Guest Post by Willis Eschenbach
This is a follow-on from my previous post entitled Greenhouse Equilibrium. If you haven’t read it, you might want to, as it introduces many of the concepts I’ll discuss in this post.
I got to thinking about the oft-repeated claim that a doubling of CO2 increases top-of-atmosphere (TOA) radiative forcing by 3.7 watts per square meter (W/m2) … and that in turn, the additional 3.7 W/m2 of TOA forcing causes a ~3° warming of the temperature. In other words, they say that ~ 1.2 W/m2 of additional radiative forcing causes one degree of warming.
What set me to thinking was the Stefan-Boltzmann equation. It relates temperature to the amount of thermal radiation emitted. It turns out that the radiation varies as the fourth power of the temperature, T4. What this means is that the warmer an object is, the more energy needs to be added to the object to raise the object’s temperature by each additional degree.
So how much extra energy does it take to raise the temperature of the earth (which is at about 15°C) by one degree C?
Per the S-B equation, it requires an additional ~ 5.2 W/m2 to raise the temperature of the earth by one degree C. But as discussed in my previous post, only ~ 80% of the surface absorbed energy is expressed as temperature. This means that to warm the earth by 1°C requires 5.2 / .8 = 6.5 W/m2 absorbed energy at the surface per 1° warming.
Now, recall that their claim is that 1.2 W/m2 of TOA forcing causes one degree of warming … which in turn requires 6.5 W/m2 at the surface.
Presumably, their claim is that various feedbacks amplify the change in radiative forcing. But turning 1.2 W/m2 at the TOA into 6.5 W/m2 at the surface? That’s a neat trick. I’m not seeing that happening at all.
Now, let me back up to a graphic from my previous post, along with the caption.
Figure 1. Greenhouse multiplier. The multiplier is calculated as upwelling longwave surface radiation divided by incoming solar radiation (after albedo reflections). A multiplier of 2 would mean that the surface would be radiating two W/m2 of energy for each one W/m2 of solar energy actually entering the system. This shows that the greenhouse has increased the incoming solar radiation by about two-thirds, as measured at the surface.
Now, over the period of the CERES record, greenhouse gas forcing increased by about 0.7 W/m2.
Theoretically, this would be increased by feedback in the ratio 6.5/1.2 to the value at the surface. in this case, it converts the 0.7 TOA W/m2 to 3.8 W/m2 at the surface.
This allows us to see what the change in the greenhouse efficiency shown in Figure 1 should look like if the absorbed surface radiation increased by 3.8 W/m2. Figure 2 is the same as Figure 1, but including the expected change from the additional 3.8 W/m2 absorbed.
Figure 2. As in Figure 1, but including the trend in the multiplier that would be expected from the increase in TOA greenhouse gas forcing.
Hmmm … several points.
First, I simply don’t believe their numbers. Their claim is that a doubling of CO2 gives an additional 3.7 W/m2 at the TOA, and it results in 3°C of surface warming. That’s about 1.2 W/m2 per degree of warming.
But we know that it takes 6.5 W/m2 to raise the earth’s temperature by one degree …
I’m not seeing any physical processes by which the 1.2 W/m2 could somehow be increased to 6.5 W/m2.
Second, even if the warming were only 1°C per doubling of CO2, we still would be able to see it in the graphic. Figure 3 shows that result.
Figure 3. As in Figure 2, but with the CO2 forcing figured at one degree of warming per doubling of CO2, which is one degree per 3.7 W/m2.
But we don’t see that lesser trend in the multiplier either. Instead, the multiplier has a slight but not significant decrease, and it’s nothing like what we’d see if increasing GHGs actually were increasing the surface temperature.
However, at least that lesser trend is a bit believable since the increase from the TOA to the surface is from 3.7 W/m2 to 6.5 W/m2. Still a big reach, though … it would require strong positive feedback, and I haven’t seen that anywhere.
Now, the important thing to remember about this measurement of the efficiency of the system is that it is end-to-end. By that I mean we start with the energy entering the system (solar minus reflections) and we end up with surface temperature.
In between the sun and the surface, we have a range of emergent climate phenomen. Inter alia they include variable cloud shortwave and longwave radiation effects, changes in surface albedo and TOA albedo, massive variable advection of energy from the tropics to the poles, changes in aerosols, the La Nina/El Nino pump, variations in timing and strength of thunderstorms, variations in sensible/latent heat loss from the surface … and changes in greenhouse gases.
And what appears to be happening is that, as I’ve said for years, the changes in greenhouse gases are being counteracted by some combination of the other emergent climate variables included above.
What a marvelously complex world we inhabit!
w.
PS—As with the previous post, please stick to the topic. Claims that the greenhouse effect isn’t real or that downwelling radiation doesn’t exist have no place in the comments on this post, and they will be frowned upon from a great height. You are welcome to discuss those issues … just not on this particular post.
My Usual—I can defend my own words. I cannot defend your (mis)interpretation of my words. Please QUOTE THE EXACT WORDS you are discussing in your comments, so we can all understand who and what you are replying to.
