on the singularity of the Bode equation is one theoretical CONDITION to achieving oscillation. [In practice one must exceed that singularity ever so slightly, impose limiting (or rely on the limiting of power supply rails), and accept a small measure of harmonic distortion.] The Bode singularity is not a mechanism that causes the individual reversals. It is a condition that indicates the circuit polarity reversals can occur.
      Is it possible that you are conflating the condition with the mechanism?
      Joe’s circuit is first-order and not an oscillator (see my graphs above). Well – it does “oscillate” at DC – it is an integrator at the singularity. Its impulse response is a step. Its step response is a linear ramp (as I stated).
      I am talking electronics here – nothing about climate. But I think we have to get the electronics (cowering on a lab bench) understood first.

      • All we need to do is understand how the Bode equation is actually used in climate models. It represents a physical reality in an electronic circuit; it does not represent a physical reality in the climate.

      • You said “It represents a physical reality in an electronic circuit; it does not represent a physical reality in the climate.”
        Likely so. But, sorry to say, it appears you don’t understand the electronics.

  82. It would be easier to instead note where the climate models have gone right, its a much shorter list, e.g. they spell “climate” correctly. Not sure there is anything else for this list.

      • I had not read any of Lockwood’s recent papers. However, out of curiosity, I read http://www.eiscat.rl.ac.uk/Members/mike/publications/pdfs/2014/308_OSF1_jgra51127.pdf
        “5. Conclusions
        We have studied the putative discontinuity in the international sunspot number record in around 1 January 1946. Our results confirm the conclusion of Svalgaard [2011] that the discontinuity is present in the widely used data set that is available from most data centers. However, Svalgaard’s estimate that a 20% correction is here shown to be an overestimate. Using the RGO/SOON spot area, Svalgaard [2011] actually found an 18% correction (it is not clear from his paper how this was quantified) that he rounded up to 20%, but both values are far out on the far tail of the probability distribution found here. We suggest preferred value should be based on sunspot data alone, maintaining its independence from geomagnetic data: we have demonstrated problems with early IDV data caused by a failure to maintain that independence. Hence, we recommend an optimum correction of 11.6%, with the 2σ uncertainty range being 8–14%. The geomagnetic data provide broad confirmation of this with IDV giving and optimum correction of 10.3% and IDV(1d) giving 7.9%. “

        • Lockwood is usually behind the curve with usually flawed papers and this one is no exception. He knows quite well [but pretends not to] that the Locarno sunspot overcount is determined by direct comparison between the weighted and unweighted sunspot counts, as explained here:
          http://www.leif.org/research/Locarno-Overcount.png
          But not to worry, give him a few years and he will catch up as he always does. It is just a pity that he carpet bombs the field with bad papers.

    • so, you disagree with Lockwood when he shows that he agrees with me? His Figure 2.
      Now, probably we are both a bit wrong in the derivation of the solar wind speed [V]. The slow increase from 1870 until today is likely to be an artifact caused by not taking into account [we don’t precisely know how to] the decreasing main field of the Earth, which causes geomagnetic activity to be a bit higher than it should be for equal solar wind.

  83. I say let us see how this prolonged solar minimum plays out before saying with 100% certainty this is how it is ,this is how it will be.
    If this prolonged solar minimum becomes established going forward answers should be coming? At least I hope so.
    Right now for me it is wait and see. I think unexpected scenarios will arise going forward. However ,I have no thought if it will favor any ones particular stance or not.
    The more I look into this the more I feel that is not known rather then what is known. To much gray area is out there for my taste.

    • Mike Borgelt

      Global warming occurs when the incoming solar energy from the sun exceeds the outgoing electromagnetic energy emitted by the Earth.

      Electromagnetic energy, eh? Are you sure that’s not long wave thermal energy emitted from the earth into space?

  84. Lord M: Grist for another of your mills:
    Climatic Change
    DOI 10.1007/s10584-015-1343-
    “The social cost of atmospheric release” by Drew T. Shindell
    http://download.springer.com/static/pdf/498/art%253A10.1007%252Fs10584-015-1343-0.pdf?auth66=1426965671_834f21d7c410f4d1f1bd3906430c9cce&ext=.pdf
    His arguments are entirely based on a ‘high discount rate’. As you have shown several times, mitigation is much cheaper when the discount rate is high. A response from you to this paper would invite an animated discussion here. I look forward to it!

