The Science of Doom

In On Having a Laugh – by Gerlich and Tscheuschner (2009) I commented that I had only got to page 50 and there were 115 pages in total.

Because there were so many errors already spotted, none central to the argument (the argument hadn’t started even at page 50), it seemed a pointless exercise to read it further. After all, many interesting papers await, on the thermohaline circulation, on models, on stratospheric cooling..

Perhaps most important of the criticisms was that Gerlich and Tscheuschner didn’t appear at all familiar with the climate science they were “debunking” – instead of commenting on encyclopedia references or throwaway comments in introductions to works unrelated to proving the inappropriately-named “greenhouse effect” they should be commenting on papers like Climate Modeling through Radiative-Convective Models by Ramanathan and Coakley (1978).

Clearly they were “having a laugh”

However, after noticing that a recent commenter actually cited Gerlich and Tscheuschner I went back and reviewed their paper. And in doing so I realized that many many misinformed comments by enthusiastic people on other popular blogs, and also this one, were included in the ground-breaking On Falsification Of The Atmospheric CO2 Greenhouse Effects by Gerlich and Tscheuschner.

It’s possible that rather than enthusiastic commenters obtaining misinformation from our duo that instead our duo have combined a knowledge of theoretical thermodynamics with climate science that they themselves obtained from blogs. The question of precedence is left as an exercise for the interested reader.

Miseducation

It is hard to know where to start with this paper because there is no logical flow.

Conductivity

The paper begins by reviewing the conductivity of various gases.

It is obvious that a doubling of the concentration of the trace gas CO2, whose thermal conductivity is approximately one half than that of nitrogen and oxygen, does change the thermal conductivity at the most by 0.03% and the isochoric thermal diffusivity at the most by 0.07 %. These numbers lie within the range of the measuring inaccuracy and other uncertainties such as rounding errors and therefore have no significance at all.

Clearly conductivity is the least important of means of heat transfer in the atmosphere. Radiation, convection and latent heat all get a decent treatment in studies of energy balance in the atmosphere.

If our duo had even read one book on atmospheric physics, or one central paper they would be aware of it.

Uninformed people might conclude from this exciting development that they have already demonstrated something of importance rather than just agreeing wholeheartedly with the work of atmospheric physicists.

Pseudo-Explanations to be Revealed in Part Two? Or Left as an Exercise for the Interested Student?

Following some demonstrations of their familiarity with mathematics and especially integration, they provide three conclusions, one of which refers to the Stefan-Boltzmann law, j=σT⁴:

The constant appearing in the T⁴ law is not a universal constant of physics. It strongly depends on the particular geometry of the problem considered.

and finish with (p21):

Many pseudo-explanations in the context of global climatology are already falsified by these three fundamental observations of mathematical physics.

Unfortunately they don’t explain which ones. The climate science world waits with baited breath..

The footnote to their comment on Stefan-Boltzmann:

For instance, to compute the radiative transfer in a multi-layer setup, the correct point of departure is the infinitesimal expression for the radiation intensity, not an integrated Stefan-Boltzmann expression already computed for an entirely divergent situation.

Sadly they are unfamiliar with the standard works in the field of the radiative-convective model.

Solar Energy Breakdown and A Huge Success in Miseducation

Solar Radiation Breakdown

They followed up this table with the hugely popular comment:

In any case, a larger portion of the incoming sunlight lies in the infrared range than in the visible range. In most papers discussing the supposed greenhouse effect this important fact is completely ignored.

First, a comment on the “benefit” of this miseducation – being able to separate out solar radiation from terrestrial radiation is a huge benefit in climate understanding – it allows us to measure radiation at a particular wavelength and know its source. But many people are confused and say we can’t because 50% of the solar radiation is “infrared”. Infrared means >0.7μm. Conventionally, climate scientists use “shortwave” to mean radiation < 4μm and “longwave” to mean radiation > 4μm. As less than 1% of solar radiation is >4μm this is a very useful convention. Any radiation greater than 4μm is terrestrial (to 99% accuracy).

Many uninformed people who have become miseducated are certain that much solar radiation is >4μm – possibly due to confusing infrared with longwave.

We don’t speculate on motives on this blog so I’ll just point out that Gerlich and Tscheuschner know very little about any climate science, and from this comment probably don’t even understand the inappropriately-named “greenhouse” effect.

Why? Well, what has the visibility of the radiation have to do with the “greenhouse” effect? Of course it’s ignored. Our duo are just demonstrating their ignorance of the absolute basics.

Or they have some amazing insight into how the visibility or not of solar radiation affects the radiative transfer equations. All to be shared in part two probably..

The Core Question – the Radiative Transfer Equations

After a brief explanation of Kirchoff’s law, our duo discuss the core equations, the radiative transfer equations (RTE):

LTE [local thermodynamic equilibrium] does only bear a certain significance for the radiation transport calculations, if the absorption coefficients were not dependent on the temperature, which is not the case at low temperatures. Nevertheless, in modern climate model computations, this approach is used unscrupulously.

Absorption and emission coefficients get a very thorough treatment in the numerical solutions to the RTE, however, our duo are only familiar with work around the 1900’s and skip all modern work on the subject. Perhaps a more accurate statement would be:

We have no idea what anyone does but we read somewhere that stuff wasn’t done right..

Or they could actually show what effect that dependency actually had..

Then they decide to support the RTE:

Fantastic, 50 pages in we find the real RTE. This is what atmospheric physicists use to calculate the absorption and re-emission of radiation for each layer in the atmosphere. They follow this up with:

The integrations for the separate directions are independent of one another. In particular, the ones up have nothing to do with the ones down. It cannot be overemphasized, that differential equations only allow the calculation of changes on the basis of known parameters.

