# Physical Constraints on the Climate Sensitivity

Guest essay by George White

For matter that’s absorbing and emitting energy, the emissions consequential to its temperature can be calculated exactly using the Stefan-Boltzmann Law,

1) P = εσT4

where P is the emissions in W/m2, T is the temperature of the emitting matter in degrees Kelvin, σ is the Stefan-Boltzmann constant whose value is about 5.67E-8 W/m2 per K4 and ε is the emissivity which is 1 for an ideal black body radiator and somewhere between 0 and 1 for a non ideal system also called a gray body. Wikipedia defines a Stefan-Boltzmann gray body as one “that does not absorb all incident radiation” although it doesn’t specify what happens to the unabsorbed energy which must either be reflected, passed through or do work other than heating the matter. This is a myopic view since the Stefan-Boltzmann Law is equally valid for quantifying a generalized gray body radiator whose source temperature is T and whose emissions are attenuated by an equivalent emissivity.

To conceptualize a gray body radiator, refer to Figure 1 which shows an ideal black body radiator whose emissions pass through a gray body filter where the emissions of the system are observed at the output of the filter. If T is the temperature of the black body, it’s also the temperature of the input to the gray body, thus Equation 1 still applies per Wikipedia’s over-constrained definition of a gray body. The emissivity then becomes the ratio between the energy flux on either side of the gray body filter. To be consistent with the Wikipedia definition, the path of the energy not being absorbed is omitted.

A key result is that for a system of radiating matter whose sole source of energy is that stored as its temperature, the only possible way to affect the relationship between its temperature and emissions is by varying ε since the exponent in T4 and σ are properties of immutable first principles physics and ε is the only free variable.

The units of emissions are Watt/meter2 and one Watt is one Joule per second. The climate system is linear to Joules meaning that if 1 Joule of photons arrives, 1 Joule of photons must leave and that each Joule of input contributes equally to the work done to sustain the average temperature independent of the frequency of the photons carrying that energy. This property of superposition in the energy domain is an important, unavoidable consequence of Conservation of Energy and often ignored.

The steady state condition for matter that’s both absorbing and emitting energy is that it must be receiving enough input energy to offset the emissions consequential to its temperature. If more arrives than is emitted, the temperature increases until the two are in balance. If less arrives, the temperature decreases until the input and output are again balanced. If the input goes to zero, T will decay to zero.

Since 1 calorie (4.18 Joules) increases the temperature of 1 gram of water by 1C, temperature is a linear metric of stored energy, however; owing to the T4 dependence of emissions, it’s a very non linear metric of radiated energy so while each degree of warmth requires the same incremental amount of stored energy, it requires an exponentially increasing incoming energy flux to keep from cooling.

The equilibrium climate sensitivity factor (hereafter called the sensitivity) is defined by the IPCC as the long term incremental increase in T given a 1 W/m2 increase in input, where incremental input is called forcing. This can be calculated for emitting matter in LTE by differentiating the Stefan-Boltzmann Law with respect to T and inverting the result. The value of dT/dP has the required units of degrees K per W/m2 and is the slope of the Stefan-Boltzmann relationship as a function of temperature given as,

2) dT/dP = (4εσT3)-1

A black body is nearly an exact model for the Moon. If P is the average energy flux density received from the Sun after reflection, the average temperature, T, and the sensitivity, dT/dP can be calculated exactly. If regions of the surface are analyzed independently, the average T and sensitivity for each region can be precisely determined. Due to the non linearity, it’s incorrect to sum up and average all the T’s for each region of the surface, but the power emitted by each region can be summed, averaged and converted into an equivalent average temperature by applying the Stefan-Boltzmann Law in reverse. Knowing the heat capacity per m2 of the surface, the dynamic response of the surface to the rising and setting Sun can also be calculated all of which was confirmed by equipment delivered to the Moon decades ago and more recently by the Lunar Reconnaissance Orbiter. Since the lunar surface in equilibrium with the Sun emits 1 W/m2 of emissions per W/m2 of power it receives, its surface power gain is 1.0. In an analytical sense, the surface power gain and surface sensitivity quantify the same thing, except for the units, where the power gain is dimensionless and independent of temperature, while the sensitivity as defined by the IPCC has a T-3 dependency and which is incorrectly considered to be approximately temperature independent.

A gray body emitter is one where the power emitted is less than would be expected for a black body at the same temperature. This is the only possibility since the emissivity can’t be greater than 1 without a source of power beyond the energy stored by the heated matter. The only place for the thermal energy to go, if not emitted, is back to the source and it’s this return of energy that manifests a temperature greater than the observable emissions suggest. The attenuation in output emissions may be spectrally uniform, spectrally specific or a combination of both and the equivalent emissivity is a scalar coefficient that embodies all possible attenuation components. Figure 2 illustrates how this is applied to Earth, where A represents the fraction of surface emissions absorbed by the atmosphere, (1 – A) is the fraction that passes through and the geometrical considerations for the difference between the area across which power is received by the atmosphere and the area across which power is emitted are accounted for. This leads to an emissivity for the gray body atmosphere of A and an effective emissivity for the system of (1 – A/2).

The average temperature of the Earth’s emitting surface at the bottom of the atmosphere is about 287K, has an emissivity very close to 1 and emits about 385 W/m2 per Equation 1. After accounting for reflection by the surface and clouds, the Earth receives about 240 W/m2 from the Sun, thus each W/m2 of input contributes equally to produce 1.6 W/m2 of surface emissions for a surface power gain of 1.6.

Two influences turn 240 W/m2 of solar input into 385 W/m2 of surface output. First is the effect of GHG’s which provides spectrally specific attenuation and second is the effect of the water in clouds which provides spectrally uniform attenuation. Both warm the surface by absorbing some fraction of surface emissions and after some delay, recycling about half of the energy back to the surface. Clouds also manifest a conditional cooling effect by increasing reflection unless the surface is covered in ice and snow when increasing clouds have only a warming influence.

Consider that if 290 W/m2 of the 385 W/m2 emitted by the surface is absorbed by atmospheric GHG’s and clouds (A ~ 0.75), the remaining 95 W/m2 passes directly into space. Atmospheric GHG’s and clouds absorb energy from the surface, while geometric considerations require the atmosphere to emit energy out to space and back to the surface in roughly equal proportions. Half of 290 W/m2 is 145 W/m2 which when added to the 95 W/m2 passed through the atmosphere exactly offsets the 240 W/m2 arriving from the Sun. When the remaining 145 W/m2 is added to the 240 W/m2 coming from the Sun, the total is 385 W/m2 exactly offsetting the 385 W/m2 emitted by the surface. If the atmosphere absorbed more than 290 W/m2, more than half of the absorbed energy would need to exit to space while less than half will be returned to the surface. If the atmosphere absorbed less, more than half must be returned to the surface and less would be sent into space. Given the geometric considerations of a gray body atmosphere and the measured effective emissivity of the system, the testable average fraction of surface emissions absorbed, A, can be predicted as,

3) A = 2(1 – ε)

Non radiant energy entering and leaving the atmosphere is not explicitly accounted for by the analysis, nor should it be, since only radiant energy transported by photons is relevant to the radiant balance and the corresponding sensitivity. Energy transported by matter includes convection and latent heat where the matter transporting energy can only be returned to the surface, primarily by weather. Whatever influences these have on the system are already accounted for by the LTE surface temperatures, thus their associated energies have a zero sum influence on the surface radiant emissions corresponding to its average temperature. Trenberth’s energy balance lumps the return of non radiant energy as part of the ‘back radiation’ term, which is technically incorrect since energy transported by matter is not radiation. To the extent that latent heat energy entering the atmosphere is radiated by clouds, less of the surface emissions absorbed by clouds must be emitted for balance. In LTE, clouds are both absorbing and emitting energy in equal amounts, thus any latent heat emitted into space is transient and will be offset by more surface energy being absorbed by atmospheric water.

The Earth can be accurately modeled as a black body surface with a gray body atmosphere, whose combination is a gray body emitter whose temperature is that of the surface and whose emissions are that of the planet. To complete the model, the required emissivity is about 0.62 which is the reciprocal of the surface power gain of 1.6 discussed earlier. Note that both values are dimensionless ratios with units of W/m2 per W/m2. Figure 3 demonstrates the predictive power of the simplest gray body model of the planet relative to satellite data.

Figure 3

Each little red dot is the average monthly emissions of the planet plotted against the average monthly surface temperature for each 2.5 degree slice of latitude. The larger dots are the averages for each slice across 3 decades of measurements. The data comes from the ISCCP cloud data set provided by GISS, although the output power had to be reconstructed from radiative transfer model driven by surface and cloud temperatures, cloud opacity and GHG concentrations, all of which were supplied variables. The green line is the Stefan-Boltzmann gray body model with an emissivity of 0.62 plotted to the same scale as the data. Even when compared against short term monthly averages, the data closely corresponds to the model. An even closer match to the data arises when the minor second order dependencies of the emissivity on temperature are accounted for,. The biggest of these is a small decrease in emissivity as temperatures increase above about 273K (0C). This is the result of water vapor becoming important and the lack of surface ice above 0C. Modifying the effective emissivity is exactly what changing CO2 concentrations would do, except to a much lesser extent, and the 3.7 W/m2 of forcing said to arise from doubling CO2 is the solar forcing equivalent to a slight decrease in emissivity keeping solar forcing constant.

Near the equator, the emissivity increases with temperature in one hemisphere with an offsetting decrease in the other. The origin of this is uncertain but it may be an anomaly that has to do with the normalization applied to use 1 AU solar data which can also explain some other minor anomalous differences seen between hemispheres in the ISCCP data, but that otherwise average out globally.

When calculating sensitivities using Equation 2, the result for the gray body model of the Earth is about 0.3K per W/m2 while that for an ideal black body (ε = 1) at the surface temperature would be about 0.19K per W/m2, both of which are illustrated in Figure 3. Modeling the planet as an ideal black body emitting 240 W/m2 results in an equivalent temperature of 255K and a sensitivity of about 0.27K per W/m2 which is the slope of the black curve and slightly less than the equivalent gray body sensitivity represented as a green line on the black curve.

This establishes theoretical possibilities for the planet’s sensitivity somewhere between 0.19K and 0.3K per W/m2 for a thermodynamic model of the planet that conforms to the requirements of the Stefan-Boltzmann Law. It’s important to recognize that the Stefan-Boltzmann Law is an uncontroversial and immutable law of physics, derivable from first principles, quantifies how matter emits energy, has been settled science for more than a century and has been experimentally validated innumerable times.

A problem arises with the stated sensitivity of 0.8C +/- 0.4C per W/m2, where even the so called high confidence lower limit of 0.4C per W/m2 is larger than any of the theoretical values. Figure 3 shows this as a blue line drawn to the same scale as the measured (red dots) and modeled (green line) data.

One rationalization arises by inferring a sensitivity from measurements of adjusted and homogenized surface temperature data, extrapolating a linear trend and considering that all change has been due to CO2 emissions. It’s clear that the temperature has increased since the end of the Little Ice Age, which coincidently was concurrent with increasing CO2 arising from the Industrial Revolution, and that this warming has been a little more than 1 degree C, for an average rate of about 0.5C per century. Much of this increase happened prior to the beginning the 20’th century and since then, the temperature has been fluctuating up and down and as recently as the 1970’s, many considered global cooling to be an imminent threat. Since the start of the 21’st century, the average temperature of the planet has remaining relatively constant, except for short term variability due to natural cycles like the PDO.

A serious problem is the assumption that all change is due to CO2 emissions when the ice core records show that change of this magnitude is quite normal and was so long before man harnessed fire when humanities primary influences on atmospheric CO2 was to breath and to decompose. The hypothesis that CO2 drives temperature arose as a knee jerk reaction to the Vostok ice cores which indicated a correlation between temperature and CO2 levels. While such a correlation is undeniable, newer, higher resolution data from the DomeC cores confirms an earlier temporal analysis of the Vostok data that showed how CO2 concentrations follow temperature changes by centuries and not the other way around as initially presumed. The most likely hypothesis explaining centuries of delay is biology where as the biosphere slowly adapts to warmer (colder) temperatures as more (less) land is suitable for biomass and the steady state CO2 concentrations will need to be more (less) in order to support a larger (smaller) biomass. The response is slow because it takes a while for natural sources of CO2 to arise and be accumulated by the biosphere. The variability of CO2 in the ice cores is really just a proxy for the size of the global biomass which happens to be temperature dependent.

The IPCC asserts that doubling CO2 is equivalent to 3.7 W/m2 of incremental, post albedo solar power and will result in a surface temperature increase of 3C based on a sensitivity of 0.8C per W/m2. An inconsistency arises because if the surface temperature increases by 3C, its emissions increase by more than 16 W/m2 so 3.7 W/m2 must be amplified by more than a factor of 4, rather than the factor of 1.6 measured for solar forcing. The explanation put forth is that the gain of 1.6 (equivalent to a sensitivity of about 0.3C per W/m2) is before feedback and that positive feedback amplifies this up to about 4.3 (0.8C per W/m2). This makes no sense whatsoever since the measured value of 1.6 W/m2 of surface emissions per W/m2 of solar input is a long term average and must already account for the net effects from all feedback like effects, positive, negative, known and unknown.

Another of the many problems with the feedback hypothesis is that the mapping to the feedback model used by climate science does not conform to two important assumptions that are crucial to Bode’s linear feedback amplifier analysis referenced to support the model. First is that the input and output must be linearly related to each other, while the forcing power input and temperature change output of the climate feedback model are not owing to the T4 relationship between the required input flux and temperature. The second is that Bode’s feedback model assumes an internal and infinite source of Joules powers the gain. The presumption that the Sun is this source is incorrect for if it was, the output power could never exceed the power supply and the surface power gain will never be more than 1 W/m2 of output per W/m2 of input which would limit the sensitivity to be less than 0.2C per W/m2.

Finally, much of the support for a high sensitivity comes from models. But as has been shown here, a simple gray body model predicts a much lower sensitivity and is based on nothing but the assumption that first principles physics must apply, moreover; there are no tuneable coefficients yet this model matches measurements far better than any other. The complex General Circulation Models used to predict weather are the foundation for models used to predict climate change. They do have physics within them, but also have many buried assumptions, knobs and dials that can be used to curve fit the model to arbitrary behavior. The knobs and dials are tweaked to match some short term trend, assuming it’s the result of CO2 emissions, and then extrapolated based on continuing a linear trend. The problem is that there as so many degrees of freedom in the model, it can be tuned to fit anything while remaining horribly deficient at both hindcasting and forecasting.

The results of this analysis explains the source of climate science skepticism, which is that IPCC driven climate science has no answer to the following question:

What law(s) of physics can explain how to override the requirements of the Stefan-Boltzmann Law as it applies to the sensitivity of matter absorbing and emitting energy, while also explaining why the data shows a nearly exact conformance to this law?

References

1) IPCC reports, definition of forcing, AR5, figure 8.1, AR5 Glossary, ‘climate sensitivity parameter’

2) Kevin E. Trenberth, John T. Fasullo, and Jeffrey Kiehl, 2009: Earth’s Global Energy Budget. Bull. Amer. Meteor. Soc., 90, 311–323.

3) Bode H, Network Analysis and Feedback Amplifier Design assumption of external power supply and linearity: first 2 paragraphs of the book

4) Manfred Mudelsee, The phase relations among atmospheric CO content, temperature and global ice volume over the past 420 ka, Quaternary Science Reviews 20 (2001) 583-589

5) Jouzel, J., et al. 2007: EPICA Dome C Ice Core 800KYr Deuterium Data and Temperature Estimates.

6) ISCCP Cloud Data Products: Rossow, W.B., and Schiffer, R.A., 1999: Advances in Understanding Clouds from ISCCP. Bull. Amer. Meteor. Soc., 80, 2261-2288.

7) “Diviner Lunar radiometer Experiment” UCLA, August, 2009

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January 5, 2017 6:14 pm

I’m particularly interested in answers to the question posed at the end of the article.
George

January 5, 2017 6:43 pm

There is no need explain an overriding of the law because there is no need to do so. The observed increase in temperature from a perfect black body to where we are today is entirely consistent with the law and can be estimated by anyone who has finished a second year heat transfer course. An exact calculation is more complex, but not beyond your average graduate mechanical engineer.

January 5, 2017 7:09 pm

And the same is true for a non ideal black body, also called a gray body. Unfortunately, consensus climate science fails to make this connection. They simply can’t connect the dots between the sensitivity of the gray body model and the claimed sensitivity which differ by about a factor of 4.

Germinio
January 6, 2017 12:08 am

The simple answer is probably that the Stefan Boltzmann law only applies to bodies in thermal equilibrium.
As long as the concentrations of CO2 are changing the earth is storing energy and will continue to do so for
several thousand years after CO2 levels stabilise (due to energy being stored in the ocean).
It should be also be pointed out that that neither Fig. 1 or Fig. 2 conserve energy. In each case there is
energy missing meaning that the analysis is wrong.

January 6, 2017 12:18 am

Germinio,
“As long as the concentrations of CO2 are changing …”
The planet has completely adapted to all prior CO2 emissions, except perhaps some of the emissions in the last 8-12 months. If the climate changed as slowly as it would need to for your hypothesis to be valid, we would not even notice seasonal change, nor would hemispheric temperature vary by as much as 12C every 12 months, nor would the average temperature of the planet vary by as much as 3C during any 12 month period.

Germinio
January 6, 2017 4:45 am

No. It just means that the earth has a fast and a slow response to any perturbations. Both together need
to be considered before any claims that the earth is in thermal equilibrium and that the Stefan Boltzmann
law can be applied.

george e. smith
January 6, 2017 10:15 am

Earth rotates. So it never ever will be in thermal equilibrium.
PS I agree with your assertion as to the necessity for equilibrium. It is not sufficient.
SB also assumes it is isothermal. Well silly me, so does thermal equilibrium require isothermality.
G

January 6, 2017 2:10 am

CART BEFORE HORSE?
Hi again Michael,
I wrote above:
“Atmospheric CO2 lags temperature by ~9 months in the modern data record and also by ~~800 years in the ice core record, on a longer time scale.”
In my shorthand, ~ means approximately and ~~ means very approximately (or ~squared).
It is possible that the causative mechanisms for this “TemperatureLead-CO2Lag” relationship are largely similar or largely different, although I suspect that both physical processes (ocean solution/exsolution) and biological processes (photosynthesis/decay and other biological) play a greater or lesser role at different time scales.
All that really matters is that CO2 lags temperature at ALL measured times scales and does not lead it, which is what I understand the modern data records indicate on the multi-decadal time scale and the ice core data records indicate on a much longer time scale.
This does not mean that temperature is the only (or even the primary) driver of increasing atmospheric CO2. Other drivers of CO2 could include deforestation, fossil fuel combustion, etc. but that does not matter for this analysis, because the ONLY signal that is apparent signal in the data records is the LAG of CO2 after temperature.
It also does not mean that increasing atmospheric CO2 has no impact on temperature; rather it means that this impact is quite small.
I conclude that temperature, at ALL measured time scales, drives CO2 much more than CO2 drives temperature.
Precedence studies are commonly employed in other fields, including science, technology and economics. The fact that this clear precedence is consistently ignored in “climate science” says something about the deeply held unscientific beliefs in this field – perhaps it should be properly be called “climate religion” or “climate dogma” – it just doesn’t look much like “science”.
Happy Holidays, Allan

Bob Osborn
January 6, 2017 8:25 am

Its not normal science. Its post normal science. The key characteristic of post normal science is to question the certainty of normal science. Its a reversal of the burden proof regarding our freedom to do things without first proving no harm. The pressure on this is occurring on every farm, home, beach, city in the world. Thus any amount of normal science suggesting that it is not likely that CO2 is a problem is going to be inadequate. The “sandpile” theory of Al Gore is the operative principle here. Catastrophe always results from piling sand too high. The fact that climate science fails is irrelevant. You must keep feeding the machine until they get it right. And of course they will never get it right because all the models will continue to feature CO2 as the operative principle of the greenhouse effect as they did in AR5 after the science opinion changed from all the warming to half the warming. The models continue to push for all. There are no science arguments to change this. The change can only occur politically and via retaining our culture of individual initiative.