  85. It seems to me that errors in thinking are evident in many of the posts that are made in this thread. One error is to think that all mathematical relations from the variable X to the variable Y are functional relations. Another is to think that this functional relation is linear. If and only if the relation is functional and linear, the ratio of Y to X is a constant. This kind of thinking leads amateur and professional climatologists alike to the conclusion that there is necessarily the constant that is called the “climate sensitivity” when this conjecture is untestable from the nonobservability of Y, the “equilibrium surface air temperature.”

  86. Climate Change зависит от солнечной активности “has solar activity influence on the Earth’s global warming?” http://eurecalert.org/e/5rst via,от альбедо Earth а альбедо зависит от формы планеты.Однобокий рост внутреннего ядра http://go.nature.com/w6iks3 деформируя кору изнутри http://shar.es/lnJxx0 изменяет форму Earth.”Een acute aanvalvan ontlastingsdrang die “ERNSTIG EN NAKEND” is”. http://www.davidhanauer.com/buckscounty/rindingrocks,http://www.bbc.com/news/science-environment-31322817.Monumental Earth Changes приводит к изменению гравитации планеты http://news.discovery.com/earth/global-wrming/earths-gravity-dips-from-antarcticice-loss-141001.htm изменяет наклон Earth от которого тоже зависит альбедо “Earth Mattres:Earth’s tilt bringsbigshanges during seasons of the year -altoonaMirror.com-Altoon,PA/News,Sports,jobsComunity information-the Altoona Mirror http://shar.es/1fFoSQ and орбиту Earth от которой также зависит альбедо http://wp.me/p7y41-vDW.Эти и другие изменения подтверждающие ссылки на которые я пока не нашёл продолжаются поэтому происходит колебание солнечной радиации и зависящее от уровня солнечной радиации в атмосфере Earth давление в верхних слоях атмосферы.От давления в атмосфере зависит преобладание ветров а значит и погоды в различных регионах Earth http://www.newsweek.com/speking-green-tongues-scientist-discovers-new-plant-language-264734

  87. Okay, a wrap-up.
    Lord Monckton has given an intelligible answer to only one of the three main issues I raised in the post to which the head post here was supposedly a response. My post was principally directed to Monckton et al.’s “transience fraction” r_t, one of the “parameters” of their model.
    Monckton et al.’s Table 2 gives r_t values that are implausible. Among the reasons I find them implausible is the one I gave upthread: negative-feedback step responses sometimes exceed positive-feedback ones. I therefore asked that the authors explain how they obtained the Table 2 values from the Gerard Roe paper, whose Fig. 6 was ostensibly the source.
    That graph provided only one curve—or, arguably, three—yet Monckton et al.’s Table has five rows. It should have been a simple matter to explain how the authors thus multiplied curves. Instead, Lord Monckton merely said, “If Mr Born disagrees with Dr Roe’s curve, he is of course entirely free to substitute his own.” Why the evasion?
    The use of r_t in Monckton et al.’s Table 4 to arrive at temperature-increase value implies there’s warming yet to be realized from the CO2-concentration increase we’ve already experienced: the already-experienced 0.8 K divided by an r_t value of 0.6 yields 1.3 K ultimately expected, or 1.3 K – 0.8 K = 0.5 K yet to be realized. But their §6 seems to draw just the opposite inference: “[T]he model fairly reproduces the change in global temperature since then, suggesting that the 0.6 K committed but unrealized warming mentioned in AR4, AR5 is non-existent.” In explanation, Lord Monckton variously just referred us to Table 4 or served up this credulity-challenging assertion: “The definition of “committed but unrealized warming” that the IPCC has in mind is not the warming to equilibrium that has not yet occurred as a result of our past sins of emission, but the warming that it considers ought to have occurred to date.” Be that as it may, I do think I can conclude that I interpreted their use of r_t correctly, which was my real concern; some confusingly described IPCC assertion and the inference Monckton et al. drew with regard to it probably aren’t too important.
    Lord Monckton actually did give a straight answer (in the midst of inapposite ones) in response to my observation that in applying their model Monckton et al. computed the response to forcing that increased over time as though it had appeared all at once at the beginning of the interval. His answer was, yes, they do treat the stimulus as having arrived all at once, but the resultant difference in temperature-change output is not large.
    But whether you consider it large depends on how you’re using it. Let’s say that over the past 75 years CO2 concentration has doubled, we have observed the (arguably) resultant change in global-average temperature, and we want to infer the equilibrium climate sensitivity from that transient climate response. As Monckton et al. teach, we multiply the resultant forcing by the product of the transience fraction r_t values for t=75 and the corresponding equilibrium climate-sensitivity parameters \lambda_\infty=\lambda_0/(1-\lambda_0f) for respective feedback-coefficient values f. Let’s say we find that the observed temperature matches the resultant fourth-row value: the feedback coefficient thereby inferred is 2.1 watts per square meter per Kelvin, which implies an equilibrium climate sensitivity of 3.4 K.
    But that’s the inference drawn from assuming that the entire forcing increase occurred 75 years ago rather than steadily over the last 75 years. If we make the latter, more correct assumption instead, we conclude that the observed temperature increase is closer to what we would expect from the table’s last-row feedback coefficient f=2.9 watts per square meter per Kelvin—which corresponds to an equilibrium climate sensitivity of 12 K, not 3.4 K—than from the fourth-row feedback coefficient f=2.1 watts per square meter per Kelvin. If we had a denser table, we could conclude that the feedback coefficient f is actually around 2.6 watts per square meter per Kelvin, from which we would infer an equilibrium climate sensitivity of 6.2 K rather than the 3.4 K that the Monckton et al. approach would suggest.
    In other words, although there may be cases in which the two approaches yield similar results, it takes quite a bit of care to avoid misleading results from the Monckton et al approach.