The initial values (or boundary conditions) cannot be derived from the differential equations to be solved. In particular, this even holds for this simple integral.

What do they mean? Of course you need boundary conditions to solve all real-world equations.

The separate directions are independent of one another? Yes, you find that in all treatments of radiative transfer.

So Gerlich and Tscheuschner agree that the RTE can be used to solve the problem? Or not? No one can tell from the comments here. If they do, the paper should be over now with support for the inappropriately-named “greenhouse effect”, unless they demonstrate that they can solve them for the atmosphere and get a different result from everyone else.

But they don’t.

Fortunately for those interested in what our duo really know and understand – they tell us..

The Modern Solution to the RTE – or How to Miss an Important 100 Years

After surveying works from more than 100 years ago, they conclude:

Callendar and Keeling, the founders of the modern greenhouse hypothesis, recycled Arrhenius’ discussion of yesterday and the day before yesterday by perpetuating the errors of the past and adding lots of new ones.

In the 70s and 80s two developments coincided: A accelerating progress in computer technology and an emergence of two contrary policy preferences, one supporting the development of civil nuclear technology, the other supporting Green Political movements. Suddenly the CO2 issue became on-topic, and so did computer simulations of the climate. The research results have been vague ever since.

No explanation of Callendar and Keeling’s mistakes – this is left as an exercise for the interested student.

And no mention of the critical work in the 1960s and 1970s which used the radiative transfer equations and the convective structure of the atmosphere to find the currently accepted solutions.

In fact, the research results haven’t been vague at all. Regular readers of this blog will know about Ramanathan and Coakley 1978, and there are many more specific papers which find solutions to the RTE – using boundary conditions and separation of upward and downward fluxes, as wonderfully endorsed by our comedic duo.

More recent work has of course refined and improved the work of the 1960s and 1970s. And the measurements match the calculations.

But what a great way to write off a huge area of research. Show some flaws in the formative work 100 or so years ago and then skip the modern work and pretend you have demonstrated that the modern theory is wrong.

As we saw in the last section, our duo appear to support the modern equations – although they are careful not to come out and say it. Luckily, they are blissfully ignorant of modern work in the field, which all helps in the miseducation of the uninformed.

The main work of the paper should now be over, but our duo haven’t realized it. So instead they move randomly to the radiative balance concept..

Radiative Balance and Mathematical Confusion

In every introduction to atmospheric physics you find the concept of radiative balance – solar energy absorbed = terrestrial radiation emitted from the top of the atmosphere. These concepts are used to demonstrate that the atmosphere must absorb longwave (terrestrial) radiation.

This concept can be found in CO2 – An Insignificant Trace Gas? Part One

After looking at the basics of the energy balance, they comment – on the right value for albedo (or ‘1-albedo’):

In summary, the factor 0.7 will enter the equations if one assumes that a grey body absorber is a black body radiator, contrary to the laws of physics. Other choices are possible, the result is arbitrary.

Being obscure impresses the uninformed. However, the informed will know that the earth’s emissivity and absorptivity will of course be different because the solar radiation is centered on 0.5μm while the terrestrial radiation is centered on 10μm. And the emissivity (and absorptivity) around 10um is very close to 1 (typically 0.98) while around 0.5μm the absorptivity is somewhat lower.

At this point, if we were to do a parody of our duo, we would write how their physics is extremely poor and do a three page derivation of absorptivity and emissivity as a function of wavelength.

Now follows many pages of maths explaining the impossibility of working out an average temperature for the earth during which they make the following interesting comment:

While it is incorrect to determine a temperature from a given radiation intensity, one is allowed to compute an effective radiation temperature Terad from T averages representing a mean radiation emitted from the Earth and to compare it with an assumed Earth’s average temperature Tmean

What they are saying is that for energy balance if we work out the radiation emitted from the earth we have dealt with the problem.

Fortunately for our intrepid duo, they are unacquainted with any contemporary climate science so the fact that someone has already done this work can be safely ignored. Earth’s Global Energy Budget by Trenberth, Fassulo and Kiehl (2008) covers this work.

To compute these effects more exactly, we have taken the surface skin temperature from the NRA at T62 resolution and 6-hour sampling and computed the correct global mean surface radiation from (1) as 396.4 W/m². If we instead take the daily average values, thereby removing the diurnal cycle effects, the value drops to 396.1 W/m² or a small negative bias. However, large changes occur if we first take the global mean temperature. In that case the answer is the same for 6 hourly, daily or climatological means at 389.2 W/m². Hence the lack of resolution of the spatial structure leads to a low bias of about 7.2 W/m². Indeed, when we compare the surface upward radiation from reanalyses that resolve the full spatial structure the values range from 393.4 to 396.0 W/m².

The surface emissivity is not unity except perhaps in snow and ice regions, and it tends to be lowest in sand and desert regions, thereby slightly offsetting effects of the high temperatures on longwave (LW) upwelling radiation. It also varies with spectral band (see Chédin et al. 2004 for discussion). Wilber et al. (1999) estimate the broadband water emissivity as 0.9907 and compute emissions for their best estimated surface emissivity versus unity. Differences are up to 6 W/m² in deserts, and can exceed 1.5 W/m² in barren areas and shrublands.

So there is potential variation of a few W/m² depending on the approach, and Trenberth et al settles on 396 W/m² average – at least the values can be calculated, whereas our duo decided it was computationally impossible – perhaps as they saw the problem as requiring a totally accurate GCM.

With this information, the radiative balance problem can be resolved and we can see that there is a discrepancy between the solar energy absorbed and the terrestrial radiation emitted which requires explanation. The inappropriately-named “greenhouse effect”.

