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## Natural Variability, Attribution and Climate Models #2

In #1 we looked at some examples of natural variability – the climate changes from decade to decade, century to century and out to much longer timescales.

How sure are we that any recent changes are from burning fossil fuels, or other human activity?

In some scientific fields we can run controlled experiments but we just have the one planet. So instead we need to use our knowledge of physics.

In an attempt to avoid a lengthy article I’m going to massively over-simplify.

## “Simple Physics”

Some concepts in climate can be modeled by what I’ll call “simple physics”. It often doesn’t look simple.

Let’s take adding CO2 to the atmosphere. We can do this in a mathematical model. If we “keep everything else the same” in a given location we can calculate the change in energy the planet emits to space for more CO2. Less energy is emitted to space with more CO2 in the atmosphere.

The value varies in different locations, but we just calculate it in lots of places and take the average.

As less energy is leaving the planet (but the same amount is still being absorbed by the sun) the planet warms up.

In our model, we can keep increasing the temperature of the planet in our model until the energy emitted to space is back to what it was before. The planetary energy budget is back in balance.

So we’ve calculated a new surface temperature for, say, a doubling of CO2.

To see the whole article, visit the new Science of Doom on Substack page and please consider suscribing, for notifications on new articles.

### 33 Responses

1. on April 27, 2023 at 9:11 am | Reply Barry D. Jacobson

Here is the thing. If CO2 absorbs or blocks the Sun’s energy, it should be a two-way street. If it blocks rays from getting out, thus trapping heat, it should block energy from getting into Earth on way down from Sun, originally. You can see this in the extreme case of using a heavy black blanket which is extremely absorptive of the Sun’s rays. On a hot day, throw it on your parked car. Clearly, your car will be cooler, not warmer, because it will block heat from getting inside to begin with. Yes, it traps all rays emanating from the car. But it traps the rays which came down from the Sun to begin with so the car receives less in the first place. The answer to this which climate worriers must posit is that it is not a two-way street. The frequency of rays coming in differs from those going out. Going in, CO2 is transparent to that frequency, but going back out CO2 is more absorptive to the new frequency. But linear systems cannot change frequency. Radio waves that bounce off a building are the same as those that arrived. So the claim is some kind of quantum nonlinear effect in the way atoms of the earth behave as they absorb and reradiate photons, changing their frequency. This is not simple or obvious science at all.

• Barry,

The incoming solar radiation is centered on 0.5um. Visible electromagnetic radiation. The surface of the sun has a temperature around 5800K.

The outgoing radiation is centered on 10um. The surface of the earth has a temperature around 288K on average.

You write, “But linear systems cannot change frequency. Radio waves that bounce off a building are the same as those that arrived”

The first sentence is irrelevant. The second sentence is correct.

The solar radiation that is reflected from the earth’s surface is still centered on 0.5um.

The terrestrial radiation that is emitted from the earth’s surface is not centered on 0.5um. It is centered on 10um.

This is basic thermal radiation. Look up Wien’s displacement law. Take a look at Thermal Radiation.

• on April 27, 2023 at 9:54 am Barry Jacobson

You have not explained how the frequencies change from being centered on one value on way in to being centered on a second on way back out. If somebody was heating the earth by putting it in a frying pan or lighting fires or blowing numerous hairdryers on surface of Earth, then we could look at the surface temperature and use Wien’s law to get the radiation distribution which would be centered on 10 uM. But the source of the Earth’s heat is not internally generated. It is generated by the very photons that arrive from the Sun. If you want to claim that in the Sun’s distribution, although most are in the 0.5 uM range, but still a significant number will be in the 10 uM range, then they would be blocked by CO2 before they arrived on Earth to cause heating. But if you claim that the 0.5 uM photons that get through the CO2 layer are what heat the Earth, and that causes 10 uM photons to be emitted back out, then you owe an explanation of how photons are able to change frequency or to be absorbed into a material and cause emission of a different frequency of photon on way out. It isn’t simple. Dipole oscillations of atoms would be expected to occur at same frequency as applied excitation.

