*Part II: How the central estimate of pre-feedback warming was exaggerated*

*By Christopher Monckton of Brenchley*

In this series I am exploring the cumulative errors, large and small, through which the climatological establishment has succeeded in greatly exaggerating climate sensitivity. Since the series concerns itself chiefly with equilibrium sensitivity, time-dependencies, including those arising from non-linear feedbacks, are irrelevant.

In **Part I**, I described a small error by which the climate establishment determines the official central estimate of equilibrium climate sensitivity as the inter-model mean equilibrium sensitivity rather than determining that central estimate directly from the inter-model mean value of the temperature feedback factor *f. *For it is the interval of values for *f *that dictates the interval of final or equilibrium climate sensitivity and accounts for its hitherto poorly-constrained breadth [1.5, 4.5] K. Any credible probability-density function for final sensitivity must, therefore, center on the inter-model mean value of *f*, and not on the inter-model mean value of Δ*T, *skewed as it is by the rectangular-hyperbolic (and hence non-linear) form of the official system gain equation *G *= (1 – *f*)^{–1}.

I showed that the effect of that first error was to overstate the key central estimates of final sensitivity by between 12.5% and 34%.

Part II, which will necessarily be lengthy and full of equations, will examine another apparently small but actually significant error that leads to an exaggeration of reference or pre-feedback climate sensitivity Δ*T*_{0} and hence of final sensitivity Δ*T.*

For convenience, the official equation (1) of climate sensitivity as it now stands is here repeated. There is much wrong with this equation, but, like it or not, it is what the climate establishment uses. In Part I, it was calibrated closely and successfully against the outputs of both the CMIP3 and CMIP5 model ensembles.

Fig. 1 illuminates the interrelation between the various terms in (1). In the current understanding, the reference or pre-feedback sensitivity Δ*T*_{0} is simply the product of the official value of radiative forcing Δ*F*_{0} = 3.708 W m^{–2} and the official value of the reference sensitivity parameter λ_{0} = 3.2^{–1} K W^{–1} m^{2}, so that Δ*T*_{0} = 1.159 K (see e.g. AR4, p. 631 fn.).

However, as George White, an electronics engineer, has pointed out (pers. comm., 2016), in using a fixed value for the crucial reference sensitivity parameter λ_{0} the climate establishment are erroneously treating the fourth-power Stefan-Boltzmann equation as though it were linear, when of course it is exponential.

This mistreatment in itself leads to a small exaggeration, as I shall now show, but it is indicative of a deeper and more influential error. For George White’s query has led me to re-examine how, in official climatology, *λ*_{0} came to have the value at or near 0.312 K W^{–1} m^{2} that all current models use.

**Fig. 1 **Illumination of the official climate-sensitivity equation (1)

The fundamental equation (2) of radiative transfer relates flux density *F _{n} *in Watts per square meter to the corresponding temperature

*T*in Kelvin at some surface

_{n}*n*of a planetary body (and usually at the emission surface

*n*= 0):

(2) | Stefan-Boltzmann equation

where the Stefan-Boltzmann constant *σ* is equal to 5.6704 x 10^{–8} W m^{–2} K^{–4}, and the emissivity *ε** _{n}* of the relevant surface

*n*is, by Kirchhoff’s radiation law, equal to its absorptivity. At the Earth’s reference or emission surface

*n =*0, a mean 5.3 km above ground level, emissivity

*ε*

_{0}, particularly with respect to the near-infrared long-wave radiation with which we are concerned, is vanishingly different from unity.

The Earth’s mean emission flux density *F*_{0} is given by (3),

where *S*_{0}* = *1361 W m^{–2 }is total solar irradiance (SORCE/TIM, 2016); *α* = 0.3 is the Earth’s mean albedo, and 4 is the ratio of the surface area of the rotating near-spherical Earth to that of the disk that the planet presents to incoming solar radiation. Rearranging (2) as (4) and setting *n *= 0 gives the Earth’s mean emission temperature *T*_{0}:

A similar calculation may be performed at the Earth’s hard-deck surface *S*. We know that global mean surface temperature *T** _{S}* is 288 K, and measured emissivity

*ε*

*≈ 0.96. Accordingly, (3) gives*

_{S}*F*

_{S}*as 374.503 W m*

^{–2}. This value is often given as 390 W m

^{–2}, for ε

*is frequently taken as unity, since little error arises from that assumption.*

_{S}The first derivative *λ*_{0} of the Stefan-Boltzmann equation relating the emission temperature *T*_{0}* *to emission flux density *F*_{0} before any radiative perturbation is given by (5):

The surface equivalent λ* _{S}* =

*T*

_{S}*/ (4*

*F*) = 0.192 K W

_{S}^{–1}m

^{2}(or 0.185 if ε

*is taken as unity).*

_{S}The official radiative forcing in response to a doubling of atmospheric CO_{2} concentration is given by the approximately logarithmic relation (6) (Myhre *et al., *1998; AR3, ch. 6.1). We shall see later in this series that this value is an exaggeration, but let us use it for now.

Then the direct or reference warming in response to a CO_{2} doubling is given by

A similar result may be obtained thus: where *F*_{μ}* *= *F*_{0} + Δ*F*_{0} = 238.175 + 3.708 = 241.883 W m^{–2}, using (2) gives *T** _{μ}*:

Then –

a little less than the result in (7), the small difference being caused by the fact that *λ*_{0} cannot have a fixed value, because, as George White rightly points out, it is the first derivative of a fourth-power relation and hence represents the slope of the curve of the Stefan-Boltzmann equation at some particular value for radiative flux and corresponding value for temperature.

Thus, the value of *λ*_{0}, and hence that of climate sensitivity, must decline by little and little as the temperature increases, as the slightly non-linear curve in Fig. 2* *shows.

**Fig. 2 **The first derivative *λ*_{0} = *T*_{0}* */ (4*F*_{0}) of the Stefan-Boltzmann equation, which is the slope of a line tangent to the red curve above, declines by little and little as *T*_{0}, *F*_{0} increase.

The value of *λ*_{0} may also be deduced from eq. (3) [here (10)] of Hansen (1984), who says [with notation altered to conform to the present work]:

“… for changes of solar irradiance,

“Thus, if *S*_{0} increases by a small percentage δ, *T*_{0} increases by δ/4. For example, a 2% change in solar irradiance would change *T*_{0} by about 0.5%, or 1.2-1.3 K.”

Hansen’s 1984 paper equated the radiative forcing Δ*F*_{0} from a doubled CO_{2} concentration with a 2% increase Δ*F*_{0} = 4.764 W m^{–2} in emission flux density, which is where the value 1.2-1.3 K for Δ*T*_{0} = Δ*F*_{0}*λ*_{0} seems first to have arisen. However, if today’s substantially smaller official value Δ*F*_{0} = 3.708 W m^{–2} (Myhre *et al., *1998; AR3, ch. 6.1) is substituted, then by (10), which is Hansen’s equation, Δ*T*_{0} becomes 0.991 K, near-identical to the result in (7) here, providing further confirmation that the reference or pre-feedback temperature response to a CO_{2} doubling should less than 1 K.

The Charney Report of 1979 assumed that the entire sensitivity calculation should be done with surface values *F** _{S}*,

*T*

*, so that, for the 283 K mean surface temperature assumed therein, the corresponding surface radiative flux obtained via (2) is 363.739 W m*

_{S}^{–2}, whereupon

*λ*

*was found equal to a mere 0.195 K W*

_{S}^{–1}m

^{2}, near-identical to the surface value

*λ*

*= 0.192 K determined from (5).*

_{S}Likewise, Möller (1963), presenting the first of three energy-balance models, assumed today’s global mean surface temperature 288 K, determined from (2) the corresponding surface flux 390 W m^{–2}, and accordingly found *λ** _{S}* = 288 / (4 x 390) = 0.185 K W

^{–1}m

^{2}, under the assumption that surface emissivity ε

*was equal to unity.*

_{S}Notwithstanding all these indications that λ_{0} is below, and perhaps well below, 0.312 K W^{–1} m^{2} and is in any event not a constant, IPCC assumes this “uniform” value, as the following footnote from AR4, p.631, demonstrates [with notation and units adjusted to conform to the present series]:

“Under these simplifying assumptions the amplification of the global warming from a feedback parameter *c* (in W m^{–2} K^{–1}) with no other feedbacks operating is 1 / (1 – *c* λ_{0}), where λ_{0} is the ‘uniform temperature’ radiative cooling response (of value approximately 3.2^{–1} K W^{–1 }m^{2}; Bony et al., 2006). If *n *independent feedbacks operate, *c* is replaced by (*c*_{1} + *c*_{2} +… + *c** _{n}*).”

How did this influential error arise? James Hansen, in his 1984 paper, had suggested that a CO_{2} doubling would raise global mean surface temperature by 1.2-1.3 K rather than just 1 K in the absence of feedbacks. The following year, Michael Schlesinger described the erroneous methodology that permitted Hansen’s value for Δ*T*_{0} to be preserved even as the official value for Δ*F*_{0} fell from Hansen’s 4.8 W m^{–2} per CO^{2} doubling to today’s official (but still much overstated) 3.7 W m^{–2}.

In 1985, Schlesinger stated that the planetary radiative-energy budget was given by (11):

where *N*_{0}* *is* *the net radiation at the top of the atmosphere, *F*_{0} is the downward flux density at the emission altitude net of albedo as determined in (3), and *R*_{0}* *is the long-wave upward flux density at that altitude. Energy balance requires that *N*_{0} = 0, from which (3, 4) follow.

Then Schlesinger decided to express *N*_{0} in terms of the surface temperature *T*_{S}* *rather than the emission temperature *T*_{0} by using *surface *temperature *T** _{S}* as the numerator and yet by using

*emission*flux

*F*

_{0}in the denominator of the first derivative of the fundamental equation (2) of radiative transfer.

In short, he was applying the Stefan Boltzmann equation by straddling uncomfortably across two distinct surfaces in a manner never intended either by Jozef Stefan (the only Slovene after whom an equation has been named) or his distinguished Austrian pupil Ludwig Boltzmann, who, 15 years later, before committing suicide in despair at his own failure to convince the world of the existence of atoms, had provided a firm theoretical demonstration of Stefan’s empirical result by reference to Planck’s blackbody law.

Since the Stefan-Boltzmann equation directly relates radiative flux and temperature at a single surface, the official abandonment of this restriction – which has not been explained anywhere, as far as I can discover – is, to say the least, a questionable novelty.

For we have seen that the Earth’s hard-deck emissivity ε* _{S}* is about 0.96, and that its emission-surface emissivity ε

_{0}, particularly with respect to long-wave radiation, is unity. Schlesinger, however, says:

“*N*_{0} can be expressed in terms of the surface temperature *T** _{S}*, rather than [emission temperature]

*T*

_{0}by introducing an effective planetary emissivity

*ε*

*, in (12):*

_{p}so that, in (13),

This official approach embodies a serious error arising from a misunderstanding not only of (2), which relates temperature and flux at the same surface and not at two distinct surfaces, but also of the fundamental architecture of the climate.

Any change in net flux density *F*_{0} at the mean emission altitude (approximately 5.3 km above ground level) will, via (2), cause a corresponding change in emission temperature *T*_{0} at that altitude. Then, by way of the temperature lapse rate, which is at present at a near-uniform 6.5 K km^{–1} just about everywhere (Fig. 3), that change in *T*_{0} becomes an identical change *T** _{S}* in surface temperature.

**Fig. 3 **Altitudinal temperature profiles for stations from 71°N to 90°S at 30 April 2011, showing little latitudinal variation in the lapse-rate of temperature with altitude. Source: Colin Davidson, pers. comm., August 2016.

But what if albedo or cloud cover or water vapor, and hence the lapse rate itself, were to change as a result of warming? Any such change would not affect the reference temperature change Δ*T*_{0}: instead, it would be a temperature feedback affecting final climate sensitivity Δ*T*.

The official sensitivity equation thus already allows for the possibility that the lapse-rate may change. There is accordingly no excuse for tampering with the first derivative of the Stefan-Boltzmann equation (2) by using temperature at one altitude and flux at quite another and conjuring into infelicitous existence an “effective emissivity” quite unrelated to true emissivity and serving no purpose except unjustifiably to exaggerate *λ*_{0} and hence climate sensitivity.

One might just as plausibly – and just as erroneously – choose to relate emission temperature with surface flux, in which event λ_{0} would fall to 254.6 / [4(390.1)] = 0.163 K W^{–1} m^{2}, little more than half of the models’ current and vastly-overstated value.

This value 0.163 K W^{–1} m^{2} was in fact obtained by Newell & Dopplick (1979), by an approach that indeed combined elements of surface flux *F _{S}* and emission temperature

*T*

_{0}.

The same year the Charney Report, on the basis of hard-deck surface values *T*_{S}* *and *F*_{S}* *for temperature and corresponding radiative flux density respectively, found λ* _{S}* to be 0.192 K W

^{–1}m

^{2}.

IPCC, followed by (or following) the overwhelming majority of the models, takes 3.2^{–1}, or 0.3125, as the value of λ_{0}. This choice thus embodies two errors one of modest effect and one of large, in the official determination of λ_{0}. The error of modest effect is to treat λ_{0} as though it were constant; the error of large effect is to misapply the fundamental equation of radiative transfer by straddling two distinct surfaces in using it to determine λ_{0}. As an expert reviewer for AR5, I asked IPCC to provide an explanation showing how λ_{0} is officially derived. IPCC curtly rejected my recommendation. Perhaps some of its supporters might assist us here.

In combination, the errors identified in Parts I and II of this series have led to a significant exaggeration of the reference sensitivity Δ*T*_{0}, and commensurately of the final sensitivity Δ*T, *even before the effect of the errors on temperature feedbacks is taken into account. The official value Δ*T*_{0} = 1.159 K determined by taking the product of IPCC’s value 0.3125 K W m^{–1} for *λ*_{0} and its value 3.708 W m^{–2} for Δ*F*_{0} is about 17.5% above the Δ*T*_{0} = 0.985 K determined in (9).

Part I of this series established that the CMIP5 models had given the central estimate of final climate sensitivity Δ*T* as 3.2 K when determination of the central estimate of final sensitivity from the inter-model mean central estimate of the feedback factor *f *would mandate only 2.7 K. The CMIP 5 models had thus already overestimated the central estimate of equilibrium climate sensitivity Δ*T* by about 18.5%.

The overstatement of the CMIP5 central estimate of climate sensitivity resulting from the combined errors identified in parts I and II of this series is accordingly of order 40%.

This finding that the current official central estimate climate sensitivity is about 40% too large does not yet take account of the effect of the official overstatement of λ_{0} on the magnitude of that temperature feedback factor *f. *We shall consider that question in Part III.

For now, the central estimate of equilibrium climate sensitivity should be 2.3 K rather than CMIP5’s 3.2 K. Though each of the errors we are finding is smallish, their combined influence is already large, and will become larger as the compounding influence of further errors comes to be taken into account as the series unfolds.

Table 1 shows various values of *λ*_{0}, compared with the reference value 0.264 K W^{–1} m^{2} obtained from (8).