Without this information we can delight in much maths and pretend that nothing can be known about anything.

Why Conduction Can be Safely Ignored and Why We Just Demonstrated It

In many climatological texts it seems to be implicated that thermal radiation does not need to be taken into account when dealing with heat conduction, which is incorrect. Rather, always the entire heat flow density q must be taken into account..  It is inadmissible to separate the radiation transfer from the heat conduction, when balances are computed..

Unfortunately, the work on even the simplest examples of heat conduction problems needs techniques of mathematical physics, which are far beyond the undergraduate level.

In fact in many texts on atmospheric physics conduction is safely ignored due to the very low value of heat conduction through gases. Strictly speaking, if we write an equation then all terms should be included, including latent heat and convection. Why just radiation and conduction?

As Ramanathan and Coakley pointed out in their 1978 paper, convection is what determines the temperature gradient of the atmosphere but solving the equations for convection is a significant problem – so the radiative convective approach is to use the known temperature profile in the lower atmosphere to solve the radiative transfer equations.

Still, no thought of conduction as that term is so insignificant – as our intrepid duo go on to realize..

Commenting on the insolubility of heat flow via conduction they take a “typical example”:

If the radius of the Moon were used as the characteristic length and typical values for the other variables, the relaxation time would be equivalent to many times the age of the universe.

Therefore, an average ground temperature (over hundreds of years) is no indicator at all that the total irradiated solar energy is emitted. If there were a difference, it would be impossible to measure it, due to the large relaxation times. At long relaxation times, the heat flow from the Earth’s core is an important factor for the long term reactions of the average ground temperature; after all, according to certain hypotheses the surfaces of the planetary bodies are supposed to have been very hot and to have cooled down. These temperature changes can never be separated experimentally from those, which were caused by solar radiation.

So heat flow by conduction is so low that achieving balance by this method will take more than the age of the universe. Therefore, it is insignificant in comparison with convection and radiation.

Good so we can move on and climate scientists are right to ignore it. Was that the point that Gerlich and Tscheuschner were making? Yes, although possibly without realizing it..

Finally, the Imaginary Second Law of Thermodynamics

In their almost concluding section we see where countless climate enthusiasts have obtained their knowledge (or the reverse).

First, here’s an extract from a contemporary work on thermodynamics. This is from Fundamentals of Heat and Mass Transfer, 6th edition (2007), by Incropera & Dewitt:

As can be seen in the text, radiation can be absorbed by a higher temperature surface from a lower temperature surface and vice versa. Of course, the net result is a heat transfer from the hotter to the cooler.

The same uncontroversial description can be found in any standard thermodynamics work, unless they consider it too unimportant to mention. Certainly, none will have a warning sign up saying “this doesn’t happen”.

The explanation of the “greenhouse effect” is that the earth’s surface warms the lower atmosphere by radiation (as well as convection and latent heat transfer). And the atmosphere in turn radiates energy in all directions – one of which is back to the earth’s surface. Believers in the imaginary second law of thermodynamics don’t think this can happen. And this is possibly due to the miseducation by our intrepid duo. Or perhaps they learnt their thermodynamics from many “climate science” blogs.

The result of the actual climate situation is that the earth’s surface is warmer than it would have been without this atmospheric radiation. Pretty simple in concept.

Here’s how Gerlich and Tscheuschner explain things:

Everyone agrees.

Now the confusion. What are they saying? This isn’t what atmospheric physicists describe. The net heat transfer is from the earth’s surface (which was warmed by the sun) to the atmosphere.

Are they saying that it is impossible for any radiation to transfer heat from the atmosphere to the earth? It would appear so –

Following their diagram above, they comment, first quoting Rahmstorf:

Some `sceptics’ state that the greenhouse effect cannot work since (according to the second law of thermodynamics) no radiative energy can be transferred from a colder body (the atmosphere) to a warmer one (the surface). However, the second law is not violated by the greenhouse effect, of course, since, during the radiative exchange, in both directions the net energy flows from the warmth to the cold.

Rahmstorf’s reference to the second law of thermodynamics is plainly wrong. The second law is a statement about heat, not about energy. Furthermore the author introduces an obscure notion of “net energy flow”. The relevant quantity is the “net heat flow”, which, of course, is the sum of the upward and the downward heat flow within a fixed system, here the atmospheric system. It is inadmissible to apply the second law for the upward and downward heat separately redefining the thermodynamic system on the fly.

Our duo first attempt to confuse, as they frequently do in their opus by claiming that a clear explanation is obscure because precise enough terms aren’t used. It’s not obscure because they make the “correction” themselves.

Then add their masterstroke. It is inadmissible to apply the second law for the upward and downward heat separately redefining the thermodynamic system on the fly.

What on earth do they mean? Our comedic duo are the ones separating the system into upward and downward heat, followed by an enthusiastic army on the internet. Everyone else considers net heat flow.

As we saw in a standard work on thermodynamics, now in its 6th edition after two or three decades in print, there is no scientific problem with radiation from a colder to a hotter body – so long as there is a higher radiation from the hotter to the colder.

At this point I wonder – should I revisit the library and scan in 20 thermodynamic works? 50? What would it take to convince those who have been miseducated by our intrepid duo?

Perhaps Gerlich and Tscheuschner can now turn their attention to all of the unscientific text books like the one shown at the start of this section..

Conclusion

There is much to admire in Gerlich and Tscheuschner’s work. It can surely become a new standard for miseducation and we can expect its deconstruction by psychologists and those who study theories of learning.

From a scientific point of view, there is less to admire.