There is no GHE, you idiots.
That is akin to stating there is no GOD.
Like GOD, GHE is a belief system. Your statement is an expression of religious intolerance. If people want to believe in the GHE then they should be free to do so.
I took a similar view to you when I first saw it being taken seriously on skeptic forums. Then I realised that I should not be intolerant of religious beliefs.
I do draw the line when is see the GHE effect being connected to the energy balance on Earth.
What I like about the last two posts from WE is that he has verified what I have been stating for a few years – GHE is not altering Earth’s energy balance. In the convoluted world of climate phiisics he has arrived at what real physics already informed those who grasp the topic.
That is akin to stating there is no GOD.
Or in this case MOD.
That’s what Anthony Watts is doing to me right now because I accused Willis of being a sophist. In short I am being moderated.
griff is ok though because griff is harmless.
Obviously, the science is settled.
Nope. You are being moderated for attempted threadjacking despite polite requests to stop doing it. But sure, keep whining … it makes you look so strong.
w.
So it is Willis’ ball and I can’t play.
Boohoo.
WE, you say “But we know that it takes 6.5 W/m2 to raise the earth’s temperature by one degree …”.
Q1. From what source?
Q2. Do you mean earth surface or near-earth air temperature.
No way. A 6.5W/m2 full spectrum solar radiation is not the same as single spectrum 15um photons.
Frequency matters and in the context of re-radiation, the quantity is not additive in order to create a (im)balance.
Willis, I humbly want to ask a simple (and probably stupid) question. In your “Greenhouse Efficiency” post yesterday (9/2/22), the first graph of your CERES data show a minimum of 240-241 w/m^2 incoming and a significantly larger 397-398 w/m^2 outgoing solar radiation. I would have expected the energy balance to be approximately the same. What did I miss (or am missing)?
On my planet, the only stupid question is the one I don’t ask, ’cause then I’ll never learn.
The ~ 400 W/m2 is upwelling from the surface, not emitted to space.
w.
Dear Willis:
Taking your advice to heart, before reading further I went to your earlier post Greenhouse Equilibrium, where I immediately found this phrase: “A Prologue: The earth is much warmer than the moon, which receives the same amount of solar energy.”
That’s my first misunderstanding-or-disagreement, which I hope you will clarify.
I think both moon and earth receive the same solar energy per unit subtended area (for practical purposes, ignoring details of minor time-varying distances from the sun), but as the cross-sectional area of the moon (as seen from the sun) is much less than the earth’s, it seems to me that the moon must receive less solar energy than the earth.
I am loathe to read further in your earlier post when I have such a large disagreement-or-misunderstanding about your initial premiss. What am I missing?
I should have said “the same amount of solar energy per unit area”. I’ve fixed the head post there. Read on.
w.
Willis is misusing the Stefan-Boltzmann equation and is again confusing energy flux and energy. He writes:
“So how much extra energy does it take to raise the temperature of the earth (which is at about 15°C) by one degree C?
Per the S-B equation, it requires an additional ~ 5.2 W/m2 to raise the temperature of the earth by one degree C”
Now what is true is that if your raise the temperature of a black body from 15C to 16C then it will radiate an extra 5.2 W/m^2 — or at least that is what I am assuming that Willis meant by his statement above. But that is very different from how much energy you need to raise the temperature by one degree. Plus there is no mention of the time taken to raise the temperature — a small change in energy flow will produce a large temperature change if you wait long enough.
Furthermore due to the greenhouse effect the surface temperature of the earth can change dramatically without the amount of energy radiated by the earth changing at all. The amount of energy radiated by the earth is set by the amount received from the sun which is approximately constant while the surface temperature depends strongly on how the amount of greenhouse gases in the atmosphere.
The greenhouse effect gets saturated very quickly. Partly due direct effects and partly due to overlap with other energy absorption. After saturation is achieved no more warming occurs. The CO2 warming effect saturates well below 200 ppm. Adding more CO2 after than point likely spreads energy latitudinally better, but no additional warming.
If you believe in the GHE then you should be extremely alarmed about runaway global warming because atmospheric water is steadily increasing this century and I am informed by NASA that water vapour is the MOST POWERFUL GHG.
Charts below from this link:
https://www.researchgate.net/publication/353672425_A_Total_Precipitable_Water_Product_and_Its_Trend_Analysis_in_Recent_Years_Based_on_Passive_Microwave_Radiometers
Not sure if you missed the word “saturated” or don’t understand its use in this context.
Energy absorption by specific gases has essentially been proven by satellite measurements. That is the basic GHE. I also believe the Earth is not flat.
Once all the surface energy is absorbed at the frequencies where absorption occurs, then no more warming is possible. Doesn’t matter how much of the gas is present.
As the following graph shows, most of the relevant GHGs are already saturated.
https://qph.cf2.quoracdn.net/main-qimg-eb091259a205b597f832adfd61707ca1-pjlq
The link only demonstrates the overlap of water and CO2. The transmission through water vapour is not saturated. That depends entirely on the distribution of water through the atmosphere and it is has been found to be rising this century.
