Guest essay By Christopher Monckton of Brenchley
This series discusses climatology’s recently-discovered grave error in having failed to take due account of the large feedback response to emission temperature. Correct the error and global warming will be small, slow, harmless and net-beneficial. The series continues to attract widespread attention, not only here but elsewhere. The ripples are spreading.
My reply to Roy Spencer’s piece on our discovery at drroyspencer.com has attracted 1400 hits, and the three previous pieces here have attracted 1000+, 350+ and 750+ respectively. Elsewhere, a notoriously irascible skeptical blogger, asked by one of his followers whether he would lead a thread on our result, replied that he did not deign to discuss anything so simple. Simple it is. How could it have been thought the feedback processes in the climate would not respond to the large pre-existing emission temperature to the same degree as they respond to the small enhancement of that temperature caused by adding the non-condensing greenhouse gases to the atmosphere? That is a simple point. But simple does not necessarily mean wrong.
The present article develops the math, which, though not particularly complex, is neither simple nor intuitive. As with previous articles, we shall answer some of the questions raised in comments on the earlier articles. As before, we shall accept ad interim, ad argumentum or ad experimentum all of official climatology except what we can prove to be incorrect.
Let us conduct a simple Gedankenexperiment, running in reverse the model of Lacis et al. (2010), who found that, 50 years after removing all the non-condensing greenhouse gases from the atmosphere, the climate would have settled down to a new equilibrium, giving a slushball or waterbelt Earth with albedo 0.418, implying emission temperature 243.3 K. We shall thus assume ad experimentum that in 1800 there were no greenhouse gases in the atmosphere. For those unfamiliar with the logical modes of argument in scientific discourse, it is not being suggested that there really were no greenhouse gases in 1800.
Lacis found that, only 20 years after removal of the non-condensing greenhouse gases, global mean surface temperature would fall to 253 K. Over the next 30 years it would fall by only 1 K more, to 252 K, or 8.7 K above the emission temperature. Thus, subject to the possibility that the equatorial zone might eventually freeze over, surface temperature in Lacis’ model settled to its new equilibrium after just 50 years.
One question which few opponents in these threads have answered, and none has answered convincingly, is this: What was the source of that additional 8.7 K temperature, given that there were no non-condensing greenhouse gases to drive it? Our answer is that Lacis was implicitly acknowledging the existence of a feedback response to the 243.3 K emission temperature itself – albeit at a value far too small to be realistic. Far too small because, as shown in the previous article, Lacis allocated the 45.1 K difference between the implicit emission temperature of 243.3 K at the specified albedo of 0.418 and today’s global mean surface temperature of 288.4 K (ISCCP, 2018) as follows: Feedback response to emission temperature 252 – 243.3 = 8.7 K; warming directly forced by the naturally-occurring, non-condensing greenhouse gases (288.4 – 252) / 4 = 9.1 K, and, using Lacis’ feedback fraction 0.75, feedback response to warming from the non-condensing greenhouse gases 27.3 K: total 45.1 K. This asymmetric apportionment of the difference between emission temperature and current temperature implies that the 8.7 K feedback response to emission temperature is only 3.6% of 243.3 K, while the 27.3 K feedback response to greenhouse warming is 300% of 9.1 K. Later we shall demonstrate formally that this implausible apportionment is erroneous.
It will be useful to draw a distinction between the pre-industrial position in 1850 (the first year of the HadCRUT series, the earliest global temperature dataset) and the industrial era. We shall assume all global warming before 1850 was natural. That year, surface temperature was about 0.8 K less than today (HadCRUT4) at 287.6 K, or 44.3 K above emission temperature. Lacis’ apportionment of the 44.3 K would thus be 8.7 K, 8.9 K and 26.7 K.
We shall assume that Lacis was right that the directly-forced warming from adding the naturally-occurring, non-condensing greenhouse gases to the air was 8.9 K. Running the experiment in reverse from 1850 allows us to determine the feedback fraction implicit in Lacis’ model after correction to allow for a proper feedback response to emission temperature. Before we do that, let us recall IPCC’s current official list of feedbacks relevant to the derivation of both transient and equilibrium sensitivities:
IPCC’s chosen high-end feedback sum implies Charney sensitivities somewhere between minus infinity and infinity per CO2 doubling. Not a particularly well constrained result after 30 years and hundreds of billions of taxpayers’ dollars. IPCC’s mid-range feedback sum implies a mid-range Charney sensitivity of only 2.2 K, and not the 3.0-3.5 K suggested in previous IPCC reports, nor the 3.3 K in the CMIP3 and CMIP5 ensembles of general-circulation models. No surprise, then, that in 2013, for the first time, IPCC provided no mid-range estimate of Charney sensitivity.
None of the feedbacks listed by IPCC depends for its existence on the presence of any non-condensing greenhouse gas. Therefore, in our world of 1800 without any such gases, all of these feedback processes would be present. To induce a feedback response given the presence of any feedback process, all that is needed is a temperature: i.e., emission temperature. Since feedback processes are present, a feedback response is inevitable.
Emission temperature is dependent on just three quantities: insolation, albedo, and emissivity. Little error arises if emissivity is, as usual, taken as unity. Then, at today’s insolation of 1364.625 Watts per square meter and Lacis’ albedo of 0.418, emission temperature is [1364.625(1 – 0.418) / d / (5.6704 x 10–8)]0.25 = 243.3 K, in accordance with the fundamental equation of radiative transfer, where d, the ratio of the area of the Earth’s spherical surface to that of its great circle, is 4. Likewise, at today’s albedo 0.293, emission temperature would be 255.4 K, the value widely cited in the literature on climate sensitivity.
The reason why official climatology has not hitherto given due weight (or, really, any weight) to the feedback response to emission temperature is that it uses a degenerate form of the zero-dimensional-model equation, ΔTeq = ΔTref / (1 – f ), where equilibrium sensitivity ΔTeq after allowing for feedback is equal to the ratio of reference sensitivity ΔTref to (1 minus the feedback fraction f). The feedback-loop diagram for this equation (below) makes no provision for emission temperature and none, therefore, for any feedback response thereto.
The feedback loop in official climatology’s form of the zero-dimensional-model equation ΔTeq = ΔTref / (1 – f )
Now, this degenerate form of the zero-dimensional-model equation is adequate, if not quite ideal, for deriving equilibrium sensitivities, provided that due allowance has first been made for the feedback response to emission temperature. Yet several commenters find it outrageous that official climatology uses so simple an equation to diagnose the equilibrium sensitivities that the complex general-circulation models might be expected to predict. A few have tried to deny it is used at all. However, Hansen (1984), Schlesinger (1985), IPCC (2007, p. 631 fn.), Roe (2009), Bates (2016) are just a few of the authorities who cite it.
Let us prove by calibration that official climatology’s form of this diagnostic equation, when informed with official inputs, yields the official interval of Charney sensitivities. IPCC (2013, Fig. 9.43) cites Vial et al. (2013) as having diagnosed the CO2 forcing 
, the Planck parameter 
and the feedback sum 
from simulated abrupt 4-fold increases in CO2 concentration in 11 CMIP5 models via the linear-regression method in Gregory (2004). Vial gives the 11 models’ mid-range estimate 
of the feedback sum as 
W m–2 K–1, implying 
, and the 
bounds of 
as 
, i.e. 
.
The implicit CO2 forcing ![clip_image006[1]](http://wattsupwiththat.files.wordpress.com/2018/04/clip_image0061.png?quality=75 "clip_image006[1]"){kind=small}
, in which fast feedbacks were included, was 
W m–2 compared with the 
W m–2 in Andrews (2012). Reference sensitivity 
, taken by Vial as 
, was 
above the CMIP5 models’ mid-range estimate 
. Using these values, official climatology’s version of the zero-dimensional-model equation proves well calibrated, yielding Charney sensitivity 
on 
, near-exactly coextensive with several published official intervals from the CMIP3 and CMIP5 climate models (Table 2).
From this successful calibration it follows that, though the equation assumes feedbacks are linear but some feedbacks are nonlinear, it still correctly apportions equilibrium sensitivities between forced warming and feedback response and, in particular, reproduces the interval of Charney sensitivities projected by the CMIP5 models, which do account for nonlinearities. Calibration does not confirm that the models’ value 
for the feedback fraction or their interval of Charney sensitivities is correct. It does confirm, however, that, at the official values of f, the equation correctly reproduces the official, published Charney-sensitivity predictions from the complex general-circulation models, even though no allowance whatsoever was made for the large feedback response to emission temperature.
Official climatology trains its models by adjusting them until they reproduce past climate. Therefore, the models have been trained to account for the 33 K difference between emission temperature of 255.4 K and today’s surface temperature of 288.4 K. They have assumed that one-quarter to one-third of the 33 K was directly-forced warming from the presence of the naturally-occurring, non-condensing greenhouse gases and the remaining two-thirds to three-quarters was feedback response to that direct warming. Therefore, they have assumed that the feedback fraction was two-thirds to three-quarters of equilibrium sensitivity: i.e., that f was somewhere between 0.67 and 0.75.
As a first step towards making due allowance for the feedback response to emission temperature, official climatology’s version of the zero-dimensional-model equation can be revised to replace the delta input and output signals, indicating mere changes in temperature, with entire or absolute values. Note that the correct form of any equation describing natural occurrences (or any natural law) must be absolute values: the use of deltas is only permissible if the delta-equations are correctly derived from the absolute equation. Accordingly, ΔTeq = ΔTref / (1 – f ) should be Teq = Tref / (1 – f ). The revised feedback loop diagram is below:
After amendment to replace delta inputs and outputs with absolute values, official climatology’s form of the zero-dimensional model equation becomes
Teq = Tref / (1 – f )
To find f where the reference and equilibrium temperatures are known, this revised equation can be rearranged as f = 1 – Tref / Teq. In the reverse Lacis experiment, reference temperature Tref before feedback is the sum of emission temperature TE and the additional temperature ΔTE = 8.9 K that is the direct warming from adding the naturally-occurring, non-condensing greenhouse gases to the air. Thus, Tref = TE + ΔTE = 243.3 + 8.9 = 252.2 K. Equilibrium temperature Teq = 287.6 K is simply the temperature that obtained in 1850, after 50 years of the reverse Lacis experiment. Then f = 1 – Tref / Teq = 1 – 252.2 / 287.6 = 0.123, only a fifth to a sixth of official climatology’s value. The reason for the difference is that, unlike official climatology, we are taking correct account of the feedback response to emission temperature.
Next, how much of the 35.4 K difference between Tref = 252.2 K and Teq = 287.6 K is the feedback response to emission temperature TE = 243.3 K, and how much is the feedback response to the direct greenhouse-gas warming ΔTE = 8.9 K? Simply take the product of each value and f / (1 – f) = 0.14, thus: 243.3 x 0.14 = 34.1 K, and 8.9 x 0.14 = 1.3 K. We prove that this is the correct apportionment by using the standard, mainstream form of the zero-dimensional-model equation that is universal in all dynamical systems except climate. The mainstream equation, unlike the degenerate climate-science form, explicitly separates the input signal (in the climate, the 255.4 K emission temperature) from any amplification (such as the 8.9 K warming from adding the non-condensing greenhouse gases to the atmosphere).
The mainstream zero-dimensional model equation is Teq = Tref μ / (1 – μβ), where Tref is the input signal (here, emission temperature); μ = 1 + ΔTref / Tref is the gain factor representing any amplification of Tref such as that caused by the presence of the naturally-occurring, non-condensing greenhouse gases; β is the feedback fraction; μβ is the feedback factor, equivalent to f in climatology’s current version of the equation; and Teq is equilibrium temperature at re-equilibration of the climate after all feedbacks of sub-decadal duration have acted.
The feedback loop for this corrected form of the zero-dimensional-model equation is below:
The feedback loop diagram for the standard zero-dimensional-model equation
Teq = Tref μ / (1 – μβ)
One advantage of using this mainstream-science form of the zero-dimensional model is that it explicitly and separately accounts for the input signal Tref and for any amplification of it via the gain factor μ in the amplifier, so that it is no longer possible either to ignore or to undervalue either Tref or the feedback response to it that must arise as long as the feedback fraction β is nonzero.
It is proven below that the apportionment of the 35.4 K difference between Tref = 252.2 K and Teq = 287.6 K in 1850 derived earlier in our Gedankenexperiment is in fact the correct apportionment. Starting with the mainstream equation, in due time we introduce the direct or open-loop gain factor μ = 1 + ΔTref / Tref. The feedback factor μβ, the product of the direct or open-loop gain factor μ and the feedback fraction β, has precisely the form that we used in deriving the feedback fraction f as 1 – (243.3 + 8.9) / 287.6 = 0.123, confirming that our apportionment was correct.
Note in passing that in official climatology f is at once the feedback fraction and the feedback factor, since official climatology implicitly (if paradoxically) assumes that the direct or open-loop gain factor μ = 1. In practice, this particular assumption leads official climatology into little error, for the amplification of emission temperature driven by the presence of the non-condensing greenhouse gases is a small fraction of that temperature.
But was it reasonable for us to assume that the 287.6 K temperature in 1850, before Man had exercised any noticeable influence on it, was an equilibrium temperature? Well, yes. We know that in the 168 years since 1850 the world has warmed by only 0.8 K or so, and official climatology attributes all of that warming to Man, not Nature.
Was it reasonable for us to start with Lacis’ implicit emission temperature of 243.3 K, reflecting their specified albedo 0.418 on a waterbelt Earth in the absence of the non-condensing greenhouse gases? Why not start with Pierrehumbert (2011), who said that a snowball Earth would have an albedo 0.6, implying an emission temperature 221.5 K? Let’s do the math. The feedback fraction f = μβ would then be 1 – (221.5 + 8.9) / 287.6 = 0.20.
Thus, from a snowball Earth to 1850, the mean feedback fraction is 0.20; from a waterbelt Earth to 1850, it is 0.12; and at today’s albedo 0.293, implying an emission temperature 255.4 K, it is 1 – (255.4 + 8.9) / 287.6 = 0.08. Which is where we came in at the beginning of this series. For you will notice that, as the great ice sheets melt, the dominance of the surface albedo feedback inexorably diminishes, whereupon the feedback fraction falls over time.
Though the surface albedo feedback may have dominated till now, what about the biggest of all the feedbacks today, the water-vapor feedback? The Clausius-Clapeyron relation implies that the space occupied by the atmosphere may (though not must) carry near-exponentially more water vapor – a greenhouse gas – as it warms. Wentz (2007) found that total column water vapor ought to increase by about 7% per Kelvin of warming. Lacis (2010) allowed for that rate of growth in saying that if one removed the non-condensing greenhouse gases from today’s atmosphere and the temperature fell by 36 K from 288 to 252 K, there would be about 10% of today’s water vapor in the atmosphere: thus, 100% / 1.0736 = 9%.
Specific humidity (g kg–1) at pressure altitudes 300, 6000 and 1000 mb
However, though the increase in column water vapor with warming is thus thought to be exponential, the consequent feedback forcing is approximately logarithmic (just as the direct CO2 forcing is logarithmic). What is more, a substantial fraction of the consequent feedback response is offset by a reduction in the lapse-rate feedback. Accordingly, the water-vapor/lapse-rate feedback response is approximately linear.