They have no understanding of modern climate science, content to dwell on works from over 100 years ago and ignoring any modern work. They appear to believe that the basis for the “greenhouse” effect is an actual greenhouse (as was covered in On Having a Laugh) even though no serious work on the subject relies on greenhouses. (Some don’t even mention it, some mention it to point out that the atmosphere doesn’t really work like a greenhouse).

In fact, the serious work of the last few decades relies on the radiative transfer equations – equations apparently endorsed by our duo, although their comments are “obscure”.

They take many other snipes at climate science by the approach of pointing out a term or dependency has been “neglected” (for example, like conduction through the atmosphere) without showing that the neglect has a significant impact – except in the case of conduction where (unwittingly?) they appear to show that conduction should definitely be ignored!

Someone could take issue with even modern work on climate science by the fact that they ignore relativistic effects.

Within the frame of modern physics, climate science is badly flawed to ignore relativity

And after 18 pages of unnecessary re-derivation of general relativity we find that “it’s therefore impossible to calculate this and the problem is insoluble“..

Well, although they haven’t read any modern climate science, it’s hard to see how they could be so confused about the application of the 2nd law of thermodynamics.

Perhaps in their follow up work they can explain why all the thermodynamics works are wrong, and especially where this 15μm (longwave) radiation comes from:

Measured downward longwave radiation at the earth's surface

According to their interpretation of the 2nd law of thermodynamics this can’t happen. No heat can flow from the colder atmosphere to the warmer surface as that would be a “perpetuum mobile” and therefore impossible.

Where is it coming from Gerlich and Tscheuschner?

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Recap

This post is a follow on from my original article: American Thinker – the Difference between a Smoking Gun and a Science Paper.

Gary Thompson who wrote the article in American Thinker that prompted my article was kind enough to make some comments and clarifications. Instead of responding in the comments to the first article, I thought it was worth a new post, especially to get the extra formatting that is allowed in posts rather than comments.

I appreciate him commenting and I’m sure he has a thick skin, but just in case, any criticisms are aimed at getting to the heart of the matter, rather than at him – or anyone else who has different views.

For people who have landed at this post and haven’t read the original.. the heart of Gary’s article were 3 papers, of which I examined one (the first). The paper compared two 3-month periods 27 years apart in the East and West Pacific. Gary commented that the actual OLR (outgoing longwave radiation) was higher in the later period in the important CO2 band (or what we could see of it).

His claim – the theory says that more CO2 should lead to less emission at those wavelengths and therefore the theory has been disproved.

My point – Gary doesn’t understand the theory. The temperature was higher in the later period in this region and therefore the radiation leaving the earth’s surface would be higher. We’ll see this explained again, but did I mention that you should read Gary’s article and my article before moving forward? Also at the end of the Science of Doom post you can see Gary’s comments. Always worth reading what people actually wrote rather than what someone (me) with the opposite point of view highlighted from their words..

The Unqualified Statements in Papers

Gary started by saying:

I know why the authors of the papers were using climate models to simulate the removal of effect from surface temperatures and humidity and that the ‘theory’ says you must do that. But my problem lies in two peer reviewed papers that casts doubt on that theory and that method.

And cites two papers. The first, a 1998 paper: The Trace Gas Greenhouse Effect and Global Warming by the great V. Ramanathan (I will continue to call him ‘great’ even though he didn’t reply to my email about his 1978 paper.. possibly busy, but still..).

I recommend this 1998 paper to everyone reading this article. Even though it is 12 years old, it is all relevant and a very readable summary.

The Great Ramanathan

Gary pointed out page 3 where statements appeared to back up his (Gary’s) interpretation of the later OLR study. Here’s what Ramanathan said:

Why does the presence of gases reduce OLR? These gases absorb the longwave radiation emitted by the surface of the earth and re-emit to space at the colder atmospheric temperatures. Since the emission increases with temperature, the absorbed energy is much larger than the emitted energy, leading to a net trapping of longwave photons in the atmosphere. The fundamental cause for this trapping is that the surface is warmer than the atmosphere; by the same reasoning decrease of temperature with altitude also contributes to the trapping since radiation emitted by the warmer lower layers are trapped in the regions above.

By deduction.. an increase in a greenhouse gas such as CO2 will lead to a further reduction in OLR. If the solar absorption remains the same, there will be a net heating of the planet.

Gary commented on the last part of this:

Notice there is no clarifying statement about having to use model simulated graphs to ‘correct’ for surface temperatures and water vapor before seeing that OLR reduction.

And on the first part:

“since the emission increases with temperature, the absorbed energy is much larger than the emitted energy, leading to a net trapping of longwave photons in the atmosphere.” – here the author stated clearly that even taking into account higher emissions from warmer surfaces, the net will still be a reduction.

For half the readers here, they are shaking their heads.. But for Gary and the other half of the readership, let’s press on.

First of all, if we took any of 1000 papers on the “greenhouse” effect and observations, models, theoretical adjustments, impacts on GCMs – I bet you could find at least 700 – 900 of them at some point will make a statement that could be pulled out which has no “clarifying statement”. That “cast doubt” on the theory. Perhaps 1000 out of a 1000.

Context, context, context as they say in real estate.

Where to begin? Let’s look at “the theory” first. And then come back and examine Ramanathan’s statements.

The Theory

There are a few basics. For newcomers, you can take an extended look at the theory in CO2 – An Insignificant Trace Gas? It’s in seven parts! Actually it’s a compressed treatment.

This is itself is a clue.

In the books I have seen on Atmospheric Physics many tens of pages are devoted to radiation, including absorption and re-radiation – the “greenhouse” effect – and many tens of pages are devoted to convection. Understanding the basics is critical.

