The Science of Doom

It is not surprising that the people most confused about basic physics are the ones who can’t write down an equation for their idea.

The same people are the most passionate defenders of their beliefs and I have no doubts about their sincerity.

I’ll meander into what it is I want to explain..

I found an amazing resource recently – iTunes U short for iTunes University. Now I confess that I have been a little confused about angular momentum. I always knew what it was, but in the small discussion that followed The Coriolis Effect and Geostrophic Motion I found myself wondering whether conservation of angular momentum was something independent of, or a consequence of, linear momentum or some aspect of Newton’s laws of motion.

It seemed as if conservation of angular momentum was an orphan of Newton’s three laws of motion. How could that be? Perhaps this conservation is just another expression of these laws in a way that I hadn’t appreciated? (Knowledgeable readers please explain).

Just around this time I found iTunes U and searched for “mechanics” and found the amazing series of lectures from MIT by Prof. Walter