  88. Further wrap-up.
    As to the circuit issue, I’m not going to revisit the substance. I don’t think that will be resolved until Lord Monckton goes back to his consultants and goes over facts such as those I raised in my post and the comments upthread. There may be some hope, because I may have detected a little walking back already. (“It is of course obvious that the Bode graph as it stands does not really represent even an electronic circuit. There are obvious asymptotic bounds preventing an infinite positive (or, above unity, negative) voltage from being output by the circuit.”) Or maybe not.
    I am cognizant of Lord Monckton’s observation that “Mr Born has so far been silent on how they actually use the equation: it is in their manner of using it that climate sensitivity ends up being prodigiously exaggerated.” I will continue to be silent about that, because I don’t know how IPCC modelers use “the Bode equation,” whatever Lord Monckton means by that. It would not surprise me at all that such modelers apply mathematics badly, but Lord Monckton has offered only conclusory statements to that effect. I’ve observed only that the arguments Lord Monckton has made about the differences between climate and circuits lack merit. True, circuits differ from climate. But saying things like “transit to the negative rail” doesn’t inspire confidence in Lord Monckton’s having identified ways in which modelers have failed to recognize relevant distinctions.
    Nor will I accept Lord Monckton’s invitation to go look up oscillators. No, I’m not an expert, but I was dealing with oscillators during the Johnson administration, so neither am I a complete tyro. I assume Lord Monckton will eventually revisit with his experts the specifics we’ve raised here and that he will then quietly drop the circuits topic or re-spin it. Anyway, I think I’ve done my part on that topic. I’ll just continue with others to cringe in vicarious embarrassment until he finally grabs the line so many of us have thrown him.

