# Top and Bottom of the Atmosphere

Guest Post by Willis Eschenbach

Some days I learn a lot. Today was one of them. Let me start at the start. Back in 1987 in a paper entitled ‘The Role of Earth Radiation Budget Studies in Climate and General Circulation Research“, a prescient climate scientist yclept Veerabhadran Ramanathan pointed out that the poorly-named “greenhouse effect” can be measured as the amount of longwave energy radiated upwards at the surface minus the upwelling longwave radiation at the top of the atmosphere, viz:

The greenhouse effect. The estimates of the outgoing longwave radiation also lead to quantitative inferences about the atmospheric greenhouse effect. At a globally averaged temperature of 15°C the surface emits about 390 W m -2, while according to satellites, the long-wave radiation escaping to space is only 237 W m -2. Thus the absorption and emission of long-wave radiation by the intervening atmospheric gases and clouds cause a net reduction of about 150 W m -2 in the radiation emitted to space. This trapping effect of radiation, referred to as the greenhouse effect, plays a dominant role in governing the temperature of the planet.

And here is what Ramanathan was talking about:

Figure 1. All-sky (both cloudy and clear) greenhouse effect. In climate science, “upwelling” means headed for space, “downwelling” means headed for the surface, “forcing” means a change in downwelling radiation, “LW” is thermal longwave radiation, and “SW” is solar shortwave radiation.

The best modern information about this question comes from the CERES Energy Balanced and Filled (EBAF) dataset that I used to make Figure 1. It combines a number of satellite and other measurements into a single coherent group of individual datasets. Interestingly, Ramanathan’s estimate of the size of the greenhouse effect was “about 150 W/m2” and modern CERES data shows a number very close to that, 158 W/m2. Well done, that man!

Today, a chance comment got me thinking about top-of-atmosphere (TOA) downwelling longwave radiation versus what happens at the surface. A doubling of CO2 is supposed to lead to a 3.7 W/m2 increase in downwelling TOA longwave radiation … but what does that do to downwelling LW at the surface?

So what I did was to calculate on a monthly basis, the change in downwelling longwave radiation at the surface for each one W/m2 change in TOA greenhouse radiation. Figure 2 shows that result.

Figure 2. Change in downwelling radiation at the surface for each 1 W/m2 change in downwelling TOA radiation.

Now, this is curious. On average the change at the surface is a little less than half the TOA greenhouse effect change. So an increase of 3.7 W/m2 at the TOA from a doubling of CO2 becomes a 1.8 W/m2 increase at the surface. I would note that this value of 0.46 agrees in general with the published study of Feldman et al. in Nature magazine who found (from observations, not models) that surface forcing is 0.43 times the TOA forcing, quite near to the above figure.

Next, I got to wondering about something I’d never looked at—just how large an additional energy flux in watts per square metre of energy is needed to increase the surface temperature by 1°C. This is a simple calculation using the Stefan-Boltzmann equation, but I’d never done it for the entire globe. Figure 3 shows that result.

Figure 3. Increase in ongoing downwelling energy flux needed to increase the surface temperature by 1°C with everything else unchanged.

In Figure 3 you can see that as Stefan-Boltzmann says, it takes more energy to raise a hot surface by 1°C than to raise a cold surface by 1°C. And for the globe, the average is about 5.5 W/m2 per degree. That was a surprise to me, I didn’t expect it to be quite that large … but then as I said, I’d never calculated it.

So here’s the summary of today’s wanderings in CERESville.

• The long-accepted value for a doubling of CO2 gives a theoretical 3.7 W/m2 increase in downwelling TOA radiation. However, because of all of the factors that affect downwelling TOA radiation (changes in clouds, temperature, water vapor, eruptions, aerosols, etc.) and the fact that the log of CO2 is essentially a straight line, it’s not possible to determine that value experimentally. Here’s the problem:

Figure 4. Ramanathan’s greenhouse radiation, along with the change in CO2 radiation over the period. The CO2 radiation change has been set to the average of the greenhouse radiation for easy comparison.

Using that accepted 3.7 W/m2 figure for a doubling of CO2, that would give an increase in downwelling surface radiation of 1.8 W/m2.

• This doubling of CO2, in turn, would warm the surface by:

1.8 watts per square metre CO2 surface forcing / 5.5 watts per square metre per degree C ≈ 0.3°C …

By comparison, the IPCC says that a doubling of CO2 would increase the surface temperature by 1.5°C to 4.5°C. If we take the midrange value of 3°C, this would imply that there is some mysterious feedback increasing the CO2-caused surface temperature change by a factor of about ten …

The general view seems to be that this mysterious ten-fold increase is somehow the result of feedback from water vapor and clouds. The problem with that theory is that the CERES measurements I’ve used above include all of those feedbacks. That is to say, the GHE value includes the feedback effects of clouds and water vapor, and the surface downwelling radiation also includes those feedbacks.

Answers gladly accepted. Here on the northern California coast, despite the screaming about “PERPETUAL CALIFORNIA DROUGHT! CLIMATE EMERGENCY!” … it’s raining again, the trees are happy, and the cat is not.

My best regards to all,

w.

NOTES: For those unclear on the physics behind the poorly-named “greenhouse effect”, it works because a sphere only has one surface, and a shell has two surfaces, inside and outside. See “The Steel Greenhouse“, “People Living In Glass Planets“, and “The R. W. Wood Experiment” for further discussion.

MY USUAL REQUEST: When you comment please quote the exact words you are discussing, so we can all be clear on your exact subject.

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January 20, 2020 10:14 pm

Willis,
“A doubling of CO2 is supposed to lead to a 3.7 W/m2 increase in downwelling TOA longwave radiation”

Is that really true? Do you have a source? Doubling is supposed to lead to a 3.7 W/m2 increase in forcing. That is, in energy flux available to result in surface warming. But I haven’t seen a claim that it would produce a measurable IR flux of that magnitude anywhere.

Antero Ollila
January 21, 2020 2:18 am

Just a comment for Figure 4. The yellow trend line has been named by “Greenhouse radiation”. It is the difference between the surface emitted radiation and the atmosphere emitted radiation. Which is normally 395 – 240 = 155 W/m2. In this trend line is the super El Nino 2015-16 included. It cannot be caused by GH effects. I think that this is a problem in using real observations. There are many – even strong impacts like ENSO – included and therefore these observations cannot be called Greenhouse effects only.

Samuel C Cogar
January 22, 2020 12:27 pm

If one measures the temperature (thermal heat energy) of the atmosphere, they are in actuality measuring the temperature of all the gas molecules (N2, O2, H2O, CO2, etc.) that are resident in the locale that the temperature is being recorded.

All atmospheric gas molecules can conduct thermal heat energy “to & from” all other gas molecules that they come in contact with.

The per se “greenhouse” (radiant) gas molecules can ALSO, both radiate and absorb IR (infrared) thermal heat energy “to & from” all other “greenhouse” gas molecules, … as well as “to & from” the earth’s surface and to outer space.

So, given the fact that both the H2O and CO2 molecules are “conducting” thermal heat energy “to & from” all other gas molecules, ….. plus radiating and absorbing IR (infrared) thermal heat energy, ….. how is it possible to accurately calculate the “role” that CO2 plays ….. “in size of the greenhouse effect”?

Cube
January 21, 2020 4:13 pm

Yes, don’t wanna use real observations when doing “science” they screw up the results. Use models or made up observations they give much better graphs.

Butch123
January 24, 2020 6:57 am

Willis,

Feldman apparently was NOT able to directly measure downwelling IR in the 15 micron band. Gero tried and failed, despite the AERI instruments being designed specifically to make that type of direct measurement. These instruments are extremely sensitive and there is no reason that the signal should not be able to be detected directly.

What Feldman did once he was brought in to evaluate why downwelling CO2 radiation could not be detected, was to create a SIMULATED signal to be combined with the actual signal received.

Viola! The result was a detectable CO2 downwelling signal. It smacks of Mannian manipulation.
I cannot put my finger on the walnut shell that actually has the pea under it but hopefully someone can

Olof R
January 21, 2020 1:09 am

I think the downwelling longwave radiation at TOA is very close to zero. The satellites that do the readings fly at an altitude of around 700 km. Only very little “cold space” back radiation there, nothing to do with atmospheric greenhouse gases.
For practical reasons TOA is sometimes calculated to be above the tropopause, say at 20 km altitude. The greenhouse effect is negative in the stratosphere..

Johanus
January 21, 2020 4:22 am

Olof,
“I think the downwelling longwave radiation at TOA is very close to zero.”

Of course it is zero because, by definition, there is no “atmosphere” to be heated beyond the TOA. The satellites measure upwelling radiation, escaping from the atmosphere to space.

Surprisingly, looking at the entire electromagnetic spectrum (“DC to daylight and beyond”) the Earth’s atmosphere is mostly opaque to EMR in general. But there are two big gaps (“windows”) in the absorption spectrum, which tend to fool us humans into believing the atmosphere is “mostly transparent”.

http://coolcosmos.ipac.caltech.edu/cosmic_classroom/ir_tutorial/irwindows.html

The first window is in the radio frequency (RF) spectrum, roughly from mediumwave to microwave, which allows radio transmissions to and from outer space.

The second window is the visible light and infra-red spectra, which includes longwave IR. However the IR window is onlypartially transparent (but very transparent around 10μm).

There are many satellites which observe this light through the atmosphere from above. For example, here’s a summary of the GOES-16 IR viewing “channels”.
https://www.weather.gov/media/crp/GOES_16_Guides_FINALBIS.pdf

Antero Ollila
January 21, 2020 5:22 am

The outgoing LW radiation is 240 W/m2 and it is a sum of two fluxes: 212 W/m2 emitted by the atmosphere (around the height of 9 kilometers, because thereafter there is no much material) and the transmitting flux from the surface 28 W/m2; totally 240 W/m2.

Kevin kilty
January 21, 2020 9:41 am

Use MODTRAN to do the calculations, and you will find that doubling (375 to 750 in this instance) produces a difference of about $3.2 W/m^2$ at the top (70km actually) of a tropical atmosphere. So, Willis’s value seems reasonable even without a reference to back it up.

January 21, 2020 3:10 pm

Kevin,
My question was whether the 3.7 W/m2 was an IR flux that could be observed. You can do a Modtran calculation, but it depends on your assumptions. Willis quoted below the section of AR5, which I’ll extract:

“RF is defined, as it was in AR4, as the change in net downward radiative flux at the tropopause after allowing for stratospheric temperatures to readjust to radiative equilibrium, while holding surface and tropospheric temperatures and state variables such as water vapor and cloud cover fixed at the unperturbed values. ERF is the change in net TOA downward radiative flux after allowing for atmospheric temperatures, water vapour and clouds to adjust,but with surface temperature or a portion of surface conditions unchanged.”

They are theoretical values with assumptions; in observation the surface temperature does not remain unchanged, but warms. In fact at equilibrium, the observed RF would be zero.

Snape
January 21, 2020 5:10 pm

@Nick Stokes

Good catch. According to Trenberth’s energy budget diagram:

Downwelling solar: 341.3 w/m2
Upwelling reflected: 101.9 w/m2
Upwelling LW: 238.5 w/m2

Net: 0.9 w/m2 downwelling

*******

I see no reason a doubling of CO2 would cause this value to change much. Like you pointed out, the 3.7 w/m2 at the TOA is a hypothetical given no surface or troposphere warming, ie. no adjustment to upwelling.

ColA
January 22, 2020 3:13 pm

There are plenty of studies that indicate that a doubling of CO2 calculates to less than 0.5 C, without following the math in detail, to agree with the IPCC models it would require Willis calculations to be out by a factor or 10, can anybody point to the 10????

Michael Hammer
January 21, 2020 1:48 pm

I firmly believe that CAGW is a false theory but even so I feel that as a scientist I need to point out a fallacy here.

The action of a green house gas is to absorb surface emission at the green house gas wavelengths (instead of it escaping to space) and replace it with radiation at those wavelengths escaping to space from the top of the green house gas column. Since the top of the green house gas column is typically the tropopause or more accurately the lower stratosphere which is colder than the surface overall emission to space is reduced.

This bimodal effect happens because for most GHG’s the atmospheric column is so thick. Spectroscopists use the term absorbance to describe the impact of absorbing substances. An absorbance of 1 means the substance (in this case the atmospheric ghg column) absorbs 90% of the incident radiation. An absorbance of 2 means it absorbs 99%, an absorbance of 3 means it absorbs 99.9% and so on. So what is the absorbance of the atmospheric CO2 gas column? Answer about 3000 absorbance!!!!! Most of the surface emission is absorbed in the first few meters!

That is WAY into saturation and begs the question, does further increase change anything? The answer is yes it does, in fact GHG’s in the atmosphere only become significant AFTER they saturate. The reason is that the absorbance profile is not a box car but rather something very close to a gaussian (actually a Lorentz profile). Gaussian profiles never go to exactly zero. One of the features of a gaussian is that convolving the spectrum with itself (equivalent to doubling the concentration) gives a new gaussian with the same mean but a greater standard deviation. Each doubling gives approximately the same increase in line width. Increasing the line width means the GHG column absorbs over a slightly greater range of wavelengths (ie: it intercepts more of the surface radiation) and this is the source of the logarithmic relationship between concentration and retained energy. Before the gas column saturates the relationship is closer to linear but the unbroadened line is so narrow that the total impact is nearly negligible. It is only when the line broadens after saturation of the line center that the impact becomes significant.

The energy retained by doubling concentration will be the additional surface radiation blocked minus the additional top of gas column radiation. This is easily calculated using Planks law but even without any calculations it is obvious that since the additional top of gas column radiation is not zero (since the top of gas column is nowhere near absolute zero) the additional surface radiation blocked must be larger than the energy retained, not less than it. I have done the Planks law calculation and it turns out that for a 3.7 watt/sqM total change in retained energy for the planet, the incremental surface radiation blocked is around 5.5 watts/sqM which corresponds to about 1C of warming before feedbacks. This seems to agree with the claims I have seem from both warmists and skeptics. The BIG issue of course is what are the feedbacks, are they positive or negative. I have reason to believe they are negative and the experimental data Willis cites seems to again confirm this.

StephanF
January 21, 2020 10:20 pm

I also anticipated that the absorption line would broaden as you did. And where it is saturated it would only lower the reabsorption height for the upwelling FIR when the concentration of CO2 increases. Then it would be interesting to know what the the time delay between absorption and re-emission is and how that would compare to the mean collision time of the gas molecules, since the absorbed energy would thermalize after a collision.

The energy imbalance in the satellite measurement could also come from this: the satellite looks at different heights in the atmosphere, depending on the absorption depth at a particular wavelength. So where CO2 is optically thick, the satellite will look at emissions at higher altitudes where the atmosphere is much colder, and where it is optically thin, it could look all the way down to the surface. On average, there should be less FIR measured than what is emitted from the surface.

But it is ‘Planck’ not ‘Plank’.

Michael Hammer
January 22, 2020 1:20 am

Stephan, you are right Planck not Plank my apologies. As regards rising CO2 reducing the reabsorption height, where does on define saturation. From an engineering point of view a reasonable point would be where the gas column absorbs 99% of the incident radiation ie: 2 abs.
But the total CO2 column is 3000 abs; 1500 times more than saturation. 99% of the surface emission at 14.7 micron is absorbed in the first 1/1500 of the gas column. The gas column extends up to the tropopause but the pressure is reducing with altitude. The first 1/1500th of the gas column is at an altitude of about 5 meters. Whether it is 5 meters or 5.5 meters is really quite irrelevant. Indeed 90% is absorbed in the first 2.5 meters. On the issue of relative time constants of emission vs thermalisation but are extremely fast (nano seconds) and we know from observation that the emission intensity depends on the bulk gas temperature not on the amount of energy being absorbed. That suggests the thermalisation time constant is faster than the emission time constant.