Over the period of the NOAA record of specific humidity at three pressure altitudes (above), there was 0.8 K global warming. Therefore, Wentz would have expected an increase of about 5.5% in water vapor. Sure enough, close to the surface, where most of the water vapor is to be found, there was a trend in specific humidity of approximately that value. But the water-vapor feedback response at low altitudes is small because the air is all but saturated already.
However, at altitude, where the air is drier and the only significant warming from additional water vapor might arise, specific humidity actually fell, confirming the non-existence of the predicted tropical mid-troposphere “hot spot” that was supposed to have been driven by increased water vapor. In all, then, there is little evidence to suggest that the temperature response to increased water vapor and correspondingly diminished lapse-rate is non-linear. Other feedbacks are not large enough to make much difference even if they are non-linear.
Our method predicts 0.78 K warming from 1850-2011, and 0.75 K was observed
One commenter here has complained the Planck parameter (the quantity by which a radiative forcing in Watts per square meter is multiplied to convert it to a temperature change) is neither constant nor linear: instead, he says, it is the first derivative of a fourth-power relation, the fundamental equation of radiative transfer. Here, it is necessary to know a little calculus. Adopting the usual harmless simplifying assumption of constant unit emissivity, the first derivative, i.e. the change ΔTref in reference temperature per unit change ΔQ0 in radiative flux density, is simply Tref / (4Q0), which is linear.
A simple approximation to integrate latitudinal variations in the Planck parameter is to take the Schlesinger ratio: i.e., the ratio of surface temperature TS to four times the flux density Q0 = 241.2 Watts per square meter at the emission altitude. At the 255.4 K that would prevail at the surface today without greenhouse gases or feedbacks, the Planck parameter would be 255.4 / (4 x 241.2) = 0.26 Kelvin per Watt per square meter. At today’s 288.4 K surface temperature, the Planck parameter is 288.4 / (4 x 241.2) = 0.30. Not much nonlinearity there.
It is, therefore, reasonable to assume that something like the mean feedback fraction 0.08 derived from the experiment in adding the non-condensing greenhouse gases to the atmosphere will continue to prevail. If so, the equilibrium warming to be expected from the 2.29 Watts per square meter of net industrial-era anthropogenic forcing to 2011 (IPCC, 2013, Fig. SPM.5) will be 2.29 / 3.2 / (1 – 0.08) = 0.78 K. Sure enough, the least-squares linear-regression trend on the HadCRUT4 monthly global mean surface temperature dataset since 1850-2011 (above) shows 0.75 K warming over the period.
But why do the temperature readings from the ARGO bathythermographs indicate a “radiative energy imbalance” suggesting that there is more warming in the pipeline but that the vast heat capacity of the oceans has absorbed it for now?
One possibility is that not all of the global warming since 1850 was anthropogenic. Suppose that the radiative imbalance to 2010 was 0.59 W m–2 (Smith 2015). Warming has thus radiated 2.29 – 0.59 = 1.70 W m–2 (74.2%) to space. Equilibrium warming arising from both anthropogenic and natural forcings to 2011 may thus eventually prove to have been 34.8% greater than the observed 0.75 K industrial-era warming to 2011: i.e., 1.0 K. If 0.78 K of that 1.0 K is anthropogenic, there is nothing to prevent the remaining 0.22 K from having occurred naturally owing to internal variability. This result is actually consistent with the supposed “consensus” proposition that more than half of all recent warming is anthropogenic.
The implication for Charney sensitivity – i.e., equilibrium sensitivity to doubled CO2 concentration – is straightforward. The models find the CO2 forcing to be 3.5 Watts per square meter per doubling. Dividing this by 3.2 to allow for today’s value of the Planck parameter converts that value to a reference sensitivity of 1.1 K. Then Charney sensitivity is 1.1 / (1 – 0.08) = 1.2 K. And that’s the bottom line. Not the 3.3 K mid-range estimate of the CMIP5 models. Not the 11 K imagined by Stern (2006). Just 1.2 K per CO2 doubling. And that is nothing like enough to worry about.
None of the objections raised in response to our result has proven substantial. For instance, Yahoo Answers (even less reliable than Wikipedia) weighed in with the following delightfully fatuous answer to the question “Has Monckton found a fatal error?”
What he does is put forward the following nonsensical argument –
1. If I take the 255.4 K temperature of the earth without greenhouse gases, and I add in the 8K increase with greenhouse gases I get a temperature of 263.4 K.
2. Now, what I’m going to say is say that this total temperature (rather than just the effect of the greenhouse gases) leads to a feedback. And if I use this figure I get a feedback of 1 – (263.4 / 287.6) = 0.08.
And the problem is … how can the temperature of the planet (255.4 K) without greenhouse gases then lead to a feedback? The feedback is due to the gases themselves. You can’t argue that the feedback and hence amplified temperature due to greenhouse gases is actually due to the temperature of the planet without the greenhouse gases! What he’s done is taken the baseline on which the increase and feedback is based, and then circled back to use the baseline as the source of the increase and feedback.
So, I’m afraid it’s total crap …
The error made by Yahoo Answers lies in the false assertion that “the feedback is due to the gases themselves”. No: one must distinguish between the condensing greenhouse gases (a change in the atmospheric burden of water vapor is a feedback process) and the non-condensing greenhouse gases such as CO2 (nearly all changes in the concentration of the non-condensing gases are forcings). All of the feedback processes listed in Table 1 would be present even in the absence of any of the non-condensing greenhouse gases.
Another objection is that perhaps official climatology makes full allowance for the feedback response to emission temperature after all. That objection may be swiftly dealt with. Here is the typically inspissate and obscurantist definition of a “climate feedback” in IPCC (2013):
Climate feedback An interaction in which a perturbation in one climate quantity causes a change in a second, and the change in the second quantity ultimately leads to an additional change in the first. A negative feedback is one in which the initial perturbation is weakened by the changes it causes; a positive feedback is one in which the initial perturbation is enhanced. In this Assessment Report, a somewhat narrower definition is often used in which the climate quantity that is perturbed is the global mean surface temperature, which in turn causes changes in the global radiation budget. In either case, the initial perturbation can either be externally forced or arise as part of internal variability.
IPCC’s definition thus explicitly excludes any possibility of a feedback response to a pre-existing temperature, such as the 255.4 K emission temperature that would prevail at the surface in the absence of any greenhouse gases or feedbacks. It was for this reason that Roy Spencer thought we must be wrong.
Our simple point remains: how can an inanimate feedback process know how to distinguish between the input emission of temperature of 255 K and a further 9 K of temperature arising from the addition of the non-condensing greenhouse gases to the atmospheric mix? How can it know it should react less to the former than to the latter, or (if IPCC’s definition is followed) not at all to the former and extravagantly to the latter? In the end, despite some valiant attempts by true-believers to complicate matters, our point is as simple – and in our submission as unanswerable – as that.
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Christopher,
Would it help clarity if you replaced your original T with a (T plus delta2T) right from the start, to show that feedbacks are operating even at what some wrongly call an equilibrium?
Then carry this through the algebra you develop above. Hope this helps and does not retard. Geoff
Mr Sherrington makes a constructive suggestion, but I fear it would make little difference. Most of those who have tried to dismiss our result in these threads know perfectly well that we are in substance right, and no amount of dressing up the actually very simple argument in other clothing would make any difference. These are not people in search of the truth: they are totalitarians wedded to the Party Line for good or ill. In due course we shall find a reasonably serious climate journal to publish our result, which will gradually become well enough known that no one will be able to ignore it, however uncongenial the true-believers may find it.
I remain open to a proper argument against our result: but none has thus far been forthcoming.
Off the top of my head I believe you can decompose an infinite geometric series into T + delta T and from there show that the climatology definition of feedback is a special case of the general feedback equation.
In effect decompose the signal into DC and AC and show that the sum of the sum(AC) + sum(DC) = sum(AC+DC).
done as a mathematical proof I don’t believe climatology can prevail.
The series continues to attract widespread attention, not only here but elsewhere. The ripples are spreading.
So funny.
gammacrux is right. It is amusing that the word is spreading so quickly. If our result were laughably wrong, it would not merit anything like the attention it is getting.
The essential issue here is will your paper pass peer review in time to be considered in AR6?
I know that that is out of your hands, but that must be the target.
Sorry Lord Monckton.
I meant “so funny” because your assertion is just wishful thinking.
Ah, it appears that the furtively pseudonymous “gammacrux”, having no scientific point to make, is resorting to mere yah-boo. But the evidence is against “gammacrux”. Just look up Yahoo answers. Now, why would anyone bother to try to trash our result as Yahoo has tried to do, unless our result was a lot more serious than the totalitarian shriekers here have tried to suggest?
Teq = Tref / (1 – f )
============
This is also the formula for the sum of an infinite geometric series, which is the mathematical equivalent of how feedback works physically.
It is hard to argue with this being anything other than the correct description for feedback when it is a simple enough matter to expand this formula into the underlying series, showing each of the iterations of the feedback loop.
Reply below next comment
And again, there is a much bigger mistake, which is much simpler to explain, logically more stringent and it has much more profound consequences.
Clouds make up for most of the albedo, how much exactly can be discussed. Commonly that share would be named to be 2/3s or more of the total albedo, which means something north of 2/3 * 0.31 * 342 = 70.7W/m2. I would confirm that and name the figure to be more like 80W/m2.
While this reflection of solar radiation will doubtlessly lower surface temperatures, clouds will also provide a positive radiative forcing, which then is treated as part of the GHE. As clouds have both, negative and positive effects on surface temperatures, seperating these two effects as if they had nothing to do with each other, is illogical, or straigt forward stupid.
Anyhow, the GHE of clouds is treated as a part of the total GHE, and such they will compete with other GHGs. So the bigger the share of clouds in that role, the smaller the possible contribution of vapour, CO2, methane and so on..
What the IPCC, what the consensus modellers tell us is this: clouds had a negative forcing of somewhere between 13-20W/m2 over all. There would be about +30W/m2 by (re)emission of LWIR and -44 to -50W/m2 be reflection of solar radiation. These +30W/m2 would be their contribution to a total GHE of about 155W/m2.
At that point there are logical mistakes all over the place, which are to be corrected.
1. If clouds emit 30W/m2 downward, they will also emit radiation upward. A fact that is otherwise well acknowledged, just look at the NOAA chart.
2. If clouds emit about 30W/m2 upward as well, both sides of that coin will neutralize each other.
3. The (negative) net forcing will then logically be equal to the albedo effect, which would be either 44-50W/m2, or more realistically, 70-80W/m2. That is as long as we follow the claim clouds would not at all reflect LWIR.
4. A massive negative net forcing of that kind however is not in line with any observations. Indeed, what we see are rather higher temperatures with clouds covers, than without. Ironically that seems specifically true for low clouds in the tropics. (low tropical clouds should have the strongest net negative effect of all, according to the IPCC).
5. Weather data show that temperatures during the night drop by 85% less when there is an overcast sky as compared to a clear sky. So we do know, that clouds stop LWIR from emitting at least as efficient as they block solar radiation by reflection.
6. This effect could not be achieved by merely emitting 30W/m2 of LWIR upward AND downward, which is a neutral thing after all.
7. Rather point 4 and 5 indicate, that clouds must provide a positive forcing that is at least as strong as their total negative forcing. And of course, that positive forcing is competing with other GHGs in that role.
8. As the NOAA chart (correctly!) indicates, total negative cloud forcing amounts to 79W/m2 (reflection of SWR) + 31W/m2 (emission of LWIR) = 110W/m2 (presented as 23% and 9% of 342W/m2).
9. Thus clouds must provide > 110W/m2 to the total GHE of only 155W/m2.
10. The 155W/m2 figure (which is consistent with the infamous 33K GHE) is derived from an assumed 391W/m2 surface emissions (which corresponds to an emissivity of 1 at 288K) and 236W/m2 (=(1-0.31)*342). Real surface emissivity however is not 1, but rather 0.92. Accordingly emissions will only be 360W/m2, dropping the GHE to only 124W/m2.
11. Finally the GHE constituted by all GHGs like CO2, vapour, methane.. can only be 124 – >110 = <14W/m2.
12. So the GHE itself is nothing more, than the logical consequence of deliberately wrong accounting the radiative effects of clouds.
https://de.scribd.com/document/370673949/The-Net-Effect-of-Clouds-on-the-Radiation-Balance-of-Earth-3
“It is hard to argue with this being anything other than the correct description for feedback “
It would be, if there were some system for which Tref is the input and T_eq was the output. But there isn’t.
So if clouds are 110 and total is 124 what is the H2O W/metre 2 and what is the CO2 W/metre2?
As I just wrote, all GHGs together (considering clouds are not definid as GHG), their forcing must be <14W/m2, or less than 3°K with the given numbers.
“However, Hansen (1984), Schlesinger (1985), IPCC (2007, p. 631 fn.), Roe (2009), Bates (2016) are just a few of the authorities who cite it.”
But they are, as always, not quoted. Let’s hear what they actually said.
The first two feedback diagrams are very odd. They show a loop with a feedback function but no amplifier. As an electronic circuit, they would tell you the feedback gain of a length of wire. They are not the “official climatology” model.
T_ref is not an input to a feedback loop. It is the expected output of a reference device without feedback; what would be called open loop gain. Here is Roe’s diagram:
As you’ll see, the feedback model has a change of forcing ΔR as input, and a ΔT as output. It is true that from this can be derived the relation ΔT_eq = ΔT_ref/(1-f). But that isn’t their feedback model. They are not saying that ΔT_ref is a feedback to ΔT_eq. It’s a ratio of two outputs of two different systems.
However, it is explicit that both ΔT’s are proportional to the forcing increment ΔR. That is why the ratio tends to f for small increments. It is a derivative. And why it makes no sense to introduce absolute quantities, which do not tend to zero, into such a ratio. The most you can get is a f value of 1 or -∞.
And so the equation, which first appears I think in the third diagram
ΔT_eq = T_eq -T_ref
is just wrong. ΔT_eq is the response of the feedback circuit to a ΔR. The difference T_eq -T_ref is just the difference between the operating points, possibly incremented, of two different systems. It makes no sense.
What is inside the box called “reference system”? Oh, it is the pre industrial system. So, the climate modellers failed to account for feedback within that box, as MB points out?
No, it is what would happen without feedback. Basically, the Planck sensitivity. You don’t have to worry about feedback within the box. It just has prescribed input/output behaviour. It could be an op amp, which has plenty of feedback within the box. But you just need to know the transfer function.
It is always nice when one does not have to think inside the box, and need only think outside the box!
Outside the box thinking is often wrong!
Mr Stokes finds that Dr Roe’s paper makes no sense. He should take that matter up with Dr Roe. And he seems stubbornly insistent that emission temperature, if unamplified, cannot induce a temperature feedback even where feedback processes are plainly present. In this, he is simply wrong.
“Mr Stokes finds that Dr Roe’s paper makes no sense.”