Table 1: Some values of the reference climate-sensitivity parameter λ_{0} |
||||

Source | Method | Value of λ_{0} |
x 3.7 = ΔT_{0} |
Ratio |

Newell & Dopplick (1979) | T_{0} / (4F)_{S} |
0.163 K W^{–1} m^{2} |
0.604 K | 0.613 |

Möller (1963) | T / (4_{S}F)_{S} |
0.185 K W^{–1} m^{2} |
0.686 K | 0.696 |

Callendar (1938) | T / (4_{S}F)_{S} |
0.195 K W^{–1} m^{2} |
0.723 K | 0.734 |

From (8) here |
T_{0} / (4F_{0}) |
0.264 K W^{–1} m^{2} |
0.985 K |
1.000 |

Hansen (1984) | T_{0} / (4F_{0}) |
0.267 K W^{–1} m^{2} |
0.990 K | 1.005 |

From (7) here | T_{0} / (4F_{0}) |
0.267 K W^{–1} m^{2} |
0.991 K | 1.006 |

Schlesinger (1985) | T / (4_{S}F_{0}) |
0.302 K W^{–1} m^{2} |
1.121 K | 1.138 |

IPCC (AR4, p. 631 fn.) | 3.2^{–1} |
0.312 K W^{–1} m^{2} |
1.159 K | 1.177 |

Nearly all models adopt values of *λ*_{0} that are close to or identical with IPCC’s value, which appears to have been adopted for no better reason that it is the reciprocal of 3.2, and is thus somewhat greater even than the exaggerated value obtained by Schlesinger (1985) and much copied thereafter.

In the next instalment, we shall consider the effect of the official exaggeration of λ_{0} on the determination of temperature feedbacks, and we shall recommend a simple method of improving the reliability of climate sensitivity calculations by doing away with λ_{0} altogether.

I end by asking three questions of the Watts Up With That community.

1. Is there any legitimate scientific justification for Schlesinger’s “effective emissivity” and for the consequent determination of λ_{0} as the ratio of *surface *temperature to four times *emission *flux density?

2. One or two commenters have suggested that the Stefan-Boltzmann calculation should be performed entirely at the hard-deck surface when determining climate sensitivity and not at the emission surface a mean 5.3 km above us. Professor Lindzen, who knows more about the atmosphere than anyone I have met, takes the view I have taken here: that the calculation should be performed at the emission surface and the temperature change translated straight to the hard-deck surface via the lapse-rate, so that (before any lapse-rate feedback, at any rate) Δ*T** _{S}* ≈ Δ

*T*

_{0}. This implies λ

_{0}= 0.264 K W

^{–1}m

^{2}, the value taken as normative in Table 1.

3. Does anyone here want to maintain that errors such as these are not represented in the models because they operate in a manner entirely different from what is suggested by the official climate-sensitivity equation (1)? If so, I shall be happy to conclude the series in due course with an additional article summarizing the considerable evidence that the models have been constructed precisely to embody and to perpetuate each of the errors demonstrated here, though it will not be suggested that the creators or operators of the models have any idea that what they are doing is as erroneous as it will prove to be.

Ø *Next: How temperature feedbacks came to be exaggerated in official climatology.*

References

Charney J (1979) *Carbon Dioxide and Climate: A Scientific Assessment: Report of an Ad-Hoc Study Group on Carbon Dioxide and Climate, *Climate Research Board, Assembly of Mathematical and Physical Sciences, National Research Council, Nat. Acad. Sci., Washington DC, July, pp. 22

Hansen J, Lacis A, Rind D, Russell G, Stone P, Fung I, Ruedy R, Lerner J (1984) Climate sensitivity: analysis of feedback mechanisms. Meteorol. Monographs 29:130–163

IPCC (1990-2013) Assessment Reports AR1-5 are available from www.ipcc.ch

Möller F (1963) On the influence of changes in CO_{2} concentration in air on the radiative balance of the Earth’s surface and on the climate. J. Geophys. Res. 68:3877-3886

Newell RE, Dopplick TG (1979) Questions concerning the possible influence of anthropogenic CO_{2} on atmospheric temperature. J. Appl. Meteor. 18:822-825

Myhre G, Highwood EJ, Shine KP, Stordal F (1998) New estimates of radiative forcing due to well-mixed greenhouse gases. Geophys. Res. Lett. 25(14):2715–2718

Roe G (2009) Feedbacks, timescales, and seeing red. Ann. Rev. Earth Planet. Sci. 37:93-115

Schlesinger ME (1985) Quantitative analysis of feedbacks in climate models simulations of CO2-induced warming. In: *Physically-Based Modelling and Simulation of Climate and Climatic Change – Part II *(Schlesinger ME, ed.), Kluwer Acad. Pubrs. Dordrecht, Netherlands, 1988, 653-735.

SORCE/TIM latest quarterly plot of total solar irradiance, 4 June 2016 to 26 August 2016. http://lasp.colorado.edu/data/sorce/total_solar_irradiance_plots/images/tim_level3_tsi_24hour_3month_640x480.png, accessed 3 September 2016

Vial J, Dufresne J, Bony S (2013) On the interpretation of inter-model spread in CMIP5 climate sensitivity estimates. Clim Dyn 41: 3339, doi:10.1007/s00382-013-1725-9

Jo Novas’ husband thinks the same http://www.perthnow.com.au/news/opinion/miranda-devine-perth-electrical-engineers-discovery-will-change-climate-change-debate/news-story/d1fe0f22a737e8d67e75a5014d0519c6

So this Kindergarten does draining real money down the river since 1896 :

A MATHEMATICAL discovery by Perth-based electrical engineer Dr David Evans may change everything about the climate debate, on the eve of the UN climate change conference in Paris next month.

A former climate modeller for the Government’s Australian Greenhouse Office, with six degrees in applied mathematics, Dr Evans has unpacked the architecture of the basic climate model which underpins all climate science.

He has found that, while the underlying physics of the model is correct, it had been applied incorrectly.

He has fixed two errors and the new corrected model finds the climate’s sensitivity to carbon dioxide (CO2) is much lower than was thought.

“Yes, CO2 has an effect, but it’s about a fifth or tenth of what the IPCC says it is. CO2 is not driving the climate; it caused less than 20 per cent of the global warming in the last few decades”.

Dr Evans says his discovery “ought to change the world”.

“But the political obstacles are massive,” he said.

His discovery explains why none of the climate models used by the IPCC reflect the evidence of recorded temperatures. The models have failed to predict the pause in global warming which has been going on for 18 years and counting.

“The model architecture was wrong,” he says. “Carbon dioxide causes only minor warming. The climate is largely driven by factors outside our control.”

There is another problem with the original climate model, which has been around since 1896.

___________________________

aghasting. / zum Kotzen /

David Evans’ work is very interesting. He advances a new theory of climate in which separate sensitivity calculations are performed at the emission altitudes for cloud tops, CO2, water vapor, methane etc. He finds climate sensitivity to be low.

The present series, by contrast, offers no new theory. It merely points out certain influential discrepancies between mainstream climate science and mainstream science. Mainstream climate science turns out to be wrong.

“Yes, CO2 has an effect, but it’s about a fifth or tenth of what the IPCC says it is.”

IPCC says it’s 3.2 K. A fifth of that is 0.64 K. I believe Dr. Evans is correct. Lindzen and Spencer independently calculated the climate sensitivity not from models but from empirical satellite data. They got the same value of 0.6 K indicating strong negative feedback since the no feedback sensitivity is around 1 K as demonstrated here by Lord Monckton

None of this is how the Planck response was calculated. The real method fully accounts for nonuniform temperature, lapse rate and emissivity. MERRA and ERA-Interim give an observation-based Planck response of about -3.1 W m-2 K-1.

See Soden & Held (2006, http://dx.doi.org/10.1175/JCLI3799.1 ), Bony et al. (2006, http://dx.doi.org/10.1175/JCLI3819.1) and Dessler (2010, http://dx.doi.org/10.1175/JCLI-D-11-

00640.s1).

Since the calculation is performed at the mean emission altitude, changes in lapse rate are irrelevant, since they are feedbacks and do not influence lambda-zero; emissivity at that altitude is as near unity as makes no difference; and the only significant non-uniformities in temperature are latitudinal, but they are insufficient to alter lambda-zero significantly. And Schlesinger did indeed determine lambda-zero as described, since when the models have followed, as Soden & Held’s list of values for lambda-zero makes clear.

“Since the calculation is performed at the mean emission altitude”

Your calculation does, but the one used for the IPCC result doesn’t. That calculation is done at all levels of the atmosphere as explained in the papers I cited.

Performing the calculation of lambda-zero at the mean emission altitude gives a result larger than performing it at any lesser altitude. Therefore, a calculation performed at all altitudes ought to yield a lesser value for lambda-zero than the emission-altitude value.

In any event, it is at the emission altitude that climate sensitivity should be determined. And the calculation at that altitude is uncomplicated.

_You_ calculated at an averaged mean emission altitude. The CMIP calculations are performed properly, see Section 2 in Soden & Held (2006, http://dx.doi.org/10.1175/JCLI3799.1 ). It’s less than 2 pages and it explains how the real technique is very different from what you’ve done here so anyone who’s interested in a way in which Planck feedback is commonly calculated should probably read it.

I think Soden & Held (2006) and many other papers explain very clearly why the full-physics result is different from using your simplified model and from the figures it’s pretty obvious. If you’re still struggling to grok it, I can point you to other examples.

I read Soden & Held (2006) in 2007 and have referred to it often since. It confirms the point I have been making: that the decision was made [originally in Schlesinger 1985] to model the reference sensitivity parameter incorrectly, using a mixture of top-of-atmosphere flux and surface temperature. Soden & Held’s Methodologty section confirms that this is exactly what is done, and it is an error.

“It confirms the point I have been making: that the decision was made [originally in Schlesinger 1985] to model the reference sensitivity parameter incorrectly, using a mixture of top-of-atmosphere flux and surface temperature. Soden & Held’s Methodologty section confirms that this is exactly what is done, and it is an error.”

From Soden & Held:

“The temperature feedback can be split further as lambda_T = lambda_0 + lambda_L, where lambda_0 assumes that the temperature change is uniform throughout the troposphere and lambda_L (i.e., lapse rate feedback) is the modification due to nonuniformity of the temperature change.”

The temperature change used in calculating the Planck feedback is “uniform [vertically] throughout the troposphere”. There is no change in lapse rate and whichever “emission altitude” you select, the temperature change there is identical to the surface. This addresses your issue and does better than your simplified calculations because it accounts for regional lapse rates and moisture profiles plus spectral variation in absorption.

I think your post needs to be corrected to state that you misinterpreted the way in which the Planck feedback was calculated and that all of your concerns are fully accounted for in the actual calculations. The correct result is close to the IPCC-reported 3.1 W m-2 K-1.

The furtively pseudonymous “Mie Scatter”, who has much to learn about climate sensitivity, and about the civilized manner of conducting an argument, for he hurls insults freely from behind that cowardly curtain, should read both the head posting and Soden & Held with rather more care.

Only a sentence or two before the sentence cited by “Mie Scatter”, Soden & Held make quite explicit the point I have made in the head posting: that the official value of lambda-zero, like that in Schlesinger (1985), is determined from emission-altitude flux and hard-deck surface temperature.

If “Mie Scatter” would only actually read Soden and Held, he would learn that the table of values of lambda-zero (listed as “Planck” among the feedbacks in the table) shows values in excess even of delta-T(surface) / [4 delta-F(emission)], when the correct use of the Stefan-Boltzmann equation is to relate temperature and flux at the same surface. It is for that reason, rather than because of supposed variations in emissivity, that the official value of lambda-zero is far too high.

in Soden and Held, they calculate lambda0 by translation of the temperature profile…

Two methods, same results.

“I read Soden & Held (2006) in 2007”

Maybe you should read it again ?

Don’t miss the last figure for your friend Willis…

Toncul is out of his depth. The value of lambda-zero in Soden and Held is said to be determined by reference to surface temperature and emission flux, and the list of values labeled “Planck” in the table of feedbacks in that paper are plainly calculated that way (albeit with small additional adjustments for other reasons). The method described in Soden & Held, which is described in detail but with any offered justification by Schlesinger (2985), is an erroneous method. Those unfamiliar with astrophysical equations such as the SB equation will naturally find it surprising that so basic an error can have been made and perpetuated, but that is the fact.

Monckton of Brenchley: you originally said that they included a change in the lapse rate when calculating lambda_0. Soden & Held explained “lambda_0 assumes that the temperature change is uniform throughout the troposphere” i.e. no change in the lapse rate.

Do you now agree that Soden & Held did not change the lapse rate in their calculation?

Thew correct method of determining the reference sensitivity parameter lambda-zero is to determine it as the first derivative of the fundamental equation of radiative transfer at the emission altitude, where incoming and outgoing fluxes are by definition equal, and then, having taken the product of that derivative and any forcing of interest, determine the corresponding temperature change at that altitude. Then, if the lapse-rate is to be held genuinely and undeniably constant at the pre-feedback stage, the change in temperature at the emission altitude is equal to the change in temperature at the surface.

However, doing the calculation as Schlesinger does, and as the models whose values of that parameter are listed in Soden & Held (2006) do, one is no longer retaining the uniform temperature change as between the emission altitude and the hard-deck surface, wherefore one is by implication altering the lapse-rate.

“However, doing the calculation as Schlesinger does, and as the models whose values of that parameter are listed in Soden & Held (2006) do”Maybe Schlesinger did that in 1985. GCMs do not deal with λ₀. And while S&H call Planck sensitivity λ₀, they make no mention of “emission altitude” or any equivalent global mean concept. Again I ask you to point to any occurrence of such usage in S&H 2006. It isn’t there. They do not need it.

Monckton’s “fundamental equation” is an equation made “fundamental” by Monckton.

Mr Oldberg should check the references, whereupon he will see that the equation is the official equation. Also, it has been calibrated using CMIP3 and CMIP5 outputs. He is, as usual, out of his depth here.

“Official” is not the same as “fundamental” .

Yes, this is looking more and more like a straw man argument.

I have repeatedly requested a reference to where this is stated as being “the official equation” and I have not yet seen one.

Err, no, a power is not an exponential, it’s a power term “of course”.

The linearisation of S-B is reasonably accurate within small changes, however if you are going to question the accuracy of this you cannot do so by using “global average” temperatures since you cannot meaningfully take the average unless it’s linear, and you are maintaining that it is not. I’m sure the author has an appropriate Latin phrase for that fallacy.

The fundamental problem with climate models is that they are tuned to best fit 1960-1990 period which is not representative. This means that they do not fit the early 20th c. warming, do produce the post WWII cooling and do not reproduce the pause. This is why Karl et al decided to change the data to fit the modelled behaviour, so as pretend all is well with the broken models.

As I pointed out in the last post there are published articles on the change in sensitivity in models as global temperature rises. This is probably a reflection of non-linearity of SB which is correctly used in the detail of the models.

While the intent of cataloguing all the errors and how they accumulate is a worthy one I get the impression that CoB is out of his depth already and does not have the depth of knowledge of physics and maths to make sound arguments and conclusion.