Loydo
January 21, 2020 10:30 pm

“I have reason to believe they are negative…”
So the 1°C rise since 1900 could have been more?

Michael Hammer
January 22, 2020 12:58 am

Ah Loydo; firstly, how much of the claimed 1C rise is due to “adjustments” of the historical data set – I suspect a very significant portion. Secondly, how much of the actual temperature rise is is due to causes other than rising CO2. By the way we have gone from 280ppm to 410 ppm which is only 0.55 doublings so the additional retained energy is only 2watts/sqM before feedbacks. Thus the direct impact before feedbacks would have been about 0.55C and if the feedbacks are negative the actual rise due to increasing CO2 would be well under half a degree centigrade.

By the way, the theory of CAGW is that rising CO2 reduces earths energy loss to space. Since the incoming energy is constant that creates an energy imbalance, more energy in than out which causes the Earth to warm. Energy loss to space is measured as outgoing long wave radiation or OLR for short. So if the theory is right we should be seeing OLR fall as CO2 rises. Of course as Earth’s temperature rises OLR will increase since rising temperature increases emission so the net impact should be a rise due to increasing temperature (3 watts/sqM/C) minus a fall due to rising CO2 (3.7 watt/sqM/doubling) all before feedbacks. Positive feedback due to water vapour as claimed substantially increases the negative 3.7 watts/sqM/doubling.
But if Earth is warming at an increasing rate, net OLR would have to be falling as CO2 rises.

Trouble is NOAA has been measuring OLR since the satellite era and over that time it has risen by 3 watts/sqM. Earth’s temperature has risen by less than 1C since 1980 (even warmists only claim 1C since 1900) so a rise of 3 watts/sqM is even more than could be explained by warming, assuming zero impact from changes in CO2 or feedbacks. So where is the evidence to justify the claim that rising CO2 is heating the earth by reducing energy loss to space. Also, if OLR is rising what is the source of the energy imbalance driving the warming?

The only answer I can see is that Earth’s energy input is rising and since the solar output is constant that means Earth’s albedo must be falling. ie: cloud cover is reducing. Well NOAA also measure albedo and cloud cover and guess what, both are indeed falling. So Earth is not warming because GHG’s are reducing OLR, it is warming because cloud cover is reducing which is exactly what Svensmark’s theory is suggesting (note, since clouds also reduce OLR reducing cloud cover will increase OLR but will increase absorbed energy even more). Guess we need to hear how rising CO2 is driving down cloud cover.

Carlo, Monte
January 22, 2020 7:56 am

Would you have any references handy that discuss the increase of OLR?

Michael Hammer
January 22, 2020 11:32 am

Carl; NOAA do publish the data but it is difficult to find in a convenient form. Other sites have republished the NOAA data as a convenient graph. They this site http://www.climate4you.com/GlobalTemperatures.htm#Outgoing%20longwave%20radiation%20global. Please note the 3 watts/sqM rise (980-2020) is more than one would expect even from the claimed global temperature rise in the absence of any impact form rising CO2 whatsoever.

As far as a discussion, I have not seen any rationalisations that make sense to me. If you find a rational understandable explanation I would be very interested to see it. Bottom line, the claim is CO2 causes warming by depressing OLR yet the experimental data is OLR has been on average rising for the last 40 years at least. If a theory predicts one outcome yet real world data shows the opposite outcome to me that casts VERY serious doubt on the theory. At the very least one would expect massive discussion over the issue. The fact that there is not (indeed, to my way of thinking, the silence on this issue is suspicious in itself) starts to sound to me like a coverup.

Lewis Lydon
January 20, 2020 10:27 pm

Very nice!

Neatly bypasses (i) a multitude of complex calculations, each with their own inherent (&/or applied) errors & (ii) all the various “unknowns” affecting/involved in the “Forcing Formulae” and cuts straight to the chase with a very nice simple comparative approach! 🙂

≈ 0.3°C sounds pretty reasonable to me (unlike most of the Alarmist drivel we’re subjected to)… I reckon I can live with that… 🙂

Greg Goodman
January 21, 2020 1:25 am

My personal filtering of the science and the BS leads me to expect around 0.8 deg C, Willis’ figure is surprisingly low. Not that surprise is an argument against numbers.

If we take the midrange value of 3°C

That is all part of the pseudo scientific trickery. They know that most people will be unaware of mean, median and long tailed probability distributions and that they will instinctively apply the little maths they know: add and divide by two.

That is why they keep a wide range to include the improbable high values and boost the incorrectly assumed “mid range” as being the mean. If you increase percentiles you use the lower figure does not move much but upper limit get much bigger. Plus the press always go for “may be as a much as ” figure for an exciting headline.

Willis:

No, SW is part of solar, LW is also part of solar. If that caption reflects the way the calculation is actually done it will probably affect the bottom line result.

A C Osborn
January 21, 2020 2:38 am

“The latter, usually called “LW”, is not part of sunlight”

Do what?
It may contain a lot less LWIR than at other frequencies, but it does not contain Zero.
https://en.wikipedia.org/wiki/Sunlight#/media/File:Solar_spectrum_en.svg

We have been here before Mr Eschenbach, you know how nit picky I am.

A C Osborn
January 21, 2020 2:41 am

ps LWIR may not reach the surface if it is absorbed by the Atmosphere, but it is part of Solar Radiation.

January 21, 2020 4:42 am

Is this true?
“The upwelling LW channel produced by CERES is Surface IR which is confined to the window wavelength range of 8-12 μm, this range is unaffected by GHGs. The expectation is therefore that if the cloud concentration goes up backscatter to space of incoming SW will increase but backscatter of LW towards the surface and absorption of the surface LW by the water droplets in the cloud will also increase. This means that the presence of the clouds will reduce the upwelling LW at the same time as it increases reflected solar leading to the negative correlation. This effect has nothing to do with GHGs.”
https://wattsupwiththat.com/2014/01/07/upwelling-solar-upwelling-longwave/#comment-1170207
If so, Does CERES observe surface total upwelling LWIR or is it calculated from temperature?

January 21, 2020 5:53 am

So I got an answer from Kevin Kilty: It’s calculcated from surface temperature estimates.

“The CERES surface temperatures are a skin value, derived from GEOS data. The method of producing these temperatures is complex, and involves both parameterization and maximum likelihood inverse methods. Comparison against independent temperature data, satellite and ground, suggests a precision of about 0.5°C. The amount of analysis and scientific work that goes into these efforts is well described in a series of technical documents, available online, that are well worth reading for a background in the subject.”

Seems to be two problems here: 1) Looking for how much does radiation affect temperatures while using temperature to estimate radiation. And 2) Looking for changes in radiation and temperature smaller than the error of observation.

January 21, 2020 5:55 am
A C Osborn
January 21, 2020 6:59 am

Ron, that data on Ceres is extremely interesting. It is abviously not actually measuring the things that we thought it was and is “model” based yet again.
I was a bit concerned when I saw it’s description in the top of the post ie ” CERES Energy Balanced and Filled (EBAF) dataset”.

Curious George
January 21, 2020 8:17 am

I vaguely remember that CERES has an unexplained inaccuracy of about 5 W/m2. That does not render the data useless, as it still detects changes. Rather than publishing raw instrument data, they “energy balance and fill” them to the best of their abilities. Keep in mind that the EBAF is just the best available guess.

Johanus
January 21, 2020 5:22 am

So Willis said LWIR “is not part of sunlight”. That’s wrong of course. He should have said, the LWIR part of “sunlight” is negligible, compared to “earthlight”.

Sun and Earth are both blackbody radiators, with distinctive Planck curves.
https://www.acs.org/content/acs/en/climatescience/energybalance.html

Note that the earthlight, having a lower Planck temperature (~210K), accounts for virtually all LWIR detected radiation.

The general rule of thumb for classifying detected radiation as sunlight vs earthlight is: if the wavelength is greater than 4μm, then it is “earthlight”.

January 21, 2020 6:24 am

Thanks johanus, a useful rule of thumb. Is it also true that the longer the wavelength, the lower the elctron voltage? I read that solar full spectrum radiation emanating from the sun’s surface at 5,778 K has 48 times the eV as what CO2 emits?

A C Osborn
January 21, 2020 6:56 am

Ron, you can see it for yourself by looking at the area under the curve that I posted.

There have also been a couple of posts on this forum (but not this thread) that show that CO2 Energy is ineffective to produce any warming of it’s own.

January 21, 2020 8:06 am

Thanks A C. That diagram does not display the energy implications as clearly as this one does:
?w=1000&h=796

https://rclutz.wordpress.com/2020/01/16/co2-so2-o3-a-journey-of-discovery/

A C Osborn
January 21, 2020 10:20 am

Ron, yep, I like your graph more.

Johanus
January 21, 2020 3:01 pm

@Ron Clutz
“Is it also true that the longer the wavelength, the lower the el[e]ctron voltage? “
Yes, the wavelength of a photon is inversely proportional to its _energy_ (not “voltage”), the proportion constant being the Planck h=6.62607004 × 10**-34 . So, E=h=c / λ

[FYI, “electron-volt” is defined the kinetic energy due to acceleration of one electron, starting from rest, pushed by electrostatic potential of one volt. So it is just another unit for expressing energy, but for use at a very small scale. It is not correct to call it ‘voltage’ ]

“I read that solar full spectrum radiation emanating from the sun’s surface at 5,778 K has 48 times the eV as what CO2 emits?”

You are trying to compare apples and oranges. In one hand you have the Sun’s full spectrum EMR output (“solar exitance”) which is about 63 megawatts per square meter (from the Sun’s surface). What is in the other hand? CO2 exitance? But that depends on the excitation state of the molecule and the wavelength of the emission, which could range from zero upwards. So comparing the Sun’s full spectrum output to the output of an excited molecule. ??? That does not make sense.

Perhaps you meant the ‘full spectrum output (radiant exitance) of the Earth’, which would be about 240 watts per square meter. Much smaller than solar exitance, of course, but a valid comparison.

[BTW, the solar and terrestrial exitances were shown on the ACS black-body plots in my link above]

January 21, 2020 3:39 pm

It also seems that electron volt is the proper unit of energy for photons, though I take your point that this is not voltage in the usual sense.
“When dealing with “particles” such as photons or electrons, a commonly used unit of energy is the electron-volt (eV) rather than the joule (J). An electron volt is the energy required to raise an electron through 1 volt, thus a photon with an energy of 1 eV = 1.602 × 10-19 J.

January 21, 2020 3:41 pm

Johanus, just a small nitpick to your informative comment. Your linked diagram says the area under the solar radiation curve is 63,000,000 Wm^2 compared to 250 Wm^2 for the earth radiance curve.

Johanus
January 21, 2020 7:18 pm

@Ron Clutz
“It also seems that electron volt is the proper unit of energy for photons,”

Any unit of energy, e.g. joule, BTU, horsepower, erg, is ‘proper’ for photons because they are all equivalent (up to a scale factor). But it would be proper to say that eV is convenient for photons, because of its very small scale.

aleks
January 21, 2020 9:33 am

RoHa
January 20, 2020 10:58 pm

Nice to see “yclept”. We should use it more.

BallBounces
January 21, 2020 4:29 am

Sure, but let’s not become ycleptomaniacs.

Jerry Anderson
January 21, 2020 8:07 am

Good one

Nylo
January 20, 2020 11:00 pm

Hello Willis,

I am not sure I understand some of this. Well, actually I am sure that I don’t. If the forcing at the surface is only 0.43 of the TOA forcing, where is the remaining energy going? If it doesn’t go out and it doesn’t reach the surface, then it needs to somehow stay in the middle. Warming the atmosphere itself. Some or all of its layers. And isn’t it the atmosphere’s temperature what we measure, near the surface? Can’t the atmosphere increase its temperature more than the surface itself? And can’t it do it by different means than infrared radiation? The fact that the radiation received is less doesn’t mean that it is not receiving energy in a different way, which should be accounted for. Does this make sense?

Scarface
January 21, 2020 12:00 am

“If the forcing at the surface is only 0.43 of the TOA forcing, where is the remaining energy going?”
I was wondering about the same. Would that”then maybe radiate into space during the night?

A C Osborn
January 21, 2020 1:42 am

This is a very important question.
As so little Solar Radiation reaches the surface, does the same apply to LWIR from the upper atmosphere?
If so what happens to it?

David Blenkinsop
January 21, 2020 2:32 pm

In reading the head posting, the description does make it sound as though some portion of the upwelling power flow is just disappearing into nothing? Or else causing a persistent imbalance to be sustained, cooking the planet in short order?

Alexander Vissers
January 21, 2020 12:31 am

I believe downwelling at the TOA is trapped by greenhouse gases on the way down before hitting the surface and then partly emitted as upwelling radiation.

Robert W Turner
January 21, 2020 7:27 am

This is all based on erroneous assumptions and worse – pseudoscience.

John Dowser
January 20, 2020 11:25 pm

The article seems to explore (or exploit) the subtle differences between modeled surface temperature and modeled and “measured “surface *air* temperature. Since these two relate to different models and calculations, it’s entirely unsure if there’s anything here at all.

JimW
January 20, 2020 11:56 pm

Indeed. What Willis does in his articles is to clearly expose the stupid complexity of a non-science called ‘climatology’. By cutting out 95% of erroneous waffle, he exposes the truth; there is nothing there at all.
That is not to say that climate change doesn’t happen. It does, it will always. It doesn’t mean humans don’t change their environment and affect some balances; 365/24/7 lifestyles in increasingly urban locations coupled with modern agricultural techniques is bound to affect local environments.
But Willis very cogently puts silly computer-driven forecasts into true perspective. he is able to do this because he has no axe to grind, no skin in the game.

Antero Ollila
January 20, 2020 11:40 pm

I could not figure out the basis of this clause: “Using that accepted 3.7 W/m2 figure for a doubling of CO2, that would give an increase in downwelling surface radiation of 1.8 W/m2.” I think that according to the IPCC, the radiative forcing is exactly the value of 3.7 W/m2.

How do we get the corresponding temperature? According to the IPCC, it is dT= CSP * RF. CSP (also marked by λ) is the climate sensitivity parameter. It has two values: for TCS it is 0.5 K/(W/m2) and for ECS it about 0.865 equal to the ECS value of 3.2 C, which is the average ECS value of 30 GCMs as tabulated in Appendix 9.5 in AR5. TCS value according to the equation above is 1.85 C and according to 30 GCMs in Appendix 9.5 it is 1.8 C – close enough.

By the way, this simple equation always raises fierce protests among the Finnish IPCC supporters, when I have used it in my blog stories. They say that it is not real IPCC science, but the real IPCC calculations are based on using GCMs. Then I ask that can you name the GCM accepted by the IPCC. No answer. Anyway, this simple equation works even with RCP8.5 which is the worst case (an impossible) scenario of the IPCC.

Antero Ollila
January 21, 2020 2:08 am

The definitions of RF and ERF defines in which conditions the magnitude of RF or ERF should be calculated. So far so good. But then we have only defined the driving force. We should calculate the surface temperature effect. This definition does not say anything about it. The final step in the model world is to increase the surface temperature and to find out what is the new temperature which brings the Earth back to the radiation balance, which means that the outgoing LW radiation must be the same as the incoming SW radiation. Only then we know, what we really should know – the surface temperature effect.

For example, if the case of TCS by raising the CO2 concentration from 280 ppm to 560 ppm: According to IPCC, the outgoing LW radiation at TOA will be 3.7 W/m2 less = 240-3.7 = 236.3 W/m2. It means that the Earth’s surface is not cooling with the same amount as before even though the incoming SW radiation remains the same. The GH effect has now been involved and the atmosphere radiates 3.7 W/m2 to the surface. The total SW plus LW radiation has now increased from value 510 W/m2 to 513.7 W/m2 (165 + 345 + 3.7). According to the physical laws, the surface temperature starts to increase until a new balance has been reached. According to the IPCC, it is 1.8 C. The Earth can reach a new balance value in about a year.