For Gary and his followers, the theory is on a precipice and these papers are giving us that clue. For people who’ve studied the subject the theory of the “greenhouse” effect is as solid as the theory of angular momentum, or the 2nd law of thermodynamics (the real one, not the imaginary one).

As Ramanthan says in the same paper Gary cites:

It is convenient to separate the greenhouse effect from global warming. The former is based on observations and physical laws such as Planck’s law for black-body emission. The concept of warming that results from the greenhouse effect, is based on deductions from sound physical principles. Numerous feedback processes, determine the magnitude of the warming; these feedbacks are treated with varying degrees of sophistication in GCMs and other climate models. As a result, predictions of the magnitude of the warming are not only model dependent but are subject to large uncertainties..

If I can paraphrase:

Greenhouse effect – dead solid. Global warming – lots of factors, need GCMs, pretty complicated.

Perhaps he has not realized that his words in the same paper combined with experiments demonstrate a flaw in the theory of the dead-solid “greenhouse” effect..

Back to the theory, but first..

A Quick, possibly Annoying, Diversion to the Theory of Gravity

But before we start, I thought it was worth an analogy. Analogies are illustrations, not proof of anything. They can often inflame an argument, but that’s not the intention here. Many people who are still undecided about the amazing theory of the inappropriately-named “greenhouse” effect might welcome a break from thinking about it.

The theory of planetary movements is my analogy. I picture a world where gravity – and its effects on the planets orbiting the sun – is strangely controversial. A concerned citizen, leafing through some fairly recent scientific papers notices that planets don’t really go around the sun in ellipses as the theory claims. In fact, there are some quite odd movements. And so, surprised that the scientists can’t see what’s in plain sight, this citizen draws attention to them.

When some detail-orientated commenters point out that the theory is actually (in part):

F = GMm/r²

where F= force between 2 bodies, G is a constant, M and m are the masses of the 2 bodies and r is the distance between them

And the ellipse idea is just a handy generalization of the results of the laws of graviational attraction.

And the reason why some planetary movements recently measured don’t follow an ellipse is because a few planets are a bit closer together, there’s a large asteroid flying between them and so when we do the maths it all works out pretty well.

The original concerned citizen then pulls out a few papers where, in the introduction, gravity is explained as that force that produces elliptical movements in the planets.. with no disclaimers about F=GMm/r² and claims that this theory is, therefore, under question.

Why this annoying analogy? Most “theories” in physics are developed because of some observations which get analyzed to death – and finally someone produces a “comprehensive theory” that satisfies most of the relevant scientific community. The paper with the comprehensive theory usually contains some equations, some observations, some matching of the two – but often in common everyday usage the shorthand version of the theory is used.

“The theory of gravity tells us that planets orbit the sun in an elliptical manner, and ..”

So much more tedious to keep saying F=GMm/r², and the other formulae..

(I know, I haven’t proved anything, but maybe a few readers can take a moment and see a parallel..)

Back to the Radiative-Convective Theory

First, bodies radiate energy according to Planck’s formula, which looks complicated when written down. The idea is simplified by the total energy radiated according to the Stefan-Boltzmann law which says that total energy is proportional to the 4th power of temperature.

Temperature goes up, energy radiated goes up (quite a bit more) – and the peak wavelength is a little lower. Here’s a graphical look of the Planck formula which takes away the mathematical pain:

Blackbody Radiation at 288K and 289K (15'C and 16'C)

Two curves – 288K and 289K. Now zoomed in a little where most of the energy is:

Close up of the peak energy of 288K and 289K

Total energy in the top curve (289K) is 396W/m^2, and in the bottom curve (288K) is 390W/m^2

Second, trace gases absorb energy according to a formula, which when simplifed is the Beer-Lambert law.

Absorption of Radiation as "optical thickness" increases

Without going into a lot of maths, as the concentration of a “greenhouse” gas increases, the absorption graph falls off more steeply – more energy is absorbed.

Third, re-radiation of this energy takes place according to an energy balance equation that you can see in CO2 – Part Three. The energy balance or radiative transfer equations rely on knowledge of the temperature profile in the lower atmosphere (the troposphere), because the actual temperature here is dominated by convection not radiation. (Radiation still takes place and the temperature profile is a major factor in the radiation – but this effect is not the primary determinant of the temperature profile).

When Gary says:

I know why the authors of the papers were using climate models to simulate the removal of effect from surface temperatures and humidity and that the ‘theory’ says you must do that. But my problem lies in two peer reviewed papers that casts doubt on that theory and that method.

It sounds like Gary believes this “model” is some suspicious extra that tries to deal with problems between the theory and the real world. But it’s the foundation. Anyone who had read an introduction to atmospheric physics would understand that. Someone who had tried hard to understand a few papers without a proper foundation would easily miss it.

• Higher temperatures increase OLR
• More trace gases reduce OLR in certain wavelengths

Which effect dominates in a particular situation?

It’s simple conceptually. But, if we want to find out exact results – such as, which effect dominates in a particular situation – we need a “model” = an equation or set of equations. Because if we want to quantify the effects we have to solve some tricky equations which you can see in a paper by.. the Great Ramanathan. Well, Ramanathan & Coakley 1978  – a seminal paper on Climate Modeling through Radiative-Convective Models, here’s an extract from p7:

A few equations from Ramanathan and Coakley, p7

Lots of maths. The rest of the paper is similar. Let’s move on to Ramanathan’s much later paper and what he said and meant.

Has Ramanathan given up on The Theory?

Let’s review the words Gary pulled out of the paper:

Why does the presence of gases reduce OLR? These gases absorb the longwave radiation emitted by the surface of the earth and re-emit to space at the colder atmospheric temperatures. Since the emission increases with temperature, the absorbed energy is much larger than the emitted energy, leading to a net trapping of longwave photons in the atmosphere.