So what. It has no influence on the thermostatic processes that regulate the energy balance.
How does absorption of IR in the atmosphere alters the -1.8C that sea ice forms?
How does IR absorption alter the 30C ocean surface limit regulated by atmospheric ice formation through deep convection?
These are the processes that regulate Earth’s energy uptake and loss.
You’re now making a different claim. First you claimed there was no GHE and now you claim it has “no influence”.
You then appear to ignore the part of my link that shows 100% absorption over most of the frequency bands where water vapor absorbs surface energy.
You may have some points about the effects of water in determining the climate on Earth. Denying facts won’t help your case.
[SNIPPED: AS I SAID, please don’t try to threadjack the thread with claims that the greenhouse effect doesn’t exist.]
Why is this so hard for some folks to understand?
w.
Isaac Walton –
I have no idea how your comment, which states a fact, can generate two down votes. Every time we get involved in topics regarding EM radiation on this site there is so much confusion and occasional down right nonsense that it becomes an injury to the site’s reputation.
Because WUWT is a lukewarmist website.
You’ve been downvoted too, currently -1, but I will make that 0.
Thank you, sir. I’ll return the favor though I can only take you up from -2.
“And what appears to be happening is that, as I’ve said for years, the changes in greenhouse gases are being counteracted by some combination of the other emergent climate variables included above.”
Another brilliant contribution, Willis.
But sad that Great Scientists like Brandon, Boris, Macron, Trudeau, haven’t noticed and make sure that that the Genius Experts they choose to annoint as “The Settled Science” have a BIG blind spot, right there.
Willis…have to question with your interpretation of S-B, which you interpreted as follows…”What this means is that the warmer an object is, the more energy needs to be added to the object to raise the object’s temperature by each additional degree”.
Maybe you meant something else, and I misinterpreted your meaning.
I questioning your interpretation based on the evolution of the S-B equation by Stefan. He based his work on an experiment by Tyndall in which Tyndall heated a platinum filament wire electrically till it glowed red. Then he increased the current, which caused the wire to emit higher frequency EM as its temperature rose. Someone else interpreted the colour spectrum emitted and related the colours to the the EM frequency/wavelength that should emit those colours.
The temperature of the filament varied linearly between about 700C and 1400C and the output EM radiation remained at T^4 wrt the temperature. The constant of proportionality used is only good in that temperature range and is not an absolute constant. It’s a mistake to apply the S-B equation arbitrarily at other temperature ranges, especially terrestrial temperatures.
I don’t think it’s fair to claim the equation suggests what you claim above. Obviously, more heat has to be added to raise the temperature per degree but that is not reflected in the S-B equation. The equation simply suggests that the EM emitted varies with the heat added since temperature is a measure of heat.
Some people have tried to reverse S-B to suggest a transfer of heat from cold to hot. It’s clear from Tyndall’s experiment that is not the case. Stefan’s equation was developed from a clear case of heat transfer from a much hotter object to the cooler ambient temperature of the room. It would be ingenuous to claim that heat could be transferred from the cooler room air to the hotter filament in order to raise its temperature. Yet that is a basis of the AGW theory.
This is what climate phiisics is based on. You are challenging a deeply rooted belief system.
Possibly my saddest day in the last year was to learn of the passing of Michael Mishchenko.
https://www.giss.nasa.gov/research/news/20200727/
Mishchenko provided clarity in the field of transmission of EMR within Earth’s atmosphere. He derived exact solutions for Maxwell’s electro-magnetic field equations to the scattering of EMR due to atmospheric particles.
He provided proof that radiant energy transmission via the electro-magnetic field is mono-directional at and point in time and space. The means back-radiation is contrived nonsense.
Given more time, I expect he would have played a more dominant role in correcting all that is wrong with climate phiisics.
Gordon,
If you integrate the black body spectrum over all frequencies you find the total energy
radiated by a black body and this is the modern derivation of the Stefan-Boltzman equation
and since the black body spectrum is correct for all temperatures then so is the Stefan-Boltzman equation with the constant being a universal one. See
https://en.wikipedia.org/wiki/Stefan–Boltzmann_law#Derivation_from_Planck's_law
for example.
Izaak…the problem is, Stefan developed the T^4 relationship well before Planck created his equation. Boltzmann’s contribution was to take it into the realm of statistical theory. He tried to confirm the 2nd law using statistical analysis and failed.
I understand that Planck’s work was important but it involved generalities and probabilities. Prior to Planck, electromagnetic energy was related frequency in such a manner that as frequency increased, the EM intensity would run away to infinity. Planck created the curve to which you refer by presuming that higher frequency EM would not have as great a probability of existing as the medium and lower frequencies. His curve is actually based n probability and you can see that in the exponential expression.
I think a more important application of Planck’s theory was used by Bohr to related electrons in atoms to EM radiation. Planck’s quantum factor, ‘h’, proved a basis of quantum theory and Bohr noticed that a quantum step had to be a factor in electron transitions to produce the discrete spectral lines in hydrogen.