Kevin kilty
January 21, 2020 9:50 am

I did a step-by-step illustration of what you are outlining here in a blog from last spring found here.

Ben Wouters
January 20, 2020 11:41 pm

In Figure 3 you can see that as Stefan-Boltzmann says, it takes more energy to raise a hot surface by 1°C than to raise a cold surface by 1°C.

Only if radiative balance would exist.
In the tropics we see max ~1000 W/m^2 on a good sunny day. Don’t believe the SST goes to the accompanying ~364K.
Back in the real world the sun warms the upper 5m or so directly and it takes ~21 MJ to increase the temperature of a column of 5 m^3 water 1K, pretty much regardless what the initial temperature was.

Matthew Sykes
January 20, 2020 11:51 pm

How come the SB calculation for the earth works out to a 5.5 watts for a 1C rise, when say using the MODTRAN model, it is 3.7 watts? Where is the disconnect, is it because temperatures above the average take considerably more energy to raise 1 C than those below?

If this is the case then the basic 1.2 C for the 3.5 watts, per doubling, is fundamentally wrong, and is nearer 0.8 C.

This is a big change, huge. This is the fundamental figure everyone works with.

John Finn
January 21, 2020 2:45 am

Willis

I’ll use my own terminology & very rough figures here so don’ t quote me.

Basically we currently have a surface flux of about 390 w/m2 (average temp of ~288k).

Because of the greenhouse effect only about 6o% is transmitted through the atmosphere to space, i.e. 235/390. Basically the 390 w/m2 surface flux drives a 235 w/m2 TOA flux.

If ghgs reduce TOA flux by 3.7 w/m2 the surface will need to warm so that equilibrium can be restored (i.e. 235 w./m2 is radiated back to space).

New TOA flux = 231.3 w/m2

To restore equilibrium TOA flux needs to increase by a factor of 1.016, i.e. 235/231.3
So surface flux needs to increase by a factor of 1.016

390 x 1.016 = 396.2 w/m2 which represents a temperature of 289.1 k

Therefore the surface will need to warm by 1.1 k to restore equilibrium at TOA. This is close to the 1.2 k per CO2 doubling (NO feedback) figure which is regularly cited but my figure comes from rough approximations.

Conclusion: Forcing at surface should be about 1.6x forcing at TOA.

Matthew Sykes
January 21, 2020 11:41 pm

OK, gotcha, thanks

Phil.
January 21, 2020 9:57 am

I just had a quick look at MODTRAN.
Tropical atmosphere: 400ppm CO2,
Upward IR Heat Flux 298.52 W/m2
Ground Temperature 299.7K
Increase surface by 1ºC
Upward IR Heat Flux 302.947 W/m2
Difference = 4.4 W/m2
Midlatitude summer:
Difference = 293.873-289.602 = 4.3
Midlatitude winter:
Difference = 3.7
Subarctic summer:
Difference =4.0
These values are for a surface at 299.7 and 300.7K
So MODTRAN lies between the 3.7 value and the value calculated by Willis.

Lance Wallace
January 20, 2020 11:54 pm

Willis, Ramanathan apparently assumed a global temperature of 15 C to get his 390 W/m2 emission rate. I recall looking on KNMI at the absolute (not anomalous) calculations, and being quite surprised that the the models disagreed in their estimate of current temperature by what seemed to me to be rather large: 12-15 C.

What would be the emission rate associated with 12 C? Or 13.5 C, which would correspond to the model mean?

Teerhuis
January 21, 2020 5:04 am

13.5°C should be 382.8 W/m2 (380.2 W/m2 is for 13.0°C).

Clyde Spencer
January 21, 2020 8:18 am

Willis
Since the ‘forcing’ varies with temperature, and we are dealing with a 4th power, I think a better approach would be to use the average temperatures by latitude, and then determine the average forcing instead of using a single average temperature for the globe.

Clyde Spencer
January 23, 2020 8:32 pm

Willis
My apologies for not reading more carefully.

Willem69
January 21, 2020 10:02 am

Willis,

As always, thank you for an interesting read!

One issue which has bugged me for some time,
I get the impression that 2 things are mixed up when people talk about ‘surface temperature’.
One being the temperature of the ‘ground/water surface’ used to calculate the emissions from same surface using SB. And the second being the near surface ‘air temperature’ measured some distance above the ground surface (standard 1 meter above i think). Now, as anyone who has ever walked barefoot over a non-vegetated surface (beach, road, poolside, desert etc) on a sunny day knows from direct personal observation, the difference between the two can be painfully large.

So could it be that the actual emission from the surface is in fact very different from what a calculated value using ‘air temperature’ would suggest? and what effect would that have on the ‘greenhouse effect’?

Best regards,
Willem

David A
January 22, 2020 3:46 pm

Question for you brainiacs…

Willis on surface emissions –
“12°C = 374.9 W/m2

13.5°C = 380.2 W/m2. Plus 5.3 W/m2

15°C = 390.9 W/m2. Plus 10.7W/m2

Yet if a doubling of CO2 is supposed to lead to a 3.7 W/m2 increase in downwelling TOA longwave radiation;
then how does plus 3.7 W/m2 produce progressively larger surface emissions per doubling?

As the surface warms would it not take progressively larger increases in downwelling LW radiation to produce the same affect?

Scarface
January 21, 2020 12:27 am

Thinking about the article, I got this idea for an experiment, to measure the effect of CO2.

You have a shelter, with a roof of let’s say 4m^2, on four poles, let’s says of 2m high.
You have a radiation-meter outside and one under the shelter and wait for a cloudless and calm day.
Then you blow air with increasing amounts of CO2 over the 2 meters, from 200ppm to 800ppm, steps of +50.
And you measure the readings of the one under the shelter and the one in the sun.
I think you should then see a decreasing difference between the 2 readings. If CO2 has any effect.
And if so, you could calculate that effect. Or am I totally wrong?

Scarface
January 21, 2020 2:31 pm

Thank you!

DMacKenzie
January 21, 2020 8:13 am

Scarface,
I once pointed out to a fellow engineer that the increase in atmospheric CO2 since 1850, was about the same as me opening a soft drink can in my office, which didn’t cause my office to warm up. He said “… but there is a beam length issue…”. A few minutes of calculations with the Hottel charts hanging on our wall showed him to be correct….so you can actually know quite a bit about CO2 and IR, and still be very wrong in your conclusion.

Scarface
January 21, 2020 2:34 pm

Antero Ollila
January 21, 2020 12:44 am

Willis’s story is also about the GH effect (GHE). I use real radiation values for illustrating the GHE. The first fact is the radiation fluxes must be absorbed by the Earth’s surface in order to have any temperature effect. For example, solar radiation is at TOA 340 W/m^s but only 240 is getting absorbed by the Earth and because the Earth is radiation balance, the same 240 W/m2 escapes as LW radiation into space.
The first observation is that only 165 W/m2 of solar radiation is absorbed by the surface. Now we have a problem. According to Planck’s law, the black surface temperature of 240 W/m2 is about
-18°C, and the measured surface temperature is about 15 C. This difference 33°C is a generally accepted measure of the GHE.

There must be more radiation energy absorbed by the surface because its temperature is so high. And there is. The observed LW energy flux radiated by the atmosphere to the surface is 345 W/m2. The surface does not make any difference if it is SW or LW radiation if it can be absorbed. So, totally the radiation absorbed by the surface is 510 W/m2. It 213 percent more than 240 W/m2.

The extra radiation absorbed by the surface is 510 – 240 = 270 W/m2. It is the real GHE effect and magnitude of the GHE. But this magnitude is different according to the IPCC. They define the GHE like this in AR5 / p. 126: “The longwave radiation (LWR, also referred to as infrared radiation) emitted from the Earth’s surface is largely absorbed by certain atmospheric constituents – (greenhouse gases and clouds) – which themselves emit LWR into all directions. The downward directed component of this LWR adds heat to the lower layers of the atmosphere and to the Earth’s surface (greenhouse effect).”

By simple words, the IPCC says that the GHE effect is the difference of LW radiation emitted by the surface (395 W/m^2) and the LW radiation emitted by the TOA into space (240 W/m2) = 155 W/m^2, and what is more, this absorbed radiation is the same as emited by the atmosphere to the surface. This 155 W/m2 is the same as used by Schmidt et a. (2010). The IPCC’s definition conflicts with the reality:

1) The IPCC says that the absorption (155 W/m2) is the same as the LW radiation to the surface (345 W/m2). It is against physical laws.
2) Or even though the LW radiation downwards is 345 W/m2, only 155 W/m2 have real temperature impacts. The surface cannot leave the difference 345-155 without absorption; it is against physical laws.
What is the real explanation? The downward LW radiation emitted by the atmosphere is the sum of four different energy sources: 1) solar radiation absorbed by the atmosphere 75 W/m^2, LW radiation absorbed by the atmosphere 155 W/m2, the latent heating 91 W/m2, and the sensible heating 24 W/m2. These fluxes are totally 345 W/m2 and the GHE effect is 345-75 = 270 W/m2, because the solar radiation absorption by the atmosphere cannot be part of the GHE.

What are the consequences? The contribution of CO2 is only 7.4% in the GHE responding 2.5 °C of 400 ppm CO2 concentration. According to Schmidt et al. it is 19 % and according to Kiehl & Trenberth it is 26 %. IPCC’s forcing of CO2 producing 1.8°C for 560 ppm cannot be fitted into the real GHE but the TCS value of 0.6°C can be fitted very well.

Two links to research papers of mine:
http://www.journalpsij.com/index.php/PSIJ/article/view/30149
http://www.journalpsij.com/index.php/PSIJ/article/view/30127/56520

I have published blog stories about this in Finnish blog sites. The comments of the IPCC supporters can be summarized like this: We cannot find anything wrong in your GHE definition, but the IPCC’s definition is correct because thousands of real climate scientists have evaluated IPCC´s specification and they never found any errors. My comment is that the majority of climate scientists have never read the IPCC’s GHE definition or even considered what it means. The rest of the climate scientists follow this rule: “It is better not to look a gift horse into the mouth.”

Ian W
January 21, 2020 8:11 am

There must be more radiation energy absorbed by the surface because its temperature is so high. And there is. The observed LW energy flux radiated by the atmosphere to the surface is 345 W/m2. The surface does not make any difference if it is SW or LW radiation if it can be absorbed. So, totally the radiation absorbed by the surface is 510 W/m2. It 213 percent more than 240 W/m2.

The ‘surface’ is at least 75% water. Water does not absorb IR radiation at all well, indeed it is probable that in a wind IR could cool the surface by increasing evaporation and loss of latent heat to the atmosphere. SW radiation will penetrate water and warm down to several meters, but the energy content of SW radiation is low.

I feel treating the Earth as if it was just a rock ball with an atmosphere, introduces considerable errors.

Phil.
January 21, 2020 10:37 am

On the contrary liquid water is a strong absorber of IR.

Clyde Spencer
January 23, 2020 8:37 pm

Ian
Water can evaporate in the absence of IR or even other wavelengths. Wind can supply enough energy to strip off water molecules. The key is that it takes energy to evaporate water and that energy can be of different types.

Antero Ollila
January 21, 2020 12:49 am

I do not find a way to fix printing errors in my comment. So, I have to fix it like this:

Original: “The surface cannot leave the difference 345-255 without absorption; it is against physical laws.”
It should be: “The surface cannot leave the difference 345-155 without absorption; it is against physical laws.”

Another Ian
January 21, 2020 2:23 am

Willis

IIRC Small Dead Animals uses WordPress and has editing for a time after you post

January 21, 2020 5:22 am

Oh, you can have comment editing in WordPress (but you have to have a .org site, not a .com, as a friend reminded me the other day).

It only takes the appropriate widget. BUT – doing this is a fraught exercise, to say the least. (Doing almost anything not plain vanilla with WordPress is a fraught exercise, to be honest. I note that I am still commenting without a “verified” WUWT account, for instance; there was also the mini-debacle with the comment system a while back.)

In any case, I tend to be somewhat AGAINST comment editing here. Better, like any other real science forum, publish – and then correct by publishing new content, if necessary.

January 21, 2020 5:25 am

Oh. Since my comment on comments hasn’t shown up yet… The one thing I would change about the comment system is to have a clicky-box for emailing me “replies to my comments.” The follow-up comments box all too frequently floods my email, and I still have to search for any actual replies to my input.

Antero Ollila
January 21, 2020 2:21 am

How to reach 3 C. See my comment about the RF ERF definitions.

John Finn
January 21, 2020 3:58 am

Transmission Ratio ??

TOA Flux =~ 0.6 TOA Flux

commieBob
January 21, 2020 1:06 am

The long-accepted value for a doubling of CO2 gives a theoretical 3.7 W/m2 increase in downwelling TOA radiation.

The downwelling TOA radiation is pretty much the solar constant. Any increase in downwelling radiation takes place within the atmosphere.

Nick Stokes was kind enough to provide us with this link. It shows the measured spectrum of the upwelling radiation over the arctic measured at 20 km as well as the spectrum of the downwelling radiation measured at the surface.

It’s very important that the upwelling spectrum doesn’t show any wavelengths longer than 17 um and the downwelling spectrum doesn’t show any wavelengths longer than 25 um. They miss a lot of the energy because that’s where H2O has total absorption (and therefore radiation).

The part of the spectrum attributed to CO2 is flat bottomed (or topped). To my mind, that indicates saturation. The other thing is that the CO2 absorption spectrum overlaps with the H2O absorption spectrum. The other thing to note is that arctic air has quite low specific humidity. In most of the rest of the globe, the absorption of long wave infrared (LWIR) by H2O will be greater.

The important thing vis a vis the present article is that looking down from 20 km, we see around 220 mw/m^2 at 15 um and 260 mw/m^2 looking up from the surface. ie. the observed upwelling LWIR is less than the downwelling LWIR at that wavelength. (Note that the power figures are in mw. That’s because they describe the power within a narrow band of wavelengths, not the whole spectrum.)

Antero Ollila
January 21, 2020 5:29 am

Quote: “The downwelling TOA radiation is pretty much the solar constant.”

The solar constant is about 1360 W/m2 and by dividing it by the 4, the flux value is 340 W/m^2. Because 100 W/m2 is reflected back to space, the downward SW radiation is 240 W/m^2. Basic knowledge in climate science.

January 21, 2020 4:53 pm

“The part of the spectrum attributed to CO2 is flat bottomed (or topped). To my mind, that indicates saturation.”
It indicates low optical depth. IOW, you see radiation coming from an emission layer at fairly uniform temperature. But that doesn’t mean more GHG couldn’t change that temperature. It can still raise the height of that emission layer, cooling it, which would lower the flat bottom (and so radiate less).

commieBob
January 22, 2020 2:34 pm

It seems like you’re confusing spectral response with altitude.

commieBob
January 22, 2020 2:49 pm
TimTheToolMan
January 25, 2020 1:53 am

Nick writes

It can still raise the height of that emission layer, cooling it, which would lower the flat bottom (and so radiate less).

Standard theory but that idea has never sat well with me. Emssivity of the atmosphere has increased at that altitude so it should radiate from more of the GHG molecules more often losing energy more quickly.

Here’s a thought experiment. Consider a ball of say O2 at say 20C out in space its magically held in a set volume so walls of any container cant play any part. The gas doesn’t radiate so you cant detect its temperature (Ok, I know even O2 can radiate a bit)

Now add a single CO2 molecule. You can now detect its temperature by measuring the radiation from that single CO2 molecule as it acquires energy from the O2 and radiates and slowly cools the O2 and the amount of energy radiated is limited to the frequency of emissions from the CO2 molecule which is set by the temperature.

Now add a second CO2 molecule. The temperature measured is still the same but surely the amount of energy radiated away has doubled.