Javert Chip
January 5, 2017 6:14 pm

Uh, those laws would be:
1) The law of unethical practitioner (given an accurate & accepted law of physics plus an unethical practitioner, results are unpredictable, usually catastrophically so)
2) The law of money (If you got money, I want some. When dealing with an an unethical practitioner, results are unpredictable, usually catastrophically so)
3) Stupid people (ok, those lacking minimal scientific training) can be tricked into believing stupid things. When manipulated by an unethical practitioner, results are unpredictable, usually catastrophically so)

noaaprogrammer
January 5, 2017 10:14 pm

You forgot the power law (I want to control you. When dealing with sheeple, results are predictable, they will worship and follow you even into catastrophes of their own doing.)

January 5, 2017 6:35 pm

So many mistakes in this I don’ t know where to start. If anyone wants an excellent and complete and relatively simple (for such a complicated concept) discussion of the science of CO2. I suggest taking Steve McIntyre’s advice and go visit scienceofdoom. This article isn’t sky dragons, but it is close.

January 5, 2017 6:40 pm

If you think there are so many errors, pick one and I’ll tell you why it’s not an error and we can go on to the next one. Better yet, answer the question.

January 5, 2017 6:54 pm

Figure one conflates absorptivity with emissivity. As drawn the proper coefficient is alpha, not epsilon. Though absorptivity is a function of emissivity, it isn’t the same thing and your figure is mistaken. I won’t carry on pointing out your other errors, minor and major. I’ve answered the question separately.

January 5, 2017 7:07 pm

Figure 1 places a wikipedia defined black body as its source and a wikipedia defined gray body between the black body and where the output is observed. If you keep reading and go on to figure 2, you will see a more proper diagram where the equivalence between atmospheric absorption and effective emissivity of the gray body model are related.
This is just another model and best practices for developing a model is to represent behavior in the simplest way possible. This way, there are fewer possibilities to make errors.

January 5, 2017 7:21 pm

Uhhh. Figure two is algebraically identical to figure one and still conflates emissivity with absorptivity.

January 5, 2017 7:30 pm

There is no conflation, although absorption and the EFFECTIVE emissivity of the gray body model are related to each other through equation 3.

January 5, 2017 7:31 pm

I got lost at Fig. 1. A black body source emits radiation – OK. A gray body filter absorbs it .. that’s only a half of the story, it also emits radiation back. You have to include this effect.

January 5, 2017 7:38 pm

Curious George,
Yes, you are correct and that point is addressed in Figure 2. Figure 1 simply uses the Wikipedia definitions of a black body and a gray body (one that doesn’t absorb all of the incident energy) to show how even the constrained Wikipedia definition of a gray body is just as valid for a gray body radiator and its this gray body radiator model that closely approximates how the climate system responds to incident energy (forcing), from which the sensitivity can be calculated exactly.

January 5, 2017 7:47 pm

I now look at Figure 2, assuming that the “Gray body atmosphere” is the “Gray body filter” of Fig. 1. In order to absorb all of the Black Body radiation, the Gray Body Filter would have to be black.
I have a feeling that you have a real message, but it needs work. In this form it does not get to me.

January 5, 2017 8:03 pm

Curious George,
The gray body atmosphere absorbs A, passes (1-A) and redistributes A half into space and half back to the surface. The ‘grayness’ is manifested by the (1 – A) fraction that is passed through. This is the unabsorbed energy the wikipedia definition of a gray body fails to account for.

January 5, 2017 8:00 pm

There is a box in the middle with an A. On the left there is Ps=σT^4. This is correct. On the right there are three equations with two arrows. The equation Po=Ps(1-A/2) is identical to Po=εσT^4, given that you have defined ε=(1-A/2) . This is wrong. For one thing, T atmosphere is not the same as T surface. Also, the transmitted energy is a function of absorptivity, not emissivity. The correct equation is Po=ασT^4. σ is not equal to ε. You are conflating emissivity and absorptivity. If we take the temperature of the gray body “surface” as T2, The what you are showing as Ps(A/2) is actually εσT2^4, but you have shown it to be εσT^4. T is not equal to T2. I could go on, but I won’t.

January 5, 2017 8:10 pm

John,
T atmosphere is irrelevant to this model. Only T surface matters. Beside, other than clouds and GHG’s, the emissivity of the atmosphere (O2 and N2) is approximately zero, so its kinetic temperature, that is, its temperature consequential to translational motion, is irrelevant to the radiative balance and corresponding sensitivity. You might also be missing the fact that the (1-A)Ps term is the power not absorbed by the gray body atmosphere, per the Wikipedia definition of a gray body (see the dotted line?).

Robert B
January 6, 2017 6:39 pm

“Figure one conflates absorptivity with emissivity. As drawn the proper coefficient is alpha, not epsilon. ”
Except – “To be consistent with the Wikipedia definition, the path of the energy not being absorbed is omitted.” so Figure 1 merely shows a blackbody has epsilon =1 and between 0 and 1 for the gray body. No conflating at all. Looks like you were just desperate to write “So many mistakes in this I don’ t know where to start.” rather than a honest mistake. I don’t have my glasses with me so I’ll refrain from giving it a thumbs up and i suggest that you give it a more thorough read before giving it a thumbs down.

David in Texas
January 6, 2017 10:00 am

John,
Could you recommend a video (30 to 45 min.) explaining the science and ramifications of CAGW? I have Dr. Dressler’s debate with Dr. Lindzen, but it’s a little old. I’d like your take on good video explaining CAWG.

January 5, 2017 6:45 pm

Robert Essenhigh developed a quantitative thermodynamic model of the atmosphere’s lapse rate based on the Stephan Boltzmann law:
“The solution predicts, in agreement with the Standard Atmosphere experimental data, a linear decline of the fourth power of the temperature, T^4, with pressure, P, and, at a first approximation, a linear decline of T with altitude, h, up to the tropopause at about 10 km (the lower atmosphere).” Prediction of the Standard Atmosphere Profiles of Temperature, Pressure, and Density with Height for the Lower Atmosphere by Solution of the (S-S) Integral Equations of Transfer and Evaluation of the Potential for Profile Perturbation by Combustion Emissions. Energy & Fuels, (2006) Vol 20, pp 1057-1067. http://pubs.acs.org/doi/abs/10.1021/ef050276y
Cited by

January 5, 2017 6:53 pm

How does this apply here? The only temperature in the model is the surface temperature which is at 1 ATM is still subject to the T^4 relationship. The model doesn’t care about how energy is redistributed throughout the atmosphere, just about how that energy is quantified at the boundaries and that from a macroscopic point of view of those boundaries, not only does it behave like a gray body, it must.

January 6, 2017 5:40 am

co2isnotevil. Essenhigh’s equations enable validating and extending White’s model. Earth’s average black body radiation temperature is not from at surface but in the atmosphere. White states:

Modeling the planet as an ideal black body emitting 240 W/m2 results in an equivalent temperature of 255K and a sensitivity of about 0.27K per W/m2 which is the slope of the black curve and slightly less than the equivalent gray body sensitivity represented as a green line on the black curve.

Essenhigh calculates temperature and pressure with elevation. He includes average absorption/emission of H2O and CO2 as the two primary greenhouse gases:

Allowing also for the maximum absorption percentages, R°, of these two bands for
the two gases, respectively, 39% for water and 8.5% for CO2, these values then support the dominance of water (as gas and not vapor) at about 80%, compared with CO2 at about 20%, as the primary absorbing/emitting (“greenhouse”) gas in the atmosphere.

From these, a detailed thermodynamic climate sensitivity could calculated from Essenhigh’s equations.

January 5, 2017 6:46 pm

George says with regard to incoming energy : “If more arrives than is emitted, the temperature increases until the two are in balance.”

This is not necessarily true, especially when considering what happens when the incoming energy melts ice or evaporates water. The temperature remains constant while energy is absorbed, until the ice completely melts, or the water completely evaporates. Only after melting or evaporation ends can the temperature of the remaining mass begin to increase. Since there is both a lot of ice, and a lot of water on the planet earth, this presents a problem with this over-simplified model of the temperature response of our planet to incoming energy from the sun.

January 5, 2017 6:58 pm

Rob,
Consider the analysis to be an LTE analysis averaged across decades or more. The seasonal formation and melting of ice, evaporation of water and condensation as rain all happens in approximately equal and opposite amounts and more or less cancel. Any slight imbalance is too far in the noise to be of any appreciable impact. There’s also incoming energy turned into work that’s not heat. Consider the origin of hydroelectric power, although it eventually turns into heat when you turn on your toaster.

January 5, 2017 7:10 pm

You have a point there co2isnotevil, consider the electromagnetic emissions visible in this picture. They do not follow the Stf-Boltz temperature relationship. They are not toasters, but a lot of sodium vapor lamps. http://spaceflight.nasa.gov/gallery/images/station/crew-30/hires/iss030e010008.jpg

January 5, 2017 7:28 pm

Even LED’s emit heat, but isn’t the light still just photons leaving the planet?

January 5, 2017 7:36 pm

Sodium vapor lamps and LEDs do not produce photons like an incandescent lamp. Since an incandescent lamp is using heat to generate the photons, it follows the Stf-Bltz equations. Yes the sodium vapor lamps and LEDs produce small amounts of heat, but they are not using heat to generate the photons they emit. So the emissions you see in the picture, being mostly sodium vapor lamps and powered by a hydroelectric dam, would not follow the Stf-Bltz law.

January 5, 2017 7:52 pm

Rob,
So, the biggest anthropogenic influence by man is emitting light into space (Planck spectrum or not) which means that less LWIR must leave for balance and the surface cools. Before man, the biggest influence came from fireflies.
I think you’re confusing whether its a Planck spectrum or not with whether or not its emitted energy must conform to the SB Law. Consider that the clear sky emissions of the planet have a color temperature representing the surface temperature, but have an SB equivalent temperature that is lower owing to attenuation in GHG absorption bands.
In effect, we can consider a sodium lamp (or even a laser) a gray body emitter with lots of bandwidth completely attenuated from its spectrum accompanied with broad band attenuation making it seem the proper distance away such that the absolute energy emitted by the lamp measured at some specific distance matches what would be expected based on the color temperature of the lamp.

January 5, 2017 8:01 pm

You missed the point co2isnotevil. The Stf-Blz analysis is inappropriate for the earth system, because there are numerous ways that incoming solar energy is stored/distributed on Earth than is reflected by a temperature differential. My point is that the analysis in this article neglects important details that make the analysis invalid.

January 5, 2017 8:12 pm

Rob,
My point is that the exceptions are insignificant, relative to the required macroscopic behavior. Biology consumes energy as well and turns it into biomass. But you add all this up and you will be hard pressed to find more than 1%.

January 5, 2017 8:05 pm

Consider this co2isnotevil: The ” ε ” value for the Earth is not constant, but is a non-linear function of T. The best example would be comparing the ” ε ” value for Snowball Earth, versus the ” ε ” for Waterworld.

January 5, 2017 8:28 pm

Rob,
Absolutely the emissivity is a function of T and here it that function:
None the less, in LTE and averaged across the planet, it has an average value and that’s all I’m considering here. The only sensitivity that matters is the long term change in long term averages. Because my analysis emphasizes sensitivity in the energy domain (ratios of power densities), rather than the temperature domain (IPCC sensitivity), the property of superposition makes averages more meaningful.
You can also look here to see other relationships between the variables provided by and derived from the ISCCP cloud data set. Of particular interest is the relationship between post albedo input power and the surface temperature, whose slope is about 0.2C per W/m^2. Where this crosses with the relationship between planet emissions and temperature is where the average is.

mellyrn
January 5, 2017 11:03 pm

“Biology consumes energy as well and turns it into biomass.”
co2isnotevil, how much energy is “consumed” by increasing the volume of the atmosphere? Warmed gases expand, yes? It’s something I’ve not seen addressed, though maybe I missed it.

January 5, 2017 11:13 pm

mellyrn,
“Warmed gases expand, yes?”
Yes, warmed gases expand and do work against gravity, but it’s not enough to be significant relative to the total energies involved.

Keith J
January 6, 2017 6:00 am

What a load of complications you present. Lapse rate, can you explain it? Why is the stratosphere, well, stratified? How about that pesky lapse rate back at its shenanigans in the mesosphere? And then stratification again in the thermosphere?
These questions persist because some think they know the answer but have not questioned assumptions. Just like assuming no bacteria could live at a pH of under 1 and with all sorts of digestive enzymes. ..helicobacter pylon ring a bell?

January 6, 2017 9:22 am

Keith,
“Lapse rate, can you explain it?”
Gravity. None the less, as I keep trying to say, what happens inside the atmosphere is irrelevant to the model. This is a model of the transfer function between surface temperature and planet emissions. The atmosphere is a black box characterized by the behavior at its boundaries. As long as the model matches at the boundaries, how those boundaries get into the state they are in makes no difference. This is standard best practices when it comes to reverse engineering unknown systems.
Anyone who thinks that the complications within the atmosphere have any effect, other than affecting the LTE surface temperature which is already accounted for by the analysis, is over thinking the problem. Part of the problem is that consensus climate science adds a lot of unnecessary complication and obfuscation to framing the problem. Many are bamboozled by the complexity which blinds them to the elegant simplicity of macroscopic behavior conforming to macroscopic physical laws.

January 10, 2017 7:15 am

My point is that the exceptions are insignificant,

No they are not insignificant, they’re the cause of the changing emissivity in your graph.
It is sign of regulation.

January 10, 2017 8:50 am

micro6500,
“they’re the cause of the changing emissivity in your graph.”
I’ve identified the largest deviation (at least the one around 273K) as the consequence of the water vapor GHG effect ramping up and not as the result of the latent heat consequential to a phase change. The former represents a change to the system, while the later represents an energy flux that the system responds to. Keep in mind that the gray body model is a model of the transfer function that quantifies the causality between the behavior at the top of the atmosphere and the bottom. This transfer function is dependent on the system, and not the specific energy fluxes and at least per the IPCC, the sensitivity is defined by the relationship between the top (forcing) and bottom of the atmosphere (surface temp).

January 10, 2017 9:28 am

This transfer function is dependent on the system

I understand.
I’m just pointing out that there is a physical reason for emissivity to be changing, it is the atm adapting to the differing ratios of humidity and temperature as you sweep from equator to pole and the day to day swings in temp (which everyone seems to want to toss out!). The big dips are where the limits of the regulation are reached because you’ve hit the min and max temps of your working “fluid”. But in between, you’ve seeing the blend of 2 emissivity rates getting averaged.
Do all of the measurements line up on a emissivity line in Fig 3?
So what I haven’t solved is the temp/humidity map that defines outoging average radiation for all conditions of humidity under clear skies. In the same black box fashion, if you have an equation that defines that line in Fig 3 (instead of an exp regression of the data points), a physical equation based on this changing ratio, would have to have the same answer, right.

January 10, 2017 9:42 am

micro6500,
“if you have an equation that defines that line in Fig 3”
The green line in Figure 3 is definitely not a regression of the data, but the exact relationship given by the SB equation with an emissivity of 0.62 (power on X axis, temp on Y axis). It’s equation 1 in the post.

January 10, 2017 10:14 am

The green line in Figure 3 is definitely not a regression of the data, but the exact relationship given by the SB equation with an emissivity of 0.62 (power on X axis, temp on Y axis). It’s equation 1 in the post.

So the average of this is about e=.62?

January 10, 2017 11:08 am

Yes, the average EQUIVALENT emissivity is about 0.62. To be clear, this is related to atmospheric absorption by equation 3 and atmospheric absorption can be calculated with line by line simulations which gets approximately the same value of A corresponding to an emissivity of 0.62 (within the precision of the data). So in effect, both absorption (emissivity of the gray body atmosphere) and the effective emissivity of the system can be measured and/or calculated to cross check each other.

January 5, 2017 7:33 pm

Rob, you are attempting to apply local physical conditions to a global radiation model of limits on the radiation. The energy that goes to melting ice or evaporating water stays in the system, without changing the system temperature until it affects one or both of the physical boundaries- the surface or the upper atmosphere emissions.

January 5, 2017 7:38 pm

Seeing that oceans comprise almost 70% of the surface of the planet, you cannot call them “local.”

Keith J
January 6, 2017 6:10 am

Condensation happens around 18000 feet above MS on average. That corresponds to the halfway point on atmospheric mass distribution. It is also where flight levels start in the US because barometric altimetry gets dicey and one must rely on in route ATC to maintain separation …enough aviation, back to meat and taters.
Average precipation is about 34″ rain per year. The enthalpy escapes sensible quantification via thermometry but once at 18,000 feet, it heats the upper troposphere and even some of the coldest layers of the stratosphere where it RISES…

Richard Petschauer
January 5, 2017 9:33 pm

This is not quite true. Ice colder than the melting point will warm. Evaporation of water will only change if it warms (for a given humidity). The cooling effect of the evaporation will reduce the warming but not eliminate it. This misunderstanding is behind the reason the large negative feedback effect of evaporation cooling is largely ignored. Latent heat is moved from the surface (mostly the oceans) to the clouds when it condenses.and part is radiated to space from cloud tops.

January 5, 2017 9:47 pm

Richard,
Covered this in a previous thread, but the bottom line is that the sensitivity and this model is all about changes to long term averages that are multiples of years. Ice formation and ice melting as well as water evaporation and condensing into rain happens in nearly equal and opposite amounts and any net difference is negligible relative to the entire energy budget integrated over time.

January 5, 2017 6:49 pm

“Atmospheric GHG’s and clouds absorb energy from the surface, while geometric considerations require the atmosphere to emit energy out to space and back to the surface in roughly equal proportions.”
It goes wrong there. It’s true very locally, and would be true if the atmosphere were a thin shell. But it’s much more complex. It is optically dense at a lot of frequencies, and has a temperature gradient (lapse rate). If you think of a peak CO2 emitting wavelength, say λ = 15 μ, then the atmosphere emits upward in the λ range at about 225K (TOA). But it emits to the surface from low altitude, at about 288K. It emits far more downward than up.