I prefer Stefan’s work because it is based on actual physical reality and corroborates the 2nd law. It’s interesting that S-B can be derived from Planck’s equation but Planck based his work on Boltzmann’s statistical analysis and it stands to reason he created the equation to reflect the work of Stefan, for whom Boltzmann was a student.
Furthermore, Planck’s equation applies to one temperature at a time, as I understand it. Stefan developed the basic S-B equation from real data that covered a 1000 degree C range of temperatures.
“Furthermore, Planck’s equation applies to one temperature at a time”
As I understand it both Planck and S-B require the radiating object to be in thermal equilibrium – i.e. one temperature at a time. If the object is not in thermal equilibrium then conduction/convection, even within the object itself, will cause the radiation from the body to be different.
Gordon,
why is it a problem when Stefan developed his theory? Newton developed his theory of gravity centuries before Einstein but we can still derive Newton’s theory from Einstein’s. Similarly the Stefan-Boltzman law can be derived trivially from Planck’s Blackbody spectrum just by integrating over all frequencies and solid angles. And the blackbody spectrum can be derived using Einstein’s 1917 work on stimulated and spontaneous emission.
Planck’s blackbody spectrum is also based on actual physical reality and furthermore has been shown to have a universal validity — look at the cosmic microwave background for example. The microwave background is at roughly 2K and if you integrated it over all frequencies you would find that the answer was given by the Stefan-Boltzmann equation extending its validity far beyond what they originally applied it to.
For black bodies in space. That means it is misapplied to anything on Earth’s surface.
But my infrared lamp works here on the Earth. Funny, that.
For radiative heat transport you have both: transfer of heat from hot to cold and, at the same time, transfer from cold to hot. The important thing is that the difference, the net heat transfer, of these two opposite streams is alwas positive from hot to cold.
What willis has been doing is looking at these streams separately, and not at the net stream.
When you look at the net stream you have heat transfer from the sun to the earth, and from the earth into space. This means from hot to warm to cold. Now depending on the details of the system, the “warm” temperature of earth could be anywhere between the temperature of the sun and the tempetature of space, without violationg the laws of physics.
It is therefore feasible that the changes of the properties of the atmosphere move the temperature slightly closer to the temperature of the sun.
This should not be misunderstood as the cold atmosphere warming the warmer surface of the earth. It is still the sun that is doing the warming of the surface. But the atmosphere can inhibit the cooling into space
Nope, the radiant energy transport is mono-directional. Proven by the great NASA/GISS physicist Michael Mishchenko and restated in this paper:
https://opg.optica.org/DirectPDFAccess/33B19AC8-EC5C-4DE3-BAD4A42301A02518_205485/oe-18-19-19770.pdf?da=1&id=205485&seq=0&mobile=no
Mishchenko is no longer with us but he has made significant contributions to measuring EMR energy transport in Earth’s atmosphere.
He cringed at Trenbarths/IPCC energy diagram showing back-radiation.
You are still confusing net heat transport, and radiation components.
Net heat transport is always monodirectional, the detailed components can have multiple directions.
I am going to try to explain this to you, as you are embarrassing yourself. Heat flows from warm things to cooler things. Yes the atmosphere has a temperature, and the surface has a temperature.
Climate so-called Scientists Claim that the Atmosphere can heat the surface. But the Atmosphere cannot generate any energy. Where does this energy come from?
Do not believe everything you read. The Atmosphere cannot warm the surface, as it is cooler that the surface. Pyrgeometers are the same thing as infrared thermometers. Buy one, point it it the sky, find out for yourself.
That is all you get from me, what a foolish issue…
Moon
The last two posts from WE has “proven”, using climate phiisics, that the GHE does not alter the energy balance.
So, in a convoluted way, using their own form of phiisics, he has verified the GHE does nothing. That is what I have been trying to get into his head for a few years now.
Small steps. Maybe he will ask himself – If it does nothing to the energy balance; does it matter?
I will not be paying to read this paper but I have read a number of Mishchenko papers.
https://opg.optica.org/josaa/viewmedia.cfm?uri=josaa-33-6-1126&seq=0&html=true
The abstract is sufficient to make the point on what is needed to apply fundamental physics to determining Earth’s energy budget:
My bold on a key point to this post.
You can’t use the average temperature. Imagine half the world at 0K, the other half at 500K.
The average is lower but the radiation far higher.
Also surface temperature doesn’t equal air temperature and so I imagine you can’t use that either
Hello Willis,
I have some difficulty understanding, how the values for the yellow “CO2 forcing increase” curves were determined. Why is the starting point exactly the same as for the trend line of the real measurements?
Should one not determine the CO2 portion of the multiplier and scale this portion according to the claimed sensitivity?