Mike Smith
January 21, 2020 1:14 am

Interesting analysis. However, I wonder if it’s really valid to simply use an average for the earth’surface?

Not every meter squared is created equal.

A C Osborn
January 21, 2020 1:49 am

Not every Watt/m squared is equal either.
Solar watts can be used to do work, LWIR can’t because it is diffuse and does not carry the electron volt energy that SW and UV carries.
But according to the accepted science all photons are the same, regardless of what and where the come from.
So explain how UV photons penetrate metres of water and LWIR ones don’t when the are all the same.

A C Osborn
January 21, 2020 3:08 am

“To do that you have to have enough energy to kick an electron up to a higher orbit, and LWIR can’t do that.”

Thank you.

LWIR does not have the same Energy.

I wonder where is that “Energy” accounted for when comparing Watts/m2 of Solar v Watts/m2 of LWIR?

Only 8% of Solar is UV and yet UV will crisp your skin and give you cancer, whereas LWIR just warms you a bit.

Phil.
January 21, 2020 8:10 am

True IR doesn’t perform electronic excitation, that’s primarily UV, however it does perform ro-vibrational excitation which can then be transferred as kinetic energy to the surrounding gas molecules.

mobihci
January 21, 2020 1:03 pm

true that. there is a real world example of that in nearly every household called a microwave oven.

January 21, 2020 4:29 am

Good point. So how is it valid to make energy budgets that treat SW and LW radiation as additive and subtractive, i.e. equivalent?

A C Osborn
January 21, 2020 7:06 am

That is my point, we know that Solar warms the Oceans to a certain depth (metres) and that that energy is therefore Stored for some indeterminate time.
It does not get reflected (pun intended) in the “Surface Balance Calculations” because it does not necessarily immediately go out as overnight LWIR.

I think Trenberth was on to something when he said the heat was hiding in the Oceans.

Ben Wouters
January 21, 2020 7:48 am

A C Osborn January 21, 2020 at 7:06 am

That is my point, we know that Solar warms the Oceans to a certain depth (metres) and that that energy is therefore Stored for some indeterminate time.

Solar is stored for 1 season (except probably in the tropics):

It does not perpetrate below ~400m or so.

I think Trenberth was on to something when he said the heat was hiding in the Oceans.

He was fully correct, only it is not heat from the sun (and most certainly not from the atmosphere) but from the inside of the earth.
Just as the continental crust is hot in spite of the small geothermal flux (~65 mW/m^2) are the oceans hot from internal heat of the Earth.

A C Osborn
January 21, 2020 10:27 am

Ben, I am not so sure about just 1 season.
Ensos come from somewhere.

E M Smith said in one of his posts that the Sun & Atmosphere just keep the heat inside the earth and slow down it’s cooling.

Ben Wouters
January 21, 2020 12:42 pm

A C Osborn January 21, 2020 at 10:27 am

Ben, I am not so sure about just 1 season.
Ensos come from somewhere.

One of the reasons why I excluded the tropics.
In the tropics the daily amount of solar energy varies between ~15 to 25 MJ/m^2.
At high latitudes the swing is from ~0 MJ/m^2 to eg 18 MJ/m^2.
In this case in winter all stored energy will be lost to space again.

Ben Wouters
January 21, 2020 2:51 pm

A C Osborn January 21, 2020 at 10:27 am

E M Smith said in one of his posts that the Sun & Atmosphere just keep the heat inside the earth and slow down it’s cooling.

To me the flux through the crust is a basic conduction situation (Fourier).
For continental crust the flux is ~65 mW/m^2. Without sun and atmosphere, this would result in a surface temperature of ~40-50K to radiate the flux to space.
Switch on the sun, and the crust temperature will start to rise, until the Geothermal Gradient from mantle to core matches the average surface temperature for a given position, and the flux is established again, close to the original number.
(slightly different due to now lower temperature difference between mantle and surface).

Mike Smith
January 21, 2020 7:48 am

Ahhhh, thank you Willis!

Greg Goodman
January 21, 2020 1:34 am

This is a simple calculation using the Stefan-Boltzmann equation

well sigma * T^4 is simple but you also need to know “effective” emissivity of all the fertile and baron land plus the sea / ice and snow and wet snow and ice, etc at the appropriate wavelengths. Values range from about 10% to 90%.

In other words, it’s not that simple and like anything else in climate science you get the values you dictate by your assumptions.

January 21, 2020 1:45 am

I think the issue is not so much emissivity (mostly close to 1) but local back radiation. S-B gives radiation into vacuum. But if the surface warms, it warms the air above (with GHGs), and also clouds, which creates back radiation. So the net radiation going up is a lot less. It’s like the steel greenhouse, but with more transparent steel.

TimTheToolMan
January 25, 2020 2:42 am

Willis writes

You can see why the error from considering the earth as a blackbody in the IR is quite small.

With the T^4 term, emissivity is very important.

For example the difference between 1m2 of a material with emissivity at 0.98 and 0.97 at 20C is 410.4 – 406.2 = 4.2 W/m2

This is a nifty way to play with its impact https://www.omnicalculator.com/physics/stefan-boltzmann-law

This is especially important where its changing like at the effective emission altitude for example. Is never mentioned in discussion of “the green house effect” however.

(Rescued from spam bin) SUNMOD

A C Osborn
January 21, 2020 2:31 am

S-B is for solid surfaces not gases.
Water rules, not CO2, as you say real world conditions prove it.

JimW
January 21, 2020 2:43 am

Good heavens, Mr Stokes, you are agreeing with me ( probably without realising it). The only human causes of ‘warming’ are localised surface effects due to increasing urbanisation and agricultural use. This warming effects the local atmosphere , creates more clouds , and traps heat because of water vapour ( your transparent steel). Naught to do with CO2 or at least miniscule effects from that molecule.

John Finn
January 21, 2020 2:59 am

Nick

If this discussion is still focusing on the TOA/surface flux ‘discrepancy’ picked up by Willis, surely the issue ir related to the “Transmission ratio” of the atmosphere.

i.e before CO2 enhancement TR = 235/390 = 0.6 (60%)

After CO2 enhancement TR = 231.3/390 = 0.593

To restore equilibrium (235 w/m2 TOA) = 235/0.593 = 396.2 w/m2 or 1.1 k (NO feedbacks).

Herbert
January 21, 2020 4:36 am

Nick and Willis,
On the question of water vapour, has there been any resolution of –
(1) Paltridge et al 2009 showing that water vapour was negative in feedback on some readings at the tropopause.
(2) Contra: Dessler and Davis 2010.
In a discussion thread on Jo Nova at the time of the 2 papers, Garth Paltridge commented on and contested the 3 points that Dessler and Davis used to substantiate the “traditional view” that water vapour is a strong positive feedback.
I appreciate your point, Willis , that the CERES material incorporates water vapour, clouds etc. but is water vapour a negative or positive feedback or unresolved?

old construction worker
January 22, 2020 3:38 am

‘..but is water vapour a negative or positive feedback or unresolved?’ Think Swamp Cooler. Swamp coolers work great in Az but are less effective in Florida. Or, as someone, who pushes “Co2 causes global warming” agenda, wants you to believe to get warm on a cool day stand next to a water fall.

Kevin kilty
January 21, 2020 10:11 am

Vacuum is not the issue. S-B pertains to a cavity radiator in a strict sense because within a cavity the IR characteristics of whatever constitutes the surface doesn’t matter — withinm a cavity all materials behave like perfect blackbodies at equilibrium. Without a cavity one really should use the actual characteristics of the surface, which aren’t known to any great precision.

John
January 21, 2020 1:48 am

Physics revision question for me as it’s a long time since I did physics. If the Sun were to suddenly disappear (forgetting gravity, momentum and other similar interactions), would the surface of the earth have an intrinsic temperature because of atmospheric pressure? If so what would that value be? Likewise, what would be the Venusian temperature be? Would the temperatures stabilise?

John
January 21, 2020 3:58 am

What is the reason for Venus’ high surface temperature? It has a retrograde rotation where it’s day is longer than the year, an atmospheric pressure of 90 atmospheres and is closer to the sun but with a high albedo. What would the temperature be on Earth if it swapped with Venus, no other orbital/rotational/atmospheric changes?

LdB
January 21, 2020 7:39 am

Willis proof relies on showing it leads to a falsifiable conflict, if you want the technical reason why it is called the shell theorem and read and note statement 1 and 2
https://en.wikipedia.org/wiki/Shell_theorem
It was developed in classical physics but the formulation still holds in GR

All the pressure is targeted at a single point in space being the centre of mass and so if the statement was true that would be the place all the temperature would manifest. In classical physics temperature is the kinetic vibration of particles and we are talking about a point in space so you can’t connect those two things or as we say classical physics fails. In GR you are simply applying pressure on a point in the spacetime fabric and given it can take the pressure of a neutron star or blackhole it is a bit trivial and does nothing.

Richard
January 21, 2020 4:32 am

Have you ever been outside during a full eclipse of the sun. Amazing how quickly it cools.

Robert W Turner
January 21, 2020 7:34 am

The sun is the reason that there is an atmosphere in the first place. The atmosphere is a gaseous fraction of the planet, it is just as much a part of the planet as the soil under your feet. Without energy from the sun, the atmosphere would condense and absorb into the solid and liquid fraction of the planet.

Edim
January 21, 2020 1:51 am

“Today, a chance comment got me thinking about top-of-atmosphere (TOA) downwelling longwave radiation…”
WUWT? Downwelling LW at TOA? How does that work? Where does this radiation come from? Space? Sun?

Edim
January 21, 2020 4:55 am

Willis, please reply, I see other people pointed it out too. There can be no downwelling LWIR at the TOA, by definition. There is no (significant) atmosphere above TOA. If there is, it’s not TOA.

Phil.
January 21, 2020 8:26 am

Based on the measurement of upwelling LWIR at ToA which will have been emitted by excited molecules from lower in the atmosphere from which region there will be an equal amount of LWIR emitted downwards.

Edim
January 21, 2020 9:40 am

But not at ToA! There can be no downwelling (atmospheric) LWIR at ToA, there is no doubt about it. Upwelling LWIR at ToA comes from the surface (window) and various heights in the atmosphere, and clouds. Downwelling LWIR at ToA is zero, by definition.

Phil.
January 21, 2020 11:24 am

The point is that measurement of upwelling IR allows us to calculate what the amount of downwelling IR will be before it interacts with the atmosphere. That is why Ramanathan used it to estimate the Greenhouse effect.

Edim
January 21, 2020 1:11 pm

Phil, please quote where Ramanathan mentions downwelling IR at the ToA. Yes, there is downwelling IR within the atmosphere all the way down to the surface, but at the ToA? No such thing.

Edim
January 21, 2020 1:04 pm

Well, this is really frustrating.
Willis, downwelling LWIR is measured at the ToA? There is no atmosphere above the top of the atmosphere and you say it’s not the Sun, so what emits this radiation? Can you please quote where Ramanathan mentions downwelling LWIR at the ToA? From your quote:
“At a globally averaged temperature of 15°C the surface emits about 390 W m -2, while according to satellites, the long-wave radiation escaping to space is only 237 W m -2.”

Fair enough, however I disagree that this reduction of about 150 W/m2 (or greenhouse effect) is caused solely by the “trapping effect of radiation”, but I digress… At this point, I just wanna know how can there be downwelling LWIR at the ToA? It’s clearly impossible.

Phil.
January 21, 2020 6:19 pm

Edim January 21, 2020 at 1:04 pm
Well, this is really frustrating.
Willis, downwelling LWIR is measured at the ToA? There is no atmosphere above the top of the atmosphere and you say it’s not the Sun, so what emits this radiation?

I’ll try to spell it out carefully.
Any excited CO2 molecule in the vicinity of the tropopause will emit a photon in any direction with equal probability. Any of those photons heading upwards will most likely escape the atmosphere and therefore cross the ToA. Therefore when you measure the upwelling IR at the ToA there will also an equal flux of downwelling IR, that’s what we’re talking about.

Waheed Uddin
January 21, 2020 1:53 am

“there is some mysterious feedback increasing the CO2-caused surface temperature change by a factor of about ten …”
Willis.
The mysterious GHG feedback effect was invented by NASA Climate folks in pursuit to blame fossil fuel CO2 for naturally caused warming during the 1980s, 1992 1998 ElNino episodes. It was adopted by IPCC climate modelers.
It’s in the archive web pages.
Reality:
The Earth’s standard temperature at mean sea level is still 15°C used by ICAO. All that 390 W/m2 energy on the Earth’s surface is produced by the weight of the entire atmosphere. No relation to the fictitious GHG effect.
Most far or long wave IR reradiated from the Earth escapes to the space at the speed of light except the cloud effect and convention as per gas laws.
The full computational model using SB heat transfer and general gas law considering the entire atmosphere is described in our forthcoming publication.
Surface temperature of all planetary bodies such as Venus can be explained this way.

Antero Ollila
January 21, 2020 5:04 am

GHE is not fictitious. The Earth receives net energy form the Sun 240 W/m2 and the same amount is radiated back into space. This radiation corresponds to -18 C. How do you explain that the surface temperature is 15 C?

Antero Ollila
January 21, 2020 5:30 am

A printing error again: not -1 but 15 degrees.

chaswarnertoo
January 21, 2020 6:58 am

Adiabatic compression by the atmosphere. Arrhenius misunderstood Fourier. Now explain why the average whole Earth temp. is normally 21 degrees C over the last 3 billion year…..

Ben Wouters
January 21, 2020 7:53 am

chaswarnertoo January 21, 2020 at 6:58 am

The atmosphere is not being compressed and is certainly not adiabatic.
Actually the atmosphere needs internal pressure and thus (energy) to expand against gravity. Is called Hydrostatic Equilibrium.

Ben Wouters
January 21, 2020 6:50 am

Antero Ollila January 21, 2020 at 5:04 am

GHE is not fictitious.

If you accept that the atmosphere warms the surface, you implicitly also accept that the atmosphere has warmed the deep oceans, since their temperature is ~275K. THAT idea is totally fictitious.

The Earth receives net energy form the Sun 240 W/m2 and the same amount is radiated back into space. This radiation corresponds to -18 C.

255K (-18 C) is the RADIATIVE balance temperature for ~240 W/m^2 incoming radiation. On Earth RADIATIVE balance temperatures are not found. Only between sunrise and noon and again between noon and sunset for 2 moments the incoming radiation will be the same as the outgoing for a body emitting according SB.
Our moon receives ~300 W/m^2 on average (albedo .11) so its temperature SHOULD be ~270K.
Actually it is ~197K. Daytime temperatures are close to radiative balance temperatures, nighttime is much to warm (should be ~3K, actually ~80K). Otherwise the temperature would be ~150K or so.

How do you explain that the surface temperature is ~15 C?

Simple. Earths oceans were (close to) boiling when they came into existence.
Currently they are colder, but the sun only increases the shallow surface layer ~13K on average.
The solar energy that actually reaches the surface is perfectly capable to maintain that temperature during day/night and summer/winter periods.
The atmosphere just reduces the outgoing energy to space. A body at 290K emitting according SB
would radiate ~400 W/m^2. Actual loss at TOA ~240 W/m^2.
=> ENERGY balance due to the Atmospheric Insulation Effect.

Antero Ollila
January 21, 2020 8:29 am

GHE is insolation of the Earth if you like to call it by that name. Climate change contrarians do not win this battle by denying scientific facts.

Ben Wouters
January 21, 2020 10:51 am

Antero Ollila January 21, 2020 at 8:29 am

Climate change contrarians do not win this battle by denying scientific facts.

Not aware that I’m denying any scientific facts.
Since you seem to accept that our cold, low density atmosphere is capable of warming our ~4km deep oceans, I’d like to hear how this is possible.
Realize that warm water does not sink to the bottom of the oceans, only cold, dense water does (mostly AABW and some NADW)

Harry
January 21, 2020 2:25 am

Isn’t some of the problem to do with considering everything based on averages rather than considering the very real differences between the equator and the poles.