• You have not explained how the frequencies change from being centered on one value on way in to being centered on a second on way back out.

You don’t understand thermal physics. It seems like you are sure you do understand it.

I’m not going to persist. Good luck.

• Barry,

the radiation emitted from the earth’s surface is emitted from the warm surface itself. We are not talking about reflection here.

• on April 27, 2023 at 2:42 pm Barry Jacobson

• Barry,
‘energy efficient light bulbs’ (today mostly LED’s) need much less energy.
An LED with 1W produces 0.9W of visible Light and 0.1W of heat.
The light that is absorbed by the walls of your room and heat the walls.
The surfaces that absorb the energy in a room can easily have 100m2. That’s in average 0.009W/m2. The whole room is heated with 1W. Not very much.
I have absolutely no idea what your point is.

• on April 28, 2023 at 6:15 am Barry Jacobson

My point us I am looking for a mechanism by which radiation which is absorbed at one frequency can be reradiated at another. The incoming light from Sun is not blocked by CO2 because it is at a different frequency (mainly in visible region) than CO2 absorption peaks. But the outgoing radiation is now in the infrared which is trapped by CO2 and supposedly contributes to global warming. How does this frequency change take place during the energy’s time spent visiting Earth?

• Barry,

If you want to learn, ask a question and then think about the answer and do some research.

If your approach is “I know nothing about the last 100+ years of physics and clearly that time was all wasted so I’m going to point it out” then I’m just going to ban you as a commenter.

Read up on thermal radiation. For example, nuclear fusion at the centre of the sun creates gamma rays (very high energy, very short wavelength radiation). But radiation from the surface of the sun in visible light (lower energy, longer wavelength). How does this happen?

Maybe you can revolutionise astrophysics as well. Who knows?

But take a pause. Read a few wikipedia articles on thermal radiation.

If your next comment demonstrates that the last 100+ years of physics has passed you by, I’ll just delete the comment and put in a block on future comments.

2. You are mistaken when you assume that more CO2 will always absorb more energy.
CO2 only absorbs Earth radiation in a narrow wavelength range, 14-16 microns. At present, there is enough CO2 to absorb ALL of the radiation in this range.
Thus more CO2 cannot cause more absorption and thus can not increase global warming.
To be absolutely exact, CO2 can absorb trivial amounts of energy in some other wavelengths, which could lead to a trivial increase in global temperature, a small fraction of 1 degree.
That is the known physics of the situation.
bobhisey, PhD

• The effect of additional CO2 decreases exponentially with concentration. This is well known. (Unless one is ideologically blinded).
I think there is still a small effect.
But I would also be interested in what can be achieved by reducing CO2 emissions. How fast would the concentration in the atmosphere decrease?
(Assuming we could afford to completely destroy the world economy).

• Bob,

CO2 only absorbs Earth radiation in a narrow wavelength range, 14-16 microns. At present, there is enough CO2 to absorb ALL of the radiation in this range.
Thus more CO2 cannot cause more absorption and thus can not increase global warming.

Do you have a reference for your invented idea?

Visualizing Atmospheric Radiation – Part Seven – CO2 increases

– you will see that CO2 has absorption/emission lines in a much wider range.

I’ll repeat the conclusion of that article:

Simple considerations of transmissivity of radiation in the most absorbing wavelengths of CO2 have led many people in the blog world to conclude that increases in CO2 will have no impact on outgoing radiation and that CO2 is “already saturated”.

Others have stated that water vapor totally overwhelms the effect of CO2.

We can see that these both misunderstand the actual, more complex, situation.

The data for the model comes from the HITRAN database (reference below) compiled over decades by spectroscopy professionals. The formula for absorption is the Beer-Lambert law. The formula for emission is the Planck emission law, modified by the emissivity at the wavelength in question. The formula for line width changes under atmospheric conditions have been known for 50 years or more and published in hundreds of papers.