How would this look like for a sensitivity of 0.36°C per douling of CO2? This was the result from my analysis:
https://osf.io/huxge/
Regarding the slight negative trend of the measured values:
Is it possible that it is caused by the slight shift towards higher frequencies of the heat radiation spectrum? The flux increase within the absorption bands of Water and C02 is less than the total change in flux due to this shift.
However the scatter of the multiplier is so tiny, that if dispayed without the extreme “zoom” it would look like a straight horizontal line.
Dear all,
This question may not be placed well here, but do you know if somebody has looked at the positive long term feedback from CO2 increasing plant growth and thereby increasing albedo?
https://www.nasa.gov/feature/goddard/2016/carbon-dioxide-fertilization-greening-earth
Willis work suggests that the climate change of the last 20 years is mostly due to a change in albedo, so this question may be relevant.
More recent versions of climate models incorporate the biosphere in some way. Despite the science being settled decades ago, the climate models still continue to be massaged by incompetent dills to make ever more complex and outrageous predictions in order to produce whatever the politics demand.
There is some prospect of the whole NutZero thingy collapsing before 2030 and the politicians will then require the models to show CO2 has no direct influence. Which I have often stated.
There are significant aspects of trees related to moisture content over land. Remove the trees and the land inevitably becomes a low altitude divergence zone meaning they get less rain. So trees beget trees through local moisture retention in the atmosphere. The Amazon rain forest is the perfect example of what trees can do to attract water. But the models do not have the ability to resolve convection so this contribution to stabilising climate is not identified. When the fundamental concept is flawed, there is no prospect of climate models replication Earth’s climate no matter how complex they get.
Forests can help store water, but do they also increase convective heat transport between the ground and the upper end of the troposphere?
If yes, how large is the change in convective heat transport compared to the change in energy absorption due to change in albedo?
Convective towers resulting from atmospheric instability are the primary engine that power the entire atmospheric motion and most of the ocean circulations.
Over tropical ocean warm pools regulating at 30C they advect 190W/m^2 to adjacent cooler columns. They pump up the troposphere to 14,000m.
In tropical rain forests, the convective towers are even more powerful because the land can warm up in a day and cycle faster than the towers over water so land dominates over adjacent ocean. The trees in the Amazon dominate over the tropical Atlantic causing mid level convergence that draws considerable water from the ocean to land about a month ahead of what would occur if it was water rather than trees on land.
There are more details here:
https://climate.nasa.gov/news/2608/new-study-shows-the-amazon-makes-its-own-rainy-season/
Cutting down trees to instal wind turbines is the best way to turn habitable land into desert. Once the desert forms, it takes at least decades to recover.
Thank you, but I do understand that tropical convection patterns are the main reason for the tropics being cooler than the subtropics. Similar in other regions.
My question was about studies of the effect of more plant growth on the albedo.
I went through Willis last two posts again, and came to one important conlusion: heat flux from convection is eliminated from the caculation of the multiplier in his graphs! Therefore only the albedo effect of forests and other growing plantlife could be visible in the graphs and not the convection effect.
An increase in albedo would reduce the slope of the multiplier curve over time, or create a negative slope.
An increase in radiative forcing would increase the slope of the multiplier curve.
Since the slope is almost exactly zero, the warming effects from change in albedo from CO2 is the same as the change of radiative heat transport. Both values may be small, but both values may be large.
Anything can happen in the world of climate phiisics. The graphs that WE has produced are based on climate phiisics. They are physical nonsense.
Deep convection is the prime mover in Earth’s climate. It drives the whole climate system, converting as much solar EMR as is needed to keep the system stable. If there was no ability for the atmosphere to form a level of free convection then Earth would be a snowball.
Sea ice is also a significant factor by retaining energy in the system.
Earth’s climate system is temperature controlled between ocean surface limits of 30C and -1.8C. Water held on land by the biomass can influence the convection that sets the 30C limit. Far more important than any albedo changes due to trees.
https://wattsupwiththat.com/2022/07/23/ocean-atmosphere-response-to-solar-emr-at-top-of-the-atmosphere/
Trees and other vegetation make the land respond more like the ocean surface because they retain moisture that is available to the atmosphere to drive the convective towers. Once trees are eliminated, the surface can get much hotter and they become perpetual low altitude divergence zones that do not attract water. The Sahara is an example of that.
THe only significant body of water that does not regulate at 30C is the Persian Gulf. It has reasonably high ground level humidity but the dry air from the north prevent the formation of an LFC. The surface temperature of the PG can reach 35C. And it is not due to being shallow because the deep water is much colder and constantly replenished from the Arabian Sea.
Hello Willis
You have been asking about a mechanism that could “amplify” the 3.7W/m^2 at the top of the atmosphere towards the ground.
Note that the IPCC assumes an effective temperature at the top of the atmosphere of 255K. But we got 288K at the ground. This means assuming the same CO2 concentration that there is a change of 288^4/255^4 = 1.6
This results in a radiative sensitivity at the ground of 6W/m^2 per doubling of CO2
Obviusly this does not explain the claimed temperature sensitivity of 3K at the ground, but at least a third of this.