For example, apparently warming is quite modest at the equator. Wouldn’t this be because a large amount of incoming solar radiation is absorbed at the surface, what is reflected is mostly dominated by the action of the very humid atmosphere. So any extra CO2 is only operating on a very small amount of remaining energy and adding this small amount to an already large amount of energy absorbed at the surface.

At the poles the opposite is true. Very little humidity and high albedo mean that very little energy is being absorbed at the surface and very little of the large amount of reflected energy down-welled by water vapour. In this environment, added CO2 would provide additional down-welling of this large percentage of energy which would be significant compared to the little that is directly absorbed, hence warming is larger at the poles.

angech
January 21, 2020 2:26 am

“Back in 1987 in a paper entitled ‘The Role of Earth Radiation Budget Studies in Climate and General Circulation Research“, Ramanathan pointed out that the “greenhouse effect” can be measured as the amount of long wave energy radiated upwards at the surface minus the upwelling long wave radiation at the top of the atmosphere, viz:

The greenhouse effect. The estimates of the outgoing longwave radiation also lead to quantitative inferences about the atmospheric greenhouse effect. At a globally averaged temperature of 15°C the surface emits about 390 W m -2, while according to satellites, the long-wave radiation escaping to space is only 237 W m -2. Thus the absorption and emission of long-wave radiation by the intervening atmospheric gases and clouds cause a net reduction of about 150 W m -2 in the radiation emitted to space.”

Lost me on square 1.
Help.
First problem
At the top of the atmosphere – Incoming energy from the sun balanced with outgoing energy from the earth.
Is this correct?
If so then there cannot be any net reduction of about 150 W m -2 in the radiation emitted to space.”
What goes in is coming out.
How can we have extra free heat continually trapped forever by GHG. Not possible.

Problem 2
the surface area of the earth is 510.1 million km², radius 6371 km
The Kármán line, at 100 km (62 mi), or 1.57% of Earth’s radius,
gives a TOA of 526,2 million km².
The IR radiation at the TOA is coming off a much bigger sphere surface than at the earth surface. Ramanathan is unlikely to have mad such an elementary mistake but the question remains.
You cannot take directly to compare or subtract a surface of earth energy measure from a TOA energy measure without changing the energy to surface area amounts to the same total surface area.
Though the radius change is small the total change in energy might be much larger.
The 390 W m -2, at the surface might attenuate to 237 [239] W m -2, at TOA to keep that perfect balance of energy in to energy out without any retained heat at all. just from emitting from a larger surface area. [may be a 4th power attenuation??
Anyway needs working through and explaining if anyone has the knowledge I lack.

There seems to be some confusion over retained energy, needing to be hot enough to radiate the IR outwards and actual energy transfer. [ see Knobs Willis Eschenbach / December 9, 2010″] Global Energy Flows.

First up the surface emits about 390 W m -2, but only receives 161 W m -2 from the sun, the rest is the same recycled energy as it makes its way out. The 390 W m -2 is being double counted, none is retained, it is only 161 W m -2 of real energy to go back out.
According to satellites, the long-wave radiation escaping to space is only 237 W m -2.
But this is in balance, 161 from the original IR emitted by the earth, 30 W m -2 from clouds and 40 W m -2 from direct window transfer.
Therefore there is no absorption and emission of long-wave radiation by the intervening atmospheric gases and clouds causing a net reduction of about 150 W m -2 in the radiation emitted to space.”

This is not to deny that the surface or atmosphere has heated up but the heat needed to create the warming or cooling is not retaining new heat all the time.
Air needs an energy budget to emit the 237 it receives back to space. Yes the surface and the air heat up but this is a minuscule amount of energy in view of the vast amounts going in and coming out each day.It does not constantly keep trapping 150 W m -2. This can be seen by the large changes in air temperature over 24 hours every day. The bulk of that energy is already in the system, ocean and land and clouds.
The atmosphere holds only 1 /6th of the energy going through it , 40 W m -2 compared to 237 W m -2.

As an aside you wrote
‘And for the globe, the average is about 5.5 W/m2 per degree. That was a surprise to me, I didn’t expect it to be quite that large … but then as I said, I’d never calculated it.”
I found this funny equation on the net which seems to match your 5.5 figure
“The energy emitted by the Earth can be written as:
EO = σ * T4 (T = temperature in Kelvin, σ = 5.67 x 10-8 J/m2 sec K4)
The Earth’s temperature reaches a balance, called a steady state, when the two equations match (EI = EO). Under those conditions we can write an equation for planetary temperature.
T4 = [(1 – a) Ω] / 4 σ (T in Kelvin degrees)
The solution for this equation with measured solar flux (Harte 1988, ERBE 2005, 2007) at the top of the atmosphere yields a value of 254° K (-19.2° C, -2.6° F) for average planetary temperature.”
Not sure if it is relevant or not.

Antero Ollila
January 21, 2020 2:49 am

I try to explain two points:
1. “If so then there cannot be any net reduction of about 150 W m -2 in the radiation emitted to space.” The SURFACE radiates 395 W/m2 and at TOA outgoing LW flux is 240 W/m2. Difference is about 155 W/m2.
2. “First up the surface emits about 390 W m -2, but only receives 161 W m -2 from the sun”. See my comment about the GHE, then you see all the real radiation fluxes involved. The surface receives 165 W/m2 SW radiation directly from the Sun and 345 LW radiation from the atmosphere (270 W/m2 is the GHE effect because 345 includes 75 W/m2 solar absorption).

Arjan Duiker
January 21, 2020 3:41 am

Willis,

A very interesting post! Thank you for that. It’s highly appreciated.
I have a view questions though which I hope I can make clear:

1. I’ve always understood from the work of Roy Spencer that the limitations of CERES’s accuracy or any other device are still too large to make up balances in the order of single Watts/m2. What is your estimated order of magnitude error in all these analyses? And second, it would be interesting to hear Roy’s opinion on your analysis. Do you by any change have or have had correspondence with regard to the analysis of CERES data? Just curious…

2. Assuming your analysis is correct there still is a possibility that heat transfer by convection and evaporation etc. (non-radiant heat transfer) interfered with the thermal balance by all the radiating fluxes in a different magnitude in the concerning period than in any other period. To keep it simple: the air might have been cooled a bit extra by the oceans for example.. Since you did quite extensive analyses on these aspects as well, do you think it’s possible to figure out if the 2000-2018 period had been any different from let’s say the decade before in that manner? If not, could this strengthen your conclusion?

3. With regard to your findings, by what degree of certainty do you think we can now say that net positive feedback is demonstrated to be out of question? That would be a powerful conclusion by itself.

Patrick MJD
January 21, 2020 3:46 am

“Nick Stokes January 18, 2020 at 7:51 pm
“CO₂ is 0.04% of the atmosphere and is minimally infrared active.”
Here is an actual measured IR spectrum taken over Alaska. The big bite around 15 μm is the CO₂ absorption.

Patrick MJD January 18, 2020 at 8:35 pm
A big bite?

Patrick MJD January 18, 2020 at 9:07 pm
Note the words “cloud free atmosphere”. Got one for a non-cloud free atmosphere over any part of the earth?

Anthony Banton January 19, 2020 at 11:45 am
“Got one for a non-cloud free atmosphere over any part of the earth?”

That was the whole point of the experiment.
To determine the magnitude of changes to the forcing exerted by CO2 in the atmosphere.
So obviously (?) the experiments were conducted in cloud free skies.
(In case it’s not obvious) because then the signal is obscured by H2O
And yes we know that water absorbs at an overlap with CO2 near 15 micron (the Earth’s strongest emission) BUT there’s plenty of places in the Earth’s atmosphere where dry air predominates, most notably at altitude where the GHE is strongest.

Patrick MJD January 19, 2020 at 7:53 pm
“Anthony Banton January 19, 2020 at 11:45 am”

What is altitude at the surface looking up? What is your definition of “dry air” because I know of two. One is theoretical.”

So what is it?

Antero Ollila
January 21, 2020 5:33 am

I am a little bit surprised. There are no comments about my definition of the GH effect. Not in favor or against my theory or the IPCC’s theory. You should know that this time it is really the definition of the IPCC because they do not refer to any research studies.

The GHE is the basis of the Anthropogenic Global Warming (AGW) theory. If it is wrong – and very badly wrong – the science of the IPCC is based on the wrong theory.

I do not know what to think. Do you think that the IPCC’s definition is correct? Do you think that is according to reality and according to physical laws? If it is correct, then you should show in which way my deduction and evidence are incorrect or what is incorrect in my definition.

This time we do not need complicated theories or models. We need only to use radiation fluxes, which are commonly accepted and used in the energy balance presentations also used by the IPCC. I have not invented any energy flux figures in my presentation.

DMacKenzie
January 21, 2020 9:40 am

Antero…probably a number of WUWT faithfuls have made the mental note “….thats a very interesting way of looking at it…. now I really need to plug all these numbers into my old Trenberth diagram spreadsheet someday”. It will take a while. Your numbers are right, for whatever my opinion is worth.

Antero Ollila
January 21, 2020 1:12 pm

Willis,

I have summarized exactly in the same as you write: “The downward LW radiation emitted by the atmosphere is the sum of four different energy sources: 1) solar radiation absorbed by the atmosphere 75 W/m^2, LW radiation absorbed by the atmosphere 155 W/m2, the latent heating 91 W/m2, and the sensible heating 24 W/m2. These fluxes are totally 345 W/m2 and the GHE effect is 345-75 = 270 W/m2, because the solar radiation absorption by the atmosphere cannot be part of the GHE.”

The differences in radiation fluxes are not the point. The contributions of GH gases are calculated by Schmidt et al and Kiehl & Trenberth from the LW absorption, which is 155 W/m^2 according to the IPCC definition. In reality the GHE is much greater 270 W/m^2. Because the absorption by CO2 is about 20 W/m^2, it makes a big difference if you calculate the contribution from the total GHE effect being 155 or 270 W/m2.

The LW flux emitted to the surface having the real GH effect is not 155 W/m2. It is much greater. Everything would be scientifically correct if the LW radiation to the surface would be 75 + 155 = 230 W/m2 but is 345 W/m^2. If you think that there is no difference if it is 230 or 345 W/m^2, it would mean that that difference 345-230 = 115 has no warming effect. How do you explain that it has no warming effect and it has nothing to do with the GHE?

David Blenkinsop
January 21, 2020 5:06 pm

Yes, I recall you, W.E., posting this power flow diagram before, a few years ago wasn’t it? I do like to see the books balance like that! I remember thinking how readily one could look at this as an idealized system of just two light absorptive “smoked plates” at two different levels in the atmosphere (with the ground as such as a third absorptive/emittive “plate”, if you like). The first question, I suppose, is why climate scientist Trenberth couldn’t publish a balanced diagram in the first place. Climate scientists can’t do arithmetic, need to hire an accountant?

Anyway, what you appear to be saying is that the difference between the 392 W/m2 surface number ‘going up’ vs the 237 W/m2 upwelling number can be viewed as a determiner for surface temperature? It looks like it could be important to know where all those numbers are going?

Antero Ollila
January 21, 2020 5:41 am

A comment about the climate sensitivity value:
Quote: “By comparison, the IPCC says that a doubling of CO2 would increase the surface temperature by 1.5°C to 4.5°C. If we take the midrange value of 3°C,…”

IPCC uses both ECS (Equilibrium Climate Sensitivity) and TCS (Transient Climate Sensitivity) concepts and summarizes the differences in AR5 [48], (p. 1110): “ECS determines the eventual warming in response to stabilization of atmospheric composition on multi-century time scales, while TCR determines the warming expected at a given time following any steady increase in forcing over a 50- to 100-year time scale.” IPCC has changed the TCS to TCR (Transient Climate Response). On page 1112 of AR5 [48], IPCC states that “TCR is a more informative indicator of future climate than ECS.” According to the IPCC science for the temperature changes during this century, the right CS is TCS, which is about 1.8 C on average according to the IPCC.

Antero Ollila
January 21, 2020 5:44 am

Quote: “So an increase of 3.7 W/m2 at the TOA from a doubling of CO2 becomes a 1.8 W/m2 increase at the surface.”.
Still I do not find any groundings, why Willis make this reduction and is it based on the IPCC science or on something else.

Nick Schroeder
January 21, 2020 7:04 am

The K-T W/m^2 heat balance diagram and all its clones are thermodynamic garbage.

1.) Converting 289 K to 396 W/m^2 using S-B creates energy out of thin air, plus the surface cannot radiate BB.

2.) 333 W/m^2 continuously/perpetually looping/upwelling/downwelling/absorbing/”trapping” at 100% efficiency leaving nothing behind either place violates thermodynamics. YES IT DOES!!!

3.) 333 W/m^2 from the cold troposphere to the warm earth without added work violates thermodynamics. YES IT DOES!!!^2

4.) 288 K – 255 K = 33 C is rubbish. 288 K is pulled out of WMO’s butt. K-T uses 289 K. UCLA Diviner says 294 K. 255 K assumes the naked earth keeps the 0.3 albedo and that assumption is scientific if not criminal malfeasance.

Robert W Turner
January 21, 2020 7:40 am

It all reminds me of reading Karl Marx. First start with some arm waving, throw in some sophistry, mix it together to become a factoid, and then proceed with volumes and volumes of erroneous work based on that false premise.

Curious George
January 21, 2020 8:06 am

Nick, have heart. It is a scientific model, used to scare the hell out of children. Also to put billions in pockets of properly connected people. It is not meant to be perfect, except for these listed purposes.

DMacKenzie
January 21, 2020 9:18 am

1) no it doesn’t, and it doesn’t make sense that you think that.
2) you are confusing thermodynamic heat flow from hot to cold, with electromagnetic components in the SB equation
3) no it doesn’t, see 2)
4) thats the number that demonstrates the radiative effect using albedo of .3 to illustrate the effect to high school students. Everybody knows it’s more complicated than that.

Tim Gorman
January 21, 2020 10:13 am

DM,

“2) you are confusing thermodynamic heat flow from hot to cold, with electromagnetic components in the SB equation”

Two bodies *do* exchange heat, i.e. a heat flow, via electromagnetic components. If the earth is considered to be a separate entity from the atmosphere then radiative heat flow must be considered. Please note that this heat flow *is* an exchange. The colder body does radiate toward the hotter body as well as the other way. Energy can’t be destroyed, only transformed. If no energy is left behind then where did it go?

“3) no it doesn’t, see 2)”

Heat flow from a hotter body to a colder body via radiation increases the kinetic energy of the colder body. How do you increase kinetic energy without performing any work?

Nick Schroeder
January 21, 2020 12:38 pm

“The colder body does radiate toward the hotter body as well as the other way.”
Does not happen.
If it did there would be refrigerators without power cords.
I haven’t seem any.
You?

Antero Ollila
January 21, 2020 1:55 pm

This hopeless but anyway. How does the colder body know that it should not emit radiation according to Planck’s law because there is a warmer body somewhere in the vicinity. If you can give a scientific answer to this, you will win a Nobel prize.

LdB
January 21, 2020 4:53 pm

He is to stupid to get that problem.

Apparently the photon leaving the sun knows ahead of time that earth is cooler and the photon leaving earth knows ahead of time that the sun is hotter 🙂

Nick Schroeder
January 21, 2020 12:40 pm

Hotter lose KE.
Colder gains KE.
Until equal temperatures and energy transfer stops.

angech
January 21, 2020 4:14 pm

Nick,
Hotter lose KE.
Colder loses KE.
Colder loses KE by radiating energy until it has Virtually none left.
All bodies not at absolute zero are radiating heat.
That radiated heat adds to the energy load of any other bodies it encounters warming them a little or slowing their rate of heat loss.
Not a Stokes puppet are you?
His sort of logic.