January 5, 2017 7:02 pm

Nick,
The atmosphere is a thin shell, at least relative to the BB surface beneath it.
You should also look at the measured emission spectrum of the planet. Wavelengths of photons emitted by the surface that would be 100% absorbed show significant energy from space, even in the clear sky. In fact, the nominal attenuation is about 3db less then it would be without absorption lines.

January 5, 2017 8:18 pm

George,
The atmosphere is optically thick at the frequencies that matter. Mean free path for photons can be tens of metres. But the more important issue is temperature gradient. You want to use S-B; what is T? It varies hugely through this “thin shell”.

January 5, 2017 8:35 pm

NIck,
The atmosphere is optically thick to the relevant wavelengths only when clouds are present, but not the emissions of the clouds themselves. The clear sky lets about half of all the energy emitted by the surface pass into space without being absorbed by a GHG and more than half of the emissions by clouds owing to less water vapor between cloud tops and space. The nominal attenuation in saturated absorption bands is only about 3db (50%) owing to the nominal 50/50 split of absorbed energy.
The atmospheric temperature gradient is irrelevant for the reasons I cited earlier. The model is only concerned with the relationship between the energy flux at the top and bottom of the atmosphere. How that measured and modelled relationship is manifested makes no difference.

January 5, 2017 7:12 pm

Being Canadian, I have to say. . . . Eh? Are you suggesting that the direction of radiation from any particular particle is not completely random? Given that the energy emitted by the heated particles decreases with temperature and temperature decreases with altitude, I can’t see how emissions are preferentially directed downward. The hottest stuff is the lowest. Heat moves from hot to cool. The heat move up, not down. As do the emissions. Emissive power decreases with temperature. For any particular molecule, the odds that the energy will go to space are the same as the odds it will go to ground. I’m missing something Nick.

January 5, 2017 7:37 pm

Nick. Never mind. I see it. For others. Consider a co2 molecule at 10 meters. It gets hit by a photon from the surface. It can radiate the energy from that photon in any direction. Now consider a molecule at twenty meters. It too gets hit by a photon from the surface. It is also possible for that molecule to get hit by the photon emitted by the molecule at 10 meters. There are more molecules at 10 meters than at twenty, so there is more emission downwards. Over 10’s of meters this is hard to measure. Over 10 kilometres, a bit less. Of course the odds of the molecule at 20 meters seeing a photon are less because some of those were absorbed at 10 meters. Also, the energy of the photons emitted by the molecules at 10 meters is lower because the temperature is lower. Have you done the math Nick? Is it a wash, or is there more downward emission?

January 5, 2017 7:59 pm

John,
The density profile doesn’t really matter because the ‘excess’ emission downward are still subject to absorption before they get to the surface and upward emissions have a lower probability of being absorbed,
Also, as I talked about in the article, if the atmosphere absorbs more than about 75% of the surface emissions, then less than half is returned to the surface. If the atmosphere absorbs less than 75% of the surface emissions, then more than half must be returned to the surface. My line by line simulations of a standard atmosphere with average clouds gets a value of A about 74.1%, so perhaps slightly more than half is returned to the surface, but it’s within the margin of error. Two different proxies I’ve developed from ISCCP data show this ratio to bounce around 50/50 by a couple of percent.

January 5, 2017 7:45 pm

John, a photon at 15 μ carries the same energy regardless of the bulk temperature of the gas. The energy increases directly with the frequency. Due to collisions some molecules always have a higher energy and can emit a photon. The frequency of the photon depends on what is emitting the photon and how the energy is distributed among the electrons in the molecule or atom. The energy of the photon doesn’t depend on the temperature, but the number emitted/volume does.

January 6, 2017 8:11 am

My line by line simulations of a standard atmosphere with average clouds gets a value of A about 74.1%, so perhaps slightly more than half is returned to the surface, but it’s within the margin of error.

Does this evolve the atm conditions second by second? If it’s just a static snapshot it is meaning less.

January 6, 2017 9:49 am

“Does this evolve the atm conditions second by second?”
Not necessary, but is based on averages of data sampled at about 4 hour intervals for 3 decades.
Sensitivity represents a change in long term averages and that is all we should care about when considering what the sensitivity actually is.

January 6, 2017 10:04 am

Then it’s wrong, the outgoing cooling rate changes at night as air temps near dew point, it is not static. You can not just average this into a “picture” of what’s happening. This is another reason the results are so wrong.

January 6, 2017 10:22 am

micro6500,
“You can not just average …”
Without understanding how to properly calculate averages, any quantification of the sensitivity is meaningless and quantifying the sensitivity is what this is all about.

January 6, 2017 10:32 am

Actually sensitivity has to be very low, Min temps are only very minimally effected by co2, it’s 98-99% WV.

January 5, 2017 8:14 pm

John,
The main thing to remember is not so much the concentration gradient, but the temperature gradient. Your notion of a CO2 molecule re-radiating isn’t quite right. GHG molecules that absorb mostly lose the energy through collision before they can re-radiate. Absorption and radiation are decoupled; radiation happens as it would for any gas at that temperature.
At high optical density (say 15 μ), a patch of air radiates equally up and down. Absorption is independent of T. But the re-emission isn’t. What went down is absorbed by hotter gas, and re-emitted at higher intensity.
There is a standard theory in heat transfer for the high optical density case, called Rosseland radiation. The radiant transfer satisfies the diffusion equation. Flux is proportional to temperature gradient, and the conductivity is inversely proportional to optical depth (mean path length). This works as long as most of the energy is reabsorbed before reaching surface or space. Optical depth>3 is a rule of thumb, although the concept is useful lower. It’s really a grey body limit – messier when there are big spectral differences.
“Have you done the math Nick? Is it a wash, or is there more downward emission?”
I think the relevant math is what I said above. Overall, warmer emits more, and the emission reaching the surface is much higher than that going to space, just based on temp diff.

January 6, 2017 8:14 am

At issue is it’s not static during the night, it changes as air temps cool toward dew point, as water vapor takes over the longer wave bands (the optical window doesn’t change temp).

Bob boder
January 6, 2017 11:18 am

Nick
GHG molicules also absorb energy through collision, gas what they do with that energy.

Alex
January 5, 2017 10:22 pm

Nick
The atmosphere is a gas and therefore doesn’t emit blackbody/ graybody radiation. It only emits spectral lines. If you are considering particles like dust and water( in liquid and solid phase) then it can emit BB/GB radiation.

January 5, 2017 10:34 pm

Alex,
“It only emits spectral lines.”
Yes, but even more importantly, only a tiny percent of the gas molecules in the atmosphere have spectral lines in the relevant spectra.
Oddly enough, many think that GHG absorption is rapidly ‘thermalized’ into the kinetic energy of molecular motion which would make it unavailable for emission away from the planet (O2/N2 doesn’t emit LWIR photons) and given that only about 90 W/m^2 gets through the transparent window (Trenberth claims even less), it’s hard to come up with the 145 W/m^2 shortfall without substantial energy at TOA in the absorption bands.

Alex
January 6, 2017 12:21 am

I don’t like the term ‘thermalised’. It implies a one way direction when in fact it isn’t. Molecules can lose vibrational energy through collision, they can also obtain rotational energy through collision. It goes equally both ways. Emission and absorption are also equal. A complex interchange but always in balance(according to probability of course).
It’s all a matter of detection. Most people (including scientists) don’t know how stuff works. They are basically lab rats that don’t have a clue. They don’t need to know, they just do their job accurately and precisely. Unfortunately the conclusions they draw can be totally erroneous.
If you imagine a molecule as a sphere then it will emit in any direction. In fact over 41,000 directions if the directions are 1 deg wide. Good luck having a detector in the right place to do that. that’s why it’s easier to use absorption spectroscopy. All energy comes from one direction and there are enough molecules to ‘get in the way’ and absorb energy. There is no consideration for emission, which can be in any direction and undetectable.
The instrumentation is perfect for finding trace quantities of molecules and things. Absolutely useless for determining the total energy emitted by molecules.
Anyone who thinks they can determine emission and energy transfer through this method should have their eye removed with a burnt stick.

george e. smith
January 6, 2017 2:24 pm

Everything that is above zero K Temperature emits thermal radiation; including all atmospheric gases.
It’s called thermal radiation because it depends entirely on the Temperature and is quite independent of any atomic or molecular SPECTRAL LINES.
Its source is simply Maxwell’s equations and the fact that atoms and molecules in collision involve the acceleration of electric charge.
An H2 molecule essentially has zero electric dipole moment, because the positive charge distribution and the negative charge distribution both have their center of charge at the exact same place.
But during a collision between two such molecules (which is ALL that “heat” (noun) is), the kinetic energy and the momentum is concentrated almost entirely in the atomic nuclei, and not in the electron cloud.
The proton and the electron have the same magnitude electric charge (+/-e) but the proton is 1836 times as massive as the electron, so in a collision it is the protons that do the billiard ball collision thing, , and the result is a separation (during the collision) of the +ve charge center, and the negative charge center due to the electrons. and that results in a distortion of the symmetry of the charge distribution which results in a non-zero electric dipole moment, so you get a radiating antenna that radiates a continuum spectrum based on just the acceleration of the charges. There also are higher order electric moments, which might be quadrupolar, Octopolar or hexadecapolar moments, and they all can make very fine radiating antennas.
Yes the thermal radiation from gases is low intensity but that is because the molecular density of gases is very low. They are highly transparent (to at least visible radiation) which is why their thermal radiation isn’t black body Stefan-Boltzmann or Planck spectrum radiation.
Some of the 4-H club physics that gets bandied about in these columns, makes one wonder what it is they teach in schools these days. Well I guess I actually know that since I am married to a public school teacher.
G

January 6, 2017 3:18 pm

George E. Smith,
“Everything that is above zero K Temperature emits thermal radiation; including all atmospheric gases.”
Not at any relevant magnitude relative to LWIR and it can be ignored. In astrophysics, the way gas clouds are detected is by either emission lines if its hot enough or absorption lines of a back lit source if its not. The problem is that the kinetic energy of an atmospheric O2/N2 molecule in motion is about the same as an LWIR photon, so to emit a relevant photon, it would have to give up nearly all of its translational energy. If only laser cooling could be this efficient.
A Planck spectrum arises as molecules with line spectra merge their electron clouds forming a liquid or solid and the degrees of freedom increase as more and more molecules are involved. This permits the absorption and emission of photons that are not restricted to be resonances of an isolated molecules electron shell. In one sense, its like extreme collisional broadening.
Have you tried collision simulations based on nothing but the repulsive force of one electron cloud against another? The colliding molecules change direction at many atomic radii away from where the electrons get close enough to touch/merge. As they cool, they can get closer and the outer electron shells merge which initiates the phase change from a gas to a liquid. In fact, nearly all interactions between atoms and molecules occurs in the outer most electron shell.

angech
January 6, 2017 1:44 am

Nick StokesJanuary 5, 2017 at 6:49 pm
“Atmospheric GHG’s and clouds absorb energy from the surface, while geometric considerations require the atmosphere to emit energy out to space and back to the surface in roughly equal proportions.”
It goes wrong there. It’s true very locally, and would be true if the atmosphere were a thin shell. But it’s much more complex. It is optically dense at a lot of frequencies, and has a temperature gradient (lapse rate). If you think of a peak CO2 emitting wavelength, say λ = 15 μ, then the atmosphere emits upward in the λ range at about 225K (TOA). But it emits to the surface from low altitude, at about 288K. It emits far more downward than up.””

Nick. It goes wrong there. When you write, ” It emits far more downward than up.”
Surfaces emit upwards by definition. Very hard to emit anything when it goes inwards instead of outwards.
Nonetheless atoms and molecules emit in all directions equally.
Hence the atmosphere, not being a surface, at all levels emits upwards, downwards and sideways equally.
What you are trying to say, I guess is that there is a lot of back radiation of the same energy before it finally gets away.
This does not and cannot imply that anything emits more downwards than upwards. Eventually it all flows out the upwards plughole [vacuum], while always emitting equally in all directions except from the surface.

RW
January 6, 2017 7:28 am

Nick,
“It goes wrong there. It’s true very locally, and would be true if the atmosphere were a thin shell. But it’s much more complex. It is optically dense at a lot of frequencies, and has a temperature gradient (lapse rate). If you think of a peak CO2 emitting wavelength, say λ = 15 μ, then the atmosphere emits upward in the λ range at about 225K (TOA). But it emits to the surface from low altitude, at about 288K. It emits far more downward than up.”
Yes, significantly more IR is passed to the surface from the atmosphere than is passed from the atmosphere into space, due to the lapse rate. Roughly a ratio of 2 to 1, or about 300 W/m^2 to the surface and 150 W/m^2 into space. However, if you add these together that’s a total of 450 W/m^2. The maximum amount of power that can be absorbed by the atmosphere (from the surface), i.e. attenuated from being transmitted into space, is about 385 W/m^2, which is also the net amount of flux that must exit the atmosphere at the bottom and be added to the surface in the steady-state. By George’s RT calculation, about 90 W/m^2 of the IR flux emitted by the surface is directly transmitted into space, leaving about 300 W/m^2 absorbed. This means that the difference of about 150 W/m^2, i.e. 450-300, must be part of a closed flux circulation loop between the surface and atmosphere, whose energy is neither adding or taking away joules from the surface or nor adding or taking away joules from the atmosphere.
Remember, not all of the 300 W/m^2 of IR passed to the surface from the atmosphere is actually added to the surface. Much of it is replacing non-radiant flux leaving the surface (primarily latent heat), but not entering the surface. The bottom line is in the steady-state, any flux in excess of 385 W/m^2 leaving or flowing into the surface must be net zero across the surface/atmosphere boundary.
George’s ‘A/2’ or claimed 50/50 split of the absorbed 300 W/m^2 from the surface, where about half goes to space and half goes to the surface, is NOT a thermodynamically manifested value, but rather an abstract conceptual value based on a box equivalent model constrained by COE to produce a specific output at the surface and TOA boundaries.
Just because the atmosphere as a whole mass emits significantly more downward to the surface and upwards into space does NOT mean upwelling IR absorbed somewhere within has a greater chance of being re-radiated downwards than upwards. Whether a particular layer is emitting at 300 W/m^2 or 100 W/m^2, if 1 additional W/m^2 from the surface is absorbed, that layer will re-emit +0.5 W/m^2 and +0.5 W/m^2 down. The re-emission of the absorbed energy from the surface, no matter where it goes or how long it persists in the atmosphere, is henceforth non-directional, i.e. occurs with by and large equal probability up or down. And it is this re-radiation of absorbed surface IR back downwards towards (and not necessarily back to) the surface that is the physical driver of the GHE or the underlying mechanism of the GHE. NOT the total amount of IR the atmosphere as a whole mass passes to the surface.
The physical meaning of the ‘A/2’ claim or the 50/50 equivalent split is that not more than about half of what’s captured by GHGs (from the surface) is contributing to downward IR push in the atmosphere that ultimately leads to the surface warming, where as the other half is contributing to the massive cooling push the atmosphere makes by continuously emitting IR up at all levels. Or only about half of what’s initially absorbed is acting to ultimately warm the surface, where as the other half is acting to ultimately cool the system and surface.

RW
January 6, 2017 7:30 am

This was supposed to say:
“Just because the atmosphere as a whole mass emits significantly more downward to the surface THAN upwards into space does NOT mean upwelling IR absorbed somewhere within has a greater chance of being re-radiated downwards than upwards.”

RW
January 6, 2017 7:32 am

This also was supposed to say:
“Whether a particular layer is emitting at 300 W/m^2 or 100 W/m^2, if 1 additional W/m^2 from the surface is absorbed, that layer will re-emit +0.5 W/m^2 UP and +0.5 W/m^2 down.”

January 6, 2017 8:36 am

” It emits far more downward than up.”
Photons are emitted equally in all directions. At optical thickness below 300 meters the atmosphere radiates as a blackbody. CO2 is absorbing and emitting (and more importantly kinetically warming the transparent bulk of the atmosphere) according to its specific material properties all the while throughout this 300m section.
The specific material property of CO2 is that it is a very light shade of greybody. It absorbs incredibly well, but re-radiates only a fraction of the incident photons. It transfers radiation poorly. Radiative transfer, up or down, is simply not how it works in the atmosphere.

Clif westin
January 6, 2017 9:45 am

Admittedly, a bit out of my depth here. “Photons are emitted equally in all direction”. Is this statement impacted by geometry? By this I mean, aren’t both the black body and grey body spherical or at least circular?

January 6, 2017 10:19 am

Clif,
‘”Is this statement impacted by geometry?”
Absolutely and this explains the roughly 50/50 split between absorbed energy leaving the planet or being returned to the surface.
It’s for the same reason that we consider the average input about 341 W/m^2 and not 1366 W/m^2 which is the actual flux arriving from the Sun. It just arrives over 1/4 the area over which its ultimately emitted.

January 7, 2017 8:38 am

A blackbody has no inherent dimension or shape. It is just a concept. The word “radiation” itself implies circularity, but that’s just the way we like to think of something that goes in every imaginable direction equally.

January 6, 2017 10:08 am

gymnosperm,
“It absorbs well, but re-radiates only a fraction of the incident photons.”
Not necessarily so. The main way that an energized CO2 molecule returns to the ground state is by emitting a photon of the same energy that energized it in the first place and a collision has a relatively large probability of resulting in such emission. It’s a red herring to consider that much of this is ‘thermalized’ and converted into the translation energy of molecules in motion. If this was the case, we would see little, if any, energy in absorption bands at TOA since that energy would get redistributed across the whole band of wavelengths, nor would we see significant energy in absorption bands being returned to the surface. See the spectrums Nick posted earlier in the comments.

January 7, 2017 8:18 am

CO2 has only one avenue from the ground state to higher vibrational and rotational energy levels. This avenue is the Q branch and it gets excited at WN 667.4. This fundamental transition is accompanied by constructive and destructive rotations that intermittently occupy the range between 630 and 720. CO2 also has other transitions summarized below.
“Troposphere” was a mental lapse intended as tropopause, but I have left it because it is interestingly true.
If you are measuring light transmission through a gas filled tube and you switch off 667.4, all the other transitions must go dark as well.
The real world is not so simple and there are lots ways for molecules to gain energy.
It is well known that from ~70 kilometers satellites see CO2 radiating at the tropopause. This is quite remarkable because it is also well known that CO2 continues to radiate well above the tropopause and into the mesosphere.
The point here is that the original source of 667.4 photons is the earth’s surface. In a gas tube it is impossible to know if light coming out the other end has been “transmitted” as a result of transparency, or absorption and re-emission. What we do know is that within one meter 667.4 is virtually extinguished and the tube warms up.
The fate of a 667.4 photon leaving the earth’s surface is the question. The radiative transfer model will have it being passed between layers of the atmosphere by absorption and re-emission like an Australian rules football…

January 10, 2017 8:36 am

The fate of a 667.4 photon leaving the earth’s surface is the question. The radiative transfer model will have it being passed between layers of the atmosphere by absorption and re-emission like an Australian rules football…

I think it’s quite possible that it really doesn’t do much until water vapor starts condensing, which has a lot of node in the 15u area, so during condensing events, the water is an bright emitter, and it could stimulate the co2 @ 15u. The stuff that goes on inside gas lasers……

January 10, 2017 10:24 am

Yes.
And the satellites looking down see CO2 radiating at the tropopause, where absorption of solar radiation by ozone adds a lot of new energy. This in spite of looking down through~60 km of stratosphere reputedly cooling from radiating CO2.
http://jennifermarohasy.com/2011/03/total-emissivity-of-the-earth-and-atmospheric-carbon-dioxide/
There is a fascinating exchange between Nasif Nahle and Science of Doom.
SOD argues transmission = 1-absorption and what is absorbed must be transmitted.
Nasif calculates from measurements a column emissivity of .002, and then argues absorption must be similarly low.
Their arguments BOTH fail on Kirchoff’s law, which pertains only to blackbodies. CO2 is a greybody, a class of materials that DO NOT follow Kirchoff’s law.