One correction:
Since we are talking about radiation of a gas the stefan Bolzmann equation is not exact (but a good approximation). Instead one should use the absorption spectrum of the gas and the plank equations for more accurate results.
“This shows that the greenhouse has increased the incoming solar radiation by about two-thirds, as measured at the surface.”
–
not happy with this wording.
GHG effect cannot increase the incoming solar radiation , it is a fixed amount that can be focused but not increased.
The surface receives 161 W incoming plus
All the back radiated IR from the layer closest to the surface that can reach the surface without being absorbed.
strangely this is the same amount of IR going out from the top layer to space that cannot be reabsorbed.
while the energy from the lower layer originally came from the sun it is now coming from the GHG and it is incorrect to refer to it as incoming energy from the sun.
thanks
“and it’s nothing like what we’d see if increasing GHGs actually were increasing the surface temperature.”
The GHE of GHGs increased, but the GHE of clouds decreased. The GHG forcing is ‘converted’ to solar forcing through cloud change.
Willis said: “the changes in greenhouse gases are being counteracted”
=============
Or the radiative greenhouse theory is wrong.
Willis, the declining greenhouse efficiency in the face of increasing CO2 is strong evidence that the radiative greenhouse theory is wrong.
We learned in school that real greenhouses were warmed by glass blocking outgoing IR. This was eventually shown to be wrong. That real greenhouses warm by controlling convection.
Now you have shown that increasing CO2 is not causing increase warming, but you cling to the radiative theory without considering that the same process that warms a real greenhouse is behind the earth’s greenhouse effect.
Which “radiative greenhouse theory”? Turns out there are 2 of them which the media never mentions. The first is blocking surface radiation from reaching space and warming the air (a little like a greenhouse). The second is reducing the flow of energy from the atmosphere to space (more like insulation).
The first one is essentially saturated except from small increases from pressure broadening. It’s not surprising there would be little change to it. The second one is where the science goes astray. Willis has shown it doesn’t create any warming.
My own view is the first (slight warming) and second (slight cooling) mechanisms basically cancel each other out.
Unless you can change the lapse rate you cannot change the surface temperature.
Still haven’t seen CO2 anywhere in the formula for lapse rate.
A lot of hand waving that CO2 will change the effective radiation height, but it continues to stubbornly sit at 500mb altitude. Half mass between the surface and TOA. No coincidence.
Which is why increasing CO2 has not changed greenhouse efficiency. It has not changed the lapse rate.
Is this because the atmospheric temperature is determined by 1) the mass? Or, 2) the amount of radiating gases?
The sun determines average atmospheric temperarure.
I happen to completely agree that the effective radiation height is fixed. This sets the basis for the lapse rate. Water adds the final variable and the surface temperature is the result.
The variability in the surface temperature is due almost completely to changes in albedo. Thus your answer is probably more accurately stated using solar energy rather than “The sun”.
Less solar energy will allow the atmosphere to shrink somewhat which in turn lowers the 500 mb altitude and the surface temperature.
I was asking to see what you thought was the basis for the effective radiation height.
The lapse rate is – g / Cp.
G is gravity and Cp is specific heat of dry air. That is the basic one.
Specific heat air is changing as we add CO2. Adding CO2 will decrease the specific heat.
“What this means is that the warmer an object is, the more energy needs to be added to the object to raise the object’s temperature by each additional degree.”
.
.
This is absolutely FALSE. A calorie is 4.1868 joules, and a calorie at 2 degrees C is the same as a calorie at 40 degrees C.
Eschenbach needs a refresher course in Physics 101
3.7 joules will warm a square meter at 2°C by more than it will warm a square meter at 40°C.
Nope, I suggest you join Eschenbach in Physics 101
..
https://en.wikipedia.org/wiki/Specific_heat_capacity
What I stated is true, but the actual degree of warming in each example would of course vary with different heat capacities. You are conflating two different issues.
Greg:
Willis phrased it sloppily, but his point is well taken. He should have phrased it something like:
“The warmer an object is, the greater the additional power flux density is required to raise the object’s temperature by each additional degree, due to the need to compensate for the greater increase in the object’s emitted thermal radiation.”
What does this mean? Let’s take the derivative of the SB equation for a blackbody or graybody:
dQ/dT = 4 * epsilon * sigma * T^3
For an object at 0C (273K) with emissivity 0.95, this is:
dQ/dT = 4 * 0.95 * 5.67E-8 * 273^3 = 4.38 W/m2/K
For the same object at 30C (303K), this is:
dQ/dT = 4 * 0.95 * 5.67E-8 * 303^3 = 5.99 W/m2/K
which is 37% greater.
Thanks, Ed. I assumed that people here were switched on enough that I didn’t have to spell out every step in the statement as you have done. Clearly I was wrong, so thanks for clarifying it for those too dull to do it for themselves.
w.
Hi Willis:
Glad to help. I have noticed over the years that much of the audience here has never done the most basic energy balance calculations of the type needed for the first few weeks of an introductory thermodynamics class.