LdB
January 21, 2020 5:17 pm

Nick is busy inventing his own physics because he isn’t using any physics that the rest of us know.

The interesting question to ask Nick would be what is the temperature of a laser beam?

LdB
January 21, 2020 6:26 pm

I will have one shot at this and see if you can understand.

A photon has no temperature it a quantum entity all it has that you would recognize is energy. A laser beam is neither hot nor cold because temperature is not a fundamental property it is a classical physics construct. Your thermal emission is just a bunch of these photons it is called “thermal emission” because of the source but it actually has no temperature.

You have probably run across that fact when as a kid you used a magnifying glass and the sun to burn things … Concentrating the sunlight changed the apparent temperature at the focus point. What you are doing in concentrating the energy which becomes temperature in your classical world again. A photon in 10um infra-red (which is about the emission of a 300K earth) when concentrated forms the basis of CO2 metal cutting laser which reaches many thousands of degree at it’s focal point.

That is why your statement about cold not transmitting to hot fails …. QM doesn’t know what the temperature is it just transfers energy. So yes photons from cold sources do enter and get absorbed by hot sources because QM doesn’t know what temperature is.

DaveS
January 22, 2020 5:58 am

Imagine a metal plate heated to say 400oC dangling in a vacuum. It’ll lose heat via radiation, and its core temperature can be plotted over time. Call this temperature profile A. Now repeat, but this time dangle metal plates heated to 300oC either side of the first plate, and plot the core temperature of the first plate over time again, calling it profile B. Will profile B (i) be identical to profile A; or (ii) trend above profile A (demonstrating lower rate of heat loss)? If you are saying that (i) is the correct answer, where is the radiative heat emitted from the two cooler plates in the direction of the hotter plate going?

A C Osborn
January 21, 2020 12:41 pm

“Energy can’t be destroyed, only transformed.”

How about sent back where it came from until they reach equilibrium.
Except they never do of course, a. because the CO2 also radiates to space, thus cooling everything and b. the Sun comes up next day to do it all again.

LdB
January 21, 2020 4:55 pm

I don’t get B the sun is always shinning on Earth it’s just on the other side 🙂

Tim Gorman
January 21, 2020 2:43 pm

Antero,

“This hopeless but anyway. How does the colder body know that it should not emit radiation according to Planck’s law because there is a warmer body somewhere in the vicinity. If you can give a scientific answer to this, you will win a Nobel prize.”

You nailed it. The heat transferred is dependent upon the total flow. (flow hot-to-cold) – flow cold-to-hot) determines total flow. Flow-cool -to-hot is *not* zero.

January 21, 2020 4:26 pm

Wow, none of you guys get it. If there were heat, also known as energy, flowing from the cold body to the hot body, the hot body would get HOTTER. It does NOT, NEVER EVER!

LdB
January 21, 2020 6:37 pm

Please read my explanation above … you start with the basic question how hot is a photon (which can be asked as how hot is a laser beam). You should quickly work out that a photon has no temperature it only has energy. That is why your statement quickly becomes nonsense because classical physics breaks down and you can’t apply it to the situation.

You were taught classical physics at school and there was a emphasis on temperature but there is no such fundamental property as temperature. It is an observational construct much like a rainbow of some deeper physics.

Tim Gorman
January 22, 2020 5:40 am

Michael Moon January 21, 2020 at 4:26 pm

“Wow, none of you guys get it. If there were heat, also known as energy, flowing from the cold body to the hot body, the hot body would get HOTTER. It does NOT, NEVER EVER!”

You didn’t bother to think about what I wrote, did you?

I said: “The heat transferred is dependent upon the total flow. (flow hot-to-cold) – flow cold-to-hot) determines total flow. Flow-cool -to-hot is *not* zero.”

If the energy received by the warmer body from the cooler body is less that the energy the warmer body emits toward the cooler body then the warmer body will *not* get hotter. It will see a net loss of energy and become “cooler”.

If the cooler body receives more energy from the warmer body than it emits toward the warmer body then the cooler body will see a net increase in energy and become “warmer”.

January 22, 2020 7:14 am

Temperature is the average kinetic ENERGY of the molecules of a substance. There are many binary stars in elliptical orbits, and the temp of the hotter one never increases as the cooler one approaches perihelion. Look it up. What you do not know fills all the textbooks about thermodynamics and heat transfer, actually basic physics. Energy is the capacity to do work. Heat is the average kinetic energy of a mass.

Cooler things never heat warmer things, as when something is heated, its TEMP goes UP. This has nothing to do with the way things cool down and your example with a plate between a heater and a human is sense-free.

Phil.
January 22, 2020 7:28 am

Michael Moon January 21, 2020 at 4:26 pm
Wow, none of you guys get it. If there were heat, also known as energy, flowing from the cold body to the hot body, the hot body would get HOTTER. It does NOT, NEVER EVER!

Amazing, over 50 years of experience using radiation shields around thermocouples to get more accurate flame temperatures didn’t happen!
Detailed analysis of shielded thermocouples so old that they’re in NACA papers:
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930084456.pdf

Carlo, Monte
January 21, 2020 7:09 am

‘In climate science, “upwelling” means headed for space, “downwelling” means headed for the surface, “forcing” means a change in downwelling radiation, “LW” is thermal longwave radiation, and “SW” is solar shortwave radiation.’

Is there a formal definition of the boundary between “LW” and “SW”?

This is important because solar radiation is spectral, with units of watts per square meter per wavelength unit (um or nm). A total irradiance in W/m2 is calculated by integrating over a specific wavelength region. When total irradiance is measured with a radiometer, the instrument implicitly performs the integration (and the answer is always “colored” by its spectral transmittance).

So stating there is “156 W/m2 of LW radiation” is nearly meaningless without also stating the wavelength bounds that LW refers to.

Thermopile radiometers such as global pyranometers typically have uncertainties on the order of +/-5% at best.

Nick Schroeder
January 21, 2020 7:59 am

The Instruments & Measurements

But wait, you say, upwelling LWIR power flux is actually measured.

Well, no it’s not.

IR instruments, e.g. pyrheliometers, radiometers, etc. don’t directly measure power flux. They measure a relative temperature compared to heated/chilled/calibration/reference thermistors or thermopiles and INFER a power flux using that comparative temperature and ASSUMING an emissivity of 1.0. The Apogee instrument instruction book actually warns the owner/operator about this potential error noting that ground/surface emissivity can be less than 1.0.

That this warning went unheeded explains why SURFRAD upwelling LWIR with an assumed and uncorrected emissivity of 1.0 measures TWICE as much upwelling LWIR as incoming ISR, a rather egregious breach of energy conservation.

This also explains why USCRN data shows that the IR (SUR_TEMP) parallels the 1.5 m air temperature, (T_HR_AVG) and not the actual ground (SOIL_TEMP_5). The actual ground is warmer than the air temperature with few exceptions, contradicting the RGHE notion that the air warms the ground.

Antero Ollila
January 21, 2020 8:40 am

I think that I have seen this comment before that there is no way to measure upwelling LW radiation emitted by the surface or even the LW radiation into space. These kinds of stories are part of the conspiracy stories. USA has a government that has money to invest in several satellites measuring LW radiation emitted by the Earth and the whole thing is a fairy tale.

I have analyzed the global results of upwelling LW radiation observations originating from GEWEX project. If somebody is interested in it, he/she can find this information just by googling.

Carlo, Monte
January 21, 2020 11:03 am

My (poorly expressed) point should have been this: taking arithmetic sums or differences of these total irradiances (however measured) is simplistic because of the spectral nature of the quantities, the numeric definite integrations can’t be avoided. In other words, adding and subtracting irradiance is only valid at single wavelengths.

And I really would like to understand the spectral difference between what the climate modelers refer to as SW and LW.

For example, is it defined by specific instruments, such as pyranometers and pyrgeometers?

Both are thermopile instruments (with calibration constants of uV/W/m2). Their spectral bands are defined by the transmittance of the domes/windows: pyranometers typically have quartz or silica domes that have long-wavelength cutoffs of 2.5-4 um, pyrgeometer domes pass 4.5-42 um (I don’t what these materials are).

Based on these two instruments, the division between SW and LW would be about 4 um, is this correct?

Nick Schroeder
January 21, 2020 7:13 am

And, oh, BTW,

5.) Dividing the discular 1,368 W/m^2 ISR by 4 to get an averaged 342 W/m^2 spherical ToA ISR is simplistic and dumb and and doesn’t even remotely resemble how the earth heats and cools.

Robert W Turner
January 21, 2020 7:48 am

6) The area of Earth used in the S-B equation for both absorption and emission is approximately 196,900,000 sq mi. This is an abstract number and not a real number that should concern scientists. In reality, the absorbing surface is much higher and the emitting surface is much much higher, because the Earth is not a polished marble but rather is covered by plants, geomorphic features, and rough surface waters.

jorgekafkazar
January 21, 2020 10:29 am

If you think that’s bad, you should see Venus.

Meanwhile, back on mostly-ocean Earth, the sea is rarely smooth anywhere for long, resulting in constantly fluctuating surface area and zenith angles. Add in humidity and wind mass transport, and good luck modeling that. Using historical averages is a fool’s errand.

Nick Schroeder
January 21, 2020 12:54 pm

Your number is for the spherical area.
The entire sphere loses energy 24/7.
Because the lit side is hotter a large percentage leaves as radiation.
Because the dark side and poles are cold a rather small percentage leaves as radiation.
That’s why dividing by 4 and using averages for all flows is useless.

Steve Case
January 21, 2020 8:26 am

5.5 W/m² per degree.

And the latest Trenberth heat budget says “net absorbed 0.9 W/M²” So that’s what, a little north of 0.15 deg C of warming?

John Finn
January 21, 2020 1:34 pm

5.5 w/m2 per degree C is surface warming without feedbacks. If Trenberth’s figure refers to the TOA then surface forcing will be ~1.5 w/m2

Also, since we’ve had over 0.5 degree warming since 1980 alone perhaps the alarmists are right and there is a strong positive feedback.

Phil.
January 21, 2020 8:51 am

Feldman et al. referred to by Willis says the following:
“The climate perturbation from this surface forcing will be larger than the observed effect, since it has been found that the water-vapour feedback enhances greenhouse gas forcing at the surface by a factor of three and will increase, largely owing to thermodynamic constraints”.

Herbert
January 21, 2020 12:44 pm

Phil and Willis,
Thanks.
That answers my somewhat obtuse question in this thread about Paltridge et al (2009) as against Dessler and Davis (2010)regarding water vapour feedback.

mkelly
January 21, 2020 9:07 am

If all the comments about CO2’s ability were true then two things must happen. 1. The specific heat of dry air must be revalued. 2. An addendum to specific heat tables must be published saying something like “If IR involved in energy supplied to increase temperature of either dry air or CO2 then the forcing equation must be included.”

As of now climate science is in conflict with thermodynamics area of specific heat. Thermodynamics says the energy can be of any form. Climate science has special case for IR and CO2. Anthony’s experiment demonstrated that increased CO2 does not cause increased temperature.

Luchezar Jackov
January 21, 2020 9:28 am

I’m just wondering how everybody deals with average temperature, while in the Stefan-Boltzmann’s law the temperature is in fourth power.

In other words if you have 1 square meter of 50 deg Celsius and 1 square meter of 0 deg. Celsius, their emission won’t be equal to 2 square meters at 25 deg Celsus, will it?

Steve Case
January 21, 2020 9:46 am

Luchezar Jackov January 21, 2020 at 9:28 am

Phrase that in Kelvin and see if you get something different.

Luchezar Jackov
January 21, 2020 10:14 am

It’s still in the 4-th power.

1 sq.m. of 50C = 323.15^4 = 10904773289.97600625
1 sq.m. of 0C = 273.15^4 = 5566789756.30100625
Total: 16471563046.2770125

2 sq.m. of 25C = 15804081127.5270125

Difference: 16471563046.2770125/15804081127.5270125 = 1.0422347818493162903409232289584
i.e. 4.22% difference

In other words, it is incorrect to calculate the outgoing radiation by averaging the temperature, be it day/night temperature or equator/pole temperature.

Luchezar Jackov
January 21, 2020 2:04 pm

I’d rather name my comment a food for thought. Looking at Figure 3 and the conclusion that it takes more energy to keep a hot surface one degree hotter than a cold surface provoked it.

Let’s take the tropics for example. The energy budget there is quite different from 1362/4 W/m2. It’s close to 1362/pi W/m2 (opposed to the poles where it is much less). The land surfaces heat up to more than 50C in the day (even though the air doesn’t get that hot) and when heated, they radiate. In the night they radiate, effectively cooling probably under the air temperature. Taking the average of the air day and night temperatures and assuming this is the temperature of emitting is not correct, because of the 4-th power in Stefan-Boltzmann’s law.

In other words the hotter surfaces of the Earth dissipate much more energy than the cooler surfaces, and averaging the temperature and then calculating the dissipation based on the average temperature is incorrect.

A C Osborn
January 21, 2020 10:49 am

It will be different, but still not correct.

The average of 0C, 273.15^4 and 50C, 323.15^ is 8235781523

Whereas 25C, 298.15^4 is 7902040564

So an error of 333740959

Near enough for Government Climate work of course.

Kevin kilty
January 21, 2020 9:34 am

At a globally averaged temperature of 15°C the surface emits about 390 W m -2,

This illustrates just one of the many problems with climate science. The surface of the Earth is not a cavity radiator. Thus, the actual LWIR characteristics of surface materials matters and one cannot just use the Stefan-Boltzmann formula without some adjustment. The average emissivity of snow, vegetation, soils, water, and so forth is probably in the neighborhood of 0.97. So at 288K (i.e. about 15C). The actual emission is more like $378 W/m^2$. The difference is already nearly four times bigger than the effect of doubling CO2 in the tropics (MODTRAN calculation). The whole science is filled with big numbers multiplied by fractional quantities that are poorly known then subtracted from other large, but error riddled numbers, and so on. Given enough imprecision and inaccuracy almost anything seems possible.

Tim Gorman
January 21, 2020 10:18 am

Kevin,

+10

A C Osborn
January 21, 2020 10:35 am

Mr kilty, what is the difference between emissivity and reflectance, which during the winter in the NH is very high due to the angle of incidence.
Which means that the full range of Solar Radiation gets reflected rather than LWIR getting emitted.

Kevin kilty
January 21, 2020 11:40 am

Emissivity is a material property. It is a dimensionless quantity, and one would calculate it as the ratio of the measured power emitted from a surface by virtue of its temperature divided by the power a perfect blackbody would emit at the same temperature. Since real materials always show some angular and frequency dependence to their emitted power, we can say that “emissivity” is only an approximation to the complexity of emitted power from a surface that is not within a cavity. Emissivity is based on emitted power into a hemisphere above a flat surface.

Reflectance is the measured ratio of redirected to incident light intensity at a material interface. This definition is per the “Encyclopedia of Physics”. It is based on inteensity which is radiance energy in a pencil of radiation at some angle to a surface. You can see in this thread some disagreement over LWIR and solar radiation, and as the above definition uses the term “light” one might wonder if reflectance applies to LW radiation in the same way it does to visible or solar radiation or not. You mention that reflectance increases at low solar angle in the northern hemisphere winter, which it does, but a rough sea state probably also shows an enhanced reflectance as well.

In the context of climate science light would likely refer to solar radiation including radiation predominantly from about 2.8 um and shorter wavelengths (an Eppley PSP for instance uses this definition); while LWIR is 4 um and longer (the definition as per an Eppley PIR), leaving a no-man’s land of radiation between the two for people to fight over.

As I explained in a blog some months ago, total power travelling away from a surface is a combination of reflected and emitted power which is known as radiosity.

Steve Case
January 21, 2020 10:54 am

Kevin kilty…
The whole science is filled with big numbers multiplied by fractional quantities that are poorly known then subtracted from other large, but error riddled numbers, and so on. Given enough imprecision and inaccuracy almost anything seems possible.