• Yes. CO2 has other absorption lines, as has been known for 100+years. But these are all at the very edge of the earthly radiation curve, so have minimal effect. Refer to the black body radiation curve for 300 degree kelvin, the earths radiation temperature.
https://www.planetforlife.com/greenexplain/index.html

• Bob,

But these are all at the very edge of the earthly radiation curve, so have minimal effect.

Even the explanation you link to demonstrates you have no idea what you are writing.

“The very edge of the earthly radiation curve”?

Did you look at the page I linked? Do you know how to convert from wavenumber to wavelength?

CO2 absorbs in a very wide range – 12-18um. But this is “not at the very edge of the earthly radiation curve”. Look at your own referenced graph. Please.

3. on April 29, 2023 at 9:59 pm | Reply nobodysknowledge

Some years ago there was a “simple physics” discussion at SoD, with professor Dessler.
His argument was as follows: “Mr. Lewis suggests that one way around this is if the water vapor + lapse rate feedback are overstated b/c the atmosphere is not warming up as fast as expected (“no hot spot”). The evidence on that is mixed, with some data sets showing expected warming and others not. Obviously, some of these observational data are wrong — and my guess is that the data sets that don’t show a hot spot are wrong.
The reason I have that view is that the atmosphere and surface are tied together by pretty simple physics (see moist adiabatic lapse rate) and if the atmosphere is not warming as fast as expected, then something really weird is going on. The more parsimonious explanation is that data sets that don’t show warming are wrong.”
“Simple physics” trumps data.

We see the same type of argument in the above introduction:
“Some concepts in climate can be modeled by what I’ll call “simple physics”. It often doesn’t look simple.
Let’s take adding CO2 to the atmosphere. We can do this in a mathematical model. If we “keep everything else the same” in a given location we can calculate the change in energy the planet emits to space for more CO2. Less energy is emitted to space with more CO2 in the atmosphere.
The value varies in different locations, but we just calculate it in lots of places and take the average.
As less energy is leaving the planet (but the same amount is still being absorbed by the sun) the planet warms up.”
“Simple physics” trumps data.

This was the greenhouse effect mantra some years ago. Now we see that the longwave radiation has increased at TOA, in the satellite period. Following Mr Desslers logic there should be something wrong with observations. If we live under rule of this simple physics

The simple solution seems to be that reality is not following “simple physics”, because we cannot “keep everything else the same”. Forget about temperature variation and climate sensitivity. It is cloud cover that matters, and “science” has not managed to get it right. The recent global warming, which for the most part (ERBE and CERES) comes from more sun radiation reaching the surface (global brightening since 1983), could be part of some natural variation. Who knows? Who can tell for sure? How can we be sure?

• Again the casual, but erroneous, assumption that more CO2 = more earth radiation absorbed. The atmosphere already has enough CO2 to saturate the wavelength range (14-16 microns), so more CO2 will have no or minimal effect. See NASA Technical memorandum 103957. Appendix E.

• “Simple physics” tells us whether something is possible or not. It cannot tell us what is really going on in a complex system.
It is possible that climate change is mainly caused by humans, but for me nothing is proven.
If we wanted to reduce human impact, what would be the most efficient strategy?
I don’t know, but certainly not what Germany is doing.

• Correct, simple physics can tell us whether something is possible, or not. In this case, simple phtsics tells us that CO2 is not the cause of global warming, so we should quit the war on CO2 and find the actual culprit.

• Nothing is proven.
Nothing is disproved.

Additional CO2 in the atposphere is responsible for about 2 W/m of additional warming. That is hard to deny.

The question is what is going on in the overall system.

A warmer ocean leads to more CO2 in the atmosphere.
More CO2 leads to a warmer world (even though this effect is exponentially decreasing).
This releases even more CO2, and so on.

This would describe a system that always ends in catastrophic warming. Fortunately, this is not the description of the entire system. 😉

• Bob,

Did you look at the page I linked? Do you know how to convert from wavenumber to wavelength?