Neither have they ever worked with actual thermal systems. Otherwise they would not be mystified by the concept of a powered object getting hotter when its heat loss to a cold ambient is somehow impeded.
So I have been careful in my comments over the years to break my argument into the smallest possible steps, and to be very careful in my terminology, to minimize the possible confusion for these people. I think it has helped somewhat.
Pardon me Ed, but it doesn’t work on cranks.
[That reminds me of the old joke ending in “Pardon me Roy, is that the cat that ate your new shoes?]
Ed,
that is not what the statement means. At best it means that if you want to maintain a body at a fixed temperature that is constantly losing energy due to thermal radiation into space then the power needed increases as the fourth power of the temperature.
If you just want to raise the temperature of a body and then are not concerned with it losing heat then the Stefan-Boltzmann equation does not apply. Alternately if the body loses heat by conduction or convection both of which are much more efficient than radiation then you need to supply more power than the Stefan-Boltzmann equation would suggest.
Hi Izaak,
Willis confirmed that I surmised his intended statement correctly. Of course, when other heat transfer modes are in play, they should be included in the calculations.
But the non-linearity of the Planck feedback is the important point here, and was to me obvious from the context of his argument.
“What this means is that the warmer an object is, the more energy needs to be added to the object to raise the object’s temperature by each additional degree.”
========!
This is not correct. The SB equation says it should be true but it is not.
.
cal·o·rie
/ˈkal(ə)rē/
noun
1.
the energy needed to raise the temperature of 1 gram of water through 1 °C (now usually defined as 4.1868 joules).
2.
the energy needed to raise the temperature of 1 kilogram of water through 1 °C, equal to one thousand small calories and often used to measure the energy value of foods.
For a surface to be warmed a net 1.2°C by 3.7W/m^2, it would have to be at minus 34°C. (with emissivity = 1)
You are incorrect. The Stefan Boltzmann equation applies to EMISSION, and has no application to absorption.
3.7W/m^2 on a surface at zero K would warm it by 90K.
Greg Bacon September 4, 2022 9:59 am
It does at a steady-state condition. For example. Per S-B, an object at ~16°C emits ~ 400 W/m2. If it is at steady-state (neither cooling nor warming) it MUST also be absorbing ~ 400 W/m2 of energy from somewhere.
w.
Nice goal post move, adding “steady state condition.” Again, SB says nothing about absorption, you are adding in that factor when you move the goal posts.
Again you are confusing energy flux with energy. The statement that “ absorbing ~ 400 W/m2 of energy”
confuses two different things, power flux per square metre and energy. A light bulb for instance might radiate away 400 W/m^2 but it gets the required energy from the current and does not absorb 400 W/m^2 since the cross-section of the wire is much smaller than the emitting surface.
The Stefan Boltzmann equation applies to EMISSION, and has no application to absorption.
========
Then why is SB being used to predict how much warming will result from an increase in back radiation?
I believe you are correct, which explains why Willis incorrectly predicted it would take more energy to warm a warm object, but for the sake of Devil’s Advocate I’m asking the obvious question which is at the heart of radiative greenhouse theory.
https://www.researchgate.net/figure/Graph-of-a-function-of-total-emitted-energy-of-a-blackbody-proportional-to-the-fourth_fig2_334029343
Exactly, but will Roger get it?
Willis wrote “What this means is that the warmer an object is, the more energy needs to be added to the object to raise the object’s temperature by each additional degree.”.
Ferd replies:
This is clearly contradicted by the specific heat of liquid water. It calls into question the radiative greenhouse theory which relies heavily on S-B to predict temperatures.
Until this contradiction is resolved futher discussuon about radiative forcing is pointless.
Ferd, we’re measuring different things.
I’m talking about objects that a steady-state condition, objects that are receiving heat in some fashion and are free to radiate away the heat.
Specific heat is not measuring that at all. It assumes that the object is NOT losing heat.
Contradiction resolved. Further discussion is now pointfull.
w.
Looks like a perpetual motion machine to me.
Looks more like Eschenbach moving the goal posts to cover his error.
Willis wrote “What this means is that the warmer an object is, the more energy needs to be added to the object to raise the object’s temperature by each additional degree.”… “I’m talking about objects that a steady-state condition,”
Ferd wrote:
Willis, SB is a measure of power not energy. What SB tells you is that it takes more power to raise the temperature of a warm object vs cold. But what you said is that it took more energy. Specific heat says the energy remains the same.
Nothing to do with solid state.
It is about a steady state, not a solid state.
Greg Bacon September 4, 2022 12:44 pm
Greg, seems you must be either looking in the mirror or talking about your friends. I don’t move the goal posts. I was simply describing the difference between what Ferd and I were talking about. So you can stuff your ugly insinuations up your fundamental orifice.
w.
You are correct. Willis is wrong.
The engineering toolbox gives the isobaric specific heat of water at different temperatures as follows:
1C = 4.22 kj
10C = 4.2 kj
20C = 4.18 kj
30C = 4.18 kj
As can be seen, as water warms it actually takes less energy to warm it further. This is opposite to what S-B predicts. Another nail in the coffin.