It makes perfectly good sense. It just has nothing to do with the caricature that you provide. Nor does “official climatology”. That is why analyses like this are useless unless you actually quote the theory that you are attempting to represent.
It is a caricature of feedback, too. In your third fig, you give μ = 1 + ΔT_ref/T_ref. Now in any sensible analysis of feedback or amplifiers, gain is a property of the circuit or device. It is not a function of the perturbation (ΔT_ref) that it may be subject to.
Mr Stokes quibbles about the definition of amplifier gain in a feedback loop. Let me instruct him, then, that his proposed gain factor, which is not unitless, is simply wrong. The gain factor is nothing more nor less than the unitless factor by which the signal from the input node is amplified before being passed to the output node. As in any amplifier, one can either build in or otherwise specify or set a gain factor, and that gain factor is – as a matter of extremely elementary mathematical definition – simply 1 plus the ratio of the change and the input signal.
“As in any amplifier, one can either build in or otherwise specify or set a gain factor, and that gain factor is – as a matter of extremely elementary mathematical definition – simply 1 plus the ratio of the change and the input signal.”
Again, the gain factor is a property of the amplifier. It is the number you use to multiply the input signal to get the output. Gain being a function also of the signal (“ratio of change”) would certainly create a nonlinear response. But more importantly, the gain would no longer simply be a property of the amplifier.
And in this case, if you take out the signal dependent component, the gain is fixed at 1, which is not interesting.
Of course the gain factor is a property of the amplifier. What else could it possibly be? But that does not stop us from specifying what that gain factor is.
“But that does not stop us from specifying what that gain factor is.”
But you haven’t, as a property of the amplifier. Your definition was μ = 1 + ΔT_ref/T_ref. ΔT_ref is the signal. It is not a property of the amplifier. In the limit of small signals, μ = 1. No gain at all.
Nick –
Equations relate dependent and independent variables. It is convention to put the dependent variable (to be calculated) left of the = sign and the independent variables to the right. Thus μ = 1 + ΔT_ref/T_ref is assumed a calculation of μ, perhaps based on an observation of the temperatures signals (if known!) on the right. If solved for ΔT_ref, the very same equation might oblige one to propose a value of μ as a known. Isn’t it anyone’s choice – subject to avoiding confusion – when possible!
Bernie
“is assumed a calculation of μ”
No, it’s the definition, as is explicit in the text above:
” μ = 1 + ΔTref / Tref is the gain factor representing any amplification of Tref”
He even reproves “official climatology” for leaving out the improvement:
“Note in passing that in official climatology f is at once the feedback fraction and the feedback factor, since official climatology implicitly (if paradoxically) assumes that the direct or open-loop gain factor μ = 1.”
“Official climatology” of course does nothing like this. And as usual, no quotes.
Mr Stokes should read the head posting, where he will find plenty of references to papers discussion the zero-dimensional-model equation. If official climatology were to use the corrected form of the equation, then and only then it would accord a value greater than unity to the reference gain factor mu. That factor is dropped from official climatology’s version of the zero-dimensional-model equation because the input signal (emission temperature) is suppressed and replaced by the reference sensitivity. it is in the input that official climatology incorporates what mainstream science treats separately as the reference gain factor mu.
Lord M,
“Mr Stokes should read the head posting, where he will find plenty of references to papers discussion the zero-dimensional-model equation.”
Yes, there are plenty of references. But you never quote what they say. Which is not connected with what you write about.
Mr Stokes’ remark is mere yah-boo.
Nick – you lost me with “….The first two feedback diagrams are very odd. They show a loop with a feedback function but no amplifier. As an electronic circuit, they would tell you the feedback gain of a length of wire. …” Feedback or feedforward???
Mr. Monckton had the same misunderstanding and even quoted you as being in agreement. I am surprised that YOU missed it because you have several times posted my Fig. 6 which had a unity gain amplifier with a feedback of +2/3 around it for a gain of 3.
We assume ideal op-amps to have a VOLTAGE output of ZERO output impedance. When we move this voltage along for later use, we use a wire – same voltage and zero impedance along it. If you prefer, take the output of the first op-amp and put in a voltage-follower op-amp, or 100 of them in series, connecting them with – – – – Wires!
Perhaps more simply, put an amplifier in the feed-forward position and give it a gain of A – any number. Any number includes A = 1.
I would suppose that, in climate models, proposing a feedback mechanism is merely a rational for making a number larger than Nature apparently made it.
Bernie,
“I am surprised that YOU missed it because you have several times posted my Fig. 6 which had a unity gain amplifier with a feedback of +2/3 around it for a gain of 3”
It has a voltage gain of 1. But it has available a very large current gain, and this makes it possible for the circuit to feed back a current which is actually twice the input current, so that the current appearing at the first op amp input node is three times the current supplied; hence the gain. There is no way that a simple wire, which is what Lord M has placed in the corresponding position, could do anything like that.
As I commented, it seems to me that, if implemented as a circuit it would simply be some kind of feedback device (a resistor?) with a short from inlet to outlet. I don’t see how that could yield anything of interest, and it certainly isn’t any kind of “official climatology”.
Mr Stokes has now begun to realize how wrong the official approach to feedback is. For it is rather obvious that the feedback loop diagram in red in the head posting is precisely a representation of the form of the zero-dimensional-model equation that official climatology uses. Now that he can see that diagram, he can at once see how daft it is that the input signal and the gain block have both been suppressed, and the open-loop gain has instead been represented as though it were the input signal. Yes, it is official climatology. And yes, as Mr Stokes says, it is wrong. He has begun to get the point.
Nick – SORRY – you are wrong. Two different things here.
What you refer to as a “feedback diagram” is what an EE calls a “signal-flow-graph” and it represents either voltage (usually) or current (the “nodes” being called “state-variables” or just signals), but NOT an assortment of both; UNLESS some of the paths are not pure numbers (pure meaning “gains” – to include attenuators like 2/3) but are instead, something like a path arrow denoted 1/R (I = V/R) which specifically (mathematically – Ohm’s Law) “converts” a voltage to a current. It would be absurd to claim that a path could have ANY gain A but NOT a gain of A=1.
The circuit of my Fig. 6 is a realization of the flow-graph with voltage nodes. Here once more for convenience:
http://electronotes.netfirms.com/EN219Fig6.bmp
The state-variables (variables of the state of the network) are voltages. The exact currents are not involved (we usually just consider voltage-dividers and currents summing to zero). Op-amps are not current amplifiers, and are capable of supplying only a few milliamps (perhaps 10 ma). [By the way, the feedback gain of -2/3 is positive 2/3 because we allow for the inversion of the first op-amp.] The feedback view is an interpretation of an alternative means of setting a gain of 3. But you don’t need G = 1/(1-f) to analyze the op-amp circuit easily, and correctly.
This is standard electronics and beyond question.
As for climate – I don’t know. But, IF I were a CAGW advocate, and a temperature rise as seen in Nature were too small for my preferred agenda, and I was not able to provide a convincing argument for a direct gain of 3, I might propose an argument for positive feedback (white ice melts to dark water, etc.). But just claiming feedback, arguing over minute details of something undemonstrated, and dragging innocent (and well-established) engineering into it seems like a poor joke.
Bernie,
“it represents either voltage (usually) or current (the “nodes” being called “state-variables” or just signals), but NOT an assortment of both”
My objection is to the complete omission of a device in the forward section. You could have an amplifier of voltage gain 1, say. But ultimately, feedback has to involve feeding back a fraction of the power from the forward stage. So there has to be something there to supply power.
“Op-amps are not current amplifiers, and are capable of supplying only a few milliamps (perhaps 10 ma).”
A device is a current amplifier if it outputs more current than it took in. An op amp may output milliamps, but it should be taking in nanoamps. As a device, your circuit takes in current V_in/R. But it has very low output impedance. If you put a load R from output to earth, the current flowing through it would be 3*V_in/R, after taking in V_in/R. Something has amplified current.
“and dragging innocent (and well-established) engineering into it seems like a poor joke”
But the enthusiast for doing this is Lord M. And there are others at WUWT. You won’t see circuit diagrams in the IPCC reports. And Arrhenius long predated circuits, amplifiers, Bode and all, and still got a sensitivity of 4 K/doubling.
“For it is rather obvious that the feedback loop diagram in red in the head posting is precisely a representation of the form of the zero-dimensional-model equation that official climatology uses.”
It isn’t at all obvious until you quote what “official climatology” actually uses. Not your version, theirs. I showed Roe’s diagram – it was nothing like this. Your red diagram does not represent anything in climatology. It is yours alone.
Nick said (12:02 PM) “…. My objection is to the complete omission of a device in the forward section. You could have an amplifier of voltage gain 1, say. But ultimately, feedback has to involve feeding back a fraction of the power from the forward stage. So there has to be something there to supply power.. . .”
Nope – just supply voltage. First off – there is something there – the first op-amp or the “error amplifier” of the flowgraph. Just as good a voltage source (or an algebraic numerical variable) as any amplifier A (or mu). Keep in mind also that the structure is a LOOP. As you could have multiple feedbacks, you could have multiple input/output points. Feedback for one could be feedforward for another. It just IS what it is and knows not what you call it.
Secondly, it is not “Power” (like Watts) that is fed back, but voltage. This does not require the amplifier to give up anything. If I feed back 1 volt of a 10 volt signal, the amplifier output remains 10 volts and does not go to 9.
Nick also said: “A device is a current amplifier if it outputs more current than it took in. An op amp may output milliamps, but it should be taking in nanoamps.”
Not true – an ideal op-amp TAKES IN ZERO current (typical real input bias is in p-amps) – that’s the basic design principle. The op-amp does require a few ma from its power supply pins for housekeeping and the output supplies or sinks currents (including unbalanced Vin/R types), and may drive a modest current to a later stage. This “collecting-up magic” is through the MASSIVE amounts of negative feedback already considered in all the usual op-amp configurations. But it does NOT amplify current. Current plays the role in an op-amp circuit that currency does in a financial network – balances the books.
[A basic transistor can amplify current – we used to design using the parameter hfe (beta). A special IC called an “operational transconductance amplifier” has a current as an output. But op-amps deal with voltages.]
Nick also said “As a device, your circuit takes in current V_in/R. But it has very low output impedance. If you put a load R from output to earth, the current flowing through it would be 3*V_in/R, after taking in V_in/R. Something has amplified current.”
NOPE again. If you put on a resistor R as a load, true Vout/R could flow as long as it did not (net) exceed the rated current output. If it did, the operating negative feedback would fail.
Perhaps more to the point BTW, I think if one wants to promote or criticize feedback as an electronics/climate comparison one should emphasize the “active” feedback of the electronics case (power supply required) as opposed to the seemingly passive climate case. ( I think Frank and some others suggested this as well.)
Nick also said:
“ But the enthusiast for doing this is Lord M.”
If I understand Monckton correctly this is because he (unwisely?) has chosen to accept all climate doctrine except the limited areas where he chooses to contest. Kind of like a boxing match where you freely allow your opponent to punch you at will except perhaps in the left elbow!
And feedback ideas predate electronics and Bode, etc., like steam engine “governors”. Old engineering counts.
Bernie
“First off – there is something there – the first op-amp or the “error amplifier” of the flowgraph”
Are we looking at the same graph? The top, red one. Do you mean the first junction with the big +? I don’t see any transfer numbers associated with that.
“an ideal op-amp TAKES IN ZERO current”
Ideal. But ideal is the limit of very large current gain. No real device can give a response to a signal of zero power. And if an input signal has finite (non-zero) power, it must input finite current.
“If I feed back 1 volt of a 10 volt signal, the amplifier output remains 10 volts and does not go to 9.”
Well, you actually feed back current. In your case, (2/3)*V_out/R = 2*V_in/R. It’s pretty hard to quantify a voltage that is fed back, since the input is held at 0.
But there is still the mystery of how you can feed back a current larger than the input (V_in/R) if there is no current amplification.
“true Vout/R could flow as long as it did not (net) exceed the rated current output”
That is only three times the input current. There is surely an operating range where that is possible. And then it is an amplified current output.
For Nick Stokes at April 8, 2018 at 11:57 pm
“…Are we looking at the same graph? The top, red one. Do you mean the first junction with the big +? I don’t see any transfer numbers associated with that. …”
That is not a junction or a multiplier– it’s a summer, which is what the + sign is for. Monckton has shown three flowgraphs with three corresponding (completely equivalent) sets of equations, and all six seem exactly right. I think he agrees this is (simple) high-school algebra. Either the flowgraphs OR the equations are sufficient – I prefer the flowgraphs myself.
“… Ideal. But ideal is the limit of very large current gain. No real device can give a response to a signal of zero power. And if an input signal has finite (non-zero) power, it must input finite current…. . . . . . .”
I think I see a MAJOR element of your not understanding. Voltage is an “intensive quantity” that distributes freely (like temperature, pressure, etc.) while current (time derivative of countable charge) is an “extensive quantity” (like mass, energy, etc.) and is subject to conservation (zero-sum, as in Kirchoff’s law).
Non-ideal op-amps are interesting for AC circuits at MHz or above, but for DC circuits (such as we are considering all to be here), op-amps are essentially ideal. They have real open-loop gains of 10^7 (ideally infinite), tiny input bias currents in pa (ideally zero), and output impedances (with negative feedback operating) of perhaps an Ohm (ideally zero). Any current needed to maintain an output voltage Vout into any load RL (that is, Vout/RL) is supplied (ACTIVELY, within ratings) courtesy of the supply pins. Vout adjusts itself (via negative feedback) so that the inputs V(+) and V(-) are equal.
Some additional confusion results from not considering the differences between an op-amp (the infinite gain triangle) and the “configuration” surrounding it which make it useful.
Note that if we INCREASED all the resistors in my Fig. 6 by a factor of 10, all the voltages would remain the SAME, and the currents flowing in the configuration would DIVIDE by 10. STILL, if your proposed load RL did NOT increase, the output current would NOT change in the slightest from Vout/RL.
I know it is helpful here to have been doing this for 45 years!
The opponents seem to be sniping from prepared positions but CMoB and his learned colleagues have bypassed them and are closing on CAGW HQ. When the final redoubt is stormed I hope that something stirring by Jimmy Hendrix with plenty of feedback will be playing. ‘The Anacreontic Song’ would be my choice.
“Voice, Fiddle, and Flute,
“no longer be mute,
“I’ll lend you my Name and inspire you to boot,
“And, besides I’ll instruct you, like me, to intwine
“The Myrtle of Venus with Bacchus’s Vine.”
I hope that Nigel S will sing for us once our result is accepted, published and announced worldwide. We shall of course also welcome a song or two of consolation if we are found to have made a significant error. So far, we do not think that has happened,.
My father (Fifth Indian Division Signals) told me that they came across dead Japanese snipers left behind tied to trees by their retreating comrades as the ‘Forgotten Army’ closed on Rangoon, hence the sniping comment. I look forward to singing lustily!
All Monckton has done is simply pointed out with simple arithmetic that the models were never based on the physics. They were based on a mathematical lie that could never support its own weight. When you start with a false theory and bend over backwards by conspiring to falsify data and call skeptics deniers and make sure that with government money to fund the falsehood with 1000’s of fraudulent climate science papers Dont expect that us skeptics will have any sympathy for anybody involved in this hoax. One lie has inevitably led to a 1000 lies. Criminals soon find out the consequences of that simple mathematical fact of falsehoods.