In answer to Greg, References establishing that the official sensitivity equation is just that are on the slide illustrating the equation, whose elements are also sourced and described in the text.

A fourth-power relation is by definition an exponential relation.

The head posting has already pointed out that the error arising from the official assumption that lambda-zero is constant is small: indeed, a graph of the underlying equation shows a near-linear curve.

I have verified that latitudinal temperature and flux differences do not materially affect the global calculations shown in the head posting.

The extent of my knowledge of physics and math is not the issue. The issue is the physics and math shown in the head posting.

Monckton of Brenchley September 3, 2016 at 11:18 pm said, in error, as Greg points out:

“A fourth-power relation is by definition an exponential relation.”

Want to think about that? If x is a variable, e^x or any a^x is exponential. x^n is a power, a term of a polynomial. Both are non-linear (in general) – if I recall correctly!

I do not propose to quibble about semantics. Let us agree that a fourth-power relation is not a linear relation.

You were happy to quibble when you thought you were right, now it’s ‘semantics’. If you want to attack the IPCC ( which is merit worthy ) , don’t make it too easy for the warmists to shoot you down.

So why are you bitching about the IPCC “erroneously ” assuming it’s linear? Yet it fine when you do it. There seems to be goose / gander issue here.

Greg is quibbling. I said the error arising from non-linearity was small but pointed to a larger error.

F(x) = x^n where the exponent, n, is held constant and the base, x, varies is a polynomial function.

F(x) = n^x where the exponent, x, varies, and the base n is a constant is an exponential function.

F(x, y) = x^y where both x and y vary is plotted as a surface and is called general exponentiation.

m^n where both m and n are constants is simply a constant.

Having taught mathematics and computer science since 1970, a BIG difference is taught in courses in the design & analysis of algorithms between polynomial-time algorithms and exponential-time algorithms. Obviously, for the sake of faster running algorithms, one usually prefers a polynomial-time designed algorithm over an exponential-time algorithm that does the same calculation. (Look up the P vs. NP problem which is still unsolved.)

Monckton of Brenchley:

Greg is quibbling. I said the error arising from non-linearity was small but pointed to a larger error.Nevertheless, Greg is correct. I’d be happier (fwiw) if you simply admitted a small error in nomenclature, apologized, and moved on.

What “error of nomenclature” is Mr Marler talking about? IPCC is cited in the head posting as stating that the reference sensitivity parameter is a “uniform” response when it is not in fact “uniform”. The head posting correctly states that the error makes little difference to the sensitivity calculation, but that it points to a larger error – the use in the models (see e.g. Soden & Held, 2006) of a mixture of surface temperature and emission-surface flux in determining that parameter.

From the equation three, it is clear that the estimate relates to assumption of 0.3 and 4. Nobody knows on the accuracy of these assumptions. Based on such assumed values we are trying to establish sensitivity factor. Then, how accurate this will be a big question mark.

Dr. S. Jeevananda Reddy

Equation 3 is not contentious. It shows the flux density at the Earth’s emission surface.

I would have thought the defining the

emissionflux density by using theincomingradiation is at least questionable.The mean emission altitude is the mean altitude at which, by definition, incoming and outgoing fluxes are equal.

And if Greg considers IPCC’s use of net incoming radiation at the emission altitude as the basis for determining emission temperature to be incorrect, let him address his concern not to me but to the IPCC secretariat.

I am working on global solar and net radiation issues since 1970. I did not question equation 3 but I questioned the constants — 0.3 and 4.

Dr. S. Jeevananda Reddy

Dr Reddy questions the appropriateness of assuming that the Earth’s albedo (or reflectance, i.e., the fraction of incoming radiation reflected harmlessly straight back into space) is 0.3. However, that is the value that most models assign to it. If Dr Reddy does not like that value, he must say why, and propose and justify a different value.

Dr Reddy also questions the fact that the ratio of the surface area of the disk that the Earth presents to solar radiation to that of the rotating sphere of identical radius is 1:4. However, the surface area of a disk is pi times the square of the radius, and the surface area of a sphere of identical radius is 4*pi times the square of the radius, from which the ratio 1:4 is self-evident.

I’m waiting on Anthony to publish a submission that directly addresses the question of why an albedo of 0.3 is too low.

I take issue here with your presentation. If you want to substitute incoming for out going you need to explain why. It is not the basic definition outgoing flux. Now you have said why you are doing that, it makes more sense.

Don’t quibble.

Equation 3 uses an albedo estimate with one (1) significant figure (two at most implied from other discussions), and yet, the derived flux is given to six (6) significant figures! That is a basic error in the handling of calculations, not unlike what undergraduate students did routinely when slide rules were replaced by hand calculators. If albedo is a fundamental component of sensitivity estimation, then we really are limited in what we can say about the precision of intermediate and end calculations.

The output of the calculation in the head posting is a final sensitivity expressed to a single digit of precision. Intermediate calculations, as is usual, retain the available precisions.

But you are claiming to establish small and accumulating errors using grossly uncertain calculations.

Which calculations are “grossly uncertain”, and why does Greg consider them uncertain?

You say just above that you are only claiming single digit accuracy in key values, so any result cannot be more accurate than that. This can not provide a basis for showing “small errors”.

Don’t quibble. Small errors are those which affect sensitivity by some tents of a degree – the precision to whic the outcome is presented,

When I took Statics & Dynamics in college the use of the pocket calculator was first approved. The text ant the answers in th back of the book all assumed the use of a slide rule. As a result, most of the answers that the students using pocket calculators got did not agree with the book.Since you are dealing with the difference in sin, tan or cos, cot of small differences in angles and the calculator was taking these differences to eight or ten places the result was a large difference in the answer, as much as an order of magnitude in some cases. Students would rework “wrong” answers several times and get frustrated. The professor then made answer sheets for each chapter fo the calculator to solve the problem.

Excellent article.

Many thanks.

There is a paper ” Hug & Barrett vs IPCC ” , Oct 11, 2001 . In section 4, it reaches the same conculsion as you have. In that they state ” Mount Pinatubo reduced Earth’s temperature by 0.3 K and and the estimated reduction in forcing of 2 w/m^2. It gives a sensitivity of 0.15 w/m^2. ”

All of the papers I’ve seen trace back to TSI being at 1368 – 1370… round up of course … Since 1368 – 1370 was shown to be in error from defective instrumentation, and the new TSI is 1360 – 1362, How did they get any of the numbers to Match?

They also estimate a lot, then mix in numbers that are significant in number, then claiming they are accurate. From what I can see, the new TSI should have given them a 0.8 K rather than 1.2 K. That is a third.

A small difference in the any of the incoming or outgoing estimates, have a big impact on the final numbers. For example, it is only an assumption that the TSI varies no more than 0.12%, which is a reduction of 1.6 w/m^2. That is conviently below the 2 w/m^2 That caused a reduction in temperature of 0.3 K . A mere additional 0.08 % change in TSI in either direction, changes the final numbers substantially.

Based on the TSI from 1370 w/m^2 to 1360 w/m^2, would have in the math reduced the warming from co2 by 1.5 K with the sensitivity at 0.15 w/m^2. At the IPCC level at 0.67 w/m^2, it’s 4 times that.

Would the IPCC accept a mathematical reduction of 6.0 K ?

In a previous post, you already “demonstrated” (at least, this is what uou thought…) that equilibrium climate sensitivity cannot be larger than1.6 K. So why are you discussing such details now ? …

Your present post is stupid for two reasons.

– First, the reference warming is not used in climate sensitivity calculations, whatever from what. So whatever you find, your conclusion is wrong.

– Second, your calculation is wrong… For such a simple calculation using global means, a simple derivative show that lambda_0 = T0/(4xF0). Your equation 9. Except that in this equation, you should have used the surface temperature TS (and in that case the effective emissivity is not 1 and equal to F0/sigma/TS^4) rather than T0. So you should have written : lambda_0 = TS/(4xF0). Think about it : the relationship you want to use necessary relates a flux at TOP OF THE ATMOSPHERE (where the forcing is defined) and SURFACE temperature.

I shall not be drawn on what final sensitivity will be whiten the present series is complete.

The reference sensitivity is of course used in climate-sensitivity calculations. See e.g. AR3, ch. 6.1, for a discussion. Feedbacks are quantified as forcings denominated in Watts per square meter of the reference warming.

And,as explained in the head posting, the SB equation must be applied to a sing,e surface only. It is an erroneous use of the equation to do as Schlesinger did and attempt to relate surface temperature and emission-altitude flux via the SB equation.

The correct procedure is to determine the temperature change from the flux change at the emission altitude. Subject only to lapse-rate feedback, the emission-altitude temperature change and the surface temperature change will be approximately equal.

Your reference to IPCC looks wrong, but because you speak about AR3 : just tell me which page of the AR3 report deltaT0 is used to get ECS… In fact, I think it is done somewhere in a IPCC report, BUT it doesn’t mean that you necessary need deltaT0 to get the sensitivity. The “reference sensitivity” (deltaT0, or related parameter lambda0) is used for a feedback decomposition. Then, if you can decompose the response you can also recompose the response, and get the sensitivity. But you can also DIRECTLY get the sensitivity without doing such decomposition.

As an example, let’s take … your OWN calculation! Here :

https://wattsupwiththat.com/2016/08/03/ipcc-has-at-least-doubled-true-climate-sensitivity-a-demonstration/

You did NOT use lambda0 or deltaT0 to get the final 1.6 K estimate (which was wrong for other reasons : first, it was not a ECS calculation but a TCR). And I already detailed the calculation to show you that this is the case. Do I show it again ?

About the second point :

The correct equation is not an exact application of SB, and relates a flux at top of the atmosphere and a surface temperature change, so at different levels. Of course, you have no problem with that, because the equation that appears in all your posts and that you have used to get te 1.6 K value (not correctly), relate a flux at top of the atmosphere (deltaF0) and a surface temperature change (deltaTeq), so at different levels. Note that you now remove the “eq” of “deltaTeq” to hide the fact that this temperature change is necessary an equilibrium one. See revious discussions).

In addition, applying the equation with the emission temperature is stupid (if done correctly) : I explain why.

In equilibrium F0 is 240 Wm-2 and the emission temperature is 255 K (or about 33 K smaller than the mean surface temperature).

If CO2 is added, albedo unchanged, and equilibrium reached, then F0 is .. 240 Wm-2 and the emission temperature is … UNCHANGED (with no lapse rate change, temperature change at a given altitude is the surface change, yes, BUT the emission altitude increases).

Toncul misunderstands atmospheric dynamics. At the start of a sensitivity calculation, emission flux is 238 W/m2 and emission temperature is 255 K. After a forcing and before feedbacks, the flux and temperature have increased to 241 and 256, at that altitude. And after feedbacks the flux and temperature at that altitude have increased again. Via the broadly invariant lapse rate, and subject only to the lapse-rate feedback, the surface temperature will rise by about the same amount as the temperature at the altitude that was, at the start of the calculation, the emission altitude, and the new emission altitude will be higher.

And it does not matter by what methods the models reach their exaggerations of climate sensitivity. Eq, 1, when informed with the forcing and feedback values officially deduced by the models, reproduces the climate sensitivities reported by or deduced from the models. But once corrections are made to allow for the errors in the official position, far lower sensitivities emerge, demonstrating that in some fashion the models indeed embody the errors.

Indeed. At any equilibrium state of the climate, overall thermal energy is constant so energy-in equals energy-out. Consider two equilibrium states. If albedo is unchanged between the two states then energy-in will be the same. So energy-out must also be the same. But the temperature of the emission altitude is pretty much defined by energy-out via Stephan-Boltzmann. Hence this must also be the same.

First, there is nothing about atmospheric dynamics, here…

Then, whatever you can say : the emission temperature in equilibrium will be still 255 K if albedo is unchanged. Because the emission temperature doesn’t care about what Mr Monckton of Brenchley think. the emission temperature care about the energy emitted, that has to be 240 Wm-2 in equilibirum whatever you do to the climate system, if albedo is unchanged.

From your reasonning, the emission temperature change is the same as the surface change.

So if we follow your reasoning the surface temperature change in equilibirium should be 0, whatever the forcing…

deltaT0 is a value obtained from simple calculations, or from climate models (all calculation agree with roughly 1 degree of warming for CO2 doubling). Whatever the method you use to get deltaT0, evenby using the wrong method of Monckton of Brenchley, it would not change the response of a climate model to CO2. And it would also not change your stupid 1.6 K calculation in your first post. This is so easy to understand. So easy.

(my comment above is for MR Monckton of Brenchley).

Toncul persists in not understanding the dynamics of the atmosphere under perturbation by a forcing. Before the forcing, in a presumed pre-existing steady state, the mean emission altitude is, say, 5.3 km. At that altitude, where by definition incoming and outgoing fluxes of radiation are equal, the net incoming solar radiation is known to be about 238 W/m2, and the measured emissivity is at or very close to unity. From the SB equation, temperature at that altitude is 254.5 K or thereby.

Now, add a forcing of 3.7 W/m2. The flux at the emission altitude at 5.3 km increases from a little over 238 to a little under 242 W/m2, and temperature at that altitude rises by about 1 K to around 255.5 K.

Since this temperature is greater by about 1 K than the emission surface, the old emission surface is no longer the emission surface. Instead, the new emission surface is around 150 m higher than before.

In the other direction, assuming no variation in the lapse-rate (for, if there were one, it would count as a feedback), the Earth’s surface and all altitudes in between warm by about the same amount as the old emission surface – i.e., 1 K.

Of course, the IPCC assumes – contrary to a growing body of evidence – that the increase in water vapor in the tropical mid-troposphere will reduce the mean lapse-rate somewhat. But the story of the glaringly missing tropical mid-troposphere hot-spot is another story, and not for today.

Finally, it does not matter by what method the models incorporate any or all of the errors that I am describing in this series. For I began by carefully and successfully calibrating the official climate-sensitivity equation against the models’ output, and I showed that it does fairly represent the climate sensitivity interval that they predict.

Since correction of the errors modifies the form of the equation and alters the values of its independent variables, the consequence of the corrections is that climate sensitivity will. In that event, a discrepancy will have arisen between the results of the modified official equation and the results from the models. If readers become convinced that most or all of the errors I shall be identifying in this series are indeed errors, then honest modelers would want to modify their models to make the necessary corrections. If, on the other hand, I am wrong, no corrections will be necessary.

Meanwhile, the world continues to warm at a rate considerably below what IPCC had predicted in 1990, forcing IPCC itself almost to halve its original projections of medium-term global warming (while keeping its job by leaving the longer-term predictions unadjusted).

“the surface temperature will rise by about the same amount as the temperature at the altitude that was”

Really? If the surface is absorbing and radiating an extra 3.7W/m2 its temperature would rise from 288K to 288.68K.

Mr Monckton of Brenchley,

Writting long (unclear) comments and partly changing subject doesn’t make you being right…

What I said above was clear. And what Ian H was clear too.

In equilibrium and with no albedo change, it is self evident that the emission temperature is unchanged.