The Wijngaarden and Happer 2020 paper* calculates a sensitivity of +1.4C for doubling of CO2 at fixed absolute humidity and +2.3C for fixed relative humidity. The latter number includes a feedback process that raises the amount of H2O in the atmosphere with temperature, which amplifies the effect of raising the CO2 level. So the extra warming is down to H2O. I note that these numbers are somewhat less than the figures quoted in Willis’ 2nd paragraph above.
These figures are for clear sky only – the real world has something like 2/3rds of its surface covered by clouds of various kinds. I don’t believe that there is any straightforward calculation available that deals with the cloud covered portions of the world. So, what the real world sensitivity looks like is really an unknown – an unknown caused by our limited understanding of clouds.
It is also not clear that fixed relative humidity applies in the real world, at least not everywhere. Dr Roy Spencer has a graph showing that for the tropics, the atmosphere does not follow fixed relative humidity as the temperature of the surface rises, so that the implied extra warming from feedback does not apply there.
* ”Dependence of Earth’s Thermal Radiation on Five Most Abundant Greenhouse Gases”
https://arxiv.org/abs/2006.03098v1
If W/H 2020 was correct we should have seen some change in the GHE over the 20 years of CERES data. Water vapor should have enhanced it. I think their physics is solid. However, they are only considering radiation. I suspect this is where their divergence from observations begins. Accepting the observations are correct, then clearly there are feedbacks not yet considered in determining Earth’s atmospheric energy flows. A radiation model alone is insufficient.
Agreed that a radiation-only model is insufficent. Dealing with clouds is in reality dealing with a complex system of convection and heat & moisture transport. However, I think that the figures quoted by Willis and the W&H paper are all based on “clear sky” calculations. Any other calculations are extremely hard and would depend on all kinds of variables many of which are not well understood.
Nope. Unless specified, all of my graphs and charts are for all-sky conditions.
w.
Takes an object at temp T radiating 1 watt. Double the temp to 2T. By S-B it will now radiate 2^4 = 16 watts.
So the question is, did it take 16 – 1 = 15 watts to double the temperature of the object.
The problem is that watts are power, not energy. So you need to know how long it takes to warm the object.
And what specific heat tells us is that since the energy remains the same, the time to change the temperature must decrease as radiation power increases.
Thus the contradiction. The radiative greenhouse theory bases temperature on power while specific heat bases temperature on energy.
Climate science ignores mass, time, energy, and specific heat so no contradiction exists because these properties don’t exist.
But now there is a new contradiction, because mass, time, energy, and specific heat do exist.
This explain why Willis has found yet another example of a climate science prediction that has proven false.
Doesn’t it take just 1 failed prediction to prove a theory false? Why does WUWT cling so strongly to the underlying assumptions? It is a marvel to me.
To simplify – a watt is a joule/sec. It takes “x” amount of joules to raise the temperature of an object a certain amount. So if you know the power flow (in joules/sec) and how many joules you need then you can calculate how long it will take. (nbr of joules)/(joules/sec) = sec.
The number of joules you need *is* dependent on mass and specific heat.
The dimension of specific heat is Joules/ (kilogram * K). So to get the number of joules required you multiply the specific heat by the mass and the temperature change.
(mass * ΔK) * joules/(mass*K) = joules.
Willis wrote:
I’m talking about objects that a steady-state condition, objects that are receiving heat in some fashion and are free to radiate away the heat.
Ferd replies
The Radiative Greenhouse Theory rests on the notion that since N2 and O2 are not greenhouse gases they are not free to radiate heat away.
While ignoring that N2 and O2 both delay cooling by transporting energy from hot places to cold, thus decreasing the effective temperature of radiation.
And it is this delay and decrease in the temperature of radiation that in fact is the principle behind the greenhouse effect.
And in a similar fashion the ocean currents also delay cooling and decrease the effective temperature of radiation.
Ferd,
Unfortunately for GHE believers, N2 and O2, like all other matter, do radiate energy – continuously – if above absolute zero.
The atmosphere acts to decrease maximum surface temperatures, and increase minimum surface temperatures. The Moon, when at the same distance from the Sun, provides examples of far greater maxima, and far lower minima, compared with the Earth.
Even on Earth, the greatest diurnal variations (and the highest temperatures) occur in arid deserts with the least amount of GHGs (H2O) in the atmosphere above.
Wot, an inverse GHE? Very strange, this “climate” physics!
Today’s commonly used temperature measurement units are Celcius and Fahrenheit, named after two gentlemen who lived in temperate climates where water (or brine) freezes seasonally.
In the 18th century tropics 99.99% of inhabitants never saw frozen water; they also couldn’t understand what ‘snow’ is. They might have made a unit C named after Coconut oil, which has its melting point at 25 Celcius / 78 Fahrenheit 😀
Perfectly argued. Using their own figures compared with observations proves CO2 is not the control knob they want it to be.