January 10, 2017 11:30 am

SOD argues transmission = 1-absorption and what is absorbed must be transmitted.

It’s to simplistic a solution.

January 10, 2017 1:54 pm

“It’s to simplistic a solution.”
What’s not transmitted is absorbed and eventually re-transmitted.
The difference between transmission and re-transmission is that transmission is immediate and across the same area as absorption while re-transmission is delayed and across twice the area. It’s the delayed downward re-transmission that makes the surface warmer than it would be based on incident solar input alone. Clouds and GHG’s contribute to re-transmission where the larger effect is from clouds.

Gary G.
January 14, 2017 6:45 am

The only thing necessary to grasp in this perceived “torrent of words”, a tour de force unlike any on the matter, is George’s explication of the ‘gray body’.
It is that simple. Bravo.

KevinK
January 5, 2017 7:22 pm

Well, all of this “average” radiation calculation stuff is really good fun.
But, the correct way to analyze this problem is to follow each instance of a “ray” of light (with it’s corresponding energy) through a complex system and apply the known and very well verified laws of refraction, transmission, scattering, etc to each and every “ray” of light moving through the system.
Once this is done properly one quickly concludes that the “Radiative Greenhouse Effect” simply delays the transit time of energy through the “Sun/Atmosphere/Earth’s Surface/Atmosphere/Energy Free Void of the Universe” system by some very small time increment, probably tens of milliseconds, perhaps as much as a few seconds.
Given that there are about 86 million milliseconds (or 86,000 seconds) in each day this delay of a few tens/hundredths of milliseconds has NO effect on the average temperature at the surface of the Earth,
I again suggest that folks “read up” about how optical integrating spheres function. The optical integrating sphere exhibits what a climate scientist would consider nearly 100% forcing (aka “back-radiation”) and yet there is no “energy gain” involved,
Yes, a “light bulb” inside an integrating sphere will experience “warming” from “back radiation” and this will change it’s efficacy (aka efficiency). BUT in the absence of a “power supply”, a unit that can provide ‘unlimited” energy (within some bounds, say +/- 100%) this change in efficacy cannot raise the average temperature of the emitting body,
This is all well known stuff to folks doing absolute radiometry experiments. “Self absorption” (aka the green house effect) is a well known and understood effect in radiometry. It is considered a “troublesome error source” and means to quantify and understand it are known, if only to a small set of folks that consider themselves practitioners of “absolute radiometry”
Thanks for your post, Cheers KevinK.

angech
January 6, 2017 1:51 am

KevinK January 5, 2017 at 7:22 pm
But, the correct way to analyze this problem is to follow each instance of a “ray” of light (with it’s corresponding energy) through a complex system and apply the known and very well verified laws of refraction, transmission, scattering, etc to each and every “ray” of light moving through the system.
“Radiative Greenhouse Effect” simply delays the transit time of energy by some very small time increment, probably tens of milliseconds, perhaps as much as a few seconds.”
Kevin a slight problem is that that ray of light/energy package may actually hit millions of CO2 molecules on the way out. A few milliseconds no problems but a a thousand seconds is 3 hours which means the heat could and does stay around for a significant time interval. Lucky for us in summer I guess.

KevinK
January 6, 2017 8:08 pm

angech, please consider that light travels at 186,000 miles per second (still considered quite speedy). So even if it “collides” with a million CO2 molecules and gets redirected to the surface it’s speed is reduced to (about) 0.186 miles per second (186,000 / 1 million). That is still about 669 miles per hour (above the speed of sound, depending on altitude).
So, given that the vast majority of the mass of the atmosphere around the Earth is within ten miles of the surface, at ~669 miles per hour the “back radiation” has exited to the “energy free void of space” after 0.014 hours (10 miles / 669 mph) which equals (0.014 hours * 60 minutes/hr) = 0.84 minutes = (0.84 minutes * 60 minutes/second) = 50.4 seconds.
it is very hard to see how a worst case delay of ~50 seconds can be reasonably expected to change the “average temperature” of a system with a “fundamental period” of 86,400 seconds…..
Cheers, KevinK

January 9, 2017 10:18 am

KevinK,
“it is very hard to see how a worst case delay of ~50 seconds …”
While this kind of delay out into space has no effect, its the delay back to the surface that does it. Here’s a piece of C code that illustrates how past emissions accumulate with current emissions to increase the energy arriving at the surface and hence, its temperature. The initial condition is 240 W/m^2 of input and emissions by the surface, where A is instantly increased to 0.75. You can plug in any values of A and K you want.
#include
int main()
{
double Po, Pi, Ps, Pa;
int i;
double A, K;
A = 0.75; // fraction of surface emissions absorbed by the atmosphere
K = 0.5; // fraction of energy absorbed by the atmosphere and returned to the surface
Ps = 239.0;
Pi = 239.0;
Po = 0.0;
for (i = 0; i < 15; i++) {
printf("time step %d, Ps = %g, Po = %g\n", i, Ps, Po);
Pa = Ps*A;
Po = Ps*(1 – A) + Pa*(1 – K);
Ps = Pi + Pa*K;
}
}

January 6, 2017 8:16 am

Have you noticed the cooling rate at night decays exponentially?

KevinK
January 6, 2017 7:28 pm

micro, thanks for the compliment.
I have not considered the decay of the cooling rate. Seems like some investigation is needed, where do I apply for my grant money ???
Cheers, KevinK

January 9, 2017 5:42 am

If you find some, let me know. We’ll it looked like it was reaching equilibrium, but my ir thermometer kept telling me the optical window was still 80 to 100F colder, same as it was when it was cooling fast.

James at 48
January 5, 2017 7:31 pm

Thanks for doing physics here. It’s a great refresher. Some of it I’ve not revisited since I was at uni.

KevinK
January 5, 2017 7:40 pm

Ok, here are some references for folks to read at their leisure;
Radiometry of an integrating sphere (see section 3,7; “Transient Response”)
Tech note on integrating sphere applications (see section 1.4, “Temporal response of an Integrating Sphere”)
https://www.labsphere.com/site/assets/files/2551/a-guide-to-integrating-sphere-theory-and-applications.pdf
Note, Optical Integrating Spheres have been around for over a century, well known stuff, very little “discovery/study” necessary.
Another note; the ‘Transient Response” to an incoming pulse of light is always present, a continuous “steady state” input of radiation is still impacted by this impulse response. However the currently available radiometry tools cannot sense the delay when the input is “steady state”. The delay is there, we just cannot see/measure it.
Cheers, KevinK.

willhaas
January 5, 2017 8:04 pm

One also has to include the fact that doubling the amount of CO2 in the Earth’s atmosphere will slightly decrease the dry lapse rate in the troposphere which offsets radiative heating by more than a factor of 20. Another consideration is that H2O is a net coolant in the Earth’s atmosphere. As evidence of this the wet lapse rate is signifficlatly lower than the dry lapse rate. So the H2O feedback is really negative and so acts to diminish any remaining warming that CO2 might provide. Another consideration is that the radiant greenhouse effect upon which the AGW conjecture depends has not been obsered anywhere in the solar system. The radiant greenhouse effect is really ficititious which renders the AGW conjecture as ficititious. If CO2 really affected climate then one would xpect that the increase in CO2 over the past 30 years would have caused at least a measureable increase in the dry lapse rate in the troposphere but such has not happened.

Brett Keane
January 5, 2017 11:42 pm

@ willhaas
January 5, 2017 at 8:04 pm : Thanks, Wil.. Radiation is ineffective because of optical depth below 5km, except in the window. We do know that the faster and mightier conduction-thermalisation-water vapour convective and condensate path totally dominates in clearing the opaque bottom half of the troposphere, and then some.. As per Standard Atmospheres. But it still works on Venus and Titan, for starters.

J Mac
January 5, 2017 8:30 pm

A simple model, based on known physics and 1st principles, yields an estimate of ‘climate sensitivity’ that approximates physical evidence while illustrating (yet again) that climate sensitivity estimates from complex software models of planetary climate are unrealistically way too high!
Very interesting. Thank you, George White!

January 5, 2017 8:32 pm

It’s time to show some real spectra, and see what can be learnt. Here, from a text by Grant Petty, is a view looking up from surface and down from 20km, over an icefield at Barrow at thaw time.
If you look at about 900 cm^-1, you see the atmospheric window. The air is transparent, and S-B from surface works. In the top plot, the radiation follows the S-B line for about 273K, the surface tempeerature. An looking up, it follows around 3K, space.
But if you look at 650 cm^-1, a peak CO2 frequency, you see that it is following the 225K line. That is the temperature of TOA. The big bite there represents the GHE. It’s that reduced emission that keeps us warm. And if you look up, you see it following the 268K line. That is the temperature of air near rhe ground, which is where that radiation is coming from. And so you see that, by eye, the intensity of radiation down is about twice up.
In this range radiation from the surface (high) is disconnected from what is emitted at TOA.

January 5, 2017 8:41 pm

NIck,
You are conflating a Planck spectrum with conformance to SB. If you apply Wein’s displacement law the average radiation emitted by the planet, the color temperature of the planets emissions is approximately equal 287K while the EQUIVALENT temperature given by SB is about 255K owing to the attenuation you point out in the absorption bands. Moreover; as I said before, the attenuation in a absorption bands is only about 3db and it looks basically the same from 100km except for some additional ozone absorption.
Where do you think the 255K equivalent temperature representing the 240 W/m^2 emitted by the planet comes from?

January 5, 2017 9:13 pm

George,
“Where do you think the 255K equivalent temperature representing the 240 W/m^2 emitted by the planet comes from?”
It’s an average. As you see from this clear sky spectrum, parts are actually emitted from TOA (225K) and parts from surface (273K). If you aggregate those as a total flux and put into S-B, you get T somewhere between. Actually, it’s more complicated because of clouds, which replace the surface component by something colder (top of cloud temp), and because there are some low OD frequencies where the outgoing emission comes from various levels.
But the key thing is that you can’t make your assumption that the atmosphere re-radiates equally up and down. It just isn’t so.

January 5, 2017 9:27 pm

Nick,
“But the key thing is that you can’t make your assumption that the atmosphere re-radiates equally up and down. It just isn’t so.”
What do you think this ratio is if its not half up and half down?
The sum of what goes up and down is fixed and the more you think the atmosphere absorbs (Trenberth claims even more than 75%), the larger the fraction of absorption that must go up in order to acheive balance.

January 5, 2017 9:38 pm

George,
“What do you think this ratio is if its not half up and half down?”
It’s frequency dependent. At 650 cm^-1, in that spectrum, it is 100:55. But it would be different elsewhere (than Barrow in spring), and at other frequencies. There is no easy way to deduce a ratio; you just have to add it all up. But 1:1 has no basis.

January 5, 2017 9:53 pm

Nick,
“you just have to add it all up.”
Yes, and I’ve done this and its about 50/50, but it does vary spatially and temporally a little bit on either side and the as system varies this ratio, it almost seems like an internal control valve, none the less, it has a relatively unchanging long term average. But as I keep having to say, the climate sensitivity is all about changes to long term averages and long term averages are integrated over a whole number of years and over the relevant ranges of all the dependent variables they are dependent on.

January 6, 2017 8:20 am

it almost seems like an internal control valve

Alex
January 5, 2017 10:56 pm

The images are reading different things. Blind Freddy can see that they are the inverse of each other.
The only way you could get a spectrum like the 2nd image is by looking at the sun. Black space won’t give you that spectrum. Both images are looking through the atmosphere with a background ‘light’. Looking at the same thing -the atmosphere.
Please explain why the photons from the sun aren’t absorbed by the atmosphere while the photons from earth are.

January 6, 2017 12:25 am

“Black space won’t give you that spectrum.”
You aren’t seeing black space, except in the atmospheric window (around 900 cm^-1). You are seeing thermally radiating gases, mainly CO2 and H2O. Unless you are Blind Freddy.

Alex
January 6, 2017 12:34 am

Nick
Give me a link to the paper. I can’t find it. Don’t be rude. I actually like you, so don’t make enemies if you don’t have to. I feel that your ‘cut and paste’ from some source is biased (by someone). The 2 images you’ve shown are different. one is an emission spectrum and the other is an absorption spectrum. It’s clearly visible. I would like to reassure myself that the information is correct. I am certain that you would like some reassurance too

Alex
January 6, 2017 12:49 am

Nick
‘Please explain why the photons from the sun aren’t absorbed by the atmosphere while the photons from earth are.’

January 6, 2017 1:37 am

Alex,
“Give me a link to the paper. “
It’s a textbook, here. And yes, one spectrum is looking down, the other up. It shows the GHG complementary emission from near surface air and TOA.
“Please explain why the photons from the sun aren’t absorbed by the atmosphere “
We’re talking about thermal IR. There just aren’t that many coming from the sun in that range, but yes, they are absorbed in that range.
Someone will probably say that at all levels emission increases with temperature, so the sun should be emitting more. Well, it emits more per solid angle. You get more thermal IR from the sun than from any equivalent patch of sky. But there is a lot more sky. Thermal IR from sun is a very small fraction of total solar energy flux.

January 5, 2017 11:11 pm

Nick,
The other part of the question has not been addressed yet. While you don’t yet accept that the gray body model accurately reflects the relationship between the surface temperature and emissions of the planet and since in LTE Pin == Pout this relationship sets an upper bound on the sensitivity to forcing, how can you explain Figure 3 and especially the tight distribution of samples (red dots) around the predicted transfer characteristic (green line)? BTW, of all the plots I’ve done that show one climate variable against another, the relationship in Figure 3 has the tightest distribution of samples I’ve ever seen. It’s pretty undeniable.

January 6, 2017 12:32 am

” While you don’t yet accept that the gray body model accurately reflects the relationship between the surface temperature and emissions of the planet”
Because the concepts are all wrong. You confound surface temperature with equivalent temperature. The atmosphere is nothing like what you model. It has high opacity in frequency bands, at which it is also highly radiative. It has a large range of vertical temperature variation. Surface temperatures are very largely set by the amount of IR that is actually emitted by lower levels of the atmosphere. And they of course depend on the surface.
At times you seem to say that you are just doing Trenberth type energy accounting. But Trenberth has no illusions that his accounting can determine sensitivity. The physics just isn’t there.

January 6, 2017 12:40 am

“You confound surface temperature with equivalent temperature.”
The two track changes in each other exactly. It’s a simple matter to calibrate the absolute value.
“The atmosphere is nothing like what you model.”
I don’t model the atmosphere, I model the relative relationship between the boundaries of that atmosphere. One boundary at the surface and another at TOA. What happens between the surface and TOA are irrelevant, all the model cares about is what the end result is.
“It has high opacity in frequency bands, at which it is also highly radiative. It has a large range of vertical temperature variation.”
This is why averages are integrated across wavelength and other dependent variables. This way, the averages are wavelength independent as are all the other variables.
“Surface temperatures are very largely set by the amount of IR that is actually emitted by lower levels of the atmosphere.”,
No. Surface temperature are set by the amount of IR the surface radiates and absorbs, which in the steady state are equal. If it helps, consider a water world and/or worlds without water, GHG’s and/or atmospheres.

RW
January 6, 2017 8:18 am

Nick,
Another way of looking at this:
The total IR flux emitted by the surface which is absorbed by the atmosphere is roughly 300 W/m^2, which happens to (coincidently) be roughly the same as the amount of IR the atmosphere as a whole mass passes to the surface.
You don’t really think or believe the contribution of 300 W/m^2 of DLR at the surface is entirely sourced from and driven by the re-radiation of this 300 W/m^2 initially absorbed by the atmosphere from the surface, do you? Clearly there would be contributions from all three energy flux input sources to the atmosphere — the energy of which also radiates downward toward and to the surface.
Keep in mind there are multiple energy inputs to the atmosphere besides just the upwelling IR emitted from the surface (and atmosphere) which is absorbed. Post albedo solar energy absorbed by the atmosphere and re-emitted downward to the surface would not be ‘back radiation’, but instead ‘forward radiation’ from the Sun whose energy has yet to reach the surface. And in addition to the radiant flux emitted from the surface which is absorbed there is significant non-radiant flux moved from the surface into the atmosphere, primarily as the latent heat of evaporated water, which condenses to forms clouds — whose deposited energy within (in addition to driving weather), also radiates substantial IR downward to the surface. The total amount of IR that is ultimately passed to the surface has contributions from all three input sources, and the contribution from each one cannot be distinguished or quantified in any clear or meaningful way from the other two.
Thus mechanistically, the downward IR flux ultimately passed to the surface from the atmosphere has no clear relationship to the underlying physics driving the GHE, i.e. the re-radiation of initially absorbed surface IR energy back downward where it’s re-absorbed at a lower point somewhere.
Thus it’s this re-radiated downward push of absorbed surface IR within the atmosphere that is slowing down the radiative cooling or resisting the huge upward IR push ultimately out the TOA. The total DLR at the surface is more just related to the rate the lower layers in combination with the surface are forced (from that downward re-radiated IR push) to be emitting up in order for the surface and the whole of the atmosphere to be pushing through the required 240 W/m^2 back into space.