The effective emission temperature is (Flw/sigma)^0,25 where Flw is outgoing terrestrial radiation at top of the atmosphere (roughly 240 Wm-2) and sigma is SB constant.

If you add a forcing (let’s say 4 Wm-2) then the emission temperature is reduced to (Flw/sigma)^0,25 with Flw=240-4 = 236 Wm-2. which is self evident too.

Because the system emits less than it gets, it warm up until the emission temperature is back to 255 K (if albedo is unchanged), roughly of about 1 K everywhere (if there is no feedbacks). and you agree with that :

you correctly say that the new altitude of the emission temperature is higher of about 150 m once the warming has warmed up of 1K.

For a temperature gradient of 6.5 K / km and if temperature increase of 1K everywhere, you need to go 1000/6.5 = 150 m higher to find back the altitude at which temperature is equal to 255 K.

So you agree that the emission temperature is unchanged in equilibrium (if albedo is unchanged). And you are right to agree with me. Because saying the opposite would be deeply stupid.

Toncul, who is grievously out of his depth both in science and in the manner of conducting a discussion, continues to assert the obvious, that the emission temperature remains the same unless insolation or albedo changes. However, the altitude at which the emission temperature occurs rises as the atmosphere warms, as carefully explained in a previous comment by me. Toncul appears unfamiliar with the concept of an emission altitude that is not fixed. If so, let him address his concerns to the IPCC secretariat, not to me.

In equilibrium which is selfevident. I also said that I agree with you that the emission level rise of 150 m. and you tell me that I don’t get this particular point… Do you have schizophrenia ?

Don’t be childish. Now that you have conceded that the altitude of the emission surface rises with warming, you have also conceded that at the former emission surface the temperature will have risen, whereas previously you were trying to dismiss my argument in the head posting on the ground that there would be no such rise. You are out of your depth here, and would do well to leave the discussion to others better qualified to participate and more willing to debate intelligently and politely.

I conceded nothing view that I never said the opposite…

And, as I already explained (do you read my comments before answering?), this is in agreement with the fact that the emission temperature remains 255 K in equilibrium, if albedo is unchanged (which is self-evident per definition of the emission temperature…).

Toncul now claims that he did not in fact suggest that since emission temperature always remains the same I had been in effect suggesting that the change in surface temperature must be zero. Since he now understands that, though the emission temperature always remains the same, the altitude at which that temperature obtains rises with warming, he should now understand that I was not in effect suggesting that the change in surface temperature must be zero.

Why use algebra and mind boggling math when a crystal ball and random shots at a dart board seem to suffice ?

Do I need the sarc tag .

Robert from Oz displays a formidable knowledge of the methods by which the modelers actually make their predictions. Expelliamus!

Thank you my lord .

“It took me years to figure this out, but finally there is a potential resolution between the insistence of the climate scientists that CO2 is a big problem, and the empirical evidence that it doesn’t have nearly as much effect as they say.”

Dr Evans is an expert in Fourier analysis

– and leaves taxpayers with trillions of $$ to spend for math high priests controverting about non existing ‘Catastrophic Anthropogenic Global Warming’.

Dr. S. Jeevananda Reddy: “From the equation three, it is clear that the estimate…”

Are you referring to Monckton’s estimate, or the IPCC’s? Monckton’s blog post ignores how the IPCC calculations were done and his claimed “inaccuracies” are all accounted for in those calculations. Bony et al. (2006) Appendix B gives a summary.

The simple equations in the blog post are mainly used to demonstrate a principle or for teaching in introductory textbooks, see for example Ambaum’s Thermal Physics of the Atmosphere. Atmospheric physicists understand that these are simplified expressions from which you can’t directly calculate the true global Planck response.

The IPCC nowhere explains how lambda-zero is calculated, and it refused to do so when requested. In fact, it lifts its estimate of lambda-zero from the models. And the models incorporate the error made by Schlesinger.

You really think that lambda_0 is used in climate models ? Are you such stupid ?

As I explain above, your calculation makes no sense at all.

Values of lambda-zero in the models are listed in e.e. Soden and Held, 2006, and are discussed extensively in the literature, as indicated by the references in the head posting.

If the models did not represent the fundamental equation of radiative transfer, they would not work at all.

If Your Posterior does not like this he should address his concerns to the modellers.

Yes models represent the fundamental equation of radiative transfer and we can get the value of lambda_0 from that. Of course they do not use lambda_0, because they are much complicated than the simple equation shown in your Figure 1…

Calculation from climate models agree with simple calculations from global means, such as the calculations you say are wrong but are correct, but they disagree with your calculation, that you say is correct but is wrong :).

The models embody various errors, including the error by which they inflate the value of lambda-zero by determining it from flux at one altitude and temperature at another.

Are you completely dumb ???

First there is no error.

Second, even if there were an error in lambda_0 calculation, it would not be an error embodied by climate models, but just an error in the lambda_0 calculation… view that this value is not used in climate models. It is just calculated by using climate models.

Your Posterior (for that, I think, is what “ton cul” means in French) continues to be discourteous in this thread. Whether Your Rearness likes it or not, the official equation was calibrated against the models’ output and duly reproduced their stated climate-sensitivity intervals with some precision, both for CMIP3 and for CMIP5.

The models are naturally constructed so as to be able to take account of forcings and then of the additional forcings that are temperature feedbacks. They take account of feedbacks by starting with the direct or reference temperature change in response to the initial forcing and then making appropriate adjustments throughout the atmospheric column at all latitudes to represent the additional forcing, denominated in Watts per square meter per Kelvin of the original forcing, that is the temperature feedback.

The values of the individual temperature feedbacks, model by model, and of the reference sensitivity parameter, model by model, are published. See e.g. Soden & Held (2006); Vial et al. (2013).

It matters not whether the values that are listed are derived ex post facto: what matters is that these are the official values derived from the models, and, if these values are wrong, then either the official derivation is wrong or the models are wrong. Either way, it becomes quite impossible to sustain the case for a high climate sensitivity, as will become all too apparent once this series is concluded.

Don’t you just love the classic alarmist activist ‘normal co-worker/peer friendly’ conversational mode?

Frequent direct yet obviously and absurdly incorrect ad hominems.

Complicated obtuse meandering sentences.

Stuck on willful reading miscomprehensions.

Circular logic confusing readers.

…

On and on; yapping junk yard dogs throw in willy nilly any quibble, nit pick, observations or definition denial possible, as if their attempts at effecting small perturbations of the Questions/Answers have any effect on reality.

One would think that they would take up the challenge and produce an equally illustrative and descriptive article of their own. Clearly describing both formula applications and history while providing citations and scientific extracts regarding their insistence of calculations and feedbacks.

Only that would mean taking and publishing a definitive stand on their use of relative formulas; open for explicitly detailed discussions.

Great Article, Lord Monckton!

Monckton of Brenchley: Vial et al. (2013) point to Soden & Held (2006). If you want to know how the CMIP5 values were calculated then read the Soden & Held (2006) methods section. They explain how lambda_0 is calculated using proper radiative kernels.

Yes, this is more complex than your blog post, but it’s necessary to account for how Earth’s atmosphere is not completely uniform and how infrared absorption depends on wavelength. Accounting for everything, the Planck response works out at about 3.1 W m-2 K-1 as reported by the IPCC.

The method by which lambda-zero is represented in the models is well explained in Soden & Held (2006), and it is an erroneous method. It embodies the error made by Schlesinger (1985) in pretending that one could satisfactorily obtain reference sensitivity by using emission-surface flux and surface temperature. One cannot do that and obtain a correct result. Instead, one should determine the temperature change from the flux change at the emission altitude and then, via the lapse rate, adjust surface temperature commensurately. Changes to the lapse rate are feedbacks and not part of the forcings.

Monckton of Brenchley: that’s not how they did it, I think you need to read Soden & Held’s methods section.

To check whether you understood the first part: let’s say that for one wavelength band we have a well-defined emission altitude. For a change in surface temperature of 1 K in Soden & Held’s method, what is the change in temperature at this emission altitude in their calculation?

My point in the head posting is a simple one, and, as Soden and Held demonstrate, a correct one. The official methodology determines lambda-zero as – to first order – the ratio of surface temperature to four times emission-surface flux. That is an unacceptable abuse of the fundamental equation of radiative transfer.

” The official methodology determines lambda-zero as – to first order “That is completely misleading. “To first order”?? They calculate the derivative of λ₀ with respect to T₀. But then they multiply by the derivative of T₀ wrt T_S. That is just proper chain rule, with full accuracy. Nothing “first order” about it. And it has nothing to do with “the fundamental equation of radiative transfer”.

Monckton of Brenchley: “My point in the head posting is a simple one, and, as Soden and Held demonstrate, a correct one. The official methodology determines lambda-zero as – to first order – the ratio of surface temperature to four times emission-surface flux. That is an unacceptable abuse of the fundamental equation of radiative transfer.”

It’s now clear that you’ve completely misunderstood what Soden & Held did. Could you explain, for a single atmospheric column, how you _think_ they calculated the change in top-of-atmosphere flux? This should make it easier to work out precisely where you’re going wrong.

MieScatter appears so shocked at the very notion that the modelers could have made a basic error that he persists in misunderstanding not only what they are saying but also what I am saying. The point is very simple. Lambda-zero is determined in Soden and Held on the basis of surface temperature and not (as it should be, if surface temperature is used) surface flux, but on the basis of emission-altitude flux, 5 km above ground level. The basis on which it is determined in the kernels is thus defective a priori, and leads to a considerable and unwarrantable overstatement of climate sensitivity.

“but on the basis of emission-altitude flux, 5 km above ground level”This is bizarre. I have been posting excerpts from Soden and Held, which explain just how it is done, and it is nothing like tise. Lord M offers nothing to support his claims. But the matter is easily tested. Nowhere in S&H is there any mention of exission altitude. I invite Lord M to find a single instance.

Monckton of Brenchley: Soden & Held calculate the change in top-of-atmosphere flux given a 1 C global average change in temperature at 5 km altitude (and every other altitude within the troposphere). Don’t you agree?

MieScatter — I refer to those values given along with equation 3 only — 0.3 & 4.

Dr. S. Jeevananda Reddy

Remember to multiply it by the margin of error of the equipment used too. Most of it is like 0.15°C up or down as drag and +- 0.05°C as spec. Nobody runs around verifying the calibration of these sensors either.

Climate sensitivities are emergent properties of modelsfound by analysing model behaviour, Where do you get this idea that models “adopt” a value of λ0 from anywhere?The IPCC value is a summary of the way models behave it is not a value that the IPCC provides for modellers to use.

Models are build up from basic physics ( plus some gross and likely wrong “parameters” for the key processes of climate for which they do not have “basic physics” ). The CO2 forcing is an input, the

sensitivity is an “output”.I say output in quotes because it is in face largely determined by tweaking the poorly constrained input parameters which gives the modellers a large margin to produce whatever sensitivity they wish.

This is clearly stated in Hansen 2005.The values of lambda-zero adopted in the models are listed, CMIP3 model by model, in Soden & Held (2006).

The purpose of that paper, and of Vial et al. (2013) fire the CMIP5 ensemble, is to present the various forcings and feedbacks that “emerge” from the models.

It will be evident by the time this series is concluded that the models are embodying substantial errors, or their output values for climate sensitivity would not be as high as they are.

“The values of lambda-zero adopted in the models are listed, CMIP3 model by model, in Soden & Held (2006).”Greg is right. I have shown S&H Table 1 below. The attached text (et seq) describes how they are derived from the models. They are not “adopted in the models”. They are emergent properties, as Greg says.

It matters not whether the values of lambda-zero are determined ex-post-facto or applied ab initio. If the values of lambda-zero that “emerge” from the models are excessive, then either the official method by which they were extracted is wrong or the models are wrong, or perhaps both.

Monckton of Brenchley:

It matters not whether the values of lambda-zero are determined ex-post-facto or applied ab initio. If the values of lambda-zero that “emerge” from the models are excessive, then either the official method by which they were extracted is wrong or the models are wrong, or perhaps both.That may be true (I don’t disagree), but your use of the word “adopted” has been misleading. Possibly the modelers “tune” the parameters so that the value of sensitivity they want “emerges” from the model, but I don’t think that can be convincingly shown (I am always alert to the possibility of being corrected after writing something like that.)

I am disinclined to quibble about semantics. Non notatio, sed notio.

https://judithcurry.com/2015/02/06/on-determination-of-tropical-feedbacks/

If you want to know how the mainstream modelling community rig the parameters to get high CO2 sensitivity read my article detailing how they down graded the parametrised volcanic forcing ( thus increasing the sensitivity ) in order to reconcile model output with the 1960-1990 climate record.

This is one of an infinite choice of values and leads to a similarly high CO2 sensitivity.

The GISS team under Hansen had deliberately abandoned physics based empirical values in favour or reconciling model output ( without downgrading CO2 sensitivity ).

The article is fully referenced and shows how Lacis et al probably were a lot closer in 1990 than the ‘convienient’ values later adopted.

Again read Hansen et al 2005. It is quite open about the scope for producing whatever results you like and explains a lot of detail. This is a clear and rigorous paper explaining how it all works.

If you read Roe (2009) you will see that lambda_0 is by definition a constant since it is the

constant of proportionality for an ideal system (which can be whatever you choose) between a

change in the input (here the flux) and the output (here the temperature) before any feedback

occurs. If you change the reference temperature of your system without feedback then lambda_0

will change but it will still be a constant for the rest of the calculation. Furthermore as Roe stated

in 2009 the equation is wrong since it assumes a linear system when clearly the climate is nonlinear since at the very least the Stefan-Boltzmann equation is nonlinear. Roe goes on to

present the next order equation that takes into account nonlinearities.

Fundamentally this discussion is thus flawed since we are putting numbers into an equation that

we know is wrong. It is however a good starting point to talk about feedbacks and their effects.

Furthermore computer climate models do not work by calculating feedbacks and then work out

the temperature. Rather they simulate a model climate and then derive the temperature and feedbacks from that. As far as I can tell using this “official equation” is a simple way to compare models since you can compare derive feedbacks and then see what changes in each model.

Geronimo is broadly correct. However, as the head posting points out, the non-linearity arising from the fourth-power SB equation is small.

Though the current generation of models do not use feedback values as inputs, feedback values are deductible from their outputs, which is how I was able to calibrate the official equation successfully against the models.

What I am demonstrating in this series is that the processes inbuilt into the models, reflected in the official sensitivity equation, are leading to outputs inconsistent with the underlying physics.

Based on this standard diagram

http://www.ipcc-wg1.unibe.ch/publications/wg1-ar4/faq/fig/FAQ-1.1_Fig-1.png

The absorptivity of IR radiation by the atmosphere is 350/390 = 0.90, which I think is significantly different than 1.0.

Radiation toward the surface is 324 W/m2 indicating a sky temperature of 9.13°C (48.43°F).

Radiation from the atmosphere away from the planet is (235-40) W/m2 indicating an effective sky temperature of -24.54°C (-12.17°F).

Radiation from the planet system is 235 W/m2 due to an albedo of 31.3%, as shown in the diagram. Assuming an emissivity of 1.0 that radiation suggests an effective blackbody temperature of -19.42°C (-2.96°F).