Mr Tomalty displays just a hint of justifiable anger at the manner in which climate skeptics have been treated by the well-funded totalitarian clique that has dominated climate science until now. We shall continue our own researches until we are confident either that we are wrong, in which case we shall not pursue our argument further, or that we are right, in which case we shall do our best to provide every necessary demonstration. That is how science works – not by the sneering and shrieking of climate fanatics, but by the calm discussion of scientific questions until as much of the truth as is within our power to discern is discerned.
Dr Strangelove is probably not a doctor of anything and certainly not of thermodynamics. Consider the climate at a surface temperature of 255.4 K, the emission temperature. Since there is water, ice, water vapor and cloud cover, the feedback processes caused by the presence of these forms of H2O are in existence. Therefore, at 255.4 K the climate would not be in thermal equilibrium. Therefore the feedback processes would induce a feedback response, and quite a large one. This is really not difficult, provided that one is searching for the objective truth rather than proclaiming some totalitarian Party Line or another.
“Mr Stokes overlooks the fact that the presence of an emission temperature will induce a feedback response where feedback processes such as surface albedo, cloud albedo and water vapor are present.”
How can it do that, when the emission temperature is by definition that pertaining in the absence of GHG’s?
The ET is that radiated by the Earth on receipt of 240 W/m2 at it’s surface via the S-B response.
To do that the Earth must have a transparent atmosphere to terrestrial IR – so NO cloud and WV (and so no albedo from ice).
“Consider the climate at a surface temperature of 255.4 K, the emission temperature. Since there is water, ice, water vapor and cloud cover”
No, there is NOT “water, ice, water vapor and cloud cover” …. except in the model result from Lacis et al (2010) when non-condensing GHG’s are removed by fiat.
http://www.atm.damtp.cam.ac.uk/mcintyre/co2-main-ct-knob-lacis-sci10.pdf
255K is the S-B response to the Sun’s TSI on Earth of 240 W/m2 (which is hypothetically assumed in the Lacis model to have the same albedo as the current Earth). The ET is not a temperature predicated on there being any sort of atmospheric GHG present.
In the Lacis model “water, ice, water vapor and cloud cover” is left over after non-condensing GHG’s have been removed and the system has settled sufficiently.
As Nick has said – a thought experiment.
“the feedback processes caused by the presence of these forms of H2O are in existence” …
As above – only in Lacis et al (2010) – and therefore it cannot be the emission temp as a DeltF is in play to produce it.
The emission T of Earth has an invariant F by definition from an invariant TSI ( practically )
“Therefore, at 255.4 K the climate would not be in thermal equilibrium” ……
Correct, not in the world of Lacis et Al (2010), but that is not a real world as predicated by the S-B response to an unvarying TSI (practically) of 240 W/m2.
“Therefore the feedback processes would induce a feedback response, and quite a large one”
It would – but that is not caused by the ET …. rather, to the feedback of changing forcing due to the remaining condensing GHG (WV and albedo in Lacis). It is changing the 240 W/m2 that has an invariant 255K with no feedback for Earth when the emission temp level is at the surface.
“This is really not difficult, provided that one is searching for the objective truth rather than proclaiming some totalitarian Party Line or another.”
No, it’s not and indeed … that is what scientists since the time of Arrhenius and Tyndall et al have done.
Again for your delectation … My name is Anthony Banton.
In fact your returning to this sceptics’ echo-chamber for your desired confirmation from the majority does not make your “Game over” anything of the sort.
Via some perverse conspiracy ideation as evidenced by “proclaiming some totalitarian Party Line or another.”
Mr Banton, who – now that I have revealed who he is – no longer vainly attempts to lurk behind his furtive pseudonym, is, as usual, hopelessly confused and way out of his depth. So let me explain things in the smallest possible words. We are considering three steps: first, an atmosphere without any greenhouse gases at all, where the emission temperature obtaining at the Earth’s surface would be 255 K; secondly, an atmosphere with all the forms of water now in existence but without any non-condensing greenhouse gases such as CO2, where the temperature at the Earth’s surface would be more like 278 K owing to the large feedback response of the water-based feedback processes to the emission temperature; and thirdly, an atmosphere to which the non-condensing greenhouse gases have been added as well, where the temperature would be today’s 288 K.
At present, however, official climatology – misled by the degenerate form of the zero-dimensional-model equation that it uses, which excludes the emission temperature and therefore any feedback response thereto from the feedback loop – has not appreciated that the emission temperature induces a feedback response even in the absence of the non-condensing greenhouse gases. This is a large, serious and – once it is pointed out – obvious error. Mr Banton will need to raise his game if he is to provide a valid criticism of our result.
“how can an inanimate feedback process know how to distinguish between the input emission of temperature of 255 K and a further 9 K of temperature arising from the addition of the non-condensing greenhouse gases to the atmospheric mix?”
Unlike you, the inanimate feedback process knows it responds to net energy flow and not to absolute temperature.
“IPCC’s definition thus explicitly excludes any possibility of a feedback response to a pre-existing temperature, such as the 255.4 K emission temperature that would prevail at the surface in the absence of any greenhouse gases or feedbacks. It was for this reason that Roy Spencer thought we must be wrong.”
Dr. Spencer knows you are wrong not because of IPCC’s definition but because you believe that a thermodynamic system in thermal equilibrium will induce a feedback unto itself, which is absurd because that means it could change its own temperature without external energy flows.
The feedback magic of The Lord of the Rings
” a thermodynamic system in thermal equilibrium”
Can you explain how the climate system has remained in equilibrium as more CO2 is added? Is there not a response? The IPCC thinks so. If so, why was there not a response to the CO2 that was in the atmosphere prior to 1850?
Why do you think the temperature in 1850 excludes the CO2 greenhouse effect? Or do you think the temperature in 1850 was 255 K?
Dr Strangelove
Why do you think the temperature in 1850 excludes the CO2 greenhouse effect?
Because in CM’s thought experiment CO2 was set to zero in 1850. Read the article.
Then CM’s thought experiment is wrong because obviously there was atmospheric CO2 in 1850. No wonder his conclusion is wrong
Dr Strangelove appears to have no understanding whatsoever of the scientific method. One of its processes is experiment. Running the Lacis model in reverse is one such experiment. The conditions precedent to that experiment are set out with great clarity in the head posting, and it is there expressly stated – precisely in the (vain) hope of avoiding stupidities such as that of Dr Strangelove – that one should not believe that in 1800 there were in reality no non-condensing greenhouse gases in the atmosphere.
“such as the 255.4 K emission temperature that would prevail at the surface in the absence of any greenhouse gases or feedbacks.” Thats a strawman! Nobody is arguing that the 255.4K would not be the emission temperature in the absence of greenhouse gases. What Monckton is arguing is that 255.4 emission temperature would be raised if you introduced water vapor and no CO2. In other words the water would evaporate and create most of the known greenhouse effect from the mean 239w/m2 insolation that created that 255.4k without any greenhouse gases. This runs contrary to the idea that CO2 controls water vapor, CO2 does not, water vapor is controlled by temperature, not just temperature change. We see natural processes changing temperature and feedbacks, not just CO2. Its important to note that Monckton isn’t goring all AGW science. Many are coming up with feedback sensitivities near what Monckton is calculating. The problem is the politics is still trying to sell the old discredited science based upon the argument we know of no other reason why the temperatures in the 80’s and 90’s went up so much other than CO2 and as such adopted large climate sensitivities that do not hold up to scrutiny. Monckton is driving yet another nail in that coffin. The problem is there are trillions of dollars at stake by politicians, scientists, institutions, corporations, and even nations and its hard to keep that in a box.
“The problem is there are trillions of dollars at stake …”
I confess the maths in this is beyond me (though I enjoy trying!). Bill, the one variable you missed from this indictment is the entire environmental philosophy which is at stake. The eco-activists have bet the farm on being able to demonise CO2 as the quickest way to end fossil fuel use and undermine “civilisation as we know it”. If it were otherwise they would not be supporting the environmental destruction that goes with wind and solar “farms” and would be supporting nuclear power for energy with natural gas as a stop-gap. Generally speaking, they aren’t.
Whatever the science, never forget the enviro-political imperative that has got us where we are.
Newminster makes a fair point about the wealth and power of the totalitarian movement that has co-opted environmentalism as its weapon of choice to dismantle the economic hegemony of the West. However, that movement failed when it advanced bogus scientific arguments in its attempt to declare the Jewish race subhuman, and it failed again when it advanced bogus scientific arguments to justify the soaking of seed-corn in water during the winter rather than planting it out in the autumn to toughen in readiness for the spring. As a result of these two totalitarian pseudo-scientific aberrations, some 250 million were killed worldwide. But they failed in the end, for they were anti-scientific, just as global-warming fanaticism will end, for it too is anti-scientific, and now we can prove it.
DrS,
I read it that the thermodynamic system is in equilibrium BECAUSE feedback keeps it that way. Geoff.
Yes if it is in disequilibrium, a feedback can restore it to equilibrium. But 255 K is already in equilibrium without GHG. A feedback will not magically appear unless there is a forcing (energy flux) that disturbs the equilibrium. Dr. Spencer’s analogy is a forcing is a cause, a feedback is an effect. So there is no effect without a cause. Absolute temperature is not a forcing. Change in temperature is a response to a forcing
Mr Hunter is right and “Dr Strangelove” is simply flat-out wrong. Owing to the presence of the feedback processes related to the presence of large amounts of water on Earth, at the emission temperature of 255 K the Earth would not, repeat not, repeat not be in thermal equilibrium. The feedback processes would act to bring the temperature considerably above 255.4 K – even if there were no non-condensing greenhouse gases in the atmosphere at all.
255 K is radiative equilibrium temperature without GHG (water vapor, CO2, others) but including the albedo of clouds (strictly speaking it’s water droplets not water vapor) If you add water vapor, that’s a forcing. Any temperature change is a response to the forcing and not due to 255 K temperature before water vapor was added
Dr Strangelove is entitled to his opinion that the presence of water vapor in the atmosphere constitutes a forcing. However, official climatology considers it to be a feedback. Since we are adopting all of official climatology except what we can demonstrate to be false, we too have taken all water-dependent feedback processes as feedbacks, just as official climatology does. If Dr Strangelove thinks officlal climatology is wrong in this respect, he should not trouble us with his opinions: let him contact secretariat@ipcc.ch.
Nick, further it is no doubt widely true that sensitivity was not determined as suggested by Monckton’s calculations. Instead high sensitivity was invoked by models that attempted to explain short term variations of temperature completely in terms of CO2 using argumentum ignoratium as was essentially stated in AR3.
Argumentum ignoratium is all you need to know to verify that Monckton has a strong point as a layman. That’s true because climate has always changed and we have not done a good job of explaining why.
I have enjoyed your work in this area as at least you have not donned the narrow blinders of the mainstream science that believes the most rapid warming seen is entirely CO2 warming while its clear you are looking more broadly and not putting on the blinders and gone of on a search for the missing warming.
Obviously the only reasonable response countering Monckton’s basic observation and KISS explanation is some more detailed work that ties the greenhouse effect to some overall test of reasonableness, which if not available already puts to mockery the hundreds of billions wasted on this enterprise considering Monckton’s work.
LM says: Lacis’ albedo of 0.418, emission temperature is [1364.625(1 – 0.418) / d / (5.6704 x 10–8)]0.25 = 243.3 K, in accordance with the fundamental equation of radiative transfer, where d, the ratio of the area of the Earth’s spherical surface to that of its great circle, is 4.
I still have huge disagreement with using one side of a disk but the entire surface of the sphere which includes a physical impossibility. The sun cannot shine on the opposite side.
One side absorbs (π2^2) but the whole surface emits (4π2^2) on average input = output.
One side absorbs (πr^2) but the whole surface emits (4πr^2) on average input = output.
Sorry for the typo.
I have some sympathy for Mr Kelly’s position. The derivation of the 255.4 K emission temperature that is standard fare in official climatology leaves a great deal to be desired. it does not account properly for the latitudinal variability in insolation and hence in surface temperature, and it does not account properly for the retention of ocean heat on the nightside. My own calculations suggest that the emission temperature – before allowing for any feedbacks or for the presence of the non-condensing greenhouse gases – is between 265 and 275 K. But I am not yet in a position to prove it, so, as stated in the head posting, I have simply adhered to official climatology’s value for the time being.
That sounds much more likely.
The substantial difference between Earth’s Atmosphere and that of Mars is that Earth’s Atmosphere contains substantial quantities of non GHGs, ie., nitrogen, oxygen and argon. If all the non GHGs in Earth’s Atmosphere were removed we would have an atmosphere very similar to that of the Martian Atmosphere with approximately the same mass, density and pressure.
Mars that has more molecules of GHGs per cubic metre of Martian Atmosphere, than does Earth’s Atmosphere, and is thought to have a GHE of around 1K to 1.5K.
Mars receives less solar insolation so one would expect to see less radiant GHE on Mars. If one corrects for the differences in solar insolation received then one might expect the GHGs in Earth’s Atmosphere to add around 3K of warming.
You do not need to calculate the emission temperature – you can measure it from the emitted
radiation from the top of the atmosphere.
Germonio appears confused about emission temperature. One cannot measure it from the radiation emitted from Earth, because the Earth radiates different amounts at different altitudes. Emission temperature is derived from the incoming solar irradiance and the albedo, and from nothing else.
Monckton wites: “Germonio appears confused about emission temperature. One cannot measure it from the radiation emitted from Earth, because the Earth radiates different amounts at different altitudes. Emission temperature is derived from the incoming solar irradiance and the albedo, and from nothing else.”
In other words, emission temperature is the product of a MODEL involving solar irradiation and albedo. Roe advocates using such a model as a reference state for quantifying feedbacks. However, models aren’t real and feedbacks exist independently from such reference states.
Frank, who seems to be trying to sow deliberate confusion, says that emission temperature is the product of a model. No: it is a product of observation, as he would know if he knew anything of the history of hhe relevant science. The fundamental equation of radiative transfer was derived by Stefan using empirical methods – i.e., observations and measurements. It was then theoretically demonstrated by Ludwig Boltzmann.
It is that equation that tells us the temperature at any point on the dayside of a celestial body once the insolation and albedo are known. The crude average that is represented by the 255.4 K emission temperature that is generally used throughout climatology is probably too low. If so, equiilibrium sensitivity is likely to be even less than we find it to be.
If Frank wants to call the method of arriving at that crude average a “model” he can please himself: but, for our part, as we have made plain in the head posting, we have simply accepted all of official climatology except what we can prove to be erroneous. If Frank thinks the emission temperature should be calculated on some basis other than that which official climatology uses, he should address his concerns not to me but to secretariat@ipcc.ch.
This is one of the fundamental points.
One side of the Earth, which is not a blackbody nor a perfect conductor, absorbs, whilst the entire surface emits. This simple fact cannot be stressed enough.