My favorite is from the IPCC’s AR4 Chapter 5 Executive summary page 387 where they say:

Over the period 1961 to 2003, global ocean temperature has risen by 0.10°C from the surface to a depth of 700 m.

Of course Trenberth’s Heat Budget is right in there:

The noon-day sun puts out nearly 1370 wm² and these guys are claiming they’ve added up all the chaotic movements of heat over the entire planet and have determined an imbalance of 0.9 Wm². That’s an accuracy to five places. No plus or minus error bars or anything.

What it means is, all of the components

Reflected by clouds
Reflected by aerosols
Reflected by atmospheric gases
Reflected by surface
Absorbed by the surface
Absorbed by the atmosphere
Thermals
Evaporation
Transpiration
Latent heat
Emitted by clouds
Emitted by atmosphere
Atmospheric Window
AND

need to have an accuracy to those five places or better for the 0.9 Wm² to be true.

Nick Schroeder
January 21, 2020 12:41 pm

No such thang!!

Steve Case
January 21, 2020 2:15 pm

Nick Schroeder January 21, 2020 at 12:41 pm
No such thang!!

How can you say that, it’s right there on Trenberth’s chart,
Global Energy Flows W m²Back Radiation 333

http://www.cgd.ucar.edu/staff/trenbert/trenberth.papers/BAMSmarTrenberth.pdf

Kevin kilty
January 21, 2020 1:39 pm

I understand your point, Willis, but my complaint is that the idea of radiation balance involves some numbers that make use of an effective emissivity, which we can’t possibly know better than $\pm 0.01$ and others make use of an albedo which we surely don’t know better than $\pm 0.01$
and then we mix them numerically. I understand that we can juggle the numbers to obtain a balance, and then work with differences from there, but even so, how well do we know the resulting balance, or its trend? I am always skeptical of just-so arguments.

As an ocean science sort of fellow you can appreciate an analogy that drove me bonkers for years. The oceanography textbooks, and many articles (in the old Scientific American for instance) would always explain anomalously large tides, like at Truro, as a resonance phenomena; and then they would use a rectangular basin of water to explain the resonance — they would fudge the dimensions of this basin to get the answer they wanted. But any place having anomalously large tides is never on the shore of a rectangular basin. They are always an inlet in a channel or estuary having dimensions that diminish toward the port. The criteria for resonance in such an instance isn’t anything like the fudged rectangular dimensions; and the anomalously large tides are not a resonance, but are what a person would expect from jamming water into a restricted region.

Resonance requires a very fine set of dimensions balanced against a tight specification of driving frequency. It would occur in fact almost nowhere by coincidence, but by fudging dimensions the authors of textbooks and articles would have it happen everywhere. Fudge small differences all over and get an impossible result that looks reasonable.

Well anyway, as usual, you provoke a lot of thought.

Len Werner
January 21, 2020 10:11 am

A most interesting post, and as or more interesting comments following it–all indicating that this science is far from settled. But here’s one more monkey-wrench:

This planet is not 15C; far less than 1% of it is 15C. The average temperature is closer to 3,000C, and debating a few watts per square meter controlled by 400 ppm CO2 in the air at the surface of a 3,000 degree molten ball sure is a puzzling pursuit to a geologist. It seems like me trying to do careful calculations to explain the effect of CO2 on the surface temperature of my wood stove while ignoring that there’s a fire burning inside it. This planet is molten, and only barely skinned over.

And we have as yet no idea how much internal heat is moved to the surface; black smokers were only discovered in the 70’s, explosive eruptions were impossible at Arctic Ocean depths until they were detected from a research vessel a couple of years ago, and we still have no idea how much submarine volcanism exists. We also don’t know how episodic that volcanism is; observations of volcanoes that we can see suggests that such heat delivery is not constant.

Doing detailed calculations of what a few ppm of CO2 in the atmosphere are or are not doing to temperatures at the earth’s surface seems quite premature–but I fully admit to having the biases of an earth scientist, not an atmospheric scientist. I guess only time and more research will reveal who was more down to earth.

Antero Ollila
January 21, 2020 11:09 am

I have not calculated this but other scientists have that the Earth’s surface receives 99.97 % of its energy from the Sun. On the other hand, other scientists say that below our feet is the core of the Earth having about the same temperature as the Sun – close to 6000 C. But who cares, if the deep sea has a temperature of 4 C. If that temperature would be about 15 C, then we should think otherwise.

Ben Wouters
January 21, 2020 12:48 pm

Antero Ollila January 21, 2020 at 11:09 am

On the other hand, other scientists say that below our feet is the core of the Earth having about the same temperature as the Sun – close to 6000 C. But who cares, if the deep sea has a temperature of 4 C.

4 C is ~277K, some 22K ABOVE the infamous 255K, the maximum temperature the sun is supposedly able to provide.
How did these oceans get so hot? From the enormous amounts of heat inside the Earth, of from the downwelling LW from the atmosphere?

LdB
January 21, 2020 5:08 pm

You can measure them
Heat flows of continental crust is 0.071 Watts per square meter
Heat flow of oceanic crusts is 0.105 Watts per square meter
The average is 0.090 Watts per square meter adjusted for land/sea ratio

So yeah 99.97 looks about right I didn’t do the maths.

Ben Wouters
January 22, 2020 4:09 am

Antero Ollila January 21, 2020 at 11:09 am
No answer to a simple question?

How did these oceans get so hot? From the enormous amounts of heat inside the Earth, of from the downwelling LW from the atmosphere?

Ben Wouters
January 21, 2020 1:10 pm

Len Werner January 21, 2020 at 10:11 am

I guess only time and more research will reveal who was more down to earth.

You’ll find that a lot of people believe that our cold, low density atmosphere is able to warm just about anything.
The Geothermal Flux through continental crust is on average just ~65 mW/m^2 and can supposedly be neglected.

Difficult to envision how the atmosphere can cause the increasing temperatures when moving deeper into the Earth.

Len Werner
January 21, 2020 7:50 pm

Thanks for all the responses to the suggestion that our molted earth may have different thermodynamics than present climate science suggests; I also do know the numbers quoted. I spent a good part of a career in geothermal exploration so am conversant with crustal heat flows–that we know about. Please appreciate that having measured temperatures in a lot of drill holes, that I may have a different perspective on geothermal energy than someone who has not. When you tell me what the crustal heat-flow values are–I measured a lot of them.

However, most of that career pointed out how much we don’t know. Many of these numbers I feel are subject to revision as we learn more. For example, continental crustal heat flow is certainly insignificant compared to what is being delivered to the base of oceans. From ocean bottom it convects away, so ocean bottom temperatures may not be indicative of how much heat is delivered. We don’t have a saturation of sampling of ocean bottom temperatures; if we did we would know how much volcanic activity is down there. We are only beginning that discovery. That snow doesn’t melt immediately when it falls on land is irrelevant for the majority of the planet’s surface.

Willis, with all due respect I don’t think that today’s understanding of planetary and atmospheric thermodynamics is at all complete; in 2100, when all the present postulated climate catastrophes are to have happened and will be in the rear-view mirror I’m betting we will have a far different picture of how these systems work, and the exponential increase in knowledge will have led us in as different directions as we are now thinking compared to a century ago. I don’t laugh at you, and it may be unwise to subject me to a laugh test. After all, Michael Mann thinks he knows all there is to know too, and we don’t agree. The discussion should be kept civil.

Ben Wouters
January 22, 2020 4:04 am

Len Werner January 21, 2020 at 7:50 pm

I spent a good part of a career in geothermal exploration

Len, a question I’d like to have an answer for:
How long does it take for the Geothermal Gradient to completely re-adjust to a 1K sudden warming at the surface? So 1k higher average surface temperature for continental crust, and 1K warmer ocean floor water.

From ocean bottom it convects away, so ocean bottom temperatures may not be indicative of how much heat is delivered.

Geothermal heat is disregarded since the flux is so low. Yet the entire heat CONTENT of the crust is from geothermal origin, except for the upper 10-20 m or so of continental crust.
Same for the oceans, below a certain depth the (500m 1000m ?) the influence of solar energy is zero.
Although small, the ~100 mW/m^2 geothermal flux into the oceans alone is capable of bringing the oceans from freezing to boiling in just ~500.000 years.
Every liter of water warmed at the ocean floor has to be physically transported to (mostly) Antarctica before it can surface and “vent” this energy to the atmosphere and space.
A very slow and inefficient process.

Antero Ollila
January 21, 2020 10:14 am

There are the same old stories about the radiation. For example, the cold atmosphere cannot heat up the warm surface. Here are some facts. The Earth’s surface emits LW radiation according to Plank’s law and it is about 395 W/m2 corresponding to the temperature about 16 °C. The Earth receives SW radiation 165 W/m2 and absorbs it. There is an error in energy balance of 395-165 =230 W/m^2.

What about this balance: The surface receives the SW radiation 165 and LW radiation 345, totally 510 W/m2. The following energy fluxes leave the surface: LW radiation 395, latent heating 91, and 24 sensible heating, totally 510 W/m2. No error in energy balance.

If you say that there is no energy flow from a lower temperature to the higher temperature, you are wrong. The net energy flux is from higher to lower temperature, but the lower temperature surface radiates as well according to its temperature as stated by Max Planck’s law. My cheap infrared measuring device can measure the temperatures of my room surface and it is real. They radiate, even though I am standing there with my 35 °C skin temperature. I cannot stop the radiation of the surfaces of the room even they have lower temperatures. And neither can you. The radiates about 1360 W/m2 to the Earth and the Earth radiates back 240 W/m2 with the 4 times greater surface. The sun cannot stop it.

Antero Ollila
January 21, 2020 1:23 pm

I have to say that I did not understand what you tried to formulate. The basic question was if the LW radiation emitted by the atmosphere (345 or 320 no matter) adds energy to the surface or not. I say the same as all the researchers who have published energy balances of the Earth: Yes, it does.

I understood that you say in the way. If you do not say so, please correct me.

angech
January 21, 2020 4:28 pm

”IR instruments, e.g. pyrheliometers, radiometers, etc. don’t directly measure power flux. They measure a relative temperature compared to heated/chilled/calibration/reference thermistors or thermopiles and INFER a power flux using that comparative temperature and ASSUMING an emissivity of 1.0.”
So sorry.
Obviously a Mosher clone.

angech
January 21, 2020 4:37 pm

Willis
“Compared to what? If we take away the atmosphere, the ground would be exposed to ~3 W/m2 background radiation of outer space. Instead, it’s getting ~320 W/m2 from the cold atmosphere.”

Not fair.
Both get the background radiation 3.
The atmosphere is insulating the surface from the sun remember?
“ put a metal plate at 100 C Source at 400 C A hotter object cools you?”
The atmosphere actually stops the surface getting as warm as it could if exposed to the bare sun. Surface of the moon is hotter under the sun than on earth .
Colder on the other side and most importantly has the same TOA out as the earth.
Because they both get the same in just the TOA is virtually the moon surface not 100 km radius further out and so they both radiate the same amount out.

Steve Z
January 21, 2020 10:27 am

It also depends on what is considered “top of atmosphere”–between what two altitudes? If IR radiation is emitted from the surface of the earth, most of it will be absorbed and converted to heat (kinetic energy of molecules) at low altitudes (higher atmospheric pressures), where the number of molecules of water vapor and CO2 per unit volume are the highest. With increasing altitude, atmospheric pressure decreases, as does the number of molecules of water vapor and CO2 per unit volume, so the intensity of IR radiation absorbed and converted to heat also decreases. The thinner atmosphere may not affect the temperature change, since the specific heat per unit volume also decreases with decreasing pressure, but most of the energy is absorbed in the lower atmosphere.

Also, the calculation of the IR radiation rate varies not only with temperature, but also the type of surface. On dry land, the emission rate would depend primarily on albedo and temperature, but over oceans, some of the radiant heat received from the sun is converted into latent heat to evaporate ocean water, which can have a huge effect on ocean temperature during daylight hours, and the Stefan-Boltzmann equation would not take this into account.

“By comparison, the IPCC says that a doubling of CO2 would increase the surface temperature by 1.5°C to 4.5°C. If we take the midrange value of 3°C, this would imply that there is some mysterious feedback increasing the CO2-caused surface temperature change by a factor of about ten …”

There are probably many variables that both Willis Eschenbach (in this article) and the IPCC have not taken into account.

However, it is within the realm of possibility that the IPCC may be wrong!

Nick Schroeder
January 21, 2020 12:34 pm

Molecules disappear at 32 km. That’s my ToA. All radiation after that.

EdB
January 21, 2020 1:26 pm

“With increasing altitude, atmospheric pressure decreases, as does the number of molecules of water vapor and CO2 per unit volume, so the intensity of IR radiation absorbed and converted to heat also decreases”

I cannot see much of a change in the greenhouse effect if the mean path to thermalization drops from say 5 meters to 3 meters above the surface with a doubling of CO2. The latency is still in milliseconds.

The average radiating temperature is warmer at 3 meters than at 5 meters. (abt 0.015C)

Thus the surface effect is extra heating from the average DWLR being up the Plank distribution to a more energetic level.

Seems trivially small to me.

January 21, 2020 10:47 am

This is the same answer I keep getting when looking at OHC too, and also proves strong negative feedback. If the “direct effect” of CO2 doubling is 3.7W/m^2 and this direct effect is supposed to be 1.2°C, my answer generally comes in at 1/4 that (0.3°C), not 3x that (3.6°C after + feedback).

This means the feedback is negative.

Twice now, I’ve seen articles about how the energy of N gazillion Hiroshima bombs have been input into the oceans, yet if you take the “area under the curve” of the CO2 forcing since, say, 1950, we “should have” seen MUCH more than we see, by the direct effect alone, using “top layer” of the ocean plus some mixing. Since oceans are the only true reservoir of energy of any substance on this rock, and this is a direct measurement of ocean heat (despite its troubles as a measurement), the amount of heat accumulating is nowhere near the “expected” amount. Each time it comes out to about 1/4 the “expected” amount. This agrees with your work shown here, and effectively destroys any argument about extreme ill effects or any emergencies.

So I always view these studies showing huge energy increases with great relief.

Herbert
January 21, 2020 3:01 pm

“Since oceans are the only true reservoir of energy of any substance on this rock….”
A pertinent reminder of the most appropriate measure of planetary climate.
In June 2009 Professor Robert Carter and 3 other scientists commented on the response of the Australian Chief Scientist and Will Steffen to the Wong- Fielding exchange ( Full Assessment available on line) as follows-
1. What is the most appropriate measure of planetary climate?
1.1 The government’s reply says “ When climate change scientists talk about global warming they mean warming of the climate system as a whole, which includes the atmosphere, the oceans , and the Cryosphere”, and then adds, “ in terms of a single indicator of global warming, change in ocean heat content is most appropriate.”
1.2 “
We agree that in an ideal academic discussion, and were accurate historical data available, ocean heat content might be a better criterion by which to judge global warming than would be atmospheric temperature. Use of this indicator was first pressed by Pielke (2007,2009) as a test of the dangerous warming hypothesis, but it has not been widely publicised by the IPCC.
1.3. In any case , Senator Fielding’s question was predicated upon the history of IPCC’s public advice which has consistently used the UK Hadley Centre near-surface air temperature record as the one that dominates in IPCC and government policy papers and discussion and is the criterion of judgement that both politicians and the public are familiar with.”
2. Natural variability in Air Temperature.
2.1 The government asserts that “at time scales of around a decade, natural variability can mask the atmospheric warming trend caused by the increasing concentration of greenhouse gases.”
2.2 It is widely agreed there is a considerable natural variability in air temperature on decadal timescales and longer. It is the IPCC who have previously denied the effect of natural variability.
For example the 2001 Summary for Policymakers, based on computer model simulations, that the climate system has only a limited variability. In turn, this claim was and is used to underpin the argument that carbon dioxide is the only plausible explanation for the late 20th century warming trend.
For the government to now invoke natural variability as an explanation for the elapsed temperature curve is to destroy the credibility of their previous arguments for carbon dioxide forcing.”
2.3 The government also claims that” in terms of the climate system as a whole, only about 5% of the warming since 1960 has taken place in the air”.
2.4 Using the Hadley CRU temperature record , the rise in air temperature since 1960 has been about 0,5 degrees C. Translating the 15×10 22 J of additional heat in the upper 700 metres of ocean since 1960 into a temperature rise, we find that this corresponds to an increase in upper ocean temperature of only 0.25C.
Thus, using these metrics air temperature increase since 1960 has been more than three times greater than ocean temperature increase.”