CO2 absorbs in a very wide range – 12-18um. But this is “not at the very edge of the earthly radiation curve”. Look at your own referenced graph. Please.

Here is another graphic for you:

As you can see, around 570 – 600 cm-1 (16.7 – 17.5 μm) and 730 – 770 cm-1 (13.0 – 13.7 μm) the transmittance through the atmosphere is nowhere near “saturated”.

If 1 km of atmosphere has a transmittance of 0.7 (i.e., 70% of radiation is transmitted) at some wavelengths then clearly more CO2 will reduce this transmittance.

This is from Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Nine – scroll down to figure 13.

If you keep repeating the same point and don’t engage with any scientific argument, I’ll just ban you.

Perhaps this isn’t the blog for you?

• I have two objectives, one, to spread the access info to the long buried NASA data(Nasa Technical Memorandum 103957, Appendix E) which shows total opacity from 600-700 wave number. Buried in 1992 by a bigwig Green fan at NASA new york.
Second to find someone to have a scientific debate on the validity of the NASA data vs other efforts.
Perhaps the greens might even do some experiments to determine the actual increase in absorptivity by doubling the CO2 to contradict the present literature (Peng et al) which reports no change within their experimental error.

I’m surprised you tolerated me this long.
Regards
Bob

• on May 2, 2023 at 2:49 am DeWitt Payne

The total atmosphere has an effective depth at STP of 8,000m, not 1,000m. So the wavenumber range for saturation for the atmosphere will be wider than depicted in the figure above. But there will still be wings at high and low wavenumbers where the transmittance gradually increases so that increasing CO2 will still have an effect on total transmittance. That’s the nature of the absorption and emission of IR radiation by molecules in a gas. Some random Technical Memorandum cannot change this. Atmospheric emission and absorption of IR radiation can be measured. The agreement between calculated and measured spectra is excellent.

• > A warmer ocean leads to more CO2 in the atmosphere.
More CO2 leads to a warmer world (even though this effect is exponentially decreasing). This releases even more CO2, and so on. This would describe a system that always ends in catastrophic warming.

Not at all!

If the feedback is small enough, the sum of the forcing + all the feedbacks will converge.

E.g., if the first forcing is X, and then the next feedback is X/2, and then the feedback of *that* is (X/2)/2, etc., then you get a sum that looks like:
sum = X + X/2 + X/4 + X/8 + X/16 + … = 2X

Some sums are convergent, some aren’t; it depends on the size of the feedback. In the real world, there’s an additional large negative feedback in the form of the Stefan-Boltzmann equations that keeps the temperatures from just heading off perpetually to infinity.

• You posit a positive feedback of 0.5. This is runaway, as it works this way. Input x, feedback o.5, output 1.5x; which generates a feedback of 1.5x*0.5, or 0.75, so next output is 1.5+0,75 or 2.25x; etc.
Even small positive feedbacks runaway. Think of the squeal of a loudspeaker system.
All positive feedbacks are runaway to the exhaustion of the resource. Check any book on electrical amplification.

• on May 5, 2023 at 4:25 pm Windchaser

> “You posit a positive feedback of 0.5. This is runaway, as it works this way. Input x, feedback o.5, output 1.5x; which generates a feedback of 1.5x*0.5, or 0.75, so next output is 1.5+0,75 or 2.25x; etc.”

Ah, no, the feedback is on the output, not on the input.

Consider the water vapor feedback: it operates based on *temperature*. So if you have a CO2 forcing which will, by itself, increase temperature by X, then water vapor feedback adds an additional forcing for another +c*X temperature increase. And then *that* temperature increase of +cX is subject to another, additional water vapor forcing for another +c*(cX). And so on.

So we’re left with sum = X + cX + ccX + cccX + …

This is a geometric series, and it converges so long as c < 1. It converges to X/(1-c).

https://en.wikipedia.org/wiki/Geometric_series

• all true, and interesting, but that is not the definition of feedback.
“feedback is defined as the process of returning part of the signal output from a circuit or device back to the input of that circuit or device.”
Your example has the “feedback” affecting only the output, not the input.