The problem I see with all such climate feedback models is that they assume the input and output to be separate. In reality the input and output are the same quantity, atmospheric temperature. Which implies that there is a short-circuit across the feedback loop. Input and output are, in fact, a single node.
The situation is somewhat analogous to ‘bootstrapping’ in electronics.
It is hard to see how such an arrangement could provide amplification without being unstable.
It is of course possible to have a stable negative feedback loop under such conditions. Just, not positive.
In response to Mr Macdonald, it is in fact possible to imagine a world without non-condensing greenhouse gases, but with today’s insolation, albedo and water vapor, ice and clouds. In that event, the feedback loop equation (in its corrected form, at any rate) is perfectly capable of giving us a reasonable estimate of the eventual temperature, even before non-condensing gases are added to the mix.
Whenever one encounters a problem of this kind in physics, it is useful to break it down into small pieces placed along a timeline. Following a strict timeline prevents chain-of-causality errors.
Ian
I think this is where Lorenz steps in. The system is indeed unstable and describing constant the “Lorenzian walk” that is not random but chaotic-deterministic. There is no equilibrium. This is a problem for the way this whole question is framed.
Ian,
Climate models have solar radiation as the input and the climate as the output. Or in a feedback model
the input is the change in radiative forcing Delta F and the output is a temperature change Delta T. They
are completely seperate rather than the same quantity.
Germonio has not succeeded in explaining on what rational ground he considers that the corrected form of the feedback-loop equation does not engender a feedback response where the input signal (whether amplified or not) and the feedback fraction are both nonzero. The mathematics is not particularly difficult, and it demonstrates beyond doubt that even in the absence of any amplification there will be a feedback response to emission temperature. Merely reciting the official definition of a feedback, which (perhaps deliberately) falsely attempts to exclude the feedback response to emission temperature does not advance Germonio’s argument one whit.
Do the math. Input signal 255 K. Gain factor 1 (meaning no amplification from non-condensing greenhouse gases). Feedback fraction 0.08 (since feedback processes are present where water vapor is present). Output signal 255 / (1 . 0.08) = 277 K., not 255 K.
Monckton, My rational grounds is that there is no evidence that your “corrected form” of the feedback
loop equation is valid. And you have presented not derivation for this equation from the underlying physics
but have just stated it with no justification.
My question would be in what sense is 255K an input signal? And it is an input signal to what? Once
you change the reference system which you have done then you change the gain and feedback and
as Roe states explicitly you cannot compare feedbacks from difference reference systems.
Germinio should read Bode (1945, ch. 3), where the correct form of the zero-dimensional-model equation is given and proven. That equation is applicable to all dynamical systems on which feedbacks bear. I cited Roe as one of the many papers using the incorrect form of the equation that made no provision for the input signal – in this instance, emission temperature.
Roe’s reference system is that part of the feedback loop that does not incorporate the feedback block on the return path. Properly speaking, it should have the reference temperature (i.e., emission temperature) as the input, and the warming from non-condensing greenhouse gases represented as a direct-gain factor in the mu amplifier block.
Roe, however, made the mistake of not including the reference temperature in his feedback loop. Indeed, he did not use temperature at all, but a change in radiative flux as his input. He then converted that change in flux to a temperature, doing so in that part of the circuit that would normally be occupied by an amplifier block, and then showed the temperature outputting to another radiative flux change. But one cannot go from a temperature to a flux change without a process of conversion – a process absent from Roe’s circuit diagrams.Mr Stokes, in seeking to rely on those diagrams, had not noticed that defect.
Feedbacks are denominated in Watts per square meter per Kelvin of the temperature that induced them. And climatology errs in not including the emission temperature as the input signal.
The whole global warming due to CO2 is a very simple model, just one variable!
I am of the school of adiabatic temperature profiles and I think as we explore the atmospheres of more planets, this will become accepted.
Also, if there were a positive feedback in the atmosphere, an assumption made by the Warmistas, then the planet would have zipped right up to boilibng very quickly. It clearly hasn’t, over 4.5 billion years, therefore I would suggest the assumption is hokam, no matter how frantickly arms are waved.
In response to Robert of Ottawa, we have adopted for the sake of argument all of official climatology except what we can prove to be false. Therefore, we have accepted ad argumentum that greenhouse gases cause a greenhouse effect. Our concern is not with whether such an effect exists (for that has been well established in the laboratory) but with the amplitude of its effect on temperature.
RGHE theory could not exist without the concept of “back” radiation, energy/heat moving from a cold tropospheric “surface” to a hot ground “surface.”
Consider a small heated rod of 0.5 m^2 inside a larger outer tube of 2.0 m^2.
The heated rod is fed 25 watts of electricity for a radiative flux of 50 W/m^2.
The outer tube absorbs that radiation for a radiative flux of 12.5 W/m^2.
RGHE theory says that 50 W/m^2 radiate outwards while 12.5 W/m^2 “back” radiates for a net of 37.5 W/m^2 warming the earth.
A watt is not energy, but power, energy over time: 3.412 Btu per English hour or 3.6 kJ per metric hour.
25 watts is 85.3 Btu/h.
25 W spread over area 1 is 50 W/m^2 moving 85.3 Btu/h.
25 W spread over area 2 is 12.5 W/m^2 also moving 85.3 Btu/h.
Conservation of energy demands that input and output must be equal.
The 25 W, 85.3 Btu/h, that entered as electricity must radiate to the world from surface 2, 25 W or 85.3 Btu/h.
There is exactly ZERO left over to “back” radiate.
In response to Nickreality65, a system subject to incoming and outgoing radiative fluxes, such as the Earth, will gain heat if the incoming flux exceeds the outgoing flux, and its temperature will increase until the outgoing flux again matches the incoming flux. One can heat such a system by increasing the influx (e.g. by greater solar activity), but one can also heat it by inhibiting the efflux.
It seems to me that we agree that RGHE is nonsense.
More net in, warming. Less net in, cooling. Not exactly news.
If more comes in, as it does every perihelion, warming. If less comes in, aphelion, cooling.
Same with the tilt as the poles take turns moving in and out of shadow/sun.
Earth’s albedo, which exists only because of the atmosphere, reflects away 30% of the incoming solar energy. The albedo does not actually cool the earth but makes it less hot which yields the same result.
No atmosphere means hotter earth not colder. See Volokin/Nikolov moon analog papers.
Variations in the albedo play a major, it not the major, role in the state of the climate.
The atmosphere’s thin layer of gases insulate and create a thermal gradient same as the wall of a house per U A dT.
My explanation is based on first principles which even the lay public can understand.
All the S-B BB & QED handwavium just clouds the issue.
Have several papers at WriterBeat, LinkedIn & PSI.
Also the changes in clouds, which directly impacts upon how much incoming solar insolation is reflected or gets through to the surface, whatever be the mechanism that drives the change in patterns of cloudiness, eg., simply chaos, random walks, responses to oceanic conditions, cosmic rays, or other changes in cloud seeding, the response that Willis, from time to time, suggests etc etc..
Different patterns in cloudiness are all part of the natural process, unless man pollutes particulate matter that may promote cloud seeding.
In further response to nickreality, we most certainly do not agree that the radiative greenhouse effect is “nonsense”. As the head posting makes explicit, we have adopted all of official climatology except what we can prove to be falses.
nickreality65 wrote: “Consider a small heated rod of 0.5 m^2 inside a larger outer tube of 2.0 m^2.
The heated rod is fed 25 watts of electricity for a radiative flux of 50 W/m^2.
The outer tube absorbs that radiation for a radiative flux of 12.5 W/m^2”
Unfortunately, this problem is somewhat more complicated than you describe. The inner surface of the outer tube radiates in all directions (not just perpendicular to the surface), so some of that inward radiation is absorbed by the central heated tube and some is absorbed elsewhere by the inner surface. And you need to apply Lambert’s cosine law to correctly calculate how much power is absorbed. These geometric issues are called “viewing angles” and solutions for a variety of common situations can be found on the internet. In the real world, you also need a temperature gradient for conduction to transport heat through the wall of the outer tube.
Imagine a 1 m layer of atmosphere parallel to the surface of the Earth. The atoms in that layer emit equally in all directions. Let’s decompose that emission into three components: 1) A component parallel to the ground. 2) An upward vertical component. 3) An equal downward vertical component. Hopefully you will immediately realize that the horizontal component cancel and don’t contribute anything to radiative heating or cooling of the planet. By cancel, I mean there is no net flux of energy (no heat transfer) in any horizontal direction, not that there is interference. (Interfere requires coherent light sources.) Both the upward and downward components add to the existing fluxes arrive at the layer.
Now we need to consider absorption of the upward and downward fluxes entering the layer. In a thin layer near the edge of space, the downward flux of LWR is extremely weak, so the layer absorbs very little of that flux and contributes more than it absorbs. A thin layer near the surface of the Earth receives 390 W/m2 of upward flux and can absorb more radiation that it emits. So the net result of absorption plus emission in a thin layer of atmosphere might reduce the upward flux and increase the downward flux even though it emits equally in both directions.
Planck showed that thermal radiation in equilibrium with its surroundings has an intensity given by Planck’s Function, B(lambda,T). Equilibrium means as many photons are being emitted as being absorbed. The radiation passing through the atmosphere may not be in such an equilibrium. Upward radiation has been emitted from below, where it is warmer, so more will be absorbed than emitted. The opposite is true for downward radiation. In both cases, the net influence is to bring the local fluxes closer to B(lambda,T). The rate at which those fluxes approach B(lambda,T) depended on the number of absorbing molecules and their absorption coefficient. Photons of strongly absorbed wavelengths may travel only a few meters vertically between emission and absorption and experience neglible change in local temperature. They therefore have B(lambda,T) intensity appropriate for the local temperature. Emission and absorption are equal at these wavelengths. Weakly absorbed photons may travel a kilometer of more between emission and absorption and therefore be out of equilibrium with the local temperature. It is these wavelengths that produce the GHE.
In any layer, the 2LoT is being obeyed. More photons from warmer places are being absorbed than emitted. Fewer photons from cooler places are being absorbed than emitted. Heat flow is the NET flux of radiation from one location to another.
The net result is that the intensity of DLW increase from 0 W/m2 on the cold edge of space to about 333 W/m2 at the warm surface, while OLR starts at 390 W/m2 near the warm surface and has diminished to 240 W/m2 as it finishes passing through the colder upper atmosphere. Note that this wouldn’t happen in an isothermal atmosphere, a temperature gradient is essential. Most of this change takes place in the troposphere, where temperature decreases with altitude.
The 396 W/m^2 upwelling and net 333 W/m^2 GHG energy loop as shown on the K-T power flux balance diagram (Figure 10 Trenberth et al 2011jcli24) is calculated using the S-B equation with an assumed emissivity of 1.0 and an average surface temperature of 16 C, 289 K. Because of the conductive/convective/advective/latent heat participating processes of the atmospheric molecules the actual and correct radiative emissivity is about 0.16, i.e. 63/396.
This GHG energy loop is an inappropriate calculation with zero physical reality.
Without this energy loop the radiative greenhouse effect theory fails.
Without RGHE man-caused climate change does not exist.
It’s called “science.”
Don’t be frightened, spit out the Kool-Aid and give it a try.
Here’s something I posted just now way upthread, where it might get overlooked, so I’m repeating it below:
Silber: “How have you dealt with the problem that to have a feedback there has to be initial change?”
Every 24 hours there is a change in temperature. That should be enough to get the ball rolling, no?
“Every 24 hours there is a change in temperature” – I’m not quite sure what you mean, Roger, by a change in temp every 24 hours, but that’s beside the point. Monckton is not basing his feedback on a change, but on the emission temperature itself.
“As a first step towards making due allowance for the feedback response to emission temperature, official climatology’s version of the zero-dimensional-model equation can be revised to replace the delta input and output signals, indicating mere changes in temperature, with entire or absolute values. Note that the correct form of any equation describing natural occurrences (or any natural law) must be absolute values: the use of deltas is only permissible if the delta-equations are correctly derived from the absolute equation. Accordingly, ΔTeq = ΔTref / (1 – f ) should be Teq = Tref / (1 – f ):”
This makes no sense to me. Although it’s probably the case that my math skills aren’t on par with Moncktons, I don’t see from a physical standpoint how this could be the case, and there are plenty of others who are better qualified and making the same argument. It also seems extraordinarily unlikely to me that all the teams of AGW climate modelers would commit the same error.
That said, I’m not the best person to judge because I’m prejudiced against Monckton, not as a skeptic but as a person. I’ll drop out of this conversation now, but since you asked twice I thought I should answer.
If Silber wishes to understand how it is that the correct version of the zero-dimensional-model equation is derived, try reading ch. 3 of Bode (1945), where everything is explained. The correct version of the zero-dimensional-model equation is Teq = Tref x mu / (1 – mu x beta), where mu is the direct or open-loop gain factor 1 + deltaTref / Tref, beta is the feedback fraction and mu x beta is the feedback factor.
Bode even provides a simple proof that this is the correct equation. And the only remaining question is whether the equation applies as much to the climate as to any other dynamical system (a system that changes its state over time). The answer to that question is that the mathematics of feedback is of universal application to all systems on which feedbacks bear.
Silber should remember that my co-authors include 5 PhDs, three of whom are professors, and one of whom is a professor of applied control theory.
Understanding the matheatics even of the naive feedback loop that is used in official climatology requires study and effort. Read Ch. 3 of Bode before commenting again here.
An excellent debate and well done to CM and those who made genuine challenges and to Anthony for hosting the whole thing. I am no expert, but I support CM’s case, but then I have been waiting a long time for such errors to be found. There are too many indicators that make catastrophic AGW too implausible to be real.
For me, this is also a good use of public review. Proposals either get refined to be stronger or fail miserably when subjected to this level of criticism. But where are the so called experts? Silence is often used to see off challengers. It is also often used when there is no defence. We must be getting close to this challenge requiring some sort of response from the climate establishment. It is a great pity that they will not have the confidence to make their argument here. Also, they will not wish to give this site any legitimacy. This would be a failure of judgement for them.
It would be interesting to hear what CM anticipates as being the next step in this process.
I’ll ‘second’ Schrodingers Cat’s applauding the excellent debate generated by this and CM’s previous posts!
I find I must read with scrupulous attention to detail, to follow the arguments (pro and con) presented here. The algebra is indeed straight forward but the results and implications of the arguments presented require somewhat more ‘digestion’. However the calculated lower value of climate sensitivity to CO2 doubling allies well with the historical records of our planet experiencing geologically extended cold periods of glaciation with only comparatively brief periods of warming. Almost regardless of prior variations in atmospheric CO2 content, the climate record indicates no tendency to ‘runaway’ warmth but does exhibit repeated ‘tipping points’ into brutal periods of glaciation.
Both reality and Monckton’s et.al revised feedback response model/calculations assert CO2 sensitivity must be small and non-hazardous. With acceptance of their revisions, the Catastrophic Anthropogenic Global Warming hypothesis dissipates like a child’s bad dream.
Many thanks both to Schroedinger’s Cat and to J Mac for their kind support. We think our result demonstrates that global warming will be small, slow, harmless and beneficial.