RW
January 6, 2017 7:59 am

Nick,
Yes, significantly more IR is passed to the surface from the atmosphere than is passed from the atmosphere into space, due to the lapse rate. Roughly a ratio of 2 to 1, or about 300 W/m^2 to the surface and 150 W/m^2 into space. However, if you add these together that’s a total of 450 W/m^2. The maximum amount of power that can be absorbed by the atmosphere (from the surface), i.e. attenuated from being transmitted into space, is about 385 W/m^2, which is also the net amount of flux that must exit the atmosphere at the bottom and be added to the surface in the steady-state. By George’s RT calculation, about 90 W/m^2 of the IR flux emitted by the surface is directly transmitted into space, leaving about 300 W/m^2 absorbed. This means that the difference of about 150 W/m^2, i.e. 450-300, must be part of a closed flux circulation loop between the surface and atmosphere, whose energy is neither adding or taking away joules from the surface or nor adding or taking away joules from the atmosphere.
Remember, not all of the 300 W/m^2 of IR passed to the surface from the atmosphere is actually added to the surface. Much of it is replacing non-radiant flux leaving the surface (primarily latent heat), but not entering the surface (as non-radiant flux). The bottom line is in the steady-state, any flux in excess of 385 W/m^2 leaving or flowing into the surface must be net zero across the surface/atmosphere boundary.
George’s ‘A/2’ or claimed 50/50 split of the absorbed 300 W/m^2 from the surface, where about half goes to space and half goes to the surface, is NOT a thermodynamically manifested value, but rather an abstract conceptual value based on a box equivalent model constrained by COE to produce a specific output at the surface and TOA boundaries.
Just because the atmosphere as a whole mass emits significantly more downward to the surface than upwards into space does NOT mean upwelling IR absorbed somewhere within has a greater chance of being re-radiated downwards than upwards. Whether a particular layer is emitting at 300 W/m^2 or 100 W/m^2, if 1 additional W/m^2 from the surface is absorbed, that layer will re-emit +0.5 W/m^2 up and +0.5 W/m^2 down. Meaning this is independent of the lapse rate. The re-emission of the absorbed energy from the surface, no matter where it goes or how long it persists in the atmosphere, is henceforth non-directional, i.e. occurs with by and large equal probability up or down. And it is this re-radiation of absorbed surface IR back downwards towards (and not necessarily back to) the surface that is the physical driver of the GHE or the underlying mechanism of the GHE that’s slowing down the radiative cooling of the system. NOT the total amount of IR the atmosphere as a whole mass passes to the surface.
The physical meaning of the ‘A/2’ claim or the 50/50 equivalent split is that not more than about half of what’s captured by GHGs (from the surface) is contributing to downward IR push in the atmosphere that ultimately leads to the surface warming, where as the other half is contributing to the massive cooling push the atmosphere makes by continuously emitting IR up at all levels. Or only about half of what’s initially absorbed is acting to ultimately warm the surface, where as the other half is acting to ultimately cool the system and surface.
I’ve noticed many people like yourself seem unable to separate radiative transfer in the atmosphere with the underlying physics of the GHE that ultimately leads to surface warming. The GHE is applied physics within the physics of atmospheric radiative transfer. Atmospheric radiative transfer is not itself (or by itself) the physics of the GHE. This means the underlying physics of the GHE are largely separate from the thermodynamic path manifesting the energy balance, and it is this difference that seems to elude so many people like yourself.

RW
January 6, 2017 9:07 am

Nick,
I assume it is agreed by you that the constituents of the atmosphere, i.e. GHGs and clouds, act to both cool the system by emitting IR up towards space and warm it by emitting IR downwards towards the surface. Right? George is just saying that like anything else in physics or engineering, this has to be accounted for, plain and simple.
He’s using/modeling the Earth/atmosphere system as a black box, constrained by COE to produce required outputs at the surface and TOA, given specific inputs:
https://en.wikipedia.org/wiki/Black_box
When this is applied to surface IR absorbed by the atmosphere, it yields that only about half of what’s absorbed by GHGs is acting to ultimately warm the surface, where as the other half is contributing to the radiative cooling push of the atmosphere and ultimate cooling of the system:
George is not modeling the actual thermodynamics here and all the complexities associated with the thermodynamics (which isn’t possible by such methods), but rather he’s trying to isolate the effect the absorption of surface IR by GHGs, and the subsequent non-directional re-radiation of that absorbed energy, is having amongst the highly complex and non-linear thermodynamic path manifesting the surface energy balance, so far as its ultimate contribution to surface warming.

Randy Bork
January 6, 2017 9:47 am

Nick – that post and the info contained in those graphs are fantastically educational to me [just trying to learn here]. Now I must go and try to find the paper they came from. Just wanted to say that those observations and descriptions crystallize what is otherwise difficult to visualize [for a newbie]. Thanks much.

January 6, 2017 11:49 am

Nick , are those spectra in a easily accessible tables somewhere ? Email me them or point me to them and I’ll calculate the actual radiative equilibrium temperature they imply .
co2isnotevil is right that “lapse rate” is the equilibrium expression of gravitational energy .
It cannot be explained as an optical phenomenon — which is why neither quantitative equation nor experimental demonstration of such a phenomenon has ever been presented .

January 6, 2017 12:29 pm

Bob,
A couple of things to notice about the spectra.
1) There is no energy returned to the surface in the transparent regions of the atmosphere. This means that no GHG energy is being ‘thermalized’ and re-radiated as broad band BB emissions.
2) The attenuation in absorption bands at TOA (20km is high enough to be considered TOA relative to the radiative balance) is only about 3db (50%). Again, if GHG energy was being ‘thermalized’, we would see littlle, if any, energy in the absorption bands, moreover; this is consistent with the 50/50 split of absorbed energy required by geometrical considerations.
3) The small wave number data (400-600) is missing from the 20km data looking down which would otherwise illustrates that the color temperature of the emissions (where the peak is relative to Wein’s Displacement Law) is the surface temperature and the 255K equivalent temperature is a consequence of energy being removed from parts of the spectrum manifesting a lower equivalent temperature for the outgoing radiation,
BTW, I’ve had discussions with Grant Perry about this and he has trouble moving away from this ‘thermalization’ point of view, despite the evidence. To be fair, it doesn’t really matter from a thermodynamic balance and temperature perspective (molecules in motion affect a temperature sensor in the same was a photons of the same energy), but only matters if you want to accurately predict the spectrum and account for 1), 2) and 3) above.
Of course, this goes against the CAGW narrative which presumes that GHG absorption heats the atmosphere (O2/N2) which then heats the surface by convection, rather then the purely radiative effect it is where photons emitted by GHG’s returning to the ground state are what heat the surface. One difference is that if all GHG absorption was ‘thermalized’ as the energy of molecules in motion, all must be returned to the surface, since molecules in motion do not emit photons that can participate in the radiative balance and there wouldn’t be anywhere near enough energy to offset the incoming solar energy.

January 6, 2017 12:29 pm

That is correct.
An atmosphere in hydrostatic equilibrium suspended off the surface by the upward pressure gradient force and thus balanced against the downward force of gravity will show a lapse rate slope related to the mass of the atmosphere and the strength of the gravitational field.
It is all a consequence of conduction and convection NOT radiation.
The radiation field is a mere consequence of the lapse rate slope caused by conduction and convection.
Radiation imbalances within an atmosphere simply lead to convection changes that neutralise such imbalances in order to maintain long term hydrostastic equilibrium.
No matter what the proportion of GHGs in an atmosphere the surface temperature does not change. Only the atmospheric convective circulation pattern will change.

January 6, 2017 2:44 pm

Bob A,
“Nick , are those spectra in a easily accessible tables somewhere ?”
Unfortunately not, AFAIK. As I mentioned above, the graph comes from a textbook. The caption gives an attribution, but I don’t think that helps. It isn’t recent.
I have my own notion of the lapse rate here, and earlier posts. Yes, the DALR is determined by gravity. But it takes energy to maintain it, and the flux that passes through with radiative transfer in GHG-active regions helps to maintain it.

January 7, 2017 8:00 pm

This is one of the great atmospheric experiments of all time. I agree with everything you say except that 228K is the Arctic tropopause rather than the top of the atmosphere. The top of the atmosphere is more like 160K where water is radiating in the window.
The peak CO2 frequency is actually 667.4, close enough. You can see a little spike indicating the 667.4 Q branch. Looking up, it would ordinarily be pointed down. In this case a strong surface inversion reversed it.
Long wave infrared light only comes from the earth’s surface. It does not come from the sun. It is not manufactured by Carbon dioxide, or any other greenhouse gas. These gasses absorb and re-emit long wave radiation emitted from the surface according to their individual material properties.
You say it emits down more than it emits up. I say the two emissions are disconnected. The boundary layer extinguishes the 667.4 band. Radiation in the band resumes generally at about the cloud condensation level as a result of condensation energy. CO2 radiates from the tropopause because massive amounts of new energy are added by ozone absorption.

January 5, 2017 8:39 pm

Presence in the phrase “the Climate Sensitivity” of the word “the” implies existence of a fixed ratio between the change in in the spatially averaged surface air temperature at equilibrium and the change in the logarithm of the atmospheric CO2 concentration. Would anyone here care to defend the thesis that this ratio is fixed?

January 5, 2017 8:45 pm

Terry,
It’s definitely not a fixed ratio, either temporally or spatially, but it does have a relatively constant yearly average and changes to long term averages are all we care about when we are talking about the climate sensitivity. This is where superposition in the energy domain comes in which allows us to calculate meaningful averages since 1 Joule does 1 Joule of work and no more or no less.

January 5, 2017 10:42 pm

Thank you, c02isnotevil, for taking the time to respond. That “1 Joule does 1 Joule of work” is not a principle of thermodynamics. Did you mean to say that “1 Joule of heat crossing the boundary of a concrete object does 1 Joule of work on this boundary absent change in the internal energy of this object”?

January 5, 2017 10:49 pm

The basic point is no 1 Joule is any different than any other.

January 5, 2017 11:06 pm

That “no 1 Joule is any different than any other” is a falsehood.

January 5, 2017 11:26 pm

Terry,
Energy can not be created or destroyed, only transformed from one form to another. Different forms may be incapable of doing different kinds of work, but relative to the energy of photons, it’s all the same and photons are all that matter relative to the radiative balance and a quantification of the sensitivity. The point of this is that if each of the 240 W/m^2 of incident power only results in 1.6 W/m^2 of surface emissions, the next W/m^2 can’t result in more than 4 W/m^2 which is what the IPCC sensitivity requires. The average emissivity is far from being temperature sensitive enough.
If you examine the temp vs. emissivity plot I posted in response to one of Nick’s comments, the local minimum is about at the current average temperature and the emissivity increases (sensitivity decreases) whether the temperature increases or decreases, but not by very much.

phaedo
January 6, 2017 2:05 am

Terry Oldberg, ‘Presence in the phrase “the Climate Sensitivity” of the word “the” implies existence of a fixed ratio …’ Could you explain the reasoning that led you to that statement.

January 8, 2017 9:09 am

phaedo:
I can explain that. Thanks for asking.
Common usage suggests that “the climate sensitivity” references a fixed ratio, The change that is in the numerator of this ratio is the equilibrium temperature. Thus, this concept is often rendered as “ECS” but I prefer “TECS” (acronym for “the equilibrium climate sensitivity”) as this usage makes clear that a constant is meant.
Warmists argue that the value of TECS is about 3 Celsius per doubling of the CO2 concentration. Bayesians treat the ratio as a parameter having prior and posterior probability density functions indicating that they believe TECS to be a constant with uncertain value.
It is by treating TECS as a constant that climatologists bypass the thorny issue of variability. If TECS is only the ratio of two numbers then climatologists have to make their arguments in terms of probability theory and statistics but to avoid this involvement is a characteristic of their profession. For evidence, search the literature for a description of the statistical population of global warming climatology. I believe you will find, like me, that there isn’t one.

January 8, 2017 9:59 am

Warmists argue that the value of TECS is about 3 Celsius per doubling of the CO2 concentration. Bayesians treat the ratio as a parameter having prior and posterior probability density functions indicating that they believe TECS to be a constant with uncertain value.

I have an effective cs for to extratropics for the seasonal changes in calculated station solar and it’s actually change in temp here
http://wp.me/p5VgHU-1t

January 8, 2017 10:11 am

micro6500
That’s a good start on a statistical investigation. To take it to the next level I’d identify the statistical population, build a model from a sample drawn randomly from this population and cross validate this model in a different sample. If the model cross validates you’ve done something worth publishing. The model “cross validates” if and only if the predictions of the model match the observations in the second of the two samples. To create a model that cross validates poses challenges not faced by professional climatologists as their models are not falsifiable.

January 8, 2017 10:21 am

It does, it shows up as an exponential decay in cooling rates, and the some of the data (with net rad) was from Australia, and other temp charts are from data in Ohio. And it explains everything. (Clear sky cooling performance)

January 5, 2017 8:48 pm

The climate system has a couple positive feedbacks that do not violate any laws of physics. For one thing, the Bode feedback theory does not require an infinite power supply for positive feedback, not even for positive feedback with feedback factor exceeding 1. The power supply only has to be sufficient to keep the law of conservation of energy from being violated. There is even the tunnel diode oscillator, whose only components are an inductor and capacitor to form a resonator, two resistors where one of them nonlinear to have voltage and current varying inversely with each other over a certain range (the tunnel diode), and a power supply to supply the amount of current needed to get the tunnel diode into a mode where voltage across it and current passing through it vary inversely.
As for positive feedbacks in the climate system: One that is simple to explain is the surface albedo feedback. Snow and ice coverage vary inversely with temperature, so the amount of sunlight absorbed varies directly with temperature. This feedback was even greater during the surges and ebbings of Pleistocene ice age glaciations, when there was more sunlight-reflecting ice coverage that could be easily expanded or shrunk by a small change in global temperature. Ice core temperature records indicate climate that was more stable during interglacial periods and less stable between interglacials, and there is evidence that at some brief times during glaciations there were sudden climate shifts – when the climate system became unstable until a temporarily runaway change reduced a positive feedback that I think was the surface albedo one.
Another positive feedback is the water vapor feedback, which relates to the gray body atmosphere depiction in Figure 2. One thing to consider is that the gray body filter is a bulk one, and thankfully Figure 2 to a fair extent shows this. Another thing to consider is that this bulk gray body filter is not uniform in temperature – the side facing Earth’s surface is warmer than the side facing outer space, so it radiates more thermal radiation to the surface than to outer space. (This truth makes it easier to understand how the Kiehl Trenberth energy budget diagram does not require violation of any laws of physics for its numbers to add up with its attributions to various heat flows.)
If the world warms, then there is more water vapor – which is a greenhouse gas, and the one that our atmosphere has the most of and that contributes the most to the graybody filter Also, more water vapor means greater emissivity/absorption of the graybody filter depicted in Figure 2. That means thermal radiation photons emitted by the atmosphere reaching the surface are emitted from an altitude on-average closer to the surface, and thermal radiation photons emitted by the atmosphere and escaping to outer space are emitted from a higher altitude. So, more water vapor means the bulk graybody filter depicted in Figure 2 is effectively thicker, with its effective lower surface closer to the surface and warmer. Such a thicker denser effective graybody filter has increased inequality between its radiation reaching the surface and radiation escaping to outer space.

January 5, 2017 9:23 pm

Donald,
You are incorrect about Bode’s assumptions. They are laid out in the first 2 paragraphs in the book I referenced. Google it and you can find a free copy of it on-line. The requirement for a vacuum tube and associated power supply specifies the implicit infinite supply, as there are no restrictions on the output impedance in the Bode model, which can be 0 requiring an infinite power supply. This assumed power supply is the source of most of the extra 12+ W/m^2 required over and above the 3.7 W/m^2 of CO2 ‘forcing’ that is required in the steady state to sustain a 3C temperature increase. Only about 0.6W per W/m^2 (about 2.2 W/m^2) is all the ‘feedback’ the climate system can provide. Of course, the very concept of feedback is not at all applicable to a passive system like the Earth’s climate system (passive specifically means no implicit supply).
Regarding ice. The average ice coverage of the planet is about 13%, most of which is where little sunlight arrives anyway. It it all melted and considering that 2/3 of the planet is covered by clouds anyway and mitigates the effects of albedo ‘fedeback’, the incremental un-reflected input power can only account for about half of the 10 W/m^2 above and beyond the 2.2 W/m^2 from 3.7 W/m^2 of forcing based on 1.6 W/m^2 of surface emissions per W/m^2 of total forcing. This does become more important as more of the planet is covered by ice and snow, but at the current time, we are pretty close to minimum possible ice. No amount of CO2 will stop ice from forming during the polar winters.
Regarding water vapor. You can’t consider water vapor without considering the entire hydro cycle, which drives a heat engine we call weather which unambiguously cools based on the trails of cold water left in the wake of a Hurricane. The Second Law has something to say about this as well, where a heat engine can’t warm its source of heat.

January 6, 2017 8:21 am

Amplifiers with positive feedback even to the point of instability or oscillation do not require zero output impedance, and they work in practice with finite power supplies. Consider the tunnel diode oscillator, where all power enters the circuit through a resistor. Nonpositive impedance in the tunnel diode oscillator is incremental impedance, and that alone being nonpositive is sufficient for the circuit to work.
Increasing the percentage of radiation from a bulk graybody filter of nonuniform temperature towards what warms its warmer side does not require violation of the second law of thermodynamics, because this does not involve a heat engine. The only forms of energy here are heat and thermal radiation – there is no conversion to/from other forms of energy such as mechanical energy. The second law of thermodynamics only requires net flow to be from warmer points and surfaces to cooler points and surfaces, which is the case with a bulk graybody filter with one side facing a source of thermal radiation that warms the graybody filter from one side. Increasing the optical density of that filter will cause the surface warming it to have a temperature increase in order to get rid of the heat it receives from a kind of radiation that the filter is transparent to, without any net flows of heat from anything to anything else that is warmer.
As for 2/3 of the Earth’s surface being covered by clouds: Not all of these clouds are opaque. Many of them are cirrus and cirrostratus, which are translucent. This explains why the Kiehl Trenberth energy budget diagram shows about 58% of incoming solar radiation reaching the surface. Year-round insolation reaching the surface around the north coast of Alaska and Yukon is about 100 W/m^2 according to a color-coded map in the Wikipedia article on solar irradiance, and the global average above the atmosphere is 342 W/m^2.

January 6, 2017 9:57 am

“Amplifiers with positive feedback even to the point of instability or oscillation do not require zero output impedance”
Correct, but Bode’s basic gain equation makes no assumptions about the output impedance and it can just as well be infinite or zero and it still works, therefore, the implicit power supply must be unlimited.
The Bode model is idealized and part of the idealization is assuming an infinite source of Joules powers the gain.
Tunnel diodes work at a different level based on transiently negative resistance, but this negative resistance only appears when the diode is biased, which is the external supply.
“Not all of these clouds are opaque.”
Yes, this is true and the average optical depth of clouds is accounted for by the analysis. The average emissivity of clouds given a threshold of 2/3 of the planet covered bu them, is about 0.7. Cloud emissivity approaches 1 as the clouds get taller and denser, but the average is only about 0.7. This also means that about 30% of surface emissions passes through clouds and this is something Trenberth doesn’t account for with his estimate of the transparent window.

January 6, 2017 8:27 am

More on your statement that clouds cover 2/3 of the surface: You said “After accounting for reflection by the surface and clouds, the Earth receives about 240 W/m2 from the Sun”. That is 70% of the 342 W/m^2 global average above the atmosphere.

January 6, 2017 11:04 am

co2isnotevil: Clouds can simultaneously have majority emissivity and majority transmission of incoming solar radiation. The conflict is resolved by incoming solar radiation and low temperature thermal radiation being at different wavelengths, and clouds have absorption/emissivity varying with wavelength while equal to each other, and higher in wavelengths longer than 1.5 micrometers (about twice the wavelength of border between visible and infrared) than in shorter wavelengths.