  89. As to two other issues, on which Lord Monckton has expended a lot of argument and seems to be confusing semantics with substance, I’ll give it one more go. Here’s the first one.
    Monckton of Brenchley: “The error was his assumption that a change in the altitude of the characteristic-emission surface consequent upon a radiative forcing would cause the temperature of that surface to change. No.”
    My comment about effective radiating altitude was definitional, not factual, and, although I think I was right, nothing depended on that.
    Let’s think this through. I’ll go slowly.
    The effective radiating altitude now, today, is h_{now}. A century ago it was h_{then}<h_{now} because the atmosphere's optical density then was lower then than it is now. As Lord Monckton says, the effective radiating altitude always has the same temperature T_{eff}. So the temperature at h_{then} was T_{eff} a century ago, and the temperature now at h_{now} is T_{eff}, but a century ago the temperature at h_{now} was lower: it was T_{eff}-(h_{now}-h_{then})r_{lapse}. In other words, the temperature at what is now the effective radiating altitude has increased, although the temperature at whatever is the effective radiating altitude is always T_{eff}. (Please read that last sentence again.)
    If in our model world we ignore or set to zero the various feedbacks (including lapse-rate feedback), the surface temperature a century ago was T_{then}=T_{eff} + r_{lapse} h_{then}, lower than its current value T_{now}=T_{eff} + r_{lapse} h_{now}: the surface temperature has risen by the same amount as the temperature at h_{now} (or, for that matter, at h_{then}).
    Okay, still with me? If not, go back and read again. I’ll wait.
    Ready? Okay.
    Now, the purpose of the original post's emission-altitude discussion was to define what we mean by “forcing.'' According to our model, the surface temperature is a response to “forcings.” If we ignore the transience fraction, the forcing value we use for now in our model must be greater than the forcing value we use for then if, as we just said it did, the surface temperature now exceeds the surface temperature then. If the forcing then was zero, in fact, the forcing now, according to the model without feedback, must be \Delta T_{now}/\lambda_0. This is true even if the system is at equilibrium, i.e., even if just as much radiation is being emitted as is being received.
    So how do we characterize that forcing? Well, suppose that optical density increased in an instant by the amount that we’ve been assuming it increased over a whole century. At that instant, the effective radiating altitude would increase instantaneously from h_{then} to h_{now}. But the surface temperature wouldn’t, not instantaneously. And neither would the temperature at h_{now}, even though it has just become the effective radiating altitude. That is, although we say that the effective radiating altitude’s temperature is always T_{eff}, we have assumed, for the sake of defining “forcing,” a situation in which thermal inertia would force it initially to depart from T_{eff}.
    In that situation there would be a radiative imbalance equal (in our linearized world) to (h_{now}-h_{then})r_{lapse}/\lambda_0. It is that hypothetical radiation imbalance that we take as today's value of forcing: it’s the radiative imbalance that would have occurred if the optical density had just instantaneously changed from the reference value to today’s value.
    The point of that discussion was not to assert that the effective radiation altitude is changing much in temperature; it was to adopt a definition of “forcing” that can afford us a non-zero forcing value even though there's no radiative imbalance. We have to define forcing in that way so that the zero-feedback value of \Delta T will equal \lambda_0 \Delta F. If instead we considered the forcing to be zero whenever the radiation flow is in balance, then our model would dictate \Delta T=0 when there's no imbalance, and that’s not what we want.
    That was my point in raising the radiation altitude. But suppose I’m somehow wrong about how forcing arises. Everything in my post dealt only with how the model treats the forcing we have, not with how we got it. So what does any misapprehension of mine about how forcing arises have to do the transience fraction r_t, the subject of my post?

  90. Monckton of Brenchley: “The misinterpretation—commonplace, but wrong—is in his assumption that the Planck parameter is a feedback just like all the others. No. In fact, it plays a special role in the determination of climate sensitivity, is not summed with the true feedbacks but is, uniquely, instead multiplied by their sum.”
    This is just a different way of looking at the same thing.
    Lord Monckton envisions the following block diagram. Before feedback he sees a forward block whose operation is multiplication by the “Planck climate-sensitivity parameter” \lambda_0. Once we add feedback there’s also a feedback block whose operation is multiplication by f and whose output is added to the forward block’s no-feedback input to become the composite input of the forward, multiply-by-\lambda_0 block.
    At least for present purposes, I have no quarrel with that.
    But I descend an abstraction level and look at the multiply-by-\lambda_0 block’s internals. Internal to that block for the toy, one-box arrangement I used as illustration is an integrator with -1/\lambda_0 feedback. So long as those internals’ time constant—i.e., \lambda_0c_p in my diagram—is small with respect to the time resolution of interest, that block is essentially the multiply-by-\lambda_0 block that Lord Monckton sees; I’ve just looked inside it.
    I included the internals for purposes of exposition. I put them there to show how positive feedback could slow r_t. I needn’t have employed that expedient, but it had the added virtue of showing that temperature does not respond instantaneously to radiative forcing. At the time resolution Lord Monckton was dealing with, though, that response may appear instantaneous, so there’s nothing (or nothing simple enough to describe here) wrong with Lord Monckton’s treating it as occurring instantaneously.
    What’s wrong is to imagine that anything substantive in this context turns on whether we treat the “Planck” coefficient as feedback or gain. (And, no, I don’t object to using the latter term when no power is applied.) All that matters is the behavior that flows from whatever treatment we choose.

  91. Finally: I’m afraid I’ve found this exchange disappointing.
    Monckton et al.’s innovation was to divide the step response by its t=\infty value and thereby tease out the portion that exposes the effect of feedback on equilibrium response. A significant number of this blog’s regular readers, including me, have made simple models, the essences of which are their step responses. Monckton et al. drew inferences by using their own, Table 2 series of step responses for selected levels of feedback.
    Those responses did not seem consistent with each other, so many of us were interested in precisely how Monckton et al. inferred the Table 2 values from the Gerard Roe paper. The explanation should have been easy to give. Yet the authors, or at least Lord Monckton, insisted on withholding that information.
    The paper raises other, subtler issues, but I doubt that we will ever reach them if we can’t get information about the basics.

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