The next step, of course, is peer review, where we are expecting a battle royal. The vested interests ranged against us are many, powerful and wealthy. We are under no illusions to the effect that in this field peer review will be dispassionate and fair. But, in the end, either someone finds a significant error in what we have discovered, or more and more people will find out about it, and the truth will gradually become apparent even if the gatekeepers try to slam the portcullis against us. The truth will find a way.
Anyone ever notice the hilarious fakery of claiming the cold Nitrogen bath Atmosphere is a heater, and that the light-warmed earth is warmer due to the cold nitrogen bath, than if there were no cold nitrogen bath?
This is what brings the people who’ll bark such ludicrous fraud to the point that their “science” is called
“The Sewer of Science.”
But there isn’t
====(
Not correct. 10% feedback can be represented as the infinite sum a/10^0+a/10^1+a/10^2+…
Where a=input.
which gives an output of
a*1.111111…
Which is a*1/.9
Which is out = in * 1/(1-f)
on 255 K in this gives 283.3 out.
Having now adapted the engineers’ modern flow-graph conventions, and having set down the corresponding math (admittedly, just high-school algebra), perhaps one could continue to borrow from EEs and use their “classical sensitivity”.
http://electronotes.netfirms.com/Sensitivity.jpg
This HIGHLY INTUITIVE measure “S” tells us how sensitive a performance parameter; say the area of a rectangular tabletop, is to, perhaps the length (S=1) while the area of a circular table has a sensitivity S=2 to the radius. In a network, we might have a sensitivity of -1/2 of a cutoff frequency to a particular resistor. If S =1, we break even. S=1/2 is a happy result. S=10 might be a disaster – a 5% tolerance error would be a 50% change in performance.
All we are asking is how much of a PERCENTAGE change we expect in (LOCAL) performance (experimental measurement perhaps) if there is an error (like component tolerance) of a certain PERCENTAGE. Exactly what a non-engineer would have gotten around to asking for? Engineers use S to judge general insensitivity of a proposed design and to write down “tuning equations”.
How sensitive is a gain due to feedback (G) to the feedback factor f?
Well, G = A/(1-Af) [ or 1/(1-f) for the case A=1]. Doing the calculation gives S (of G to f) = Gf. This has the happy result that if feedback f is found to be smaller, not ONLY is the gain G smaller, but the sensitivity of G to f is a smaller percentage.
Details and examples from 2016 are here:
http://electronotes.netfirms.com/AN430.pdf
but because you believe that a thermodynamic system in thermal equilibrium will induce a feedback unto itself, which is absurd because that means it could change its own temperature without external energy flows
=======
No. If the forcing is +10 and the feedback is -10, the net force on the system is zero and the system is in equilibrium with a non zero feedback.
this constitutes proof by contradiction that the IPCC is wrong. A system in equilibrium can have non zero feedbacks.
In my mind the issue is the clouds, the clouds, the clouds.
Not just the specific coverage. But at what altitude, what latitude, what time of day and what time of year.
All these factors define the if the cloud acts to warm or cool the earth and by how much. A simple average disc temperature representation of the earth is daft also given the surface temperature of the earth varies every day by at least 100C from place to place, show me how a model can model the cloud and can incorporate a variable such as CO2 changing by 20ppm and can tell us that we will be .2C warmer.
Yeh right as they say in NZ
Mr Treuren is of course right. The behavior of clouds is the largest of all the uncertainties in deriving equilibrium sensitivities. However, in the head posting we are dealing with the certainty that official climatology has at best undervalued and more usually simply overlooked the very large feedback response to emission temperature.
Monckton returns to fantasyland! According to Monckton, the GISS model used by Lacis et al can’t be trusted to predict whether a doubling of CO2 will cause 2 or 4 degC of warming, but the same model can provide useful information about our planet without any condensible GHGs after a cooling of more than 30 degC!
Are any skeptical climate scientists supporting this nonsense?
Frank continues to misunderstand some elementary concepts. Not the least of these is the concept of emission temperature, which is a function solely of insolation and albedo. As noted in the head posting (which Frank should read one day), Pierrehumbert (2011) found that on a snowball Earth the albedo would be 0.6, implying an emission temperature 221.5 K; Lacis (2010) found that on a slushball or waterbelt Earth the albedo would be 0.418, implying an emission temperature 243.3 K, and at today’s albedo of 0.293 the emission temperature is 255.4 K.
As the head posting surely makes explicit, my conclusion is that Lacis et al. have not explicitly acknowledged the existence of the large feedback response to emission temperature, but their paper does state that the temperature in the absence of the non-condensing greenhouse gases would be 252 K, which I said was considerably below the realistic value. In other words, I found that Lacis’ model did not repeat not, provide useful information about our planet without the non-condensing greenhouse gases.
It is Frank, therefore, who, as usual, is spouting nonsense.
Monckton wrotes: “Frank continues to misunderstand some elementary concepts. Not the least of these is the concept of emission temperature, which is a function solely of insolation and albedo”.
What Monckton forgets is that blackbody equivalent emission temperature comes from a MODEL – a blackbody MODEL – that has no physical reality. The most of the photons escaping from Lacis’ hypothetical planet to space (totaling about 200 W/m2) are being emitted from cloud tops (75% clouds), which are colder than the surface. Some are emitted by water vapor in the atmosphere, which is colder than the surface. And some are emitted by the surface, which Lacis’ MODEL says will be 252 K. The total number of photons emitted is equal to a blackbody model at 243 K OR a graybody model at 252 K with emissivity 0.87. Monckton’s speculation is models built upon models built upon models; equations written without bothering to consider whether they represent the underlying physics.
Monckton wrote in this post: “Thus, from a snowball Earth to 1850, the mean feedback fraction is 0.20; from a waterbelt Earth to 1850, it is 0.12; and at today’s albedo 0.293, implying an emission temperature 255.4 K, it is 1 – (255.4 + 8.9) / 287.6 = 0.08. Which is where we came in at the beginning of this series. For you will notice that, as the great ice sheets melt, the dominance of the surface albedo feedback inexorably diminishes, whereupon the feedback fraction falls over time.”
In comments about Monckton’s previous post, I repeatedly pointed out the feedbacks are not linear over more than a few degK. Monckton never admitted that I was correct. Now he has revised his amplification model and found that feedbacks do appear to vary with with temperature. But his ad hoc new models are still based on amplification and control theory. They aren’t based on fundament physics.
Monckton wrote: “As the head posting surely makes explicit, my conclusion is that Lacis et al. have not explicitly acknowledged the existence of the large feedback response to emission temperature, but their paper does state that the temperature in the absence of the non-condensing greenhouse gases would be 252 K, which I said was considerably below the realistic value. In other words, I found that Lacis’ model did not repeat not, provide useful information about our planet without the non-condensing greenhouse gases.”
What Monckton doesn’t realize is that AOGCMs don’t explicitly include feedbacks. Feedback isn’t parameterized; physics occurring inside grid cells is parameterized. Feedbacks are an emergent property of choices made when tuning a model and they are later abstracted from a variety of model experiments. Under these circumstances, it is absurd to say:
“Lacis et al. have not explicitly acknowledged the existence of the large feedback response to emission temperature”
BBeq emission temperature is not a part of Lacis’ model. Feedback is the change in net flux in response to a change in surface temperature. If we don’t trust AOGCMs to predict feedbacks within a few degC of current temperature – and I certainly do not – it is absurd to believe that anything those models say about a 30+ degC colder planet without condensable GHGs can help us predict the effect of 2XCO2. The change in temperature over the past century can tell us something useful about feedbacks, but MONCKTON CONSTANTLY FORGETS THAT WE HAVEN’T REACHED EQUILIBRIUM WARMING. Transient warming needs to be analyzed with EBMs. That has been done by Otto et al 2013 and Lewis and Curry (2015). According to ARGO, today’s forcing of about 2.5 W/m2 has been reached to about 0.7 W/m2 by current warming, meaning that current warming is 40% short of equilibrium warming.
Frank, do you or do you not acknowledge the existence of a large feedback response to the 255K emission temperature? Do you agree that MB identified a fundamental error in the climate models?
Sailboarder asked: Do you or do you not acknowledge the existence of a large feedback response to the 255K emission temperature? Do you agree that MB identified a fundamental error in the climate models?
Sailboarder: What is a “feedback response to an emission temperature”? The simplest way to think of feedback is as a change in the net flux at the TOA in response to a change in surface temperature: λ = dW/dT. Feedback can be divided into two components λ0 for the change in simple thermal emission and λ1 for the sum of all the other feedbacks. The dimensionless feedback factor f = -λ1/λ0). None of these parameters a constants independent of temperature for more than a few degK.
I’m tempted to integrate dW = λ(T)dT from 0 to T so that I can associate a feedback with a temperature, but these thoughts aren’t proving any insight to me.
The simple answer is that Monckton has not identified a fundamental error in “climate models”. Climate scientists make little use of what Monckton calls a zero-dimensional climate model. The climate models they use for most of their work (and to scare the public) are AOGCMs. Monckton’s post tell us nothing about those models. He has simply discovered that linear models give crazy results when applied to non-linear phenomena.
The only thing that matters is the value of λ that will determine our future, If it takes a 1 degK rising in Ts to emit or reflect and addition 1 W/m2 to space (λ = -1 W/m2/K), then it will take 3.7 K of warming to emit an additional 3.7 W/m2 of net radiation and eliminate the imbalance created by a doubling of CO2. When no imbalance exists, the temperature has reached a new steady state. If λ = -2 W/m2/K, then it will only take only 1.75 K of warming and there will be little need for expensive measures to reduce CO2 emissions. This is the crux of the problem. If you insist on converting these simple numbers into dimensionless amplification factors, λ = λ0 + λ1, λ0 = -3.2 W/m2/K and f = -λ1/λ0.
Monckton is telling us that we can learn something about the correct value for λ for the next few degK of warming from AOGCMs. If so, AOGCMs are saying that λ = -1 W/m2/K. Neither of us thinks models are capable of calculating that value correctly. Instead, Monckton wants to use one AOGCM to do a vastly more challenging job, make projections about a planet without any non-condensible GHGs that is 30+ degK colder than today. And somehow avoid the complications from non-linearity. This is somehow supposed to tell us something useful about λ during the next few degK of warming. This makes absolutely no sense to me. Someone who works with electrical circuits and controls systems built from linear components might look at the problem differently. That is why I’m trying to focus everyone’s attention on λ1 and λ0 (which have a physical reality and non-linearity) and not the dimensionless ratio, f, a “Tref” and a “Teq”. Monckton’s presentation has omitted all mention of λ, which the symbol used for feedback in climate science. Temperature isn’t amplifying itself! It is driven by radiation and λ is the factor that converts one into the other.
sailborder:
Yes, there’s substantial feedback at low temperatures, but, no, climate models’ finding high climate sensitivity isn’t evidence that they’ve failed to recognize it. In my comments nearby I set forth an example of nonlinear feedback T = g(R + f(T)) that resulted in the following loop gain:
http://i66.tinypic.com/2641a94.png
As you can see, the loop gain is significant–indeed, at the low end it exceeds unity–yet that model exhibited a climate sensitivity of 3.2 K. Lord Monckton is mucking about in stuff he doesn’t understand.
Frank continues to be more and more confused. Nonlinearity in feedbacks exists whether official climatology’s math or our math is deployed. But if our math is deployed the equilibrium sensitivity will inevitably be less than if the incorrect math is deployed. And our empirical calculation for the industrial era shows a feedback fraction remarkably similar to that which we obtained theoretically for the pre-industrial era.
Frank, in his desperation, resorts to the use of childish capitals. He says I have not allowed for the fact that we are not yet at equilibrium warming. Yet, if only he would actually read the head posting before wasting reams of ill-considered comments on it, he would see that we dealt with that very point, explicitly and in detail. And it didn’t make all that much difference.
Frank also says that emission temperature is “blackbody-equivalent” and says I have forgotten this. No, I haven’t: for the emission temperature is, of course, a graybody temperature, not a blackbody temperature. Frank should really study the fundamental equation of radiative transfer before presuming to lecture me on it.
Finally, Frank has written in a thoroughly arrogant and unpleasant tone throughout. This has been noticed. For, like many commenters from the totalitarian perspective here, Frank has assumed that he is dealing with a mere Classical architect who knows nothing about science or mathematics. He is, however, dealing with a body of competent co-authors who have written a paper that Frank has not yet seen – though that does not prevent him from imagining that we have made no mention of the feedback parameter lambda – and who have, between then, all the relevant qualifications to draw the conclusions we have drawn. His constant and unpleasantly-expressed assumption that I know nothing of what I am talking about, when it is he who – over and over again – has made the most childishly elementary mistakes, reflects ill on him and does us no harm at all,.
The few arrogant totalitarian shriekers here have underestimated the extent to which ordinary readers can tell by the tone of the shriekers’ remarks that they are desperate. And so they should be, for – if we are right – then, scientifically speaking, this is the end of the climate scare.
The Born Liar continues to be vicious and spiteful, saying that I am “mucking about” in matters I do not understand. He has yet to realize that his own knowledge is limited and that, even if it were as great as he pretends, his known animus renders everything he says on this subject suspect.
His contributions here have been as petty and splenetic as usual, and he has merely tried to confuse a simple issue with pointless complications. At my back I have an army of co-authors all of whom are far more knowledgeable than the Born Liar. it doesn’t matter what the Born Liar would like readers here to think of me: the result we have discovered cannot be impugned with mere petty spite.
Lord Monckton, Nick and others following our debate: Some of the confusion in our discussion arises from the horrendous terminology being used by climate scientists. Some of the confusion arises because Roe’s definition of feedback (2008) differs from the the definition used by many others.
The symbol λ is being used to stand for two different quantities, reciprocals as it turns out. Roe (2009) and other sources use λ to stand for the climate sensitivity parameter, which is climate sensitivity expressed in units of K/(W/m2). λ0 is the no-feedbacks climate sensitivity parameter. Multiply by F2x (W/m2/doubling) and you get ECS and NF-ECS (K/doubling). The glossary for AR4 defines the climate sensitivity parameter as being:
“The climate sensitivity parameter (units: °C (W m–2)–1) refers to the equilibrium change in the annual mean global surface temperature following a unit change in radiative forcing.”
https://www.ipcc.ch/publications_and_data/ar4/wg1/en/annex1sglossary-a-d.html
On the other hand, the symbol λ is also used for feedbacks, which are measured in units of W/m2/K. In Table 1 of this post, Monckton reports feedbacks in terms of W/m2/K, but he doesn’t use the symbol λ. In their classic paper on climate feedbacks, Soden and Held (2006) use λ, λ_i for individual feedback_i, and λ for the sum of all feedbacks – the overall climate feedback parameter. The AR4 glossary defines the climate feedback parameter as:
“A way to quantify the radiative response of the climate system to a global surface temperature change induced by a radiative forcing (units: W m–2 °C–1). It varies as the inverse of the effective climate sensitivity. Formally, the Climate Feedback Parameter (Λ) is defined as: Λ = (ΔQ – ΔF) / ΔT, where Q is the global mean radiative forcing, T is the global mean air surface temperature, F is the heat flux into the ocean and Δ represents a change with respect to an unperturbed climate.”