David L Hagen
January 21, 2020 12:40 pm

Willis Eschenbach
Excellent evidence and observations.
Your first figure of the difference in Long Wave Greenhouse Radiation vs TOA radiation appears related to regional rainfall and clouds. See especially the reds in the western Pacific. Comparing those may further your thermostat model.
Best wishes
David

aleks
January 21, 2020 12:55 pm

To Willis Eschenbach

To Willis Eschenbach January 21, 2020 at 12:24 am
Willis, in the Stefan-Boltzmann equation the term including albedo is missing: E(1-A) ε = σ T4 . The Earth’s surface temperature 255 K (according to IPCC) can be obtained when E = 1368/4 = 341 W/m^2, albedo A=0.3, emissivity ε =1. However, albedo varies significantly: for water it is 0.06 – 0.1, for snow and ice 0.7 – 0.9, for sand 0.35, forests 0.07 – 0.18.
https://www.e-education.psu.edu/earth103/node/1002
This invalidates the accuracy of calculating both temperature and energy using the Stefan-Boltzmann equation.

aleks
January 21, 2020 5:59 pm

Yes, Willis, albedo is included to S.-B. equation for Earth, because Earth is not a black body. I can cite one from many links: 3. New Science 8: Applying the Stefan-Boltzmann Law to Earth. http://joannenova.com.au/2015/10/new-science-8-applying-the-stefan-boltzmann-law-to-earth/
Regards, a

Herbert
January 21, 2020 3:02 pm

“Since oceans are the only true reservoir of energy of any substance on this rock….”
A pertinent reminder of the most appropriate measure of planetary climate.
In June 2009 Professor Robert Carter and 3 other scientists commented on the response of the Australian Chief Scientist and Will Steffen to the Wong- Fielding exchange ( Full Assessment available on line) as follows-
1. What is the most appropriate measure of planetary climate?
1.1 The government’s reply says “ When climate change scientists talk about global warming they mean warming of the climate system as a whole, which includes the atmosphere, the oceans , and the Cryosphere”, and then adds, “ in terms of a single indicator of global warming, change in ocean heat content is most appropriate.”
1.2 “
We agree that in an ideal academic discussion, and were accurate historical data available, ocean heat content might be a better criterion by which to judge global warming than would be atmospheric temperature. Use of this indicator was first pressed by Pielke (2007,2009) as a test of the dangerous warming hypothesis, but it has not been widely publicised by the IPCC.
1.3. In any case , Senator Fielding’s question was predicated upon the history of IPCC’s public advice which has consistently used the UK Hadley Centre near-surface air temperature record as the one that dominates in IPCC and government policy papers and discussion and is the criterion of judgement that both politicians and the public are familiar with.”
2. Natural variability in Air Temperature.
2.1 The government asserts that “at time scales of around a decade, natural variability can mask the atmospheric warming trend caused by the increasing concentration of greenhouse gases.”
2.2 It is widely agreed there is a considerable natural variability in air temperature on decadal timescales and longer. It is the IPCC who have previously denied the effect of natural variability.
For example the 2001 Summary for Policymakers, based on computer model simulations, that the climate system has only a limited variability. In turn, this claim was and is used to underpin the argument that carbon dioxide is the only plausible explanation for the late 20th century warming trend.
For the government to now invoke natural variability as an explanation for the elapsed temperature curve is to destroy the credibility of their previous arguments for carbon dioxide forcing.”
2.3 The government also claims that” in terms of the climate system as a whole, only about 5% of the warming since 1960 has taken place in the air”.
2.4 Using the Hadley CRU temperature record , the rise in air temperature since 1960 has been about 0,5 degrees C. Translating the 15×10 22 J of additional heat in the upper 700 metres of ocean since 1960 into a temperature rise, we find that this corresponds to an increase in upper ocean temperature of only 0.25C.
Thus, using these metrics air temperature increase since 1960 has been more than three times greater than ocean temperature increase.”

(Rescued from spam bin) SUNMOD

January 21, 2020 3:34 pm

Johanus, just a small nitpick to your informative comment. Your linked diagram says the area under the solar radiation curve is 63,000,000 Wm^2 compared to 250 Wm^2 for the earth radiance curve.

Butch123
January 21, 2020 4:24 pm

Feldman et al did NOT measure downwelling IR directly.
The AERI instruments were designed to be extremely sensitive and they do measure downwelling IR in a number of regions. Just not in the 15 micron band. This was a major failing per Gero prior to Feldman getting involved. Feldman created a simulated spectra and then compared it to the measured spectra which showed nothing. Viola! We now have downwelling IR appearing.

It just seems to be overly Mannomatic.

Hubert
January 21, 2020 4:31 pm

I think that on TOA the SW should balance LW and this value is not dependent of greenhouse , only Sun and albedo : so the equation becomes SW (Sun- albedo) = LW (window + green house * K)
if greenhouse is increasing, then the window part is reduced .
When greenhouse = 0, SW(sun-albedo ) = LW (window)
On surface we have LW(surface) = LW (window + greenhouse)
So if greenhouse is increasing by 3.7 Watts/m2 , the window part is reduced and the increase of the total LW(surface ) is not 3.7 watts/m2, but less because the window part is reduced .
I hope it is clear .

Antero Ollila
January 22, 2020 10:12 am

You are right. GHE has no role in the energy balance at the TOA.

Walter Sobchak
January 21, 2020 6:13 pm

“This doubling of CO2, in turn, would warm the surface by: 1.8 watts per square metre CO2 surface forcing / 5.5 watts per square metre per degree C ≈ 0.3°C …”

So Willis, you are saying that the ECS is 1/10th of the number the IPCC used. If so we are going to have to burn a lot more fossil fuel in order to to dodge the next Stadial and have any hope of ending the Quaternary period ice age.

angech
January 21, 2020 10:14 pm

“Now, this is curious. On average the change at the surface is a little less than half the TOA greenhouse effect change. So an increase of 3.7 W/m2 at the TOA from a doubling of CO2 becomes a 1.8 W/m2 increase at the surface.”
“The key is to realize that the atmosphere is not heated by just Ramanathan’s ~150 W/m2.”

Hate that diagram.
Trying to explain things
There is a TOA of 237 W/m2.
At this level 100 km above the earth the incoming energy that is not reflected exactly balances the outgoing energy 237 W/m2.
The surface of the earth is radiating at 392 W/m2.
This is amazingly higher than the 342 W/m2. from the total incoming reflected and incident solar radiation.
The GHG effect is basically to add 321 W/m2. of back radiation to the heating of the earth surface to the 169 W/m2. from the incident solar radiation that reaches the earth.
Basically the surface should be at a temperature commensurate with 490 W/m2. ie hotter than it is.
It emits however at 392 W/m2.giving I presume a temp of 15C, because the other 98 W/m2. is lost by sensible heat 10 W/m2. and latent heat 18 W/m2.

Now there is no Ramanathan 150 W/m2. being absorbed all the time. Some energy has to absorbed to raise the temperature of the air and surface but this is almost instantaneous and trivial when considering all those hydrogen bombs of energy going through the atmosphere every second. Air temperature changes very quickly night to day. Once it is warmed up there is no 150 W/m2. being drained into an atmospheric greenhouse battery all the time.
The energy in equals the energy out at the TOA.

Now why do we have a seeming TOA imbalance from the surface when there is not one at the TOA?
Because we are not comparing oranges with oranges.
The total energy absorbed at the surface is for a much smaller sphere.
Earth Surface area: 510.1 million km² Radius: 6,371 km energy emitted 392.
TOA surface area 526.2 million km² Radius: 6,471 km energy emitted 237.
Is this enough to make these 2 figures equal is what I would like someone to answer.
On the surface it does not look likely but?

One cannot take energy figures per square meter of a much larger sphere from energy figures for a much smaller sphere without doing a calibration for surface area and attenuation.

angech
January 21, 2020 11:04 pm

Hmm seems the outgoing IR is measured at the TOA 100 KM out so spread over a bigger sphere surface area but the energy going into the ground is measured at earth surface area a smaller sphere so the energy budget diagrams are technically out of whack.
Technically the two have to balance to have a TOA in the first place

OLR is a critical component of the Earth’s energy budget, and represents the total radiation going to space emitted by the atmosphere.[3] OLR contributes to the net all-wave radiation for a surface which is equal to the sum of shortwave and long-wave down-welling radiation minus the sum of shortwave and long-wave up-welling radiation.[4] The net all-wave radiation balance is dominated by long-wave radiation during the night and during most times of the year in the polar regions.[5] Earth’s radiation balance is quite closely achieved since the OLR very nearly equals the Shortwave Absorbed Radiation received at high energy from the sun. Thus, the Earth’s average temperature is very nearly stable

Mack
January 22, 2020 2:47 am

Willis,
I notice that you’ve got, (in your diagram), 321 watts/sq.m of “backradiation” from the “greenhouse” gases coming down from the atmosphere and absorbed by the surface.
According to the diagram you only get 169 watts/sq.m impinging on the surface from the sun…the sun Willis,… in summer hot enough to melt tar on the roads.
I was wondering if you leave your bacon and eggs out on the porch overnight and have them cooked for you in the morning by that backradiation from the atmosphere.?

Mack
January 23, 2020 12:24 am

Well, I thought those numbers would have pricked up your ears, Willis I would have thought that 321 watts/ sq.m. of “backradiation” belting down from the ATMOSPHERE 24/7, would have triggered some form of thought process in your head….. particularly since it’s nearly TWICE the amount of solar radiation impinging upon the surface.! Is there nothing about that which really unsettles you? Is there nothing about that which says…”hang on, there could be some mistake in these diagrams.” ?

Ben Wouters
January 23, 2020 4:03 am

Willis Eschenbach January 23, 2020 at 12:35 am

Also, if the ≈ 169 w/m2 of sunlight was the only thing heating the surface, it would be at about -40°C or so …

Why do you keep pushing this radiative balance temperature nonsense?
If the surface temperatures on Earth were in radiative balance with incoming solar we would see temperature swings from ~3K during the night to 365K or higher during the day.
Is not happening.
169 W/m^2 is ~14,6 MJ/m^2 over 24 hrs. This seems close to the world average as shown in these charts:
https://www.pveducation.org/pvcdrom/properties-of-sunlight/isoflux-contour-plots
14,6 MJ/m^2 between sunrise and sunset is enough energy to INCREASE the temperature of the upper 4 m of ocean water 1K.
Has nothing to do with RADIATIVE balance.
Backradiation does not warm the surface, it reduces the energy loss from the surface to the atmosphere. Otherwise we would see your 321 W/m^2 + ~1000 W/m^2 at noon giving temperatures of ~390K.

Ben Wouters
January 24, 2020 5:47 am

Willis Eschenbach January 23, 2020 at 10:01 am

Seriously?

Absolutely.

Average energy budgets are a very useful tool for studying the nature and size of the energy flows of the climate system.

Absolutely agree: average ENERGY budgets.
The moment you assign a SB temperature to these energy flows, you implicitly assume RADIATIVE balance.
On Earth we do NOT see radiative balance temperatures. Nigh time temperatures do not drop to ~3K, nor do daytime temperatures soar to ~364K, the RADIATIVE balance temperature for 1000 W/m^2 solar radiation.

The 169 W/m^2 average solar that actually heats the surface is enough energy to increase to temperature of ~3,5 m^3 ocean water 1K.
169 J/s/m^2 x 60 x 60 x 24 = 14,6 MJ/m^2/day.

On our moon we DO see ~radiaitve balance temperatures during the day.
Not so for the lunar night. Temperatures do not drop to ~3K as radiaitve balance would suggest, but to ~80K on average.

Difference between the two obviously our oceans vs lunar regolith.

Mack
January 24, 2020 1:16 pm

The thing that unsettles me ,Willis, is that you think the ATMOSPHERE raises the temperature of the planet from that… ” -40deg C or so” to what we have in reality of about 15deg C.

Trick
January 24, 2020 8:12 pm

“On our moon we DO see ~radiaitve balance temperatures during the day.”

No Ben, DIVINER radiometer results show brightness temperatures are always changing lunar day and night (diurnal) so no ~radiative balance. Or define your ~. Apollo derived results though show temperature unchanging diurnally about 0.3m deep in the lunar soil.

Ben Wouters
January 25, 2020 1:22 am

Mack January 24, 2020 at 1:16 pm

The thing that unsettles me ,Willis, is that you think the ATMOSPHERE raises the temperature of the planet from that… ” -40deg C or so” to what we have in reality of about 15deg C.

Compared to the moon it’s even more unsettling’.
On the moon ~90% of incoming solar is available for heating, resulting in avg temperature of ~197K. Increasing its rotation to ours should result in ~220K.
Adding an earth-like atmosphere reduces the amount of solar that actually reaches the surface to <50%. Yet this same atmosphere is supposed to heat the surface to ~290K.

Ben Wouters
January 25, 2020 1:32 am

Trick January 24, 2020 at 8:12 pm

No Ben, DIVINER radiometer results show brightness temperatures are always changing lunar day and night (diurnal) so no ~radiative balance.

See https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2011JE003987
(search for equilibrium)
Nighttime temperatures never go to 3K, the radiative balance temperature with the Cosmic Background radiation.
Noon temperature on the equator is even slightly above radiative balance temperature, reason probably the high temperature at sunrise (~100K or so) Reason for this some geothermal plus heat storage from the previous day.

angech
January 22, 2020 4:16 am

Apologies,
no offence intended.
It was a comment on the complexity of the radiation flows and trying to work through them, not on the authorship of the diagram.
You see it everywhere. I did not know it was yours.
Love it.

angech
January 22, 2020 4:35 am

Willis
Finally, the top layer is not 500 km out, or a hundred KM out. The bottom layer of the stratosphere is the effective radiating layer. We know this from the brightness temperature of the radiation. It’s at about 10 km. This difference in altitude introduces an error of 0.3% in the simplified energy diagram … lost in the noise.”

Respectfully,
I may be wrong.
I thought the Top of Atmosphere is defined as where radiation in equals radiation out by convention.
For a sphere the average distance is said to be about 100 km.
In truth the TOA is very close to the poles and further away at the equator during the day.
The effective radiating layer may be the bottom of the stratosphere but the TOA is where the energy in balances the energy out by definition.
The satellites may be out 500 km but what they are measuring is the output of IR from those top layers and formulating an overall TOA value.
Incidentally they rely on ground stations for the IR out and in at surface level because the satellites have a lot of trouble trying to assess IR levels below 800 meters and cannot do it through clouds, apparently.
CERES apparently does it’s TOA from an amalgam of satellites and a computed input from GCMs with an inbuilt warming and it is extremely variable with large margins of error and does not do clouds well.

“The idea that scientists wouldn’t notice and adjust for a potential error of is simply not reasonable.”
True.
Very hard to actually find out. Perhaps Dr Spencer could enlighten us if he is reading.

angech
January 22, 2020 4:39 am

“. Here’s my diagram of the simplified energy budget. Unlike Trenberths similar diagram, this one actually balances, with equal amounts radiated up and down from the two atmospheric levels.“
As said missed that attribution totally at the time.
Would never be deliberately that rude.

Nelson
January 22, 2020 11:51 am