Gary reads into this “here the author stated clearly that even taking into account higher emissions from warmer surfaces, the net will still be a reduction“. By which Gary thinks Ramanathan is saying something like:

..measurements from a specific location at a later date when CO2 has increased will always lead to a reduction in OLR..

-my paraphrase.

But no, he has totally misunderstood what the author is saying. Ramanathan is doing a quick drive through of the basics and explaining how the greenhouse effect works.

Lower temperatures in the atmosphere mean that the radiation to space from this lower temperature atmosphere is lower than the radiation from the surface. (This is the “net trapping”). Therefore – the “greenhouse” effect. There is no conclusion here that “at all times in all situations increases in “greenhouse” gases will lead to a reduction in OLR in these bands“. The conclusion is just that “greenhouse” gases mean that the surface is warmer than it would be without these gases

And the first claim, Ramanathan said:

By deduction.. an increase in a greenhouse gas such as CO2 will lead to a further reduction in OLR. If the solar absorption remains the same, there will be a net heating of the planet.

Gary said:

Notice there is no clarifying statement about having to use model simulated graphs to ‘correct’ for surface temperatures and water vapor before seeing that OLR reduction.

That’s because the basics of the theory are the solid foundation and don’t need to be restated as qualifiers to every statement. Ramanathan helped write the theory! For people who think that this stuff is just some added extra, read his 1978 paper and see all the maths and the explanations. This is the theory.

In the earlier part of his earlier statement he said “Since the emission increases with temperature” but didn’t qualify it with “emission increases in proportion to the 4th power of temperature“.

Is Ramanathan losing confidence in the Stefan-Boltzmann formula? Or Planck? Are these rocks crumbling?

It’s only because Gary has decided that these points are somehow rocky that he would reach these conclusions. (And I could pick 10’s of other statements in the paper which, without qualifiers, could be taken to be the beginning of the end of a specific theory).

As a general point – when we look at the hypothetical global annual average after “new equilibrium” from increased CO2 is reached – if this new equilibrium exists – the theory (1st law of thermodynamics) predicts that the “new” OLR will match the “old” OLR (global annual average). And in that case the OLR in “greenhouse” gas bands will be reduced a little, while the OLR outside of those bands will be increased a little.

But when we look at one local situation we need the theory, also known as “the model”, also known as equations, to tell us what exactly the result will be.

Ramanathan hasn’t cast any doubt on it. He believes it. His papers from the 1970s to today work it all out. He just doesn’t write qualifiers to each statement as if every line will be read by people who don’t understand the theory..

Gary’s Maths

In Gary’s comment he reproduced his back of envelope calculations of how much surface temperature should have changed over this 27 year period.

He takes the charitable approach of considering a net reduction in OLR from one of the three papers he originally reviewed – if I understood this step correctly. The figure he takes to work with is a 1K reduction. And then tries to work out how much this 1K reduction in OLR in the CO2 band would have on surface temperatures.

Like all good science this starts on napkins and the back of envelopes, because everyone studying a problem first has to attempt to quantify it using available data and available formulae. Then when the first results are worked out and it seems like something new is discovered – or something old overturned – then the scientist, patent clerk, writer now has to turn to more serious methods.

In Gary’s preliminary results he shows that a reduction in OLR due to CO2 might have contributed something like 0.3°C to surface temperature change over 30 years or so – where the GISS temperature increase for the period is something like 0.7°C. The essence of the calculation was comparing the Planck function (see the first and second graph in this post) of two temperatures 1K apart, then considering how much is in the CO2 band and so calculating the approximate change in W/m². Then by applying a “climate sensitivity” number from realclimate.org, converting that into a temperature change.

Radiative physics has the potential to confuse everyone. Perhaps if we consider the “equilibrium case”, one problem with Gary’s calculation above will become clearer.

What’s the equilibrium case? In fact, it’s one generalized result of the real theory. And because it’s easier to understand than dI = -Inσdz + Bnσdz = (I – B)dχ people start to think the generalized result under equilibrium is the theory..

Under equilibrium, energy out = energy in. This is for the whole climate system. So we calculate the incoming solar radiation that is absorbed, averaged across the complete surface area of the earth = 239 W/m².

So if the planet is not heating up or cooling down, energy out (OLR) must also = 239 W/m².

So we consider the golden age of equilibrium in 1800 or thereabouts. We’ll assume the above numbers are true for that case. Then lots of CO2 (and other stuff) was added. Let’s suppose CO2 has reached the new current CO2 level of 380ppm – and stays constant from now on. The downward radiative forcing as calculated at “top of atmosphere” from the increase in CO2 is 1.7 W/m². And nothing else happens in the climate (“all other things being equal” as we say).

Eventually we will reach the new equilibrium. Doesn’t matter how long it takes, but let’s pretend it’s 2020. Before equilibrium the planet will be heating up, which means OLR < 239 W/m² (because more energy must come into the planet than leave the planet for it to warm up). At equilibrium, in 2020, OLR = 239 W/m² – once again. (Of course, at wavelengths around 15μm the energy will be lower than in 1800 and other wavelengths the energy will be higher).

At this new equilibrium point we still have a “radiative forcing” of 1.7W/m², which is why the surface temperature is higher, but no change in OLR when measured at 1800 and again at 2020.

We’ll assume, like Gary, the realclimate.org climate sensitivity – how do we calculate the new equilibrium temperature?

The change in OLR is 0.0 W/m². Therefore, change in temperature = 0’C. Ha, we’ve proved realclimate wrong. Climate sensitivity cannot exist.