The first sentence is the traditional definition for feedback. Since additional heat lost by the planet is traditionally negative number, the overall climate feedback parameter (λ) is negative. The more formal definition for Λ switches this sign convention. The IPPC’s Table 9.5 cited by Monckton uses BOTH sign conventions. A radiative forcing change ΔQ goes into warming the ocean (ΔF), and the atmosphere (which is negligible), and the TOA radiative imbalance. ΔQ – ΔF and the change in radiative flux across the TOA (ΔR), the “radiative response” in the simpler definition. The more sophisticated definition defines the climate feedback parameter in situations that do not start and end with equilibrium (ΔF = 0).
THERE IS ABSOLUTELY NO DOUBT THAT THE TERM FEEDBACK IN CLIMATE SCIENCE MEANS A QUANTITY MEASURED IN W/m2/K, NOT A DIMENSIONLESS “GAIN”. In Table 1 in this post, Monckton reports feedback in W/m2/K. However, Roe (2009) says:
“In order to quantify the effect of a feedback, a reference system (i.e., a system without the feedback) must be defined.”
The IPCC’s definition of a climate feedback parameter doesn’t require a reference system! THIS IS THE MAIN REASON WHY MONCKTON AND I DISAGREE. If we consider the response to seasonal warming (which can be observed from space every year), we see changes in TOA OLR and reflected SWR. Those feedbacks (responses to a change in Ts) can be quantified in terms of W/m2/K without regard to any reference system. The LWR change is highly linear. Clearly we can and do quantify feedback without regard to a reference system. And if we know the overall climate feedback parameter λ, that is all one needs to know. F_2x / λ = ECS!
If one wants to understand how water vapor feedback contributes to the overall planetary climate feedback parameter OR if one wants to characterize amplification, then Roe and Monckton are right: One needs a reference system without that feedback. The only place we can get a reference system is from an AOGCM. If you don’t trust AOGCMs to produce accurate feedbacks, then you don’t have a system with and without the feedback of interest. IN OTHER WORDS, YOU CAN’T QUANTIFY FEEDBACKS AND A FEEDBACK FRACTION, IF YOU DON’T BELIEVE AOGCMs ARE ACCURATE! (If you do trust AOGCM’s, you already know ECS AND the overall planetary climate feedback parameter.)
IMO, as a skeptic of climate models, Monckton has no business using them to quantify a feedback fraction.
I continued by attempts to settle disagreements by looking into the definition of a zero-dimensional model. Roe doesn’t use this phrase. The first definition I found came from Wikipedia and is a gray-body model. It turns out to be very helpful:
(1-a)*S*(Pi*r^2) = eoT^4*(4*Pi*r^2)
eoT^4 = (1-a)*S/4 at steady state)
If we envision a slow change in Ts (say caused by a change in solar irradiation S) so the system remains in steady-state, and differentiate with respect to Ts (using the chain rule), we get feedbacks:
4eoT^3 + eoT^4*(de/dTs) + (S/4)*da/dTs = 0
4eoT^3 is Planck feedback (λ0)
(S/4)*da/dTs is SWR feedback (the change in albedo/absorptivity with Ts)
eoT^4*(de/dTs) is the change in emissivity with Ts – LWR feedback without Planck feedback.
λF (or λ1) is the sum of second and third terms for a zero-dimensional model.
Why does the emissivity of a planet change with Ts? Most of the photons escaping to space are emitted from well above the Earth’s surface – from cloud tops and GHGs high in the atmosphere. When we treat the planet as a simple gray body – a zero-dimensional model – this means that emissivity must be less than 1. The higher and colder the GHGs emitting radiation to space, the lower the emissivity. With more GHGs in the atmosphere, including water vapor, the average photon escaping to space is emitted from higher (after an instantaneous forcing). (See Lindzen’s “Taking Greenhouse Warming Seriously”). A decrease in the lapse rate due to higher humidity means the upper atmosphere warms more than the surface, increasing emissivity.
Current Earth: T = 288 K, e = 0.615, a (albedo) = 0.30.
Lacis’ Earth without non-condensible GHGs: T = 252 K, e = 0.87, albedo = 0.41
With large changes in Ts, it is easy to see that both absorptivity and emissivity change with Ts. Monckton keeps talking about a [blackbody equivalent] emission temperature, meaning emissivity is 1. However, no planet can have an emissivity approaching 1 if some of the photons escaping to space are emitted from above the surface where it is colder than Ts. If Lacis got rid of clouds and water vapor, then emissivity could approach 1 and wouldn’t change with Ts.
Monckton has asserted that that there is a feedback fraction (not feedback alone) that can be associated with any temperature. In a sense, he is correct. If we start with a blackbody Earth and move to Lacis’ model, albedo and emissivity change and those changes are feedbacks and produce a feedback fraction. If we go from Lacis’s Earth to PI Earth, we start with a changed albedo and an emissivity less than 1 and change both parameters. Those changes produce feedbacks and amplification that have accumulated within today’s planet. And with 2XCO2, there will be further changes in emissivity and absorptivity added on to the existing changes. If your reference state is a blackbody (the ideal reference state according to Roe), then changes due accumulate with rising temperature.
Above I explained how confusing terminology and symbols lead to misunderstanding. Continuing this process with some of the other terminology might help lear up other disagreements.
The AR4 Glossary doesn’t offer a definition for feedback fraction (f), aka gain (g). Monckton doesn’t seem to understand the process for obtaining a feedback fraction f from climate feedback parameters, It is clearly defined by Tsushima and Manabe, PNAS (2013) for both observations (hurrah) and models (hiss). There are few sources more definitive than a paper by Manabe:
“The feedback parameter, λ, may be divided into the feedback parameter of the first kind and that of the second kind, as expressed by
λ=λ0 +λF
The first term, λ0, denotes the change in the TOA flux of the OLR in response to uniform, 1 °C increase in the temperature of the surface–troposphere system. In other words, it denotes the rate of “basic radiative damping” of temperature perturbation that follows approximately the Stefan–Boltzmann law of black- body radiation. Soden and Held (11) estimated λ0 in the CMIP3 models. The average value of λ0 obtained from the models is 3.21 Wm−2·K−1, which is used in the present study. In addition to the primary feedback (i.e., basic radiative damping), there is the feedback of the second kind as described below.
The change in surface temperature induces not only the vertically uniform change in the troposphere but also changes in the vertical lapse rate of temperature, humidity, and cloudiness in the troposphere and in the coverage of snow and sea ice at the Earth’s surface. These changes affect the TOA flux of OLR and that of reflected solar radiation, modifying the strength of radiative feedback as indicated by λF in the right-hand side of Eq. 5. To represent the strength of the feedback of the second kind identified here, Hansen et al. (10) introduced a nondimensional metric called gain factor (g) as expressed by
g = −λF/λ0
Here, the sign of gain factor is chosen such that the feedback of the second kind weakens the overall strength of feedback, thereby enhancing the sensitivity of climate, if gain factor is positive. However, the reverse is the case if the gain factor is negative. Using the gain factor thus defined, the feedback parameter (λ) can be expressed as
λ=λ0*(1−g)”
Manabe’s gain (g) is Monckton’s “feedback fraction” (f). In my comments, I accidentally replaced Manabe’s λF with λ1, but both terms represent the sum of all other feedbacks besides Planck feedback.
Monckton writes: Official climatology trains its models by adjusting them until they reproduce past climate. Therefore, the models have been trained to account for the 33 K difference between emission temperature of 255.4 K and today’s surface temperature of 288.4 K.
This is flat-out wrong. In theory, AOGCMs are tuned so that their output agrees with the climate we observe today. A typical tuning process is described below. Only after a model has been tuned do researchers learn how well it hindcasts historic warming and what its climate sensitivity is.
https://doi.org/10.1029/2012MS000154
During a development stage global climate models have their properties adjusted or tuned in various ways to best match the known state of the Earth’s climate system. These desired properties are observables, such as the radiation balance at the top of the atmosphere, the global mean temperature, sea ice, clouds and wind fields. The tuning is typically performed by adjusting uncertain, or even non‐observable, parameters related to processes not explicitly represented at the model grid resolution. The practice of climate model tuning has seen an increasing level of attention because key model properties, such as climate sensitivity, have been shown to depend on frequently used tuning parameters. Here we provide insights into how climate model tuning is practically done in the case of closing the radiation balance and adjusting the global mean temperature for the Max Planck Institute Earth System Model (MPI‐ESM). We demonstrate that considerable ambiguity exists in the choice of parameters, and present and compare three alternatively tuned, yet plausible configurations of the climate model. The impacts of parameter tuning on climate sensitivity was less than anticipated.
However, experienced researchers have fair idea of what the consequences of the tuning choices they make will be and they can re-tune a model if it predicts too much or too little warming. Isaac Held candidly discusses whether models can be tuned to roughly produce a pre-determined outcome here:
https://www.gfdl.noaa.gov/blog_held/73-tuning-to-the-global-mean-temperature-record/
“This is flat-out wrong”
And no model has been tuned with a history that includes the total absence of CO2.
Frank and Mr Stokes are, as usual, flat-out wrong. Paper after paper after paper states that the “natural greenhouse effect”, the sum of the directly-forced warming from the non-condensing greenhouse gases and the feedback response thereto, is 33 K. As if those numerous papers were not enough, the official definition of a “feedback” explicitly excludes the possibility of a feedback response to emission temperature. The models have been tuned to take these matters into account. And that is why they exaggerate all transient and equilibrium sensitivities.
The central question raised by this series remains: how can inanimate feedback processes decide that they should not respond to emission temperature but should suddenly respond greatly to the very small enhancement of it that arises from the presence of the non-condensing greenhouse gases? For all the flim-flam, no proper answer to that key question has yet been provided by our detractors here. Until they provide one, all that they say will lack credibility.
Monckton says: “Paper after paper after paper states that the “natural greenhouse effect”, the sum of the directly-forced warming from the non-condensing greenhouse gases and the feedback response thereto, is 33 K.”
Many sources say that the greenhouse effect is 33K, but this value is obtained from A MODEL, the blackbody equivalent temperature of 255 K. That MODEL assumes an Earth without GHGs WOULD STILL HAVE TODAY’S ALBEDO (a totally absurd assumption) and that the planet would EMIT LIKE A BLACKBODY (another totally absurd assumption if water vapor and clouds are present). Lacis’ model – which lacks non-condensable GHGs, but includes water vapor and clouds does NOT emit like a blackbody, because many photons escaping directly to space are emitted from cloud tops and water vapor in the atmosphere, both of which are colder than the surface. Does anyone in their right mind think the GISS model correctly reproduces convection and cloud formation when the planet is 30+ degC colder than today?
When climate scientists say that the GHE is 33 K, the public has been FOOLED into thinking that the GHE can be reduced a single, unambiguous number. The calculation requires a MODEL for the Earth without a GHE and the standard model (constant albedo, blackbody emission) isn’t what many expect. The only definite measure of the GHE is the 150 W/m2 difference between mean surface emission (390 W/m2) and mean TOA emission (240 W/m2). The GHE IS 150 W/m2. The enhanced GHE from 2XCO2 IS about 3.5 W/m2. Climate scientists don’t know how to convert changes in radiation (W/m2) into changes in temperature. If they did, WE WOULD ALREADY KNOW ECS.
We don’t know ECS because we don’t know how big feedbacks really are and we can’t trust AOGCMs to properly calculate them! For exactly the same reasons, we can’t trust Lacis’ model for our planet without condensable GHGs to correctly extrapolate feedbacks all the way to 30+ degC colder than today. Therefore anything Monckton derives from Lacis’s and Pierrehumbert’s models is suspect.
Let me make Monckton’s propaganda easier to understand. The GHE is 150 W/m2. If we also accept that the GHE is 33 K, then the climate feedback parameter λ is 4.5 W/m2/K If F_2x is 3.7 W/m2, then ECS is 0.8 K/doubling and f is -0.2. Feedback is modestly negative, trivially different from Monckton’s positive value of 0.08. Amplified global warming therefore must be a hoax. Skip the complicated control theory.
The problem is that feedbacks are not linear. The average value for λ from 255K (or 252K or 240K or ?K) to to the present isn’t relevant to what happens in the future. Feedbacks are highly non-linear. The whole idea is absurd.
Frank continues to maunder on about nonlinearity in feedbacks. But the simple truth is that, insofar as there is any nonlinearity in feedbacks, a) it is not very great; b) it is present in the system whether the corrected or uncorrected math is used; and c) therefore, equilibrium sensitivity will be considerably less using the corrected math than using the uncorrected math, even after the small nonlinearity has been allowed for.
Nibcjtib wrutesL :Frank continues to maunder on about nonlinearity in feedbacks. But the simple truth is that, insofar as there is any nonlinearity in feedbacks, a) it is not very great; b) it is present in the system whether the corrected or uncorrected math is used; and c) therefore, equilibrium sensitivity will be considerably less using the corrected math than using the uncorrected math, even after the small nonlinearity has been allowed for.”
I pointed out that Monckton’s reference (Roe 2008) discusses how to deal with non-linearity. I applied Roe method above and found the correction was large when trying to used data from Lacis’s model for our planet without non-condensible GHGs.
Frank continues to maunder on about nonlinearity in feedbacks. He cites Roe (2009) as an authority on how to handle nonlinear feedbacks. However, he overlooks the fact that Roe makes the same mistake as everyone else in official climatology by failing to accord any value to the large feedback response to emission temperature, and by using a degenerate form of the zero-dimensional-model equation that makes no provision for the emission temperature and, therefore, no provision for any feedback response thereto.
It is precisely because official climatology does not make due allowance for the feedback response to emission temperature that it imagines, quite improperly, that nonlinearity in feedbacks is a big deal. Of course Frank will be able to make nonlinearity look serious if he continues to refuse to use the corrected form of the zero-dimensional-model equation.
Monckton writes: “Let us conduct a simple Gedankenexperiment, running in reverse the model of Lacis et al. (2010), who found that, 50 years after removing all the non-condensing greenhouse gases from the atmosphere, the climate would have settled down to a new equilibrium, giving a slushball or waterbelt Earth with albedo 0.418, implying emission temperature 243.3 K. … Lacis found that, only 20 years after removal of the non-condensing greenhouse gases, global mean surface temperature would fall to 253 K. Over the next 30 years it would fall by only 1 K more, to 252 K, or 8.7 K above the emission temperature…. ”
What does Monckton mean when he says that the “implied emission temperature” is 243.3 K? He is saying that a BLACKBODY at 243. K would emit 199 W/m2 and our planet with an albedo of 0.416 would absorb (1-0.412)*342 = 201 W/m2. Close enough to balance. WHO EVER SAID THE EARTH MUST EMIT LIKE A BLACKBODY? The current Earth emits like a graybody with emissivity 0.615 and temperature 288K. Lacis’ model has more clouds than today. If Lacis’ model has cloud tops at 235 K and a surface at 252K, it would emit about 200 W/m2. And that is before accounting for any reduction in emission due water vapor in the atmosphere.