Basically, for any of the equations to make any sense, the 40 W/m2 from the surface, thru the atmospheric window, must be accounted for separately. That gives the non-unity emissivity that must be divided into the atmosphere’s radiation numbers to obtain a more accurate effective emission temperature. Because of the lower temperature and pressure at increased altitude, the atmospheric emissivity will be significantly lower than the value computed above.

Also, since the upward and downward effective emission temperatures are significantly different (9°C vs -24°C) that completely invalidates some of the arguments made above.

Unfortunately, the IPCC has decided not to provide the derivations for any of these “magic” equations and, therefore, has proven beyond all doubt that … (I don’t want to get too negative).

It is evident from the diagram that, for a surface temperature 288 K, the corresponding radiative flux density is 390 watts per square meter, implying emissivity at the surface is 1.

It is also evident from the diagram that at the emission altitude the flux density is much as given in the head posting at eq. (3), from which it follows that at that altitude emissivity is also at or close to 1.

The reason why one should not mix two distinct surfaces when applying the SB equation, as Mr Clemenzi does here, is given in the head posting.

Talking of atmospheric energy flowcharts….. There was a discussion here recently, as to whether downwelling longwave radiation (DLR) could warm the oceans (because LWR can only penetrate the top ten microns). So I thought I would create an energy flowchart that did not include DLR warming of the oceans. And contrary to the suggestion that oceans would freeze if DLR was not absorbed by them, the flowchart is balanced. (Not sure if it is entirely logical and feasible, of course…)

The major difference in this flow diagram is the double-headed red arrow, which represents DLR from the troposphere hitting the ocean, not being absorbed, and being reradiated back up again. So this is an energy flux that is bouncing around in the atmosphere and not doing very much at all, in terms of surface heating (although it can heat the atmosphere, the land-surface, and provide the latent heat of vaporisation for the top micron of the water surface). Which would mean that oceanic warming is dependent on incident SW insolation.

The left purple upflow is ULR resulting from SW absorption by sea, and DLR-SW absorption by land.

The right blue downflow is DLR from the atmosphere being absorbed by land.

The small green-turquoise arrows represent thermic and latent heat radiation. I have split them into two, to represent flows from direct SW oceanic heating (green) and from SW-DLR heating of land surfaces (turquoise).

“The major difference in this flow diagram is the double-headed red arrow, which represents DLR from the troposphere hitting the ocean, not being absorbed, and being reradiated back up again.”It isn’t actually a major difference, which is why your plot still balances. The issue about DLR not being absorbed is a red herring. Sea surface at, say, 15°C, must radiate a whole lot of heat. To stay steady temperature, that flux must be balanced. The solar absorbed by sea comes to the surface, but is not nearly enough. DLR makes up the balance. It does not need to be absorbed.

Your accounting says DLR is re-radiated. That is a strained description of the physics, but the effect is the same. The upflux is the sum of solar and DLR, for surface heat balance.

What if DLR increases – will that warm the sea? Yes! If the sea doesn’t warm, there is now too much flux being supplied for the surface to radiate. Some absorbed solar can’t escape, and that will heat the surface (and below) until balance is restored.

Good analysis, but it misses the point. The question is not “Can DLR heat the ocean?”, the correct question is “Why doesn’t DLR heat the ocean?”. The answer is rather simple.

On land, the surface temperature drops below the atmospheric temperature almost as soon as the Sun sets. By morning, the temperature drops about 20°F. If it was not for the DLR, that change would be over 100°F.

However, the ocean temperature drops by less than 2°F and the DLR and ULR are about the same.

So, what’s the difference? When water cools, its density increases and the cold layer sinks bringing warmer water to the surface. As a result, several feet of water must lose heat for the temperature to drop. However, with solids, the outer surface continues to cool because rock and soil are pretty good thermal insulators. As a result, the lower atmosphere is cooled as its stored energy is used to limit the change in temperature (known as the greenhouse effect). Looking at radio sonde soundings will make this obvious. I have provided a few samples here

(works with Windows XP and Vista, not Windows 10).

The concept of down welling long wave radiation from the atmosphere “heating a surface” shows a misunderstanding of radiation heat transfer. There is energy going both up and down, and this is generally true for radiation between two sources, but the net effect of the back radiation is to decrease net radiation heat transfer up. There is no radiation heat transfer down unless the atmosphere is warmer than the surface. The decrease in heat transfer up caused by this back radiation then requires compensation by other heat transfer means (conduction, convection, and evapotransporation) to remove the required excess energy deposited at the surface by sunlight (there is no other significant source of this surface energy). The mechanism of the atmosphere absorbing radiation from the surface causing a temperature rise (the so called atmospheric greenhouse effect) is due only to the increase in average altitude in radiation to space (from the radiating atmosphere rather than the surface), and no other reason (assuming constant albedo and lapse rate). It is not from the back radiation heating the surface.

Mr Weinstein is broadly correct, though perhaps the clearest metaphor for the effect of CO2 is provided by Professor Christopher Essex at the University of Western Ontario. He says the interaction of photons of near-infrared radiation with CO2 molecules is akin to turning on billions of tiny radiators throughout the atmosphere. The additional heat that thus arises is then transported both upward and downward in the atmospheric column by various processes.

RC, you said, “Radiation toward the surface is 324 W/m2 indicating a sky temperature of 9.13°C (48.43°F).”

Does this “sky temperature” take into account the fact that blue light is scattered out of the dominantly green light coming from the sun?

No, the 324 W/m2 is longwave IR emitted by the atmosphere. Light from the Sun is included in the albedo and the 168 W/m2 and 67 W/m2 absorbed by the surface and atmosphere. About 70% of the absorbed energy is in the invisible IR. The blue light helps us to see (albedo), but has little effect on the temperature.

RC and others,

This “standard diagram’ shows a surface reflectance of 30 W/m2 (~9%). I have submitted an article that I hope Anthony will publish, wherein I argue that this value is too low.

Clyde Spencer: “RC and others, This “standard diagram’ shows a surface reflectance of 30 W/m2 (~9%). I have submitted an article that I hope Anthony will publish, wherein I argue that this value is too low.”

In that diagram, 198 W m-2 reaches the surface and 30 W m-2 is reflected. That’s about 15% reflection.

If you think you’ve found errors in the albedo measured by the MODIS and CERES satellite instruments, that would be fascinating and there are many journals who would be happy to publish your work.

If we are concerned about albedo or total reflectance, what is germane is the total light reflected out of the total incoming. Of 342 Watts, 30 is supposedly reflected by the surface (8.8%). The question is NOT how much of the light that doesn’t get absorbed by the atmosphere or reflected by clouds and aerosols is reflected by the surface! Maybe we can quibble about the 67 watts that get absorbed by the atmosphere because the atmosphere re-radiates it. However, that still gives about 11% reflected by the surface out of the total incoming.

The alternate diagram provided by ralfellis shows 23 watts, lowering the total reflectance even more.

Even if I wanted to go to the trouble of providing a manuscript for publication, I doubt if any journal would touch it. My credentials are not in climatology, and I’m no longer in academia. However, if my argument is sound, then people at the public trough can run with it. The concept isn’t that difficult. It just seems that the people working in the field don’t have the right background and have missed it.

Clyde Spencer September 4, 2016 at 9:04 am

FWIW, the CERES data says 24 W/m2 …

w.

24 exacerbates the situation. I have used an illustration from CERES, and judging from the average land values, it appears that snow has been left out of the mid-latitudes.

Willis, put your computer away, and go enjoy the wedding.

richard@rbaguley.plus.com September 4, 2016 at 1:46 pm

The wedding was superb, the bride was lovely, the gorgeous ex-fiancee was … well, as gorgeous as you might imagine.

My thanks to all who sent their good wishes, it was all I could imagine.

I also imagined that I looked mondo studly in my tux … as my daughter would say, “In your dreams, dad” … regardless, it was all that a man could want.

w.

“Even if I wanted to go to the trouble of providing a manuscript for publication, I doubt if any journal would touch it. My credentials are not in climatology, and I’m no longer in academia. However, if my argument is sound, then people at the public trough can run with it. The concept isn’t that difficult. It just seems that the people working in the field don’t have the right background and have missed it.”

The difference between a blog and a scientific paper is that a scientific paper is checked for common errors and clear mistakes. If it were my work, I’d want it to be checked properly. Whether you have a name in the area or not is irrelevant – Kevin Cowtan, Ken Rice, Dana Nuccitelli, Andy Skuce, Nic Lewis, Troy Masters and Grant Foster have all published papers without credentials in climatology.

If you’re right then this is groundbreaking. You could submit to Nature Climate Change or Nature Geoscience, they allow you to be anonymous for the reviews. And if you’re right, you get much more impact and recognition this way because I can’t imagine that anyone in a scientific institution takes WUWT posts seriously. But please do keep an open mind, it’s always possible that thousands of climate scientists haven’t all made the same obvious mistake.

I have found this blog to be a very unforgiving peer review. (i’ve had four guest essays published.) One even gets severely criticized by those who are ostensibly on the same side of the political spectrum. If I survive review here, then there is almost certainly value to what I present. Suggesting that presenting in WUWT will doom it to oblivion is naive. I’m sure that there are scientists out there who if they saw the importance would be all too happy to take credit for it. Because there are a few scientists with the appropriate bona fides reading this, it would be difficult to keep a lid on it if I’m right. I may well have overlooked something. It wouldn’t be the first time in my life that that I was wrong — although I’m not in the habit of making frequent serious mistakes.

With your moniker, I expect that you are in atmospheric physics. I retired as a senior remote sensing scientist, so we probably have some things in common. However, my research in the area of imaging polarimetry prepared me to see things differently from someone like yourself. I worked for an aerospace company and our focus was extracting military intelligence from imagery. Sometimes a different goal gives one a different perspective and different tools.

How many thousands of scientists made the same mistake before every paradigm shift? It is a long shot perhaps, but I have a healthy ego and I will survive if someone points out an obvious flaw.

“How many thousands of scientists made the same mistake before every paradigm shift? It is a long shot perhaps, but I have a healthy ego and I will survive if someone points out an obvious flaw.”

There are astrophysics or remote sensing journals too. Why not submit to one where your work will be checked by competent people? The worst case is that the reasons given for a rejection teach you something. Maybe there’s a mistake in your work, or you need more evidence to justify an assumption, or your presentation confuses readers. The only way you “lose” by submitting to real review is if your work is rubbish but you’re emotionally attached to it being right.

If WUWT “review” is anything like the response to this blog post then you’ll understand my skepticism. As someone in remote sensing you can tell that Christopher Monckton’s post shows the simplest of misunderstandings. It’s ignorant of radiative kernels and the importance of frequency and local atmospheric profiles of temperature and moisture. His responses shows he can’t understand the chain rule if it contradicts his beliefs. He makes simple mistakes and doesn’t seem to understand how, but after the “review” on here he seems as certain as ever that he’s definitely right. After working with remote sensing you know better – does that give you confidence in WUWT “review”?

My take on the commenters on WUWT is that they range from people with little or no science background to senior scientists; however, it would seem to be heavy on retired engineers. I’ve seen people on both sides of the argument dig in their heels and either deny facts or be obtuse in responding to key points. That is one reason I suggested Chamberlain’s Method of Multiple Working Hypotheses to Kip. I think that a large number of commenters here could benefit from reading Chamberlain’s paper. They would learn the true meaning of “skeptic.”

It is hard to teach an old dog new tricks. However, you are suggesting that at my age there are still many things I haven’t seen. That may be the case. But I actually trust this ‘community’ to be more competent and savage at evaluating my writing than an anonymous gatekeeper that might well have a vested interest.

I think my work is correct. However, I’m not emotionally attached to it. I can walk away from it if someone clearly shows that I have made a serious mistake. Furthermore, I’m more than capable of evaluating any criticism it might evoke. I know BS when I see it. And, if someone tries to pass off something that is esoteric, I’m not too proud to ask for a second opinion. However, I’m sure that other commenters will take such attempts at obfuscation to task. Once I present my case (assuming Anthony publishes it), it will be obvious that it is an oversight that needs to be corrected and publication in a ‘prestigious’ journal with gatekeepers will be anticlimactic.

I don’t need anything to add to my CV, nor do I expect to ever again be asked to provide a list of publications. My interest is getting to the Truth, and doing it as quickly as possible, and not waiting two or more years for turnaround in a journal that only academics can afford to read.

Clyde Spencer, this sounds very important. There are fast-review journals like GRL and ERL or you Discussions journals with public review. If you honestly think there’s a massive global conspiracy among climate journals then you can submit to a remote sensing or astrophysics journal while still posting on blogs.

Unless you’re confident you’re a complete expert on all of radiative transfer, plant functional types and photosynthesis, GCM land-surface schemes, CERES, MODIS and AVHRR data then it’s possible that you might have slipped up somewhere important. A journal review has a much better chance of catching this and helping you get to the “Truth”.

You have the technical background to see that Monckton’s blog post here is full of basic errors and misunderstandings that make is conclusions worthless. Yet any commenter that points out how the physics was actually done is called “cowardly” or “out of his depth” (no chicks, apparently) and the facts are ignored. This is a sign that WUWT “review” is not hugely effective.

My first four submissions were published in a day or two. I don’t know what is holding this one up other than it it like 2,700 words, or that Nick Stokes said my last submission had so many errors he didn’t know where start. After the ad hominen, he didn’t really back up his complaints.

I never said anything about a “global consipracy.” I suspect the problem is specialty blinders and CYA bias.

I never claimed to be a specialist in all the things that contribute to modeling climate effectively. In fact, one of my complaints is that there are a bunch of specialists working on GCMs, but their breadth isn’t comprehensive enough to prevent overlooking things. I suspect that you are one of those specialists. In my very first WUWT essay I complained that one problem with GCMs is, because they aren’t entirely dependent on first principles, and can be ‘tuned’ to compensate for problems with an inability to properly model things like energy exchange in clouds, it is entirely possible something has been overlooked and it has been ‘compensated’ out of the model. One doesn’t know what they don’t know.

I have asked Anthony why it hasn’t shown up yet. I will give him some more time and then I will look for an alternative place to get exposure.

[Life happens. Every submittal first passes into a single queue for automaticspam review.

If it passes through the spam filter, then every message triggers a word search by WordPress.

If a triggers/trip happens on the (modest) list of list of “key words and tricky phrases”, then the message hits an automatic “HOLD” until one of the moderators releases it for presentation.

If no “key word and tricky phrase” is triggered, and if it passes the spam filter, it is published.

.mod]

Clyde Spencer: those topics are related to albedo, which you claim is being done wrongly. I strongly recommend you submit your work to a journal if you’re interested in finding the “Truth”. Review comments will let you know whether you’ve missed anything important because the reviewers will know about things like the MODIS albedo products and how they were verified, limitations, wavelength dependence and so on.

Compare that with WUWT “review” – you have the expertise to see that this post makes really basic errors that destroy its conclusions, but how many people picked up how Monckton doesn’t even seem to understand there is a concept like a radiative kernel? Never mind how it’s used and how it depends on wavelength and all the other pesky things you need to do grown-up radiative transfer calculations.