Or, it was wrongly applied.

As trace gases like CO2 increase in concentration they absorb energy. The atmosphere warms up and re-radiates the energy in all direction. Simplifying, we say it re-radiates both up and down. The extra downward radiation is what is used to work out changes in surface temperature. Not the immediate or eventual change in OLR.

The extra downward part is usually called “radiative forcing” and comes with a number of definitions you can see in Part Seven of the CO2 series (along with my mistaken attempt to do a “back of envelope” calculation of surface temperature changes without feedback).

How do we work out the change in surface temperature?

In Gary’s case, what he will need to know is the change in downward longwave radiation. Not upwards.

Conclusion

The theory of radiative transfer in the atmosphere, at its heart, is a relatively simple one – but in application is a very challenging one computationally speaking. Therefore, it’s hard to grasp it in its details intuitively.

The theory isn’t the generalized idea of what will happen when moving from one equilibrium state to another equilibrium state with more “greenhouse” gases. That is a consequence of the theory under specific (and idealized) circumstances.

But because everyone likes shorthand, to many people this has become “the theory”. So when someone applies the maths to a specific situation it is “suspicious”. Maths becomes equated with “models” which to many people means “GCMs” which means “make-belief”. I think that if Gary had read Climate Modeling through Radiative-Convective Models by the Great Ramanthan, he might have a different opinion about the later paper and whether Ramanathan is “bailing out” on the extremely solid theory of “greenhouse” gases.

Anyone who has read a book on atmospheric physics would know that Gary’s claim is – no nice way to say it – “unsupported”. Yes – cruel, harsh, wounding words – but it had to be said.

However, most of the readers here and most on American Thinker haven’t read an undergraduate book on the topic. So it makes it worth trying to explain in some detail.

It’s also great to see people trying to validate or falsify theories with a little maths. Working out some numbers is an essential step in proving or disproving our own theories and those of others. In the example Gary provided he didn’t apply the correct calculation. (The subsequent pages of Ramanathan’s 1998 paper also run through these basics).

For those convinced that the idea that more CO2 will warm the surface of the planet is some crazy theory – these words are in vain.

But for the many more people who want to understand climate science, hopefully this article provides some perspective. The claims in American Thinker might at first sight seem to be a major problem to an important theory. But they aren’t.

Note – I haven’t yet opened the Philipona paper, but will do so in coming weeks and probably add another article about it. I didn’t want to leave Gary’s comments unanswered, and this post is already long enough..

Note on a Few Technical Matters

A few clarifications are in order, for people who like to get their teeth into the technical details.

Strictly speaking, at the very top of atmosphere there is no downward longwave forcing at all. That’s because there’s no atmosphere to radiate.

The IPCC definition of “radiative forcing” at “top of atmosphere” is a handy comparison tool of extra downward radiation before feedbacks and before equilibrium of the surface or troposphere is reached. In reality the increase in downward radiation doesn’t occur in just one location, extra downward longwave radiation occurs all throughout the troposphere and stratosphere.

In the example above, from 2010 to 2020 as surface and troposphere temperatures increased, radiative forcing would also increase slightly so it wouldn’t necessarily be constant at 1.7W/m².

Climate sensitivity is calculated by GCMs to work out the resulting long term (“equilibrium”) temperature change, with climate feedbacks, from increased radiative forcing. No warranty express or implied as to their accuracy or usefulness, just explaining how to apply the climate sensitivity value correctly.

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Many readers of this blog would like progress towards the solution of the great questions in climate science. Other readers have stopped by still pondering the basics.

Some of those pondering the basics might have read many of the exciting claims on the internet that the “greenhouse” effect can’t exist because it would violate the 2nd law of thermodynamics.

It’s not a claim that you find in any books on atmospheric physics by the way, it’s strictly an “internet phenomenon”.

Just a few basics in case this is the first post you have read from this site.

The inappropriately named “greenhouse” effect can be summed up in a few sentences:

Longwave radiation from the earth’s surface is absorbed by many trace gases, including water vapor and CO2. The absorption causes these gases to heat up and energy is radiated back out – both up and down. The upward radiation is effectively “no change”. The downward radiation adds to the energy received from the sun and heats up the surface of the earth more than if this downward radiation did not occur.

If there was no absorption of radiation by “greenhouse” gases the surface of the earth would be a lot colder. Here is a very simplified graphic to draw people’s attention to the fact that “something big” is going on:

Upward Longwave Radiation, Numbers from Kiehl & Trenberth (1997)

(TOA = top of atmosphere). If there was no absorption and re-radiation back down the two numbers would be the same. (Note that the downward radiation is not shown to crystallize the issue)

These numbers are global annual averages under a clear sky. Under a cloudy sky the numbers are different but similar – and still the radiation from the surface of the earth is a lot greater than that leaving through the top of atmosphere. For more on this take a look at CO2 – An Insignificant Trace Gas? – Part Six – Visualization and the followup CO2 Can’t Have That Effect Because.. as well as the start of the series on CO2.

Many people have said that the numbers are obviously wrong, I’m mixing up solar radiation and longwave radiation, it can’t happen, the temperature varies a lot from equator to poles so that’s why the radiation numbers are wrong..

As one person said on another blog, possibly commenting on one of these earlier posts:

I even saw one where the guy had 100 watts/m² going into the atmosphere MORE than was coming out FOREVER.

Sharp-eyed readers might notice that I haven’t drawn in the downward radiation. Energy is balanced in the atmosphere because of the downward radiation from the atmosphere (not drawn). This is the “greenhouse” effect.

Onto the Imaginary Second Law of Thermodynamics

How can a colder atmosphere add heat to a warmer surface?