January 6, 2017 11:34 am

Donald,
“Clouds can simultaneously have majority emissivity and majority transmission of incoming solar radiation”
Yes, this is correct. But again, we are only talking about long term changes in averages and over the long term, the water in clouds is tightly coupled to the water in oceans and solar energy absorbed by clouds can be considered equivalent to energy absorbed by the ocean (surface), at least relative to the long term steady state and the short term hydro cycle.

January 6, 2017 11:06 am

co2isnotevil: I did not state that a tunnel diode oscillator does not require a power supply, but merely that it does not require an infinite one. For that matter, there is no such thing as an infinite power supply.

January 6, 2017 11:40 am

Donald,
“there is no such thing as an infinite power supply.”
Correct, but we are dealing with idealized models based on simplifying assumptions, especially when it comes to Bode’s feedback system analysis. And one of the many simplifying assumptions Bode makes is that there is no limit to the Joules available to power the gain (unconstrained active gain). The error with how the climate was mapped to Bode was that the simplifying assumptions were not applicable to the climate system, thus the analysis is also not applicable.

January 6, 2017 11:10 pm

co2isnotevil saying: “And one of the many simplifying assumptions Bode makes is that there is no limit to the Joules available to power the gain (unconstrained active gain). The error with how the climate was mapped to Bode was that the simplifying assumptions were not applicable to the climate system, thus the analysis is also not applicable.”
Please state how this is not applicable. Cases with active gain can be duplicated by cases with passive gain, for example with a tunnel diode. The classic tunnel diode oscillator receives all of its power through a resistor whose resistance is constant, so availability of energy/power is limited. The analogue to Earth’s climate system does not forbid positive feedback or even positive feedback to the extent of runaway, but merely requires such positive feedback to be restricted to some certain temperature range, outside of which the Earth’s climate is more stable.

prjindigo
January 5, 2017 8:58 pm

So where’s the density component of your equations? Density is regulated by gravity alone on Earth.

January 5, 2017 9:12 pm

prjindigo,
The internals of the atmosphere, which is where density comes in, are decoupled from the model which is a model that matches the measured transfer function of the atmosphere which quantifies the causal behavior between the surface temperature and output emissions of the planet. This basically sets the upper limit on what the sensitivity can be. The lower limit is the relationship between the surface temperature and the post albedo input power, whose slope is 0.19 C per W/m^2 which is actually the sensitivity of an ideal BB at the surface temperature! This is represented by the magenta line in Figure 3. I didn’t bring it up because getting acceptance for 0.3C per W/m^2 is a big enough hill to climb.

January 5, 2017 9:05 pm

Forrest,
The satellite data itself doesn’t say much explicitly, but it does report GHG concentrations (H2O and O3) and when I apply a radiative transfer model driven by HITRAN absorption line data (including CO2 and CH4) to a standard atmosphere with measured clouds, I get about 74%, which is well within the margin of error.

January 5, 2017 9:13 pm

A black body is nearly an exact model for the Moon.
By looking out my window I can see that this is not the case, it’s clearly a gray body.
A perfect blackbody is one that absorbs all incoming light and does not reflect any.

January 5, 2017 9:32 pm

Phil,
“By looking out my window I can see that this is not the case, it’s clearly a gray body.”
Technically yes, if we count reflection as not being absorbed per the wikipedia definition, it would be a gray body, but relative to the energy the Moon receives after reflection, it is a nearly perfect black body, so the calculations reduce the solar energy to compensate. BTW, I don’t really like the wikipedia definition which seems to obfuscate the applicability of a gray body emitter (black body source with a gray body atmosphere).

January 5, 2017 10:34 pm

This is the trouble that comes when not properly allowing for the frequency dependence of ε. For the Moon, in the SW we see absorption and reflection (but not emission), which is fairly independent of frequency in that range. But ε changes radically getting into thermal IR frequencies, where we see pretty much black body emission.

January 5, 2017 10:40 pm

“allowing for the frequency dependence of ε.”
The average ε is frequency independent and that is all the model depends on.
Why is it so hard to grasp that this model is concerned only with long term averages and that yes, every parameter is dependent on almost every other parameter, but they all have relatively constant long term averages. This is why we need to do the analysis in the domain of Joules where superposition applies since if 1 Joule can to X amount of work, 2 Joules can to 2X amount of work and it takes work to warm the surface and keep it warm and the sensitivity is all about doing incremental work. So many of you can’t get your heads out of the temperature domain which is highly non linear where superposition does not apply.

January 9, 2017 6:34 am

co2isnotevil January 5, 2017 at 9:32 pm
Phil,
“By looking out my window I can see that this is not the case, it’s clearly a gray body.”
Technically yes, if we count reflection as not being absorbed per the wikipedia definition, it would be a gray body, but relative to the energy the Moon receives after reflection, it is a nearly perfect black body, so the calculations reduce the solar energy to compensate.

If you’re going to do a scientific post then get the terminology right, the moon is not a black body it’s a grey body. The removal of the reflected light is exactly what a greybody does, the blackbody radiation is reduced by the appropriate fraction in the gray body, that’s what the non unity constant is for. Also the atmosphere is not a greybody because its absorption is frequency dependent.

January 9, 2017 10:39 am

Phill,
“The removal of the reflected light is exactly what a greybody does”
This is not the only thing that characterizes a gray body. Energy passed through a semi-transparent body also implements grayness as does energy received by a body that does work other than affecting the bodies temperature (for example, photosynthesis).
My point is that if you don’t consider reflected input, the result is indistinguishable from a BB. And BTW, there is no such thing as an ideal BB in nature. All bodies are gray. Considering something to be EQUIVALENT a body black is a simplifying abstraction and this is what modelling is all about.
I don’t understand why the concept of EQUIVALENCE is so difficult for others to understand as without understanding EQUIVALENCE there’s no possibility of understanding modelling.

January 9, 2017 12:02 pm

I don’t understand why the concept of EQUIVALENCE is so difficult for others to understand as without understanding EQUIVALENCE there’s no possibility of understanding modelling.

Just to be clear for me, I understand equivalency very well. I also understand fidelity, and reusability.
I’m just trying to understand and discuss the edges that define that fidelity.

January 5, 2017 9:24 pm

“A gray body emitter is one where the power emitted is less than would be expected for a black body at the same temperature.”
A gray body emitter has a rather specific meaning, not observed here. The power is less, but uniformly distributed over the spectrum. IOW, ε is independent of frequency. This is very much not true for radiative gases.
“Trenberth’s energy balance lumps the return of non radiant energy as part of the ‘back radiation’ term, which is technically incorrect since energy transported by matter is not radiation.”
A flux is a flux. Trenberth is doing energy budgetting; he’s not restricting to radiant. The discussion here is wrong. Material transport does count; it helps bring heat toward TOA, so to maintain the temperature at TOA as it loses heat by radiation.

January 5, 2017 9:32 pm

Wiki’s article on black body is more careful and correct. It says “A source with lower emissivity independent of frequency often is referred to as a gray body.”. The independence is important.

January 7, 2017 8:41 pm

“It is why 11 μ with ε = 0, IR goes straight from surface to space, while at 15μ, where ε is high, IR is radiated from TOA and not lower, because the atmosphere is opaque.”
The energy of ALL light is frequency dependent regardless the color (black or grey) of the emitting body. Emissivity has nothing to do with frequency, except as regards the wavelengths the emitting body happens to absorb and emit.
Wiki simply has it wrong.
CO2 has very LOW emissivity at about 15 microns. Otherwise it would not be extinguished within a meter of standard atmosphere. In order for surface energy to travel to the tropopause at 15 microns it would have to TRANSMIT. It doesn’t. Transmission is 1-absorption. There is ZERO transmission to the tropopause at 15/667.4. From Science of Doom:

January 9, 2017 12:12 pm

gymnosperm
Where did this graph come from?
I would expect to find that the std atm had conditions that would lead to near 100% rel humidity for this spectrum. Do you have a link to the data to see exactly what they were doing with it.
This is what I’ve been blathering about, Or I don’t understand just exactly what (or where?) is being measured here. If this is surface up to space, it should only be like this if the rel humidity is pretty high.

January 9, 2017 12:42 pm

micro6500,
This plot looks like the inverse of absorption, which is not specifically transmission since transmission includes the fraction of absorption that is eventually transmitted into space.

January 9, 2017 2:41 pm

Except it isn’t just co2.

January 5, 2017 9:44 pm

“The power is less, but uniformly distributed over the spectrum”
As I pointed out, this is not a requirement. Joules are Joules and the frequency of the photons transporting those Joules is irrelevant relative to the energy balance and subsequent sensitivity. Again, the 240 W/m^2 of emissions we use SB to convert to an EQUIVALENT temperature of 255K is not a Planck distribution, moreover; the average emissivity is spectrally independent since it’s integrated across the entire spectrum.
“Material transport does count”
Relative to the radiant balance of the planet and the consequential sensitivity, it certainly does, since only photons can enter or leave the top boundary of the atmosphere. Adding a zero sum source and sink of energy transporter by matter to the radiant component of the surface flux shouldn’t make a difference, but it adds a layer of unnecessary obfuscation that does nothing but confuse people. The real issue is that he calls the non radiant return of energy to the surface radiation which is misrepresentative at best.

January 5, 2017 10:39 pm

“As I pointed out, this is not a requirement.”
It is a requirement of the proper definition of grey body. It is why grey, as opposed to blue or red. And it is vitally important to atmospheric radiative transport. It is why 11 μ with ε = 0, IR goes straight from surface to space, while at 15μ, where ε is high, IR is radiated from TOA and not lower, because the atmosphere is opaque.

January 5, 2017 10:48 pm

Nick,
“It is a requirement of the proper definition of grey body.”
Then the association between 255K and the average 240 W/m^2 emitted by the planet is meaningless as is the 390 W/m^2 (per Trenberth) emitted by the surface (he uses about 287.5K).
There is no requirement for a Planck distribution when calculating the EQUIVALENT temperature of matter based on its radiative emissions. This is what the word EQUIVALENT means. That is, an ideal BB at the EQUIVALENT temperature (or a gray body at an EQUIVALENT temperature and EQUIVALENT emissivity) will emit the same energy flux as the measured radiative emissions, albeit with a different spectra.

January 5, 2017 11:45 pm

“Then the association between 255K and the average 240 W/m^2 emitted by the planet is meaningless…”
Nobody thinks that there is actually a location at 255K which emits the 240 W/m2.
“as is the 390 W/m^2 (per Trenberth) emitted by the surface (he uses about 287.5K).”
No, the surface is a black body (very dark grey) in thermal IR. It is a more or less correct application of S-B, though the linearising of T^4 in averaging involves some error.
“Planck distribution when calculating the EQUIVALENT temperature of matter”
You can always calculate an equivalent temperature. It’s just a rescaled expression of flux, as shown on the spectra I included. But there is no point in defining sensitivity as d flux/d (equivalent temperature). That is curcular. You need to identify the ET with some real temperature.

January 6, 2017 12:07 am

“But there is no point in defining sensitivity as d flux/d (equivalent temperature)”
But, this is exactly what the IPCC defines as the sensitivity because dFlux is forcing. The idea of representing the surface temperature as an equivalent temperature of an ideal BB is common throughout climate science on both sides of the debate. It works because the emissivity of the surface itself (top of ocean + bits of land that poke through) is very close to 1. Only when an atmosphere is layered above it does the emissivity get reduced.

January 6, 2017 12:21 am

” this is exactly what the IPCC defines as the sensitivity “
Not so. I had the ratio upside down, it is dT/dP. But T is measured surface air temperature, not equivalent temperature. We know how equivalent temp varies with P; we have a formula for it. No need to measure anything.

January 6, 2017 12:30 am

“But T is measured surface air temperature, not equivalent temperature. ”
T is the equivalent surface temperature which is approximately the same as the actual near surface temperature measured by thermometers. This is common practice when reconstructing temperature from satellite data and the fact that they are close is why it works.

Tony
January 5, 2017 9:43 pm

“… doubling CO2 is equivalent to 3.7 W/m2 of incremental, post albedo solar power”
The sun when moving from its perihelion to aphelion each year produces as change of a massive 91 W/m2. It has absolutely ZERO impact on global temperatures, thanks to the Earth’s negative feedbacks.
Why does everyone keep ignoring them?

January 5, 2017 10:20 pm

“It has absolutely ZERO impact on global temperatures”
The difference gets buried in seasonal variability since perihelion is within a week and a half of the N hemisphere winter solstice and the difference contributes to offset some of the asymmetry between the response of the 2 hemispheres. In about 10K years, it will be reversed and N hemisphere winters will get colder as its summers get warmer, while the reverse happens in the S hemisphere.

Jocelyn
January 5, 2017 10:28 pm

Tony,
The closest (most heat rays from the sun) is in Jan. So you could think the global temperature would be the warmest then. But it is in July.
See here;
http://data.giss.nasa.gov/gistemp/news/20160816/july2016.jpg
I think the difference is mainly due to the difference in the amount of continent surface in the Northern Hemisphere vs the South.

hanelyp
January 5, 2017 10:18 pm

Where does convection as a heat transfer mechanism enter the model?

January 5, 2017 10:25 pm

hanelyp,
Convection and heat transfer are internal to the atmosphere and the model only represents the results of what happens in the atmosphere, not how it happens. Convection itself is a zero sum influence on the radiant emissions from the surface since what goes up must come down (convection being energy transported by matter) and whatever effect it has is already accounted for by the surface temperature and its consequent emissions.

January 5, 2017 11:36 pm

“since what goes up must come down (convection being energy transported by matter) “
That’s just not true. Trenberth’s fluxes are in any case net (of up and down). Heat is transported up (mainly by LH); the warmer air at altitude then emits this heat as IR. It doesn’t go back down.

January 5, 2017 11:57 pm

Nick,
“Heat is transported up”
The heat you are talking about is the kinetic energy consequential to the translational motion of molecules which has nothing to do with the radiative balance or the sensitivity. Photons travel in any direction at the speed of light and I presume you understand that O2 and N2 neither absorb or emit photons in the relevant bands.

January 6, 2017 12:10 am

” the kinetic energy consequential to the translational motion of molecules which has nothing to do with the radiative balance or the sensitivity”
It certainly does. I don’t think your argument gets to sensitivity at all. But local temperature of gas is translated directly into IR emission. It happens through GHgs; they are at the same temperature as O2 and N2. They emit according to that temperature, and the heat they lose is restored to them by collision with N2/O2, so they can emit again.

January 6, 2017 12:28 am

Nick,
“But local temperature of gas is translated directly into IR emission. It happens through GHgs; they are at the same temperature as O2 and N2. They emit according to that temperature, and the heat they lose is restored to them by collision with N2/O2, so they can emit again.”
The primary way that an energized GHG molecule reverts to the ground state upon collision with O2 or N2 is by emitting a photon and only a fraction of the collisions have enough energy to do this. You do understand that GHG absorption/emission is a quantum state change that is EM in nature and all of the energy associated with that state change must be absorbed or emitted at once. There is no mechanism which converts any appreciable amount of energy associated with such a state change into linear kinetic energy at the relevant energies. At best, only small amounts at a time can be converted and its equally probably to increase the velocity as it is to decrease it. This is the mechanism of collisional broadening which extends the spectrum mostly symmetrically around resonance and which either steals energy or gives up energy upon collision, resulting in the emission of a slightly different frequency photon.

angech
January 5, 2017 10:28 pm

“A black body is nearly an exact model for the Moon.”
No, The moon is definitely not a black body.
Geometric albedo Moon 0.12 earth 0.434
Black-body temperature (K) Moon 270.4 earth 254.0

“To conceptualize a gray body radiator, If T is the temperature of the black body, it’s also the temperature of the input to the gray body,To be consistent with the Wikipedia definition, the path of the energy not being absorbed is omitted.”
This misses out on the energy defected back to the black body which is absorbed and remitted some of which goes back to the grey body. I feel this omission should at least be noted [I see reference to back radiation later in the article despite this definition]

” while each degree of warmth requires the same incremental amount of stored energy, it requires an exponentially increasing incoming energy flux to keep from cooling.”
It requires an exponentially increasing energy flux to increase the amount of stored energy, the energy flux must merely stay the same to keep from cooling.

“The equilibrium climate sensitivity factor (hereafter called the sensitivity) is defined by the IPCC as the long term incremental increase in T given a 1 W/m2 increase in input, where incremental input is called forcing”.
but, I am lost. The terms must sound similar but mean different things.
The equilibrium climate sensitivity (ECS) refers to the equilibrium change in global mean near-surface air temperature that would result from a sustained doubling of the atmospheric (equivalent) carbon dioxide concentration (ΔTx2). a forcing of 3.7 W/m2

“The only place for the thermal energy to go, if not emitted, is back to the source ”
Well it could go into a battery, but if not emitted it could never go back to the source.

“A gray body emitter is one where the power emitted is less than would be expected for a black body at the same temperature”.
At the same temperature both a grey and a black body would emit the same amount of power.
The grey body would not get to the same temperature as the black body from a constant heat source because it is grey, It has reflected, not absorbed, some of the energy. The amount of energy detected would be the same but the spectral composition would be quite different with the black body putting out far more infrared.

January 5, 2017 10:37 pm

“Both warm the surface by absorbing some fraction of surface emissions and after some delay, recycling about half of the energy back to the surface.”
Unfortunately, when energy is emitted by the surface, the temperature must fall. Half the emitted energy returning will not return the temperature to its pre emission state.
No increase in temperature. Night is an example. Or, temperatures falling after daytime maxima.
Cheers,

Phillip Bratby
January 5, 2017 10:50 pm

Anything based on the Earth’s average temperature is simply wrong.

January 5, 2017 10:56 pm

“Anything based on the Earth’s average temperature is simply wrong.”
This is why a proper analysis must be done in the energy domain where superposition applies because average emissions do represent a meaningful average. Temperature is just a linear mapping of stored energy and a non linear mapping to emissions which is why average temperature is not necessarily meaningful. It’s best to keep everything in the energy domain and convert average emissions to an EQUIVALENT average temperature in the end.

angech
January 5, 2017 11:24 pm

“Clouds also manifest a conditional cooling effect by increasing reflection unless the surface is covered in ice and snow when increasing clouds have only a warming influence.”
Clouds reflect energy regardless of ice and snow cover on the ground,They always have an albedo cooling effect. Similarly clouds always have a warming effect on the ground whether the surface is ice and snow or sand or water. The warming effect is due to back radiation from absorbed infrared , not the surface conditions. The question is what effect does it have on emitted radiation.

“Near the equator, the emissivity increases with temperature in one hemisphere with an offsetting decrease in the other. The origin of this is uncertain”
More land in the Norther Hemisphere means the albedo of the two hemispheres is different, The one with the higher albedo receives less energy to absorb and so emits less.