Monckton continued: “One question which few opponents in these threads have answered, and none has answered convincingly, is this: What was the source of that additional 8.7 K temperature, given that there were no non-condensing greenhouse gases to drive it? Our answer is that Lacis was implicitly acknowledging the existence of a feedback response to the 243.3 K emission temperature itself – albeit at a value far too small to be realistic.”
So low cloud top temperature and water vapor can easily explain why Lacis’ model emitted only about 200 W/m2 of LWR. Just like low cloud top temperature, water vapor and non-condensable GHGs explain why our planet today only emits 240 W/m2 (a blackbody equivalent temperature of 255 K). In both cases we expect the planet to emit like a gray-body, not a blackbody: T = 288K and e = 0.615 gives a graybody emission of 240 W/m2 (like today). T = 252 and e = 0.87 emits 199 W/m2. Mystery explained.
As Frank begins to realize that the Great Cause on which he has wasted so much time is on the brink of outright collapse he becomes ever more hysterical and incoherent. Let me explain to him, yet again, how the fundamental equation of radiative transfer works.
Take a snowball Earth with albedo 0.6. The emission temperature is 221.5 K. Take a waterbelt Earth with albedo 0.418. The emission temperature is 243.3 K. Take today’s Earth, with albedo 0.293. The emission temperature is 0.293 K. None of these temperatures is a blackbody temperature, because the albedos are nonzero. Neither I nor anyone has suggested that the Earth must emit like a blackbody when, given its albedo, it must emit like a graybody.
In this post, Monckton continues to push the idea that feedback can be associated with a temperature, rather than just a temperature change. Does this idea make any sense for climate (not amplifiers or control systems)? The climate feedback parameter λ is the derivative of net radiative balance across the TOA (OLR + reflected SWR) with surface temperature. For changes of a few degK, we can treat λ as a constant, For larger changes, such as those in this post, we can not – emission varies with the FOURTH POWER of temperature. To make this clear, let’s express λ as a function of Ts
dW/dTs = λ(Ts)
dW = λ(Ts)*dTs
This equation can be integrated from T1 to T2, which would define a cumulative feedback for a temperature change from T1 to T2. Or we can imagine an indefinite integral with an unknown constant of integration C. We can evaluate C at absolute zero and find that C = 0.
Now let’s try the same mathematics with amplification, which arises from breaking λ(Ts) up into two components, Planck feedback λ0(Ts) and the sum of all other feedbacks λ1(Ts). f(Ts) = -λ1(Ts)/λ0(Ts)
dW = λ0(Ts)*dTs + λ1(Ts)}*dTs = λ0(Ts)*dTs + -f(Ts)*λ0(Ts)}*dTs
These integrals exist, so we might be able to assign a cumulative value to amplification at any temperature.
Above, I wrote that Lacis’ data fit a graybody model with T = 252, e =0.87, and albedo = 0.412 as well as T =288, e = 0.615 and albedo = 0.30. In other words, but emissivity and absorptivity are changing with temperature when we think of the planet as a gray body.
So, changing the temperature from 3K to 255K won’t induce any feedback effect, but changing the temperature from 255K to 263K will? Makes sense (or not..).
Mr Langlee is right and Frank, as usual, is flat-out wrong. Feedbacks, whether Frank likes it or not, are denominated in Watts per square meter per Kelvin. Being inanimate, they are quite incapable of distinguishing between the input signal (emission temperature) and any amplification thereof. They will simply respond to the input signal, whether amplified or not. The corrected form of the zero-dimensional-model equation makes this quite clear. And, just in case, we built a test rig to check that there is indeed a feedback response to the input signal, and then we got a national laboratory to do the same, We are right about this.
As to Frank’s point about non-linearity, that is the last refuge of a scoundrel. We have shown in the head posting that the variance in the value of the “Planck feedback” is tiny even across 33 K of temperature change. We have shown that the only significant feedback – the water vapor feedback – is approximately linear. In such circumstances, we are fully justified in taking as a working assumption that the feedback fraction is near-invariant.
In any event, to whatever extent the feedback regime in the climate system may be non-linear, correction of the error we have exposed does not have the effect of increasing that non-linearity. Therefore, correction will very substantially diminish both transient and equilibrium sensitivities.
How would Frank explain the very sharp nonlinearity by which the feedback response to emission temperature is either nil or very small, while the feedback response to the modest addition to it represented by the directly-forced warming from the non-condensing greenhouse gases is very large?
“How would Frank explain the very sharp nonlinearity by which the feedback response to emission temperature is either nil or very small, while the feedback response to the modest addition to it represented by the directly-forced warming from the non-condensing greenhouse gases is very large.”
Right — it doesn’t make sense. Moreover, the non-linearity of the system clearly works against the incremental response being greater than the absolute response:
http://www.palisad.com/co2/gf/st_ga.png
http://www.palisad.com/co2/why/pi_gs.png
Plus, each degree of warming requires incrementally more and more power to effect and sustain than the previous degree, which only further works against the incremental response being greater that the absolute response.
The real flaw though in all of this is that there really is no new starting point for the physical processes and feedbacks (mainly water vapor and clouds) since the system is never truly in balance — it perpetually oscillates to maintain an approximate steady-state. The physical processes and feedbacks from water vapor and clouds have no way to distinguish an imbalance from added GHGs from imbalances that occur as a result of the regularly occurring dynamic chaos in the system, and would respond within the same bounds.
The great Cause on which Frank invests his time is Science, not politics. Unlike politicians and attorneys, scientists are expected to tell the truth, the whole truth and nothing but the truth, with all of the ifs ands buts and caveats. However, the vast majority of climate scientists appear to have been attracted to the field to “save the world” and have forgotten their scientific ethics. They live in left-wing ivory towers and have sold out to a political organization (the IPCC) with a charter (consensus) that allegedly requires them to skip over some of the truth and almost all of the caveats. Their reports require unanimous agreement of more than 100 bureaucrats, meaning that their SPMs contain only the convenient part of the truth and none of the caveats, particularly about the fallibility of AOGCMs (their only tool for making projections). Those bureaucrats are advised/controlled by a self-perpetuating group of activist insiders who serve as prosecutor, judge and jury for our fossil-fuel based society. No defense attorneys (nor the press) are allowed to attend, just fanatic environmental organizations ready to pounce if anyone steps out of line. For that reason, it is difficult for any scientist to publicly discuss and publish science that suggests climate sensitivity is low.
Unfortunately, almost all of the science being pushed by politically active skeptics and at this blog is badly flawed. Like this post. And previous posts about the Pause: About the absence of statistically significant warming being evidence that no warming is occurring and that the GHE doesn’t exist. Confusing transient and equilibrium warming. This noise has drowned the growing real evidence that climate sensitivity is near the bottom of the IPCC’ s likely range: EBMs, all AOGCMs show ECS less than 2 when forced with historic SSTs, the weakening evidence for a strong aerosol indirect effect, weakening AR5 claims about the MWP, hurricane intensification. This progress towards a less alarmist future is being ignored because the skeptic position that get the most publicity is that AGW is a hoax. Skeptical (and alarmists) politics is all about “winning”, not uncovering scientific truth. To quote Alice Dreger (a passionate advocate for more unbiased science and research: “Only people like us, with insane amounts of privilege, could ever think it was a good idea to decide what is right before we know what is true”. In her case, the ‘insanely privileged” people she was referring to were her fellow liberal academics. Ms. Dreger’s book is subtitled “Heretics, Activists, and One Scholar’s Search for Justice”. A great read.
Monckton’s Cause is winning.
Frank misrepresents me when he says that I had suggested that the Great Pause in global temperatures indicated that there was no greenhouse effect. On the contrary, in column after column here, as the Paus grew in length to 18 years 9 months before a large el Nino brought it to an end, I made it quite plain that some warming was to be expected and that, therefore, the Pause would not continue indefinitely.
But we seem to be in agreement that equilibrium sensitivity will be well south of 2 K. That is certainly what our result shows.
Frank continues to reveal his ignorance of elementary control theory by pretending that a feedback response cannot arise in the presence of an invariant input signal. The point really is elementary. The corrected version of the zero-dimensional-model equation mandates it. But, because IPCC had attempted to define a feedback as a response only to a change rather than also to an absolute value, we built not one but two simple circuits to make sure that the theoretically-mandated feedback response even to an unamplified input signal actually occurs, and occurs at the expected value. Well, it does. And it’s no good Frank trying to muddy the waters. Control theorists will soon be looking at our result, and they will have no patience with the nonsensical notion that an invariant or unamplified input signal induces no feedback response.
The main criticism of Lord Monckton’s conjecture, if I may call it that, appears to be that one shouldn’t use the equation:
ΔTeq = ΔTref / (1 – f )
for absolute (Kelvin) temperatures i.e. in the form:
Teq = Tref / (1 – f )
But the only reason one can’t use it in this way is if the feedback parameter f were to change as a function of temperature.
If the feedback parameter f is constant across all temperatures from 0°K to 288°K, then Teq = Tref / (1 – f ) is perfectly valid, as demonstrated Monckton’s electrical feedback circuits, and a constant value of f=0.08 is appropriate to explain the single data point that we are considering here, namely that an input temperature of 263°K (the sum of the 255°K emission + 8°K non-condensing GHGs) results in an equilibrium temperature of 288°K.
However… if you make the feedback parameter f a function of temperature, let’s call it f(T), then if course you can’t use a constant value of f on the absolute temperature. Clearly Teq = Tref / (1 – f ) no longer works as it doesn’t capture the changing feedback parameter across large temperature changes. For example, if you used f=0.75 (Lacis et al) and applied it to the full input temperature of 263°K it would imply the earth’s equilibrium temperature is 263°K /(1-0.75) = 1053°K (!). So of course this is absurd.
But the another way to satisfy our single data point, namely that 263°K implies an equilibrium 288°K, is to set the feedback parameter f(T) to zero right the way from 0°K up to 263°K and then jump it up to 0.75 in the region 263°K to 288°K. Then if you would restrict the use of the equations thus:
0°K < T < 263°K ΔTeq = ΔTref / (1 – 0.0 )
263°K < T ΔTeq = ΔTref / (1 – 0.75 )
Then this too satisfies our single data point. So the previous conjecture (Hansen et al) can be thought of this way. Zero feedback until 263°K, followed by a step-change discontinuity in f(T), where it suddenly steps up to 0.75 at the magical 263°K temperature.
Now I'm not familiar with the exponential Clausius-Clapeyron relation w.r.t. temperature, and the logarithmic nature of water vapour feedback (is the end result roughly linear, so a constant feedback parameter?). But my first assumption would definitely not be an f(T) of has this odd square-wave form. What basis is there to assume that? As Lord Monckton eloquently puts it, water vapour is also present in the atmosphere at lower temperatures too, well below 263°K, so how does the mother earth know to provide zero feedback until 263°K and then suddenly crank up the feedback processes at a rate of 0.75 above the magic temperature? Being polite I'd call it: erroneous.
So given we only have one data point, the best we can do is estimate a single value. So a much better starting point would be to assume a constant f = 0.08.
(That's not to say that far more work needs to done to map out f(T) from 0°K up to 288°K, for example when an input ΔT of 2°K is enough to end an ice age and the world might become say 10°K warmer. So in this narrow temperature region f(T) could jump up to 0.8. But it could be zero or negative either side, who knows? So what does this function of f(T) look like? Why don't we know? What have climatologists done with all their funding money, counting polar bears?)
I’m most grateful to Mr Palmes for having really thought hard about our work. He has gotten the point of what we are trying to say, and he has also understood that, though feedback processes are non-linear in the climate system, they are not very non-linear, which is why assuming a single mean feedback fraction is justifiable.
It may assist Mr Palmes to know that we are not dealing with an interval of surface temperature from 0 to 288 K, but from 255 to 288 K. The feedback processes (chiefly the water-vapor and albedo feedbacks) are not concerned with any value less than the emission temperature of 255 K. That is the input temperature to which they would react even in the absence of the non-condensing greenhouse gases. So we are only dealing with an interval of 33 K. Across that interval, nonlinearities in feedbacks tend, if anything, gradually to diminish the feedback fraction rather than to increase it.
In any event, such nonlinearities as may subsist in the feedback processes subsist no less under the present system than under the corrected system. It is inevitable, therefore, that in the corrected system the equilibrium sensitivity will be considerably below its value in the present system. For our corrections do not alter any nonlinearities that may be present.
In reply to Lord Monckton, thank you, that was extremely useful response. I was getting lost down a side alley for no good reason.
In a moment of clarity I suddenly see the elegant simplicity of this. If an input temperature of 263°K (the sum of the 255°K emission + 8°K non-condensing GHGs) results in an equilibrium temperature of 288°K that implies that f=0.08. And then perturbing the input signal by a ΔT of 1.2°K (the direct temperature rise for x2 CO2) this means the input is now 263+1.2 = 264.2. This results in an equilibrium temperature of 264.2 /(1-0.08) = 289.3, which is an equilibrium temperature rise of 1.3°K.
So hang on, isn’t this even better than we thought? We only need to worry about the non-linearity in very close proximity to the current 263°K input signal? Why are we worrying about snowball earth or the feedback parameter near absolute zero. That’s completely irrelevant to the question we’re trying to answer.
I’m not sure why it’s taken me so long to get it, (perhaps led astray by Nick Stokes?)
I am glad that Mr Palmes can now see our result in his mind’s eye. The speed with which he has grasped it is commendable. It took me a great deal longer, with much fumbling around and with publication of several papers raising the questions to which I needed answers before I could finally see the whole picture.
In truth we do not really need to worry about nonlinearity at all. For our separate calculation intended to derive the industrial-era value of the feedback fraction found it to be somewhere between 0.04 and 0.28, depending on how many assumptions unduly favorable to the official position one is prepared to make. That would give an equilibrium sensitivity of 1.2-1.5 K, which is not enough for anyone to worry about.
Harry: The Clausius-Claperyon relationship is not an exponential one. The log of saturation vapor pressure varies with 1/T. 7%/K is a reasonable approximation around 288 K. IIRC, it is closer to 6%/K in the tropics and up to 10%/K around -20 degC. Just another example of Monckton not being familiar with the physics he is using. The real problem, of course, is that our atmosphere is not saturated with water vapor. Relative humidity averages 80% over the ocean and falls with altitude. The assumption that relative humidity will remain the same as the planet cools more than 30 degC is a dubious one.
I think you’ve got the right idea writing f(T) rather than just f (a constant). Don’t forget λ0 also should be written as λ0(T)> It represents simple thermal emission of radiation with varies with T^4. And there is some merit in the idea of integrating.
Frank continues to adopt a childish, hectoring, lecturing tone which is not impressing readers here. He keeps assuming that it is I whom he is having to deal with, rather than a band of expert co-authors with certificates of appropriate Socialist training in the relevant subjects.
And of course, when considering nonlinear functions such as the feedback fraction, one must consider an array of temperature-dependent values. All of that is elementary. However, the central and obvious point is this. Given that the nonlinearities in the system are the same whether one does the math incorrectly, as official climatology does by ignoring the large feedback response to emission temperature, or correctly, as we have done, it is inevitable that, following our correction, Charney sensitivity will be very considerably below what it is currently thought to be.