“Unfortunately, the IPCC has decided not to provide the derivations for any of these “magic” equations and, therefore, has proven beyond all doubt that …”

The data for the energy-budget figures come from a variety of sources, included CERES satellite data.

A common method of calculating the feedbacks, whose results were reported by the IPCC, is described fully in Soden & Held (2006)’s method section. The relevant papers are cited by the IPCC, but you can get a good idea from S&H. If you’re interested, go read it.

Christopher, thanks for continuing your exposition.

You say:

First, whenever someone says “personal communication” I get nervous.

And when the “personal communication” is a graph which offers no sources for the data shown, I get more nervous.

And when the “personal communication” shows one DAY of data and an extrapolation is given for all times and places, I get real nervous.

The problem is that I showed

that both MODTRAN and the CERES data strongly disagree with your contention that the lapse rate is the same everywhere. It differs both by location and by season. Here is the MODTRAN data for six different areas, each with 14 different cloud covers:hereAs you can see, the lapse rates are all over the board, just as they are with the CERES data. So I fear that your “personal communication” is unconvincing on this point.

As I said before (loc. cit.), this may make little difference to your claims, or it may be important … but either way, you are far from establishing your claim that the lapse rate is essentially the same everywhere. If nothing else, it must be different over a desert than over a jungle … but your “personal communication” doesn’t show that at all.

Onwards,

w.

Mr Davidson’s graph of lapse rates originally included a further image for a different time of year, but I omitted that for brevity.

In the absence of a lapse-rate feedback, there is little reason to suppose a small reference or pre-feedback warming will alter the lapse-rate, in which event any temperature change at the emission altitude will be matched at the surface.

Willis, I’m seeing (perhaps wrongly) a relatively narrow range of lapse rate (6 to 7) at 5.2 km altitude . . which to my ignorant mind does not seem like all over the board . .

JohnKnight September 4, 2016 at 3:54 am

John, you are correct. However, consider my graph in light of Christopher’s claim, that “any change in the emission altitude will be matched at the surface”. In other words, he says that in order to convert temperature changes at the effective radiation level (ERL) into surface changes all we need to do is add 6.5 °C / km altitude.

In order for that to be true, the lapse rate needs to be 1) the same at all locations, 2) the same at all times, and 3) the same at all altitudes.

But as my graph above and my analysis of the CERES data shows, it is none of these things … again, I don’t know how much this changes Christopher’s results. I’m just saying it’s not as simple as he is claiming. For example, Christopher referred me to Dick Lindzen, who said:

Christopher, however, says it is simple—just add 6.5°C per km altitude to the temperature at the ERL, and that gives you the surface temperature. Even his own diagram shows that this is not the case. Take a look at the lapse rate above the South Pole. No matter where on that line the ERL might be located, a 1°C change at the ERL will NOT be matched by a 1°C change at the surface.

Now, as I said, this may make little difference to his eventual arguments, some of which are not yet presented … but it is not something that can be ignored.

Best regards,

w.

The lapse rate is assumed to be a constant in the above analysis. If it varies with altitude that invalidates the assumption.

That sounding was taken in winter (no sun). In the day (summer) the ERL extends all the way to the surface.

In that chart, the other soundings with an inversion at the surface appear to be taken at night or early morning. Trying to argue against the 6.5°C/km ELR with that data is an error. If you look at a few years of data it should be obvious that Lord Monckton has a point.

Also, I have no problem with a “personal communication” as the source of the chart since I have plotted significantly more data than that and seen the same patterns. The one place where Lord Monckton is wrong is in assuming that “global warming” might change the ELR – it won’t. In fact, the chart he provided proves it – it shows lots of different surface temperatures but, above the boundary layer, the ELR is constant (other than a few wiggles for clouds and weather fronts). BTW, the 4.8°C/km you got from the CERES data is what is typically found in low clouds due to the heat of condensation and will change based on altitude (pressure).

Changes to the lapse rate consequent upon a radiative forcing are not part of the direct forcing: they are feedbacks. However, by straddling two surfaces – the emission surface and the hard-deck surface – the models are in effect pretending that some of the lapse-rate feedback is really a direct forcing. The effect of this error is to overstate the values of all other feedbacks.

The central point of the head posting is that in the determination of lambda-zero the lapse rate should be held fixed, and any changes to the lapse-rate resulting from the reference warming are treated as part of the lapse-rate feedback. However, the official method incorrectly determines lambda-zero, in effect implying that even before feedback there is a change in the lapse-rate. In fact, overall the lapse-rate seems to have proven quite resistant to change, but, whether or not that be the case, it is not a correct use of the Stefan-Boltzmann equation to relate temperature at the surface to flux density at an altitude where a far lesser temperature prevails – and that is the error in the official method.

Willis Eschenbach:

The problem is that I showed here that both MODTRAN and the CERES data strongly disagree with your contention that the lapse rate is the same everywhere. It differs both by location and by season.Thank you for your comment. There is no good reason to think that the distribution of the lapse rate (across latitude, time, altitude and surface temperature) will remain constant. but if there is indeed an audience out there who believe that it will remain constant, Christopher Monckton’s presentation should matter to them.

Mr Marler has misunderstood matters. The determination of lambda-zero should not involve the surface temperature at all. It should be made at the emission altitude. Then the product of lambda-zero and the radiative forcing gives the reference sensitivity, which, since it is by definition the pre-feedback sensitivity, precedes and thus precludes any change in the lapse-rate. Changes in the lapse-rate are accounted for via the lapse-rate feedback, which falls to be determined after the reference sensitivity has been determined. The point is actually quite a simple one, and it makes a considerable difference to final climate sensitivity.

“The official sensitivity equation thus already allows for the possibility that the lapse-rate may change.”That’s fortunate, for change it does as any amateur storm-chaser in the Midwest, let alone professional meteorologist can attest, and as your plot of multiple temperature profiles seems to support, despite their relative similarities.

Specifically though, I’m intrigued by the plot done at Scott90S, as it’s obviously different from nearly all the other profiles taken that day, and completely distinct from any such profile I’ve ever seen. Of course I don’t usually see plots done from the South Pole so I can’t say if this profile is atypical for that region, but it is certainly fascinating.

I can see Willis beat me to this one, and with graphs as well. ^_^

One is not talking of local and temporary changes to lapse-rate, but permanent changes over a long period, arising through alterations to the properties of the atmosphere in consequence of some forcing.

“One is not talking of local and temporary changes to lapse-rate, but permanent changes over a long period, arising through alterations to the properties of the atmosphere in consequence of some forcing.”Such as changes in composition and so forth, one assumes? Only it seemed somewhat blithe to gloss over the differences observed in wet (4.0 – 6.0 C/km) versus dry (8.0 – 10.0 C/km) lapse rates, et al., and their changes on an hourly basis otherwise, but now I think I see more clearly.

Just to be sure I have it correctly then, would it be accurate to say that we are considering only the calculation of the

meansurface temperature, which is found using the ICAO standard lapse rate (6.49 C/km, 0 – 11 km altitude) to modify themeantemperature at a specific altitude (namely, the “mean emission surface”), which itself was previously calculated using the starting flux density & S-B equations? If the discussion is in fact limited here to a large-scale homogeneous mathematical model, then this makes a good deal more sense to me, as do the resulting conclusions.I appreciate your lordship’s clarification, and am left only with Mr. Stokes criticism of finding some specific boundary layer within the atmosphere where emissivity “must” = 1. As he points out, such a “surface” may be very hard to find in practice, although as one scales to more & more complexity this may not be the confounding issue it appears on its… ah, surface.

Changes to the lapse rate consequent upon a forcing are feedbacks and not part of the reference temperature change, which was the subject of the head posting. The effect of the erroneous method described in Schlesinger (1985) and incorporated in the models, as Soden & Held (2006) show it has been, is to treat some of the lapse-rate feedback as though it were part of the original forcing. This allows the models to overestimate all other temperature feedbacks, making a considerable difference to final sensitivity.

I am not ignoring lapse-rate changes: I am saying that, to work the fundamental equation of radiative transfer properly, one should keep the feedbacks, including changes to the lapse rate, separate from the original direct forcings in the analysis. It is not a complicated point, but some commenters here are making unnecessarily heavy weather of it.

@Monckton of Brenchley:

Understood. Thank you again for your clarifications.

when someone calls a fourth power law exponential, I lose faith in all the mathematical reasoning that follows.

Mr Smith should understand that in these islands the term “exponential” is sometimes loosely used to describe any expression containing a term raised to a power greater than 1. If that usage caused confusion in the context in which it was used here, I apologise.

As Gauss used to say, Non notatio, sed notio. If Mr Smith is interested only in the notation and not in the notion, he need not spend any more time reading this series.

Monckton of Brenchley September 4, 2016 at 1:47 amMr Smith should understand that in these islands the term “exponential” is sometimes loosely used to describe any expression containing a term raised to a power greater than 1. If that usage caused confusion in the context in which it was used here, I apologize.

Maybe among journalists and their ilk but certainly not by anyone with a scientific education. The statement you made suggested a level of scientific illiteracy, especially when repeated after the error is pointed out:

“A fourth-power relation is by definition an exponential relation.”If you want to discuss science you do so using appropriate scientific language if you want to be taken seriously.

It seems the error claimed here is that in determining reference sensitivity by the product λ0 * ΔF0, regular science used a wrong value for λ0 (0.313). It should, we are now told, have used the primitive value from the Stefan-Boltzmann equation of 0.267, as also derived by Hansen’s method.

But we have been through all this before, here, where Lord M told us:

So there a value of 0.313 was asserted, based on Lord M’s Hölder study. In fact, as I pointed out with references, the difference is not due to to this MoB claim, but to absorption in the atmosphere. This is calculated, as MieScatter said above, by atmospheric modelling, which does not simplify to any “emission surface”. It was set out in detail by Soden and Held 2006, which was referenced on by the AR4.

No basis is given here for reverting from “One final adjustment is needed” to claiming that science is now in error for not using the primitive value. Does it mean that Lord M is now ditching his Hölder claim? He should, of course, but not without examining the true reason why the “final adjustment” is needed.

Mr Stokes is right that I had thought the Hoelder inequality made IPCC’s value for lambda-zero legitimate, However, I have recently recalculated and reintegrated the latitudinal values of lambda-zero and have found that the inequality makes little difference.

Roe (2009) attributes IPCC’s departure from the strict SB value to the “finite absorptivity” of the atmosphere, but, as the head posting explains, by Kirchhoff’s radiation law the absorptivity is equal to the emissivity, which falls on [0, 1] and is, therefore, self-evidently finite in all circumstances. And at the emission altitude the absorptivity is unity.

I have been unable to obtain from IPCC any indication of how lambda-zero is determined. The only clear explanation I can find in the journals is that of Schlesinger, and that explanation is erroneous, and his value is close to that which the models use.

So, if anyone can answer my question about the value of lambda-zero raised at the end of the head posting, I shall be grateful.

Kirchoff’s Law is misapplied sometimes. You and I and a million others know this law without me quoting it.

The meat of the matter is:

Emission is based on temperature.

Absorption is NOT based on temperature.

A blackbody absorbs ALL energy falling on it.

Even though the energy is absorbed by the above blackbody it does not mean it emits it.

I do my calculations (using Kirchoff’s Law), differently. I perform separate calculations on emission and absorption.

Kirchhoff’s radiation law is not up for repeal. Absorptivity equals emissivity, and is equal to unity at the emission altitude.

Gotcha. Pity about your comprehension skills I never suggested that Kirchoff’s Law should be repealed He is God to me. I only have a problem with the way some idiots apply it.

You can take that any way you like. I was being polite and informative before.

Lord Moncton

Some of the comments here clearly demonstrate the Klimate Inquisition has got you in its sights, seeking to discredit you by trying to invoke some kind of emotive response. When individuals disdanefully argue about heresy, as the Klimate Inquisition is doing here, you can pretty much rely on the fact you have touched the raw nerve of truth.

I have the strong sense that many of the attacking comments here are made by some of the high priests of the Global Warming Industry fearful of having their cosy gravy train derailed.

As a humble geologist in the private sector, I have always believed the concept of CAGW to be a complete crock, or you would be able to observe something similar in the geological record. There is, of course, a reasonable correlation between CO2 levels and global temperature in the geological record, but embarrassingly for alarmists it always shows changes in CO2 levels follow changes in temperature, not vice versa.

Keep up the good work – make them bleat some more!

Well done, Mr Miller! You have detected the mounting hysteria in the ranks of the ungodly as they begin to sense the threat to their official position that is represented by this series, in which there are many more revelations to come.

I have deliberately started slowly, with some small errors, just to draw out the troublemakers and tire them before I turn to the more serious errors that are yet to come. They sense the game is up, and they are doing their best to derail this thread before the series reaches its conclusion. In this they will fail.

Peter

You can get up off your knees now. The lord probably hasn’t noticed you.

Alex

Nice bleat!

Why are you and the rest of the Klimate Establishment – Nick Stokes excepted – so fearful of revealing your real names, preferring to snipe from beneath the dark shroud of anonymity?

“So, if anyone can answer my question about the value of lambda-zero raised at the end of the head posting, I shall be grateful.”<The primitive value is clearly not the right one. For it represents the change of emission temperature T_0 with ΔF0. But λ0 is defined (in Fig 1, for example) as the rate of change of

surfacetemperature T_S with ΔF0. You cannot expect that these will be the same. In fact, if you simply multiply .267 by (T_S/T_0) you get 0.302, not so far from .313.The proper version of this factor is given by Soden and Held (op cit)

For Planck feedback, x is T_0, and so what is required is a GCM estimate of ∂T_S/∂T_0, the correction factor to the primitive. That is found and used in their Table 1, which I have referred to before:

Note that S&H use an inverse convention; λ0 (Planck) is in W/m2/K. Just invert to get the MoB convention.

The account given by Mr Stokes amply confirms the point made in the head posting: lambda-zero is indeed being determined in the models as Schlesinger determines it: by reference to surface temperature set against emission-altitude flux. Yet the SB equation relates flux density and temperature at the same surface, not at distinct surfaces. Looks like an error to me.

It’s not an error, it the whole basis of the conceptual model that you have already used yourself (you fig 1) and that relates surface temperature changes to flux changes at the top of the atmosphere.

“Yet the SB equation relates flux density and temperature at the same surface, not at distinct surfaces. Looks like an error to me.”No, it’s the factoristion that S&H set out.

λ0 = ∂R/∂x ∂x/∂T_S = ∂R/∂T_0 ∂T_0/∂T_S

∂R/∂T_0 expresses the change of R with T_0,( the 0.267 above). But the definition is change wrt T_S. To get that, you need the second factor, which GCMs can provide.

Still looks like an error to me. The change in surface temperature following a change in emission temperature is, to first order and assuming no change in lapse rate, identical to the emission temperature change.

“to first order”Yes. They are looking for second order. As you noted, the ratio is about 7/6, not 1.

“Still looks like an error to me”

And this is very good news. What looks like correct for you is generally wrong.