Can a candle warm the sun?

There are many popular restatements of the imaginary 2nd law. These two should be a representative sample. And so follows the Q.E.D. claim that the “greenhouse” effect plainly contradicts the second law of thermodynamics.

What is the second law?

The Real Second Law of Thermodynamics

My boring thermodynamics books and I have long since had a parting of the ways, so I looked it up on Wikipedia. Not a 100% reliable source, but the (real) second law is just as I remember it so I looked no further.

It’s possible that the imaginary second law has taken a strong hold because anyone who does look it up finds statements like dS/dt>=0, where S is entropy. Wow. Clever people. What’s entropy? How does this relate to candles? Candles can’t warm the sun, so I guess the second law has just proved the “greenhouse” effect wrong..

According to Wikipedia, Clausius expressed the second law (validly) like this:

Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature

Again, that seems right and it doesn’t have any entropy involved in the description. I never did like entropy. It never seemed real.

Perhaps this formulation has been the inspiration for the imaginary second law. As a not very precise definition many people might read this and think no energy at all can flow from a cold body to a hot body.

In fact, no net energy can flow from a cold body to a hot body.

In the case of the real “greenhouse” effect and the real 2nd law of thermodynamics, net energy is flowing from the earth to the atmosphere. But this doesn’t mean no energy can flow from the colder atmosphere to the warmer ground.

It simply means more energy flows from the warmer surface to the colder atmosphere than in the reverse direction.

Another likely reason the imaginary second law has become popular is most people are much more familiar with conduction of heat than radiation. Conduction of heat only appears to flow one way.

A Thought Experiment

We’ll do a thought experiment to demonstrate why the imaginary second law of thermodynamics is wrong. It’s simpler, safer, cheaper AND more reliable than assembling equipment. After all, we are going to look at radiation and if we do an experiment we would need to ensure that no convection or conduction was taking place.

And the thought experiment will, I hope, be more powerful. Plus it will have the added benefit for those already convinced by the beguiling imaginary second law that they can say “you haven’t proven anything, it’s all in your head” and so the popular imaginary law can live on.

In our thought experiment we will consider the sun. It’s hot. It doesn’t conduct or convect any heat outside its immediate surface because space is a vacuum and heat can only travel by radiation through a vacuum.

So energy is radiated out from the sun equally in all directions. At a 1000km distance from the sun, we get our measuring instrument out and find that energy radiated is 10,000W/m² (because I can’t be bothered to work out the actual number).

Now we fly in a cold large rock and park it at 1000km from the sun. Energy from the sun is absorbed on this cold rock and it heats up to some equilibrium value where it is also radiating out what it is receiving.

The temperature of this large once-cold rock is now a toasty 648K (375’C). All is well with both the real and imaginary formulations of the 2nd law, so far.

Now, from a galaxy far far away, we fly in a new star. Before we started moving it we checked the radiation 1000km away from the star and found that it was 11,000W/m². We are careful in our relocation of this star that nothing changes in its inner generation of radiation. The new star is parked 1000km away from the once-cold rock and 1000km away from the sun.

It’s a love triangle. Due to the new star’s welcome appearance, the rock heats up further. It now receives 21,000W/m². Its new equilibrium temperature is 780K. All is still well with both the real and imaginary formulations of the 2nd law.

Trouble in Paradise

But now a problem.. the new star is radiating out in all directions. Believers in the imaginary second law have no problem with the idea that the sun receives energy from the new star. After all the sun was a little colder.

But what about the sun? It is also radiating out in all directions. Or it was before the new star arrived.

Now that the new star is parked 1000km from the sun, squarely in the path of some portion of the sun’s radiation we have to ask ourselves what actually happens?

Believers in the real second law of thermodynamics are quite happy. No cognitive dissonance there. The energy from the sun which is incident on the new star’s surface actually increases the new star’s surface temperature compared with what it was before.

11,000W/m² are flowing from the new star to the sun, and 10,000W/m² are flowing from the sun to the new star. Some kind of new equilibrium might be reached, but for real second law believers there is no angst. The net flow of energy is from the hotter to the colder.

Believers in the imaginary second law, what happens?

One obvious suggestion is that the sun’s paltry 10,000W/m² which was flowing through that exact spot now divert around the new star as if it had some kind of force field. Perhaps all the energy lines completely redistribute so that (depending on the diameter of this new star) about 10,015W/m² flow in all directions except through the location of the new star.

Another obvious suggestion is that the sun “realizes” the new star is there and energy is flowing from the new star to it so just stops radiating in that exact direction. I put “realizes” in quotes of course because we all know the sun is not sentient. It’s just terminology. Some process that drives the imaginary second law will no doubt make this happen.

And the most likely suggestion of all is that this radiation from the sun, when it strikes the surface of the new star, just bounces off. Or is absorbed but doesn’t actually heat up the surface of the new star (unlike the inner radiation of this new star which does warm the surface from the inside).

Conclusion

I can’t help thinking that all my explanations for the imaginary second law have their own problems. And so I welcome explanations from promoters of the theory for the physical processes that take place near the surface of the new star.

Perhaps the problem is in the thought experiment itself. After all, you can’t just fly a star in from another galaxy and park it close to the sun. Barking mad!

And so the Imaginary Second Law of Thermodynamics lives on!

Update – the imaginary law also covered (possibly created by) On the Miseducation of the Uninformed by Gerlich and Tscheuschner (2009)

Update – a worked example with the maths, Radiation Basics and the Imaginary Second Law of Thermodynamics

Update – and more explanation with reference to one advocates explanation of this imaginary law, Intelligent Materials and the Imaginary Second Law of Thermodynamics

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