January 5, 2017 11:48 pm

angech,
“Clouds reflect energy regardless of ice and snow cover on the ground,”
Yes, but what matters is the difference in reflection between whether the cloud is present or not. When the surface is covered by ice and snow and after a fresh snowfall, cloud cover often decrease the reflectivity!
Yes, the land/sea asymmetry between hemispheres is important, especially at the poles and mid latitudes which are almost mirror images of each other, but where this anomaly is, the topological differences between hemispheres are relatively small.

angech
January 6, 2017 1:26 am

co2isnotevil “Clouds reflect energy regardless of ice and snow cover on the ground,”
“Yes, but what matters is the difference in reflection between whether the cloud is present or not. When the surface is covered by ice and snow and after a fresh snowfall, cloud cover often decreases the reflectivity!”
Hm.
The clouds have already reflected all the incoming energy that they can reflect.Hence the ice and snow are receiving less energy than they would have.
Some of the radiation that makes it through and reflects will then reflect back to the ground and hence warm the surface again. Yes.Most will go out but I get your drift.
The point though is that it can never make the ground warmer than it would be if there was no cloud present. Proof ad absurdio would be if the cloud was totally reflective, no light, ground very cold, a slight bit of light a bit warmer, no cloud warmest.

January 6, 2017 9:02 am

“The point though is that it can never make the ground warmer than it would be if there was no cloud present.”
Not necessarily. GHG’s work just like clouds with one exception. The water droplets in clouds are broad band absorbers and broadband Planck emitters while GHG’s are narrow band line absorbers and emitters.

Tom in Oregon City
January 5, 2017 11:27 pm

“If T is the temperature of the black body, it’s also the temperature of the input to the gray body, thus Equation 1 still applies per Wikipedia’s over-constrained definition of a gray body.”
That’s just wrong.
Radiant energy has no temperature, only energy relative to its wavelength (to have temperature, there must be a mass involved). The temperature of the absorbing surface of that energy is dependent on its emissivity, its thermal conductivity, and it’s mass.

Reply to  Tom in Oregon City
January 5, 2017 11:52 pm

Tom,
“Radiant energy has no temperature, …”
Radiant energy is a remote measurement representative of the temperature of matter at a distance.

Tom in Oregon City
January 6, 2017 5:04 pm

There’s no need to quote the texbook understanding of blackbody radiation spectrum to me. Observing the peak wavelength may tell you the temperature of a blackbody, but not the temperature it will generate at the absorber. Consider this: an emitter at temperature T, with a surface area A, emits all its energy toward an absorber with surface area 4A. What is the temperature of the absorber? Never T. It’s not the WAVELENGTH of the photons that determines the temperature of the absorber, it’s the flux density of photons, or better the total energy those photons — of any wavelength — present to the absorber, that determines the heat input to that absorber. Distance from the emitter, the emissivity of the absorber, its thermal conductivity, its total mass… all these things affect the TEMPERATURE of that grey body.
Consider it another way: take an object with Mass M and perfect thermal conductivity at temperature T, and allow it to radiate only toward another object of the same composition with mass 10M at initial temperature 0K. Will the absorber ever get hotter then T/10?
I repeat: those photons do not have temperature. Only matter has temperature.
Or would you care to tell me the temperature of microwave emissions from the sun? Certainly not 5778K.

angech
January 5, 2017 11:44 pm

“Trenberth’s energy balance lumps the return of non radiant energy as part of the ‘back radiation’ term, which is technically incorrect since energy transported by matter is not radiation.”
Trenberth is simply getting the non radiant energy higher in the atmosphere where it eventually becomes radiative energy out to space [of course it does some back radiating itself as radiant energy but this part is included in his general back radiation schemata] . He is technically correct.

January 6, 2017 12:03 am

angech,
“He is technically correct.”
Latent heat cools the surface water as it evaporates and warms the droplet of water it condenses upon which returns to the surface as rain at a temperature warmer than it would be without the latent heat. The difference in what it would have been had all the latent heat been returned drives weather and is returned as gravitational potential energy (hydro electric power). The energy returned by the liquid water rain is not radiative, but nearly all the energy of that latent heat is returned to the surface as weather, including rain and the potential energy of liquid water lifted against gravity.

Tom in Oregon City
January 6, 2017 5:09 pm

“Latent heat cools the surface water as it evaporates and warms the droplet of water it condenses upon which returns to the surface as rain at a temperature warmer than it would be without the latent heat.”
Where do you find such a description? Latent heat is released in order for water vapor to condense into liquid water again, and that heat is radiated away. Have you not noticed that water vapor condenses on cold surfaces, thus warming them? At the point of condensation the latent heat is lost from the now-liquid water, not when it strikes the earth again as rain.

Reply to  Tom in Oregon City
January 6, 2017 5:35 pm

Tom,
“… that heat is radiated away. ”
Where do you get this? How was water vapor radiate away latent heat? When vapor condenses, that heat is returns to the water is condenses upon and warms it. Little net energy is actually ‘radiated’ away from the condensing water since that atmospheric water is also absorbing new energy as it radiates stored energy consequential to its temperature. In LTE, absorption == emission and LTE sensitivity is all we care about.

Tom in Oregon City
January 6, 2017 8:22 pm

This is quite pointless. Pick up a physics book, and figure out how the surface of water is cooled by evaporation: it is because in order for a molecule of water to leave the surface and become water vapor, it must have sufficient energy to break its bonds to the surface. This is what we call the heat of evaporation, or latent heat: water vapor contains more energy than liquid water at the same temperature. When water vapor condenses back into water, the energy that allowed it to become vapor is radiated away. It does not stay because… then the molecule would still be vapor.
Your avatar, co2isnotevil, I completely agree with. Where you got your information about thermal energy in the water cycle, or about the “temperature” of radiative energy, that I cannot guess. Not out of a Physics book. But I have seen similar errors among those who do not believe that radiative energy transactions in the atmosphere have any effect on the surface temperature at all, even when presented with evidence of that radiative flux striking the surface from the atmosphere above. And in that crowd, understanding of thermodynamics is sorely lacking.

Reply to  Tom in Oregon City
January 7, 2017 9:28 am

Tom,
You didn’t answer my question. You assert that latent heat is somehow released into the atmosphere BEFORE the phase change. No physics text book will make this claim. I suggest that you perform this
experiment:

Now, why is the phase change from vapor to liquid any different, relative to where the heat ends up?

Tom in Oregon City
January 8, 2017 9:59 pm

co2isnotevil wrote “You assert that latent heat is somehow released into the atmosphere BEFORE the phase change.”
That is incorrect. The phase change forces the release of the latent heat, which itself was captured at the point of escape from the liquid state. But of course, that’s not the only energy change a molecule of water vapor undergoes on its way from the surface liquid state it left behind to the liquid state it returned to at sufficient altitude: there are myriad collisions along the way, each capable of either raising or lowering the energy of that molecule, along with radiative energy transactions where the molecule can either gain or lose energy. But we are talking about the AVERAGE here, for that is what TEMPERATURE is: an average energy measurement of some number of molecules, none of which must be at that exact temperature state.
Your experiment shows nothing outrageous or unexpected: the latent heat of fusion (freezing) is 334 joules, or 79.7 calories, per gram of water, while it takes only 1 calorie to raise the temperature of one gram of water by 1 degree. Therefore, as the water freezes to ice, those ice molecules are shedding latent heat even without changing temperature, and the remaining water molecules — and the temperature probe as well as the container — were receiving that heat. Thermal conductivity slows the probe’s reaction to changes in environment, and your experiment no longer shows something unexpected. Only your interpretation is unexpected, frankly.
The heat of fusion is much smaller than the heat of vaporization, which is 2,230 joules, or 533 calories, per gram.
Latent heat is not magic, or even complicated. Water becoming water vapor chills the surface, the vapor carries the heat aloft, where it is released by the action of condensation. Any Physics text — or even “Science” books from elementary school curricula — will bear out this definition.

Reply to  Tom in Oregon City
January 8, 2017 10:27 pm

“Water becoming water vapor chills the surface, the vapor carries the heat aloft, where it is released by the action of condensation.”
I would say this,
Evaporation cools by taking energy from the shared electron cloud of the liquid water that’s evaporating, the vapor carries the latent heat aloft, where the action of condensation adds it to the energy of the shared electron cloud of the water droplet it condenses upon, warming it.
The water droplet collides with other similarly warmed water droplets (no net transfer here) and with colder gas molecules (small transfer here). Of course, any energy transferred to a gas molecule is unavailable for contributing to the radiative balance unless it’s returned back to some water capable of radiating it away.

Tom in Oregon City
January 8, 2017 10:43 pm

The only part you got right: “the vapor carries the latent heat aloft”
“shared electron cloud” — you write as if you believe liquid water is one gigantic molecule.
You neglect the physics of collisions, and the pressure gradients of the atmosphere, and pretend latent heat all returns to earth in rain. Liquid water emits radiation, “co2isnotevil”. Surely you know this. That radiative emission spreads in all directions, with a large part of it escaping from space.
I’m done. I’ve already said this discussion is pointless, and I’ve wasted more than enough time. My physics books don’t read like you do; I’ll stick with them.

Reply to  Tom in Oregon City
January 8, 2017 10:57 pm

“you write as if you believe liquid water is one gigantic molecule.”
You’re being silly. But you do understand that the difference between a liquid and a gas is that the electrons clouds of individual molecules strongly interact, while in a gas, the only such interactions are elastic collisions where they never get within several molecular diameters of each other. This is also true for a solid, except that the molecules themselves are not free to move.
Think about how close together the molecules in water are. So much so that when it freezes into a solid, it expands.

January 6, 2017 7:12 pm

Water vapour will condense under conditions of atmosphere cooler than it’s gaseous state. It most certainly not warm as a function of condensing. It will give up latent heat to sensible heat in the surrounding medium. This is generally at altitude where much of this heat will radiate away to space.

January 6, 2017 8:07 pm

John,
“It will give up latent heat to sensible heat in the surrounding medium.”
The ‘medium’ is the water droplet that the vapor condenses on.
When water evaporates, it cools the water it evaporated from. When water freezes, the ice warms, just as when water condenses, the water it condenses upon warms. When ice melts, the surrounding ice cools. This is how salting a ski run works in the spring to solidify the snow.
The latent heat is not released until the phase change occurs, which is why it’s called ‘latent’.
What physical mechanism do you propose allows the latent heat to instantly heat the air around it when water vapor condenses?

January 7, 2017 11:27 am

“What physical mechanism do you propose allows the latent heat to instantly heat the air around it when water vapor condenses?”
The latent heat goes into the environment, bubble and air. On this scale, diffusion is fast. There is no unique destination for it. Your notion that the drops somehow retain the heat and return it to the surface just won’t work. The rain is not hot. Drops quickly equilibrate to the temperature of the surrounding air. On a small scale, radiation is insignificant for heat transfer compared to conduction.
Condensation often occurs in the context of updraft. Air is cooling adiabatically (pressure drop), and the LH just goes into slowing the cooling.

January 7, 2017 12:00 pm

“Your notion that the drops somehow retain the heat and return it to the surface just won’t work.”
Did you watch or do the experiment?
You’re claiming diffusion, but that requires collisions between water droplets and since you do not believe the heat is retained by the water, how can diffusion work?
The latent heat per H2O molecule is about 1.5E-19 joules. The energy of a 10u photons (middle of LWIR range of emissions) is about 2E-20 joules. Are you trying to say that upon condensation, at many LWIR photons are instantly released? Alternatively, the kinetic energy of an N2 or O2 molecule in motion at 343 m/sec is about 2.7E-20 joules, so are you trying to say that the velocity of the closest air molecule more than doubles? What laws of physics do you suggest explains this?
How does this energy leave the condensed water so quickly? And BTW, the latent heat of evaporation doesn’t even show up until the vapor condenses on a water droplet, so whatever its disposition, it starts in the condensing water.

angech
January 5, 2017 11:52 pm

“The complex General Circulation Models used to predict weather are the foundation for models used to predict climate change. They do have physics within them, but also have many buried assumptions, knobs and dials that can be used to curve fit the model to arbitrary behavior. The knobs and dials are tweaked to match some short term trend, assuming it’s the result of CO2 emissions, and then extrapolated based on continuing a linear trend. The problem is that there as so many degrees of freedom in the model, it can be tuned to fit anything while remaining horribly deficient at both hind casting and forecasting.”
Spot on.
I think the stuff about the simple grey body model contains some good ideas on energy balance but needs to be put together in a better way without the blanket statements.
“The Earth can be accurately modeled as a black body surface with a gray body atmosphere, whose combination is a gray body emitter whose temperature is that of the surface and whose emissions are that of the planet. ”
Accurate modelling is not possible with such a complex structure though well described.

January 6, 2017 12:13 am

“Accurate modelling is not possible with such a complex structure though well described.”
Unless it matches the data which Figure 3 tests and undeniably confirms the prediction of this model. As I also pointed out, I’ve been able to model the temperature dependence of the emissivity and the model matches the data even better. How else can you explain Figure 3?
Models are only approximations anyway and the point is that this approximation, as simple as it is, has remarkable predictive power, including predicting what the sensitivity must be.

January 6, 2017 9:35 am

The GCMs do not actually forecast. They equivocate, which is not the same concept.

January 6, 2017 7:14 pm

Hah! It’s forecasting without all that silly accountability!

January 6, 2017 10:01 pm

Right!

Brett Keane
January 6, 2017 12:27 am

When we remember that radiant energy is only a result of heat/temperature/ kinetic vibration rates in EM Fields, not a cause; we can start to avoid the tail-chasing waste of time that is modern climate ‘science’. When? Soon please.

richard verney
January 6, 2017 1:02 am

For matter that’s absorbing and emitting energy, the emissions consequential to its temperature can be calculated exactly using the Stefan-Boltzmann Law,

Can you actually use the Stefan-Boltzmann Law to something like Earth’s atmosphere which is never constant, its composition continually changes not least because of changes in water vapour and the composition of gases with respect to altitude?,

January 6, 2017 2:09 am

Richard Verney
“Can you actually use the Stefan-Boltzmann Law to something like Earth’s atmosphere”
It’s a good question, not so much about the constancy issues, but just applying to a gas. S-B applies to emission from surface of opaque solid or liquid. For gases, it is more complicated. Each volume emits an amount of radiation proportional to its mass and emissivity properties of the gas, which are very frequency-banded. There is also absorption. But there is a T^4 dependence on temperature as well.
I find a useful picture is this. For absorption at a particular frequency a gas can be thought of as a whole collection of little black balls. The density and absorption cross-section (absorptivity) determine how much is absorbed, and leads in effect to Beer’s Law. For emission, the same; the balls are now emitting according to the real Beer’s Law.
Looking down where the cross-sections are high, you can’t see the Earth’s surface. You see in effect a black body made of balls. But they aren’t all at the same temperature. The optical depth measures how far you can see into them. If it’s low, the temperature probably is much the same. Then all the variations you speak of don’t matter so much.

richard verney
January 6, 2017 5:15 am

Thanks.

For gases, it is more complicated. Each volume emits an amount of radiation proportional to its mass and emissivity properties of the gas, which are very frequency-banded. There is also absorption. But there is a T^4 dependence on temperature as well.

That was partly what I had in mind when raising the question, but you have probably better expressed it than I would have.
I am going to reflect upon insight of your second and third paragraphs.

January 6, 2017 9:13 am

Richard,
Gases are simple. O2 and N2 are transparent to visible light and LWIR radiation, so relative to the radiative balance, they are completely invisible. Most of the radiation emitted by the atmosphere comes from the water in clouds which is a BB radiator. GHG’s are just omnidirectional, narrow band emitters and relative to equivalent temperature, Joules of photons are Joules of photons, independent of wavelength. The only important concept is the steradian component of emissions which is a property of EM radiation, not black or gray bodies.

January 6, 2017 6:15 am

“For emission, the same; the balls are now emitting according to the real Beer’s Law.”
Oops, I meant the real Stefan-Boltzmann law.

JohnKnight
January 6, 2017 3:25 pm

co2isnotevil,
“Most of the radiation emitted by the atmosphere comes from the water in clouds which is a BB radiator. GHG’s are just omnidirectional, narrow band emitters and relative to equivalent temperature, Joules of photons are Joules of photons, independent of wavelength.”
The directional aspects of water droplet reflection interest me, in that the shape of very small droplets is dominated by surface tension forces, which means they are spherical . . which means (to this ignorant soul) that those droplets ought to be especially reflective straight back in the direction in the light arrives from, rather than simply skittering the light, owing to their physical shape.
This hypothetical behavior might have ramifications, particularly in the realms of cloud/mist albedo, I feel, but your discussion here makes me wonder if it might have ramifications in terms of “focused” directional “down-welling” radiation as well, as in the warmed surface being effectively mirrored by moisture in the atmosphere above it . .
Pleas make me sane, if I’m drifting into crazyville here ; )

January 6, 2017 3:53 pm

John,
Wouldn’t gravity drive water droplets into tear drop shapes, rather than spheres? Certainly rain is heavy enough that surface tension does not keep the drops spherical, especially in the presence of wind.
Water drops both absorb and reflect photons of light and LWIR, but other droplets are moving around so it doesn’t bounce back to the original source, but off some other drop that passed by and so on and so forth. Basic scattering.

JohnKnight
January 6, 2017 5:03 pm

co2isnotevil.
“Wouldn’t gravity drive water droplets into tear drop shapes, rather than spheres?”
When they are large (and falling) sure, but most are not so large, of course. I did some investigating, and it seems very small droplets are dominated by surface tension forces and are generally quite spherical.
“Water drops both absorb and reflect photons of light and LWIR. . ”
That’s key to the questions I’m pondering now, the LWIR. Some years ago I “discovered” that highway line paint is reflective because tiny glass beads are mixed into it, and the beads tend to reflect light right back at the source (headlights in this case). I’ve never seen any discussion about the potential for spherical water droplets to preferentially reflect directly back at the source, rather than full scattering. It may be nothing, but I suspect there may be a small directionality effect that is being overlooked . . Thanks for the kind response.

January 6, 2017 5:59 pm

That’s key to the questions I’m pondering now, the LWIR. Some years ago I “discovered”

As rel humidity goes to nearly 100% outgoing radiation drops by about 2/3rds, one good possibility is fog that is effective in LWIR, but outside the 8-14u window because it and optical are still clear. This or both co2 and WV both start to radiate and start exchanging photons back and forth. But it drops based on dew point temperature.

JohnKnight
January 6, 2017 10:26 pm

Thanks, micro, that’s some fascinating detail to consider . .

January 6, 2017 8:59 am

Richard,
Unless the planet and atmosphere is not comprised of matter, the SB law will apply in the aggregate. People get confused by being ‘inside’ the atmosphere, rather than observing it from a far. We are really talking about 2 different things here though. The SB law converts between energy and equivalent temperature. The steradian component of where radiation is going is common to all omnidirectional emittersm broad band (Planck) or narrow band emitters (line emissions).
The SB law is applied because climate science is stuck in the temperature domain and the metric of sensitivity used is temperature as a function of radiation. What’s conserved is energy, not temperature and this disconnect interferes with understanding the system.