Nick, thanks for posting table 1. The amazing thing to me is this. The models show a lapse rate feedback that varies by a factor of 3 from small to large. Three! Their water vapor feedback varies by about 1.5 to 1. Surface albedo feedback varies by 4.5 to 1 small to large. And cloud feedback varies by an astounding 7 to 1 from small to large.

Despite that, they all do relatively well at emulating the historical changes in temperature.

This is why I laugh when people claim that the models are based on “simple physics” and the like … what we are seeing are the marvels of having lots of tunable parameters. Yes, each of them can make the elephant wiggle his trunk …

So what?

And people actually believe that if you just average all of them together they can give us the evolution of the climate for the next century …

w.

“The account given by Mr Stokes amply confirms the point made in the head posting: lambda-zero is indeed being determined in the models as Schlesinger determines it: by reference to surface temperature set against emission-altitude flux. Yet the SB equation relates flux density and temperature at the same surface, not at distinct surfaces. Looks like an error to me.”

Try reading the methods section of Soden & Held (2006) and you should see why it is not an error.

Soden & Held (2006) show quite clearly that the original error made by Schlesinger is now set in stone in the models: they are incorrectly comparing surface temperature change with emission-surface rather than hard-deck-surface flux (the two are very different), and one effect of this ghastly mismatch is to treat part of the lapse-rate feedback as though it were part of the original forcing. Another is to allow a substantial overstatement of the reference sensitivity parameter and hence of all temperature feedbacks.

Peter and the lord

I have been visiting this site since very close to it’s inception. I never have and never will be a warmist. However, If I find, or feel, a friend or enemy could be mistaken about some detail, I will point it out to them.

I use Alex because that is my name, at no point did I feel it necessary to give more than that. I don’t see the need to give my full details and home address or credit card number. My email address is registered with this site and I can be contacted at any time by the runners of this site. There are a lot of loonies out there. Yes, I’m a little paranoid.

If you want some basic bio about me then here it is:

I am 67 and retired when I was 38. I make and invent things and do a lot of study in my area of interests. You won’t find any of my products on the market because I just make things for myself. I frankly couldn’t care less about money or improving the lot of humans on the planet.

This does not mean I’m some weird guy. I’m in a long term relationship and I have acquaintances around the world that think I’m very cool and have a brain the size of a planet.

So, because I am magnanimous, there is no need to apologise

Very good article as is the work done by David Evans from a different direction. Global warming/climate change is not science nor is it happening as predicted, it is very good to see it being challenged against the consensus by people not supported by floods of government money.

Martin Mason, have you read Soden & Held (2006)? A free pdf is here:

https://www.gfdl.noaa.gov/bibliography/related_files/bjs0601.pdf

Do you think there is something wrong with their radiative kernel approach? Could you be specific?

Your insistence on citing and posting links to ‘Soden & Held (2006)’ as responses to the calculations and questions of Lord Monckton’s article above are bizarre.

If you actually read ‘S&H 2006’ you would recognize some of the calculation problems cited by Lord Monckton above.

ATheoK, “If you actually read ‘S&H 2006’ you would recognize some of the calculation problems cited by Lord Monckton above.”

This blog post is nothing like Soden & Held’s approach, it seems clear to me that Monckton either hasn’t read it or he hasn’t understood it and his entire post borders not-even-wrong.

Perhaps you understand Soden & Held’s paper better than me, in which case I’d like to learn. Two starter questions:

1) what is the change in mean temperature of a the “effective radiation level” change when the surface temperature increases by 1 K in S&H’s calculation?

2) How does the “effective radiation level” change with wavelength, and how does the S&H method account for this?

MieScatter continues to duck the central question. The reference sensitivity parameter ought to be determined solely and wholly at the emission altitude, with the lapse-rate held constant (not all that far from observation, actually), so that any change to the lapse rate is treated not as part of the forcing but as part of the lapse-rate feedback. However, S&H make it quite clear that emission-surface flux and hard-deck surface temperature are the points of comparison, and that, therefore, there are different pre-feedback temperature changes at the surface and at the emission altitude. But that implies a change in the lapse-rate, which is not a forcing but a feedback.

Monckton of Brenchley: for a global-average surface temperature change of 1 K in the Soden & Held method, what is the change in the lapse rate when they calculate the Planck response?

Did anybody considered the hidden hypotheses behind the “forcing” concept?

1- the forcings are linear

2- the forcings are independent from each other

3- the forcings act immediately (without delay).

For more details and consequences, have a look at: https://dl.dropboxusercontent.com/u/56918808/forcings_rel%2001.08.pptx

Please note I did not discuss in details the value of the parameters, as done brillantly in this post. but my analysis remain valid, from a conceptual point of view

The CO2 forcing function is actually logarithmic.

You are absolutely right. But I referred actually and specifically to the denominator term 1-F = 1-sum(fi). Which means that the individual forcings just sum up: this is what I mean with “linear” and “independent”. For the “delay” (3rd hidden hypothesis), this simplification is of paramount importance. Delayed non linear equations become easily chaotic (dynamical systems). A simple example is the rather well known”logistic equation”: x(t+1) = a*x(t)*(1-x(t)). which is nothing else than the product of a positive and a negative delayed feedback (or forcing). If you “tune” the parameter “a”, you’ll find amazing properties. The equation leads to a result that becomes rather unpredictable and which is extremely dependent on the initial conditions and the value of the parameter (for values of “a” in the range 3.6 < <4). Transposed to climate science (?), this means that if the climate system behaves in the same way (and it can be proved mathematically that it exhibits a "chaotic signature"), all the "projections" you made are extremely dependent on the exact values of the parameters used for calibrating the model: the initial conditions resulting from time series of experimental data from the past (and the associated experimental and algorithmic errors) and from the parameters (the exact value of the sum of the individual forcings, for example). On those two issues "the science is NOT settled" as shown by the abundant recent (and peer reviewed if you believe this gives some credibility) literature on the subject, not to refer to the present post and discussion. It seems thus reasonable to me, based on purely mathematical considerations, to claim that the climate system is not predictable on the long term. Different methods do exist to predict the horizon of predictability from time series. The problem is, as you know, to get this kind of work applied to climate data published.

It is good to see a discussion of the chaoticity of the Verhulst logistical model here. Indeed, the climate is sensitive to minor perturbations in the initial conditions (see e.g., Lorenz, 1963; Giorgi, 2005; IPCC AR3, para. 14.2.2.2).

However, it will become apparent when I turn to the feedback side of the official climate-sensitivity equation that the feedback forcings do not come anywhere near as close to unity as the models currently imagine.

Henry Masson: “Did anybody considered the hidden hypotheses behind the “forcing” concept?”

Yes. One relatively recent example, among a large literature on the subject:

http://dx.doi.org/10.1088/1748-9326/10/10/104010

Many thanks Mike for this interesting reference. But at first sight, it does not address the third (and probably most critical) hidden hypothesis stating that feedbacks are instantaneous, while chaotic behaviour (and extremely limited predictability) is closely linked to delays in the feedback loops (=forcing), and that obviously such delays have been spotted in experimental data (800 years time constant of the “oceans” i.e.). Also a-periodic (= not exactly periodic) and intermittent fluctuations as observed in many time series are an indication of dynamical (= chaotic) behaviour.

Feedbacks are not assumed to be instantaneous, but it’s necessary to pick some way of differentiating between feedbacks and forcing.

Check IPCC AR5 Chapter 8 discussion on effective radiative forcing and on the fixed-SST and regression method for disaggregating forcing and feedbacks in models.

Many thanks for your suggestion and comments. But I am still puzzled, as the equation in 1/(1-sum(f_i)) is typical of and only valid for linear, independent and instantaneous feedbacks, as I recalled in the dropbox link given above, and that I recall for convenience: https://dl.dropboxusercontent.com/u/56918808/forcings_rel%2001.08.pptx

In answer to M Masson, the head posting does make it clear that, since we are dealing with equilibrium sensitivity, the non-linearity of temperature feedbacks is not an issue. However, an account of the treatment of non-linear feedbacks will be found in Roe (2009), freely available on the web.

Many thanks for the reference to the work of Roe. Please note however that he is considering “red noise” (Brownian motion) and not pink noise (following a 1/f law). The amplitude distribution of Power spectrums of most climate data (and other dynamical systems) exhibit generally a pink noise signature. Such a pink noise signature is even often considered as indicative of the existence of a dynamical system (i.e. when applied to visibility graphs)

In response to M Masson, Roe explicitly entitles his paper “red noise” and also explicitly refers to the G = 1 / (1 – f) amplification function for feedback factors.

… and Roe gives in his paper a sketch exhibiting clearly my three initial claims regarding the 1/(1-sum(f_i)): the feedbacks must be linear, independent of each others and acting without any delay. Otherwise the formula does not apply. And this jeopardizes the whole “forcing” paradigm. Also, coming back to a later comment I made on Roe’s paper: “red” noise refers to Brownian motions /data. “white” noise to purely random motions /data. “pink” noise refers to a “1/frequency” law. If you look at amplitude distributions and power spectra, you’ll find that many time series describing natural / ecological /socio-economic “concepts” follow such a kind of law. Climate data is not an exception See for example John Gribbin’s “Deep Simplicity, Chaos, Complexity and the Emergence of Life” (Allen Lane /Penguin books, 2004), and more precisely the chapter 5, for having a first overview on this.

“3- the forcings act immediately (without delay).”This is irrelevant to the equilibrium sensitivity being discussed here. It describes the difference between steady states, without reference to the intermediate stages and their timing. For each such steady state, it describes the feedbacks that have become established.

You are right Nick, but the problem is that of course you never reach local equilibrium, as this requires an infinite time. The climate system is never “static”, as the Earth rotates around it axis and the incoming solar flux in each point changes thus continuously. Not to mention the even fast dynamics of clouds acting as a blanket (during the night) or a shutter (during the day). I think this is the basic flaw of the whole IPCC approach: they ignore the fact that the system is (far) away from equilibrium, even locally.

I am sorry to ask a really stupid question. Would somebody be kind enough to explain (or point me to a reference) how the all-important climate sensitivity can be reconciled to the concept of saturation whereby (as I understand it) the radiation at the relevant CO2-sensitive wavelength is all absorbed and (as I adduce) the sensitivity reduces to zero? The two phenomena seem to give quite different characteristics.

Since the CO2 forcing function is logarithmic, each doubling of concentration will increase radiative flux density by a fixed amount. At or near the Earth’s surface, the absorption wavelengths of CI2 are largely overlain by those of water vapor, but in the mid-troposphere there is still scope for some warming to be caused.

Surely the point is that CO2 absorbs all the radiation available to it at approx. 20ppm. Absorption on the shoulders of the absorption bands in the absence of water vapor should already be accounted for. At 400ppm there should be no more thermalization unless TSI increases.

Siamiam would be right as far as the surface is concerned, but the upper troposphere is drier, and it is here that the CO2 forcing begins to matter.

Monckton of Brenchley September 4, 2016 at 3:00 amAt or near the Earth’s surface, the absorption wavelengths of CI2 are largely overlain by those of water vapor, but in the mid-troposphere there is still scope for some warming to be caused.

Water vapor lines are rather sparse in the absorption region of CO2, see below for an example (top is CO2):

http://i302.photobucket.com/albums/nn107/Sprintstar400/CO2H2O.gif

Steve Borodin, does this help?

https://youtu.be/we8VXwa83FQ

MieScatter

September 4, 2016 at 9:40 am: Totally outed yourselves now, you lot. Trolls I’ve met before. Wreckers, but so predictable.

“he was applying the Stefan Boltzmann equation by straddling uncomfortably across two distinct surfaces in a manner never intended either by Jozef Stefan”There is too much reliance in this post on the notion of an emission surface. There is no such surface at which the S-B law can be applied. There are not “two distinct surfaces”. Hansen describes his T_e as an effective radiating temperature from the Earth, which he derives from the formal S-B law. He does not claim that it is a temperature of any particular location, and of course emission comes from a whole range of values. Others do likewise. It is simply a parameter determining flux, and Soden and Held show how to use it. Differential dependence of flux on the parameter is easy; what is then needed is the rate of change of that parameter with T_S. That comes from GCMs.

At the mean emission altitude around 5.3 km a.g.l., the net flux density is 238 W/m2 and, given emissivity at unity, the equivalent temperature at that altitude is 254.5 K or thereby. Change the flux density at that altitude by 3.7 W/m2 and the temperature rises by 1 K.

At the surface, temperature is 288 K and, with emissivity at or close to unity, corresponding flux density is 390 W/m2. Change the surface flux density by 3.7 W/m2 and the surface temperature rises by 0.67 K.

At any SB surface in between these two, the reference-temperature change would be between 0.7 and 1 K. I see no basis for the conclusion that it would be more than that.

“given emissivity at unity”But emissivity of what thing? Gas has an emissivity per unit depth, but it is far from unity. You can think of its Kirchhoff equivalent, absorptivity. Gas is not locally black. It may be that all incoming radiation of some wavelength will be absorbed somewhere in the air, so the whole earth looks like a black body. But there is no surface (in the air) that has absorptivity one.

T_0 is simply an analogy. It is the temperature that the Earth would have if it were a black body emitting that flux. But that doesn’t mean there is an actual black surface doing that. The point of such a parameter is that you can hope that T_S will behave something like T_0 as flux changes. In olden times, that was all they could do. But in IPCC times we can with GCM do what is required. That is to find the derivative of that parameter with respect to T_S. That is not in principle different to using the GCM to find λ_0 directly, but seems more natural, since ∂T_0/∂T_S is close to 1 – as you noted, about 7/6.

In fact, the coefficient 7/6, though it is implicit in the official method of determining lambda-zero, is inappropriate, because it arises from the improper use, ever since Schlesinger (1985), of surface rather than emission-altitude temperature as the denominator in the first derivative of the Stefan-Boltzmann equation.

Nick

I am a little puzzled by this ‘virtual surface’ thing. Is it some sort of mathematical construct with no basis in reality? I would ask the lord but he would probably tell me to read a book or quote some latin at me.

I have reasonable knowledge about fluxes etc. but I can’t for the life of me work out how you can establish an altitude where things balance. The downwelling and upwelling mix is different. There would also be latitudinal differences including the atmospheric mass. If you can’t explain briefly, then point me in a direction where It can be explained

Alex,

You can’t characterise such a surface as a flux neutral point. Total heat flux (steady) is the same at all altitude surfaces (changing slightly in intensity as the area expands with radius to centre). It is partitioned into SW, LW and convection, so you might find neutral points of some subset, but not well defined.

T_0 is just defined as (F/σ)^(1/4). F is a global average. T_0 is more often called effective emission temperature. And you can calculate a surface at which that would be attained (lapse rate), but it has no special properties. T_0 is the temperature at which a black body would emit F. The Earth isn’t black, but it is dark (for IR) so it is reasonable to think dependence on T_S might follow T_0. Lord M calls that “first order”. But it is a guess, and with GCMs you can really find out. That is what they do.

In reply to Alex (and overlooking the silly sneer in his tone), the emission surface of a planet with an atmosphere is the locus of all points at or above the hard-deck surface at which incoming and outgoing radiation are equal, since it is from that “surface” that outgoing radiation from the Earth is observed to emanate.