• on May 5, 2023 at 6:30 pm Windchaser

> all true, and interesting, but that is not the definition of feedback. “feedback is defined as the process of returning part of the signal output from a circuit or device back to the input of that circuit or device.” Your example has the “feedback” affecting only the output, not the input.

No, that’s still the same thing. The “input” in this definition is whatever the feedback operates on. It doesn’t have to be the *initial* forcing, it can also be the resulting temperature. (I.e., both forcings and temperature are “inputs” to different parts of this cycle of calculations, so the terminology may be confusing).

I think in your example (where you went from 1 -> 1.5 -> 2.25 -> etc.) you’re double-counting the feedbacks. If you want to stick to your terms, where the “input” is 1, then the first round of feedback adds +0.5, then the second round adds an additional +0.25, then an additional +0.125, etc. These feedbacks are *added* to the input – but don’t add them more than once.

If you’re double-counting, though, then *at each round*, you’re re-adding the initial feedback. E.g., first round of feedback is (0.5). Then you’re saying the next round of feedback is (0.75). That 0.75 comes from (0.5)*1.0 + (0.5)*(0.5), which means you’re adding that feedback of +0.5 from the initial 1.0, *again*. And that’s incorrect. That +0.5 feedback should only be added once to the input, not at every iteration, over and over and over.

In any case: yes, climate science feedbacks can definitely converge.

• As I said, check the definition of feedback=it operates on the input, not the output. Try making a diagram of your proposal. I like to be precise about the meaning of words.

• on May 9, 2023 at 5:33 pm Windchaser

> “As I said, check the definition of feedback=it operates on the input, not the output.”

That’s not really what the definition says – it says it `returns part of the output back to the input`. Domain-wise, we’d say it *maps* from the output to input.

Anyways, I can give another example that should be more clearly self-limiting.

Consider an initial input, X_0.
Consider a function mapping input to output: f(x) = 1 – 1/(x+1)
And consider a feedback, where the feedback at the next timestep is 1x the output at the previous timestep (unitless), and this is simply added directly to the input.

So, then, imagine X = 1 at the first timestep:
t = 0: x = 1, Out = 0.5, feedback = 0.5
t = 1, x = 1.5, Out = 0.6, feedback = 0.6
t = 2, x = 2.1, Out = 0.67, etc

Etc. The In->Out function is asymptotic, converging to 1 as input -> +infinity, so there’s no runaway effect.

• All perfectly true. However, it seems it is not a positive feedback system. It is negative, since there is a negative sign in the formula.
I t exactly conforms to a normal presentation if you consider the initial value of 1 to be the disturbance, or forcing factor, which winds down to zero.
But one can write lots of equations but experimental data is needed to confirm.
What I have not seen shown is experimental data on the effects of doubling CO2 concentration on the A, absorptivity coefficient to contradict the experimental data in the literature that all indicate very minor effect. For example, one 1960s article in Applied Optics shows an increase of 10 fold in concentration causes an increase in A of of about one half per cent. Or 2ppm of CO2 in our case.
If this is in the ball park, then doubling would cause less than a tenth of a percent in absorption. If we then accept the general notion that our 400ppm has caused 3 degrees warming, then doubling would cause about 2 hundredth of a degree.
Then we would need a positive feedback of 100 to get the 2 degrees that seem to be desired. I’m pretty sure that that big a positive feedback would be unstable but, as we agree, the climate shows a stable system over many years.
There is a lot of absorption data in the 60’s literature. None recently, it seems the field is mined out.
It is a pleasure to have a civil scientific discussion in this area. Everyone talk about warming, but noone discusses the cause of warming. I have no opinion about the degree of warming, but feel we are wasting out money and time assuming it is CO2 and warring on fossil fuels. I bet if we stopped subsidizing ‘green’ energy we might even be able to balance the US budget.

Regards
Bob

4. Yes, indeed.