January 6, 2017 1:51 am

The Earth/atmosphere system is a grey body for the period of time it takes for the first cycle of atmospheric convective overturning to take place.
During that first cycle less energy is being emitted than is being received because a portion of the surface energy is being conducted to the atmosphere and convected upward thereby converting kinetic energy (heat) to potential energy (not heat).
Once the first convective overturning cycle completes then potential energy is being converted to kinetic energy in descent at the same rate as kinetic energy is being converted to potential energy in ascent and the system stabilises with the atmosphere entering hydrostatic equilibrium.
Once at hydrostatic equilibrium the system then becomes a blackbody which satisfies the S-B equation provided it is observed from outside the atmosphere.
Meanwhile the surface temperature beneath the convecting atmosphere must be above the temperature predicted by S-B because extra kinetic energy is needed at the surface to support continuing convective overturning.
That scenario appears to satisfy all the basic points made in George White’s head post.

January 6, 2017 2:14 am

“What law(s) of physics can explain how to override the requirements of the Stefan-Boltzmann Law as it applies to the sensitivity of matter absorbing and emitting energy, while also explaining why the data shows a nearly exact conformance to this law?”
The conditions that must apply for the S-B equation to apply are specific:
“Quantitatively, emissivity is the ratio of the thermal radiation from a surface to the radiation from an ideal black surface at the same temperature as given by the Stefan–Boltzmann law. The ratio varies from 0 to 1”
From here:
https://en.wikipedia.org/wiki/Emissivity
and:
“The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time (also known as the black-body radiant emittance or radiant exitance), , is directly proportional to the fourth power of the black body’s thermodynamic temperature T:”
In summary, when a planetary surface is subjected to insolation the surface temperature will rise to a point where energy out will match energy absorbed. That is a solely radiative relationship where no other energy transmission modes are involved.
For an ideal black surface the ratio of energy out to energy in is 1 (as much goes out as comes in) which is often referred to as ‘unity’. The temperature of the body must rise until 1 obtains.
For a non-ideal black surface there is some leeway to account for conduction into and out of the surface such that where there is emission of less than unity the body is more properly described as a greybody. For example an emissivity of 0.9 but for rocky planets such processes are minimal and unity is quickly gained for little change in surface temperature which is why the S-B equation gives a good approximation of the surface temperature to be expected.
Where all incoming radiation is reflected straight out again without absorption then that is known as a whitebody
During the very first convective overturning cycle a planet with an atmosphere is not an ideal blackbody because the process of conduction and convection draws energy upward and away from the surface. As above, the surface temperature drops from 255K to 222K. The rate of emission during the first convective cycle is less than unity so at that point the planet is a greybody. The planet substantially ceases to meet the blackbody approximation implicit in the requirements of the S-B equation.
Due to the time taken by convective overturning in transferring energy from the illuminated side to the dark side (the greybody period) the lowered emissivity during the first convective cycle causes an accumulation within the atmosphere of a far larger amount of conducted and convected energy than that small amount of surface conduction involved with a rocky surface in the absence of a convecting atmosphere and so for a planet with an atmosphere the S-B equation becomes far less reliable as an indicator of surface temperature. In fact, the more massive the atmosphere the less reliable the S-B equation becomes.
For the thermal effect of a more massive atmosphere see here:
http://onlinelibrary.wiley.com/doi/10.1002/2016GL071279/abstract
“We find that higher atmospheric mass tends to increase the near-surface
temperature mostly due to an increase in the heat capacity of the
atmosphere, which decreases the net radiative cooling effect in the lower
eddies decreases with increasing atmospheric mass, resulting in further
near-surface warming.”
At the end of the first convective cycle there is no longer any energy being drawn from the incoming radiation because, instead, the energy required for the next convective cycle is coming via advection from the unilluminated side. At that point the planet reverts to being a blackbody once more and unity is regained with energy out equalling energy in.
But, the dark side is 33K less cold than it otherwise would have been and the illuminated side is 33K warmer than it should be at unity. The subsequent complex interaction of radiative and non- radiative energy flows within the atmosphere does not need to be considered at this stage.
The S-B equation being purely radiative has failed to account for surface kinetic energy engaged in non-radiative energy exchanges between the surface and the top of the atmosphere.
The S-B equation does not deal with that scenario so it would appear that AGW theory is applying that equation incorrectly.
It is the incorrect application of the S-B equation that has led AGW proponents to propose a surface warming effect from DWIR within the atmosphere so as to compensate for the missing non-radiative surface warming effect of descending air that is omitted from their energy budget. That is the only way they can appear to balance the budget without taking into account the separate non-radiative energy loop that is involved in conduction and convection.

paqyfelyc
January 6, 2017 3:45 am

I really don’t think that
“The Earth can be accurately modeled as a black body surface with a gray body atmosphere”
This is utterly inaccurate because of the massive energy flux between those, that make them behave as a single thing : the tiny pellicle of the whole Earth, which also include ocean water a few meter deep, and other thing such like forests and human building. This pellicle may seem huge and apt to be separated in components from our human very small scale, but from a Stefan-Boltzmann Law perspective this shouldn’t be done.
AND
remember that photosynthesis has a magnitude ( ~5% of incoming energy) greater than that of the so called “forcing” or other variations. It just cannot be ignored… but it is !

January 6, 2017 9:09 am

paqyfelyc,
“The Earth can be accurately modeled as a black body surface with a gray body atmosphere”
Then what is your explanation for Figure 3? Keep in mind that the behavior in Figure 3 was predicted by the model. This is just an application of the scientific method where predictions are made and then tested.

January 6, 2017 7:21 pm

Photosynthesis is a process of conversion of electromagnetic energy to chemical potential energy. In total and over time, all energy fixed by photosynthesis is given up and goes back to space. Photosynthesis may retain some energy on the surface for a time but that energy is not thermal and has virtually no effect on temperature.

January 6, 2017 8:15 pm

John,
“This is utterly inaccurate because of the massive energy flux between those”
The net flux passing from the surface to the atmosphere is about 385 W/m^2 corresponding the the average temperature of about 287K. Latent heat, thermals and any non photon transport of energy is a zero sum influence on the surface. The only effect any of this has is on the surface temperature and the surface temperature adjusted by all these factors is the temperature of the emitting body.
Trenberth messed this up big time which has confused skeptics and warmists alike by the conflating energy transported by photons with the energy transported by matter when the energy transported by matter is a zero sum flux at the surface. What he did was lump the return of energy transported by matter (weather, rain, wind, etc) as ‘back radiation’ when non of these are actually radiative. As best I can tell, he did this because it made the GHG effect look much larger than it really is.

Thomas Homer
January 6, 2017 5:44 am

” … warm the surface by absorbing some fraction of surface emissions and after some delay, recycling about half of the energy back to the surface.”
Ahhh, there’s the magic! The surface warms itself.

Thomas Homer
January 6, 2017 6:34 am

Are the laws of physics suspended during the “delay”? What’s causing the delay?
What is the duration of the delay since those emissions are travelling at the speed of light?
What’s the temperature delta of the surface between the emission and when it’s own energy is recycled back?
If the delay and the delta are each insignificant, then the entire effect is insignificant.

January 6, 2017 9:27 am

Thomas,
“What’s causing the delay?”
The speed of light. For photons that pass directly from the surface to space, this time is very short. For photons absorbed and re-emitted by GHG’s (or clouds), the path the energy takes is not a straight line and takes longer, moreover; the energy is temporally stored as either the energy of a state transition, or energy contributing to the temperature of liquid or solid water in clouds.

Thomas Homer
January 6, 2017 11:03 am

co2isnotevil replied below with: “For photons absorbed and re-emitted by GHG’s (or clouds), the path the energy takes is not a straight line and takes longer”
I’m asking how much longer, twice as long? Show me where and how long the duration is of any significant delay. Is it the same order of magnitude as the amount of time a room full of mirrors stays lit after turning out the lights? IOW, insignificant?
Now, instead of considering these emissions as a set of photons, consider them as a relentless wave and you’ll see there is no significant delay.

January 6, 2017 11:30 am

At 1 ns per foot, it takes on the order of a milisecond for a photon to pass directly from the surface to space. Photons delayed by GHG absorption/re-emission will take on the order of seconds to as much as a minute. Photons of energy delayed by being absorbed by the water in clouds before being re-emitted is delayed on the order of minutes. It’s this delayed energy distributed over time and returned to the surface that combines with incident solar energy and contributes to GHG/cloud warming which of course is limited by the absorption of prior emissions.
The delay doesn’t need to be long, just non zero in order for ‘old energy’ from prior surface emissions to be combined with ‘new energy’ from the Sun.

richard verney
January 6, 2017 12:50 pm

But the sun does not shine at night (over half the planet).
That is one of the facts that the K&T energy budget cartoon (whatever it should be called)fails to note.

January 6, 2017 1:15 pm

Richard,
“But the sun does not shine at night (over half the planet).”
This is one of the factors of 2 in the factor of 4 between incident solar energy and average incident energy. The other factor of 2 comes from distributing solar energy arriving in a plane across a curved surface whose surface area is twice as large. Of course, we can also consider the factor of 4 to be the ratio between the surface area of a sphere and the area that solar energy arrives from the Sun, half of this sphere is in darkness at all times.
The Earth spins fast enough and the atmosphere smooths out night and day temps, so this is a reasonable thing to do relative to establishing an average. Planets tidal locked to its energy source (for example Mercury), would only divide the incident power by 2.

Thomas Homer
January 6, 2017 1:23 pm

[ co2isnotevil –
“Photons of energy delayed by being absorbed by the water in clouds before being re-emitted is delayed on the order of minutes” ]
Order of minutes? So, the laws of physics are being suspended then.
A photon can bounce from the surface up to 40 Kilometers and back 3200 times per second if it were reflected without delay. And your claim is that it is delayed an order of minutes? I find that extremely doubtful. The transfer of heat is relentless. Do all of those photons take a vacation in the clouds?
But my question also asked what the surface temperature delta is for the duration of your claimed delay. I’ll give you two minutes, what is the temperature delta in two minutes? That vacationing photon was emitted from the surface at some temperature, what is the surface temperature when it returns to the surface? Has it lost more energy than the surface during its vacation in the clouds?
[ co2isnotevil –
“The delay doesn’t need to be long, just non zero in order for ‘old energy’ from prior surface emissions to be combined with ‘new energy’ from the Sun.” ]
But the duration of the delay is precisely the point, that’s how long this “old energy” is available to combine with “new energy”. It’s insignificant. You’re imagining that this “old energy” is cumulative, it is not.
Does the planet Mercury make the sun hotter since it’s emitting photons back towards the sun’s surface?

January 6, 2017 2:49 pm

Thomas,
“Order of minutes? So, the laws of physics are being suspended then.”
Why do you think physics needs to be suspended? Is physics suspended when energy is stored in a capacitor? How does storing energy as a non ground state GHG molecule, or as the temperature of liquid/solid water in a cloud any different? What law of physics do you think is being suspended?
Each time a GHG absorbs a photon, temporarily storing energy as a time varying EM field, and emits another photon as it returns to the ground state, the photon goes in a random direction. The path the energy takes can be many 1000’s of times longer than a direct path from the surface to space.

Thomas Homer
January 6, 2017 5:06 pm

“The path the energy takes can be many 1000’s of times longer than a direct path from the surface to space.”
How about 384,000? Is that “many of 1000’s”? That’s two minutes of bouncing 40K @ 3200 trips per second.
Think of it rather as a wave, a relentless wave. Heat continually seeks escape, it does not delay.

January 6, 2017 5:31 pm

“Think of it rather as a wave, a relentless wave. Heat continually seeks escape, it does not delay.”
But we are taking about photons here and to escape means either leaving the top of the atmosphere or leaving the bottom and returning to the surface and being massless, the photon has no idea which was is up or down. And 100’s of thousands of ‘bounces’ between GHG molecules is not unreasonable. But the absolute time is meaningless and in fact the return to the surface of absorbed emissions from one point in time are spread out over a wide region of time in the future. All that matters is that the round trip time from the surface and back to the surface is > 0.

beng135
January 6, 2017 6:29 am

Very interesting analysis, but this is far too complicated for climate scientists/MSM and will be ignored.

January 6, 2017 9:24 am

“but this is far too complicated …”
Actually, its not complicated enough.

January 6, 2017 6:57 am

What law(s) of physics can explain how to override the requirements of the Stefan-Boltzmann Law as it applies to the sensitivity of matter absorbing and emitting energy, while also explaining why the data shows a nearly exact conformance to this law?

Because another force exceeds it. Water vapor over powers all of the co2 forcing.
Here https://micro6500blog.wordpress.com/2016/12/01/observational-evidence-for-a-nonlinear-night-time-cooling-mechanism/
And measured effective sensitivity at the surface.
here https://micro6500blog.wordpress.com/2016/05/18/measuring-surface-climate-sensitivity/

January 6, 2017 9:29 am

“Because another force exceeds it.”
Water vapor is not a force, but operates in the same way as CO2 absorption, except as you point out, H2O absorption is a more powerful effect. When I talk about the GHG effect, I make no distinction between CO2, H2O or any other LWIR active molecule.

January 6, 2017 9:40 am

well I was referring to the force of it’s radiation as it was being emitted, but fair enough. Also since they over lap there could be some interplay between them that is not expected.

January 6, 2017 7:00 am

References:
Trenberth et al 2011jcli24 Figure 10
This popular balance graphic and assorted variations are based on a power flux, W/m^2. A W is not energy, but energy over time, i.e. 3.4 Btu/eng h or 3.6 kJ/SI h. The 342 W/m^2 ISR is determined by spreading the average 1,368 W/m^2 solar irradiance/constant over the spherical ToA surface area. (1,368/4 =342) There is no consideration of the elliptical orbit (perihelion = 1,416 W/m^2 to aphelion = 1,323 W/m^2) or day or night or seasons or tropospheric thickness or energy diffusion due to oblique incidence, etc. This popular balance models the earth as a ball suspended in a hot fluid with heat/energy/power entering evenly over the entire ToA spherical surface. This is not even close to how the real earth energy balance works. Everybody uses it. Everybody should know better.
An example of a real heat balance based on Btu/h follows. Basically (Incoming Solar Radiation spread over the cross sectional area) = (U*A*dT et. al. leaving the lit side perpendicular to the spherical surface ToA) + (U*A*dT et. al. leaving the dark side perpendicular to spherical surface area ToA) The atmosphere is just a simple HVAC/heat balance/insulation problem.
http://earthobservatory.nasa.gov/IOTD/view.php?id=7373
“Technically, there is no absolute dividing line between the Earth’s atmosphere and space, but for scientists studying the balance of incoming and outgoing energy on the Earth, it is conceptually useful to think of the altitude at about 100 kilometers above the Earth as the “top of the atmosphere.” The top of the atmosphere is the bottom line of Earth’s energy budget, the Grand Central Station of radiation. It is the place where solar energy (mostly visible light) enters the Earth system and where both reflected light and invisible, thermal radiation from the Sun-warmed Earth exit. The balance between incoming and outgoing energy at the top of the atmosphere determines the Earth’s average temperature. The ability of greenhouses gases to change the balance by reducing how much thermal energy exits is what global warming is all about.”
ToA is 100 km or 62 miles. It is 68 miles between Denver and Colorado Springs. That’s not just thin, that’s ludicrous thin.
The GHE/GHG loop as shown on Trenberth Figure 10 is made up of three main components: upwelling of 396 W/m^2 which has two parts: 63 W/m^2 and 333 W/m^2 and downwelling of 333 W/m^2.
The 396 W/m^2 is determined by inserting 16 C or 279K in the S-B BB equation. This result produces 55 W/m^2 of power flux more than ISR entering ToA, an obvious violation of conservation of energy created out of nothing. That should have been a warning.
ISR of 341 W/m^2 enter ToA, 102 W/m^2 are reflected by the albedo, leaving a net 239 W/m^2 entering ToA. 78 W/m^2 are absorbed by the atmosphere leaving 161 W/m^2 for the surface. To maintain the energy balance and steady temperature 160 W/m^2 rises from the surface (0.9 residual in ground) as 17 W/m^2 convection, 80 W/m^2 latent and 63 W/m^2 LWIR (S-B BB 183 K, -90 C or emissivity = .16) = 160 W/m^2. All of the graphic’s power fluxes are now present and accounted for. The remaining 333 W/m^2 are the spontaneous creation of an inappropriate application of the S-B BB equation violating conservation of energy.
But let’s press on.
The 333 W/m^2 upwelling/downwelling constitutes a 100% efficient perpetual energy loop violating thermodynamics. There is no net energy left at the surface to warm the earth and there is no net energy left in the troposphere to impact radiative balance at ToA.
The 333 W/m^2, 97% of ISR, upwells into the troposphere where it is allegedly absorbed/trapped/blocked by a miniscule 0.04% of the atmosphere. That’s a significant heat load for such a tiny share of atmospheric molecules and they should all be hotter than two dollar pistols.
Except they aren’t.
The troposphere is cold, -40 C at 30,000 ft, 9 km, < -60 C at ToA. Depending on how one models the troposphere, average or layered from surface to ToA, the S-B BB equation for the tropospheric temperatures ranges from 150 to 250 W/m^2, a considerable, 45% to 75% of, shortfall from 333.
(99% of the atmosphere is below 32 km where energy moves by convection/conduction/latent/radiation & where ideal S-B does not apply. Above 32 km the low molecular density does not allow for convection/conduction/latent and energy moves by S-B ideal radiation et. al.)
But wait!
The GHGs reradiate in all directions not just back to the surface. Say a statistical 33% makes it back to the surface that means 50 to 80 W/m^2. A longer way away from 333, 15% to 24% of.
But wait!
Because the troposphere is not ideal the S-B equation must consider emissivity. Nasif Nahle suggests CO2 emissivity could be around 0.1 or 5 to 8 W/m^2 re-radiated back to the surface. Light years from 333, 1.5% to 2.4% of.
But wait!
All of the above really doesn’t even matter since there is no net connection or influence between the 333 W/m^2 thermodynamically impossible loop and the radiative balance at ToA. Just erase this loop from the graphic and nothing else about the balance changes.
BTW 7 of the 8 reanalyzed (i.e. water board the data till it gives up the right answer) data sets/models show more power flux leaving OLR than entering ASR ToA or atmospheric cooling. Trenberth was not happy. Obviously, those seven data sets/models have it completely wrong because there can’t possibly be any flaw in the GHE theory.
The GHE greenhouse analogy not only doesn’t apply to the atmosphere, it doesn’t even apply to warming a real greenhouse. (“The Discovery of Global Warming” Spencer Weart) It’s the physical barrier of walls, glass, plastic that traps convective heat, not some kind of handwavium glassy transparent radiative thermal diode.
The surface of the earth is warm for the same reason a heated house is warm in the winter: Q = U * A * dT, the energy flow/heat resisting blanket of the insulated walls. The composite thermal conductivity of that paper thin atmosphere, conduction, convection, latent, LWIR, resists the flow of energy, i.e. heat, from surface to ToA and that requires a temperature differential, 213 K ToA and 288 K surface = 75 C.
The flow through a fluid heat exchanger requires a pressure drop. A voltage differential is needed to push current through a resistor. Same for the atmospheric blanket. A blanket works by Q = U * A * dT, not S-B BB.
The atmosphere is just a basic HVAC system boundary analysis.
Open for rebuttal. If you can explain how this upwelling/downwelling/”back” radiation actually works be certain to copy Jennifer Marohasy as she has posted a challenge for such an explanation.