My contention is that climate-sensitivity calculations should be performed at the emission surface. However, Schlesinger (1985) adopted a novel notion – that a legitimate differential of the fundamental equation of radiative transfer could be obtained by taking the ratio of hard-deck surface temperature to emission-surface net radiative flux density.

This leads to a considerable overstatement of lambda-zero and hence not only of pre-feedback warming but also of each individual feedback.

The models have since found it expedient to emulate this questionable device, since otherwise climate sensitivity falls quite a bit.

As to “finding a balance”, it’s not too difficult. Since the emission surface is defined as I have defined it (or, rather, as Professor Lindzen has defined it, for it is his definition that I am using), the net flux density is known and the emissivity are known, from which the emission temperature can be calculated (either by a global mean or by latitudinal means), and, given the known lapse rate, the mean altitude of the emission surface (about 5.3 km a.g.l.) can be readily determined.

“In reply to Alex (and overlooking the silly sneer in his tone), the emission surface of a planet with an atmosphere is the locus of all points at or above the hard-deck surface at which incoming and outgoing radiation are equal, since it is from that “surface” that outgoing radiation from the Earth is observed to emanate.”None of this makes much sense. Outgoing radiation is not observed to emanate from such a surface. It is the sum of emanation from various levels, influenced by frequency, including about 20% which comes direct from “hard-deck” in the atmospheric frequency window.

But the surface definition makes little sense. The net heat flux (averaged over time and area, and spectral frequency) at any level is equal to the small heat loss from Earth’s interior. At TOA, that means that incoming radiation (mainly SW) and outgoing IR are equal. Coming down to the troposphere, part of the upward flux is taken over by convection (and LH advection), so in general down radiation will exceed up.

And if you don’t average, you have a complete mess. Where is that locus at night? But while averaging is fine for accounting for conserved quantities like heat (hence temperature) it doesn’t make sense for defining a surface for radiation, which responds to current circumstances.

I think link to Lindzen is needed.

Monckton of Brenchley September 4, 2016 at 11:54 amIn reply to Alex (and overlooking the silly sneer in his tone), the emission surface of a planet with an atmosphere is the locus of all points at or above the hard-deck surface at which incoming and outgoing radiation are equal, since it is from that “surface” that outgoing radiation from the Earth is observed to emanate.

No, the ’emission surface’ model which you use is the equivalent black body emitter which emits the same flux as is received by the planet. Such a surface would be at a temperature of ~255K which in a standard atmosphere would at ~5.3 km. Such a surface does not exist and using it to calculate sensitivity etc. as Monckton does, given the nonlinearities involved, is inappropriate (especially if you’re doing so to claim that the detailed calculations are in error).

For example, in the tropical atmosphere (cloudless), CO2 emission near the peak of the emission spectrum at ~15microns is at ~220K ( 12.5km), the Q-branch spike is at ~35km. In contrast the ‘window’ region between 10 and 13 microns emits directly to space from the surface at ~300K. Add some stratus clouds around 1km and the emission from the cloud tops is at ~290K, add some cumulus and it drops to ~280K. All these effects are supposed to be accounted for by the assumed ’emission surface’ in Monckton’s model.

If “Phil.” wants to take up with the IPCC secretariat the issue of their using emission-altitude flux as part of the basis for their calculations, let him do so. However, the virtue of that approach is that the emission-altitude flux is easily measured by cavitometers on satellites.

From that flux, the emission temperature of the Earth – which is the temperature that it would possess at the surface if the surface were a blackbody and if there were no atmosphere and no change in today’s albedo – may be determined directly via the SB equation, and there is in fact a mean altitude at which that temperature obtains. It is about 5 km a.g.l.

Monckton of Brenchley says: ” the emission-altitude flux is easily measured by cavitometers on satellites.”

..

WRONG..

http://www.bsuir.by/online/showpage.jsp?PageID=93100&resID=119941&lang=en&menuItemID=120098

…

Cavitometers do not measure emission flux.

Monckton of Brenchley September 5, 2016 at 4:34 pmIf “Phil.” wants to take up with the IPCC secretariat the issue of their using emission-altitude flux as part of the basis for their calculations, let him do so.

No I’m taking it up with you, because it is you, not they, who is misusing the concept in order to incorrectly claim that they have made an error. Note that any addition of CO2 will increase emission from ~12.5km (~220K).

The S-B relationship you use is the integral across all wavelengths of the Planck’s Law equation, in the case of the atmosphere where emission is from a variety of temperatures it’s appropriate to integrate using the actual temperatures at each wavelength. Using Line by Line calculations in the relevant parts of the spectrum as the models do. The average emission altitude is a simple means of illustrating the way the GHG effect works, given the non-linearities involved you can’t use it to accurately calculate the sensitivity.

I notice that you have made no attempt to address the error in your claim that:

“the absorption wavelengths of CI2(sic.) are largely overlain by those of water vapor”Mr Baguley incorrectly asserts that I had stated that cavitometers on satellites measure emission flux. No: I said they measure emission-surface flux, for, by definition, the incoming radiation measured by the cavitometers is, at that altitude, equal to the outgoing radiation. See Lindzen’s talks on the definition of what he calls the “characteristic-emission altitude”.

Monckton of Brenchley, let me make it simpler so even you can understand.

..

Satellites don’t have cavitometers..

Get it?

Particularly with respect to the long-wave radiation with which we are here concerned, the emissivity of the emission “surface” is as near unity as makes no difference.

as seen in another post of yours above, there is too much reliance on the output of various cfd modelers. the modeling of airflow over the surface of aircraft wings has yet to be perfected ,as evidenced by various stabilisers and airflow interruption devices attached post production in the test phase. the notion that any cfd model gets remotely close to accurately modeling the atmosphere is delusional in the extreme .

in the case of the cost to humanity in implementing measures to halt cagw, near enough is just not good enough.

I suggest you check out the contribution that Tony Jameson’s CFD modeling of wings has made to the redesign of wings, notably for Boeing and Airbus.

http://aero-comlab.stanford.edu/Papers/AirplaneDesignShanghai.pdf

The leader of the 737 Aerodynamics program stated: “Without the understanding gained from CFD there would not have been a 737-300 Program!

Well, this is all a bit irrelevant really:

https://www.theguardian.com/environment/2016/sep/03/breakthrough-us-china-agree-ratify-paris-climate-change-deal

And arctic sea ice extent at second lowest in the record.

Parts of the world which count recognise man made climate change and the evidence for it plainer than ever.

Even those pushing the Arctic sea ice meme realize this years low is the result of storms. The fact anyone would mention it in regards to man made climate change shows denial of reality. Have you always been prone to delusions?

As for the Paris agreement? It is not worth the paper it was written on as many AGW supporters realize. It has no teeth.

Griff,has been taken to school on this,on other websites and here too just recently. as you pointed out,hat powerful WIND driven storms for ALL three low years of 2007,2012 and 2016 were the main cause of low summer ice extent.

He also fails to account for the evidence that Arctic region have been mostly or totally ice free in the summer for many years,in the early part of the Holocene.

Richards M: “Even those pushing the Arctic sea ice meme realize this years low is the result of storms. The fact anyone would mention it in regards to man made climate change shows denial of reality. Have you always been prone to delusions?”

It seems that summer Arctic sea ice extent is the lowest in at least 1,450 years (Kinnard et al., 2011 http://dx.doi.org/10.1038/nature10581 ).

Did we get storms in the Arctic for the first time in 1,450 years?

“And arctic sea ice extent at second lowest in the record.”

Sounds impressive huh? But that’s a record which is only 35y long in a climate system which is known to have a strong circa 60y periodicity, which was at its coolest in in 1975 and peaked around 2005. I suspect that 2012 will be the trough of the ice cycle for the next few decades.

In 2007 we were told it is was “run away” melting , climate meltdown, death spiral etc. Then the canary in the coal mine started to feel better. In 2012 we had another OMG moment but in 2013 NH sea ice volume increased by 50% in a single year. WTF? That is more like a sign of a strong negative feedback.

Hardly compatible with the tipping point hyperbole. So alarmists suddenly went quiet about it for a couple of years and started bed-wetting about millennial scale “melt-down” in Antarctic.

Now they think the Arctic is worth bemoaning again but this time because it’s the lowest winter max. EVAH ( ie in the last 35y of the warm part of the AMO cycle ).

So what Griff the grifter probably needs to ask himself is why , after the lowest winter max EVAH we are only seeing the second lowest summer ice coverage. Odd that this ice which is has been subject to the worst AGW since the dawn of man is now melting so slowly that even starting at a low point in winter does not lead to a new summer minimum.

As for the much heralded “agreement” with China , it would be wise to see EXACTLY what POTUS says, when he actually does ( rather than the froth and lather that MSM are fluffing up before it actually happens ) and exactly now he intends to sign a treaty that he has no constitutional authority to sign.

IMO this will turn out to be a “joint statement” of intent with little substance and lots of puff.

MieScatter doesn’t appear to understand what “extensive uncertainties remain” means. He seems to think the paper he referenced is based on data. Face-palm. You need to go back to the turnip farm.

‘Kinnard et al., 2011’ use ‘high resolution land based proxies’ to postulate Arctic Sea ice in an area greater than 14-15 million square kilometers.

From their proxy analysis they find that the recent warming is consistent with anthropological warming influence.

Correlation does not mean causation.

A lack of definitive certification of proxy accuracy implies massive possibilities for errors. Definitely not a definitively accurate analysis.

Leaps to vague assumptions with the CAGW religious faithful promoting ‘consistent with’ to absolute certainty.

Translation: They haven’t solved any puzzles. The Inuit verbal history is still the best historical source until the satellite era began.

Rising greenhouse gases are modeled to increase positive NAO/AO giving a more northerly jet stream track. That can only cool the Arctic.

http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch10s10-3-5-6.html

The rational explanation for the increase in the negative NAO/AO that has driven the AMO and Arctic warming since 1995, is the decline in solar wind strength.

have a look the same time next year. all that open water is no longer insulated by ice ,resulting in much heat being lost to the atmosphere.

bit chilly, there’s some interesting work been done on this, including the importance of inversions. See e.g. Bintanja et al. (2011, http://dx.doi.org/10.1038/ngeo1285 )

At or near the Earth’s surface, the absorption wavelengths of CO2 are largely overlain by those of water vaporSuch sentences I have read nearly everywhere, just like those claiming that CO2 merely absorbs around 15µ and nowhere else in the spectrum.

I’m not a physicist and therefore can’t say by own knowledge wether or not it is correct. All I can do is to read papers and consult web sites informing about the topic.

To be clear: I’m not at all interested here about the relevance of CO2 as a GHG, but solely in obtaining a (scientific) comfirmation of (or contradiction to) what follows.

The first I have read is that Earth’s IR emission near its surface, with temperatures from say 35 °C in the Tropics till say -60 °C in Antarctica, should range from about 9.5µ up to about 13.5 µ. That’s what you are told when consulting

http://spectralcalc.com/blackbody_calculator/blackbody.php

Quite in the near you find

http://spectralcalc.com/spectral_browser/db_intensity.php

from which you obtain, for the wavelength range above, and selecting the default database (HITRAN2012)

http://fs5.directupload.net/images/160904/93kwvitf.png

1,741 absorption lines for H2O, and

http://fs5.directupload.net/images/160904/nvktqojl.png

27,100 for CO2 (note that selecting older material, e.g. HITRAN2004, gives less absorption lines for both gases: 603 for H2O resp. 3,214 for CO2).

This would mean that CO2‘s ability to absorb IR certainly is not less than that of H2O. Water vapor’s higher IR absorption would then solely be due to the fact that it is by far more abundant in the atmosphere (at least below 10 km).

So if somebody happened to read this comment and to

exactly (!!!) knowwether or not this assumption is correct, s/he should feel free to answer!Omissions are inevitable as it seems.

It must be noted that the two plots above possibly give a distorted impression, as they have a logarithmic scale. Using a linear scale gives a different view.

H2O:

http://fs5.directupload.net/images/160904/iage4rwk.png

CO2:

http://fs5.directupload.net/images/160904/79njt5is.png

But I obviously don’t know the exact scientific interpretation of the difference.

Yes, and furthermore, half the smog of rotational lines they are fond of showing around the important vibrational lines are destructive and reduce the energy of the molecule. The “p” and “r” rotational lines are a couple orders of magnitude weaker than the central “q” vibration. The destructive “r” lines are a bit stronger than the constructive “p”, so the net effect of the rotational smog is a small loss of energy to the molecule.

Those are vacuum spectra plots for a single molecule. They change considerably at atmospheric pressure, temperate, and abundance. In the lower troposphere, about 50% of the CO2 spectra overlaps with water vapor. In the stratosphere, there is no overlap because water is only 5 ppm, it is 10,000 ppm in the lower troposphere.

Bindidon To apply this spectroscopic data, use quantitative Line By Line (LBL) radiation/absorption models. e.g.

Intercomparison of Far Infrared Line By Line Radiative Transfer Models Kratz et al. 2005

One of the models is HARTCODE by Ferenc M. Miskolczi as applied in Fig 2, Fig 4 and Fig 5 in

The Greenhouse Effect and the Infrared

Radiative Structure of the Earth’s Atmosphere 2014.

Thank you David L. Hagen, I have a pdf “First light from the Far-Infrared Spectroscopy of the Troposphere

(FIRST) instrument” on disk. The second link is very interesting though a bit harder to digest.

But what I’m looking for is rather to be seen in the context of publications like

http://newscenter.lbl.gov/2015/02/25/co2-greenhouse-effect-increase/

http://www.nature.com/nature/journal/vaop/ncurrent/full/nature14240.html

Suddenly I remember to have read this

http://www.drroyspencer.com/2010/08/comments-on-miskolczi%E2%80%99s-2010-controversial-greenhouse-theory/

years ago…

Thanks for the Co2 paper. Separate Miskolczi’s quantitative LBL from his first order equilibrium atmospheric modeling. Next need to add 2nd order issues to (and refine translation issues into English).

And… what about even this?

https://wattsupwiththat.com/2014/05/01/top-ten-skeptical-arguments-that-dont-hold-water/

??? Address the issues Spencer raised.

Robert Clemenzi on September 4, 2016 at 8:14 pm

Thanks.

They change considerably at atmospheric pressure, temperate,and abundance.Spectralcalc has a radio button selector to activate a scaling by atmospheric abundance but this didn’t change anything. Maybe it’s behind their paywall.

Sorry, the red line not blue.

You have only shown a small part of the CO2 spectrum, the Earth’s IR emission covers ~5-25 microns, the 15 micron band is close to the energy peak of the emission.

You are right Phil, but the focus was here I guess on the IR emitted at surface.

HITRAN tells us that CO2 absorbs/emits even till 30µ, i.e. -150 °C or 23 km (probably the altitude where it emits to outer space).

HITRAN is just a catalogue of spectral lines, so a graph of that will produce just lines. in the real world the lines are not just lines, they are much broader and will mesh with other lines in the series. not only are the lines wider for all molecules, but water vapour is special in that it forms a continuum. see-

http://www.sciencedirect.com/science/article/pii/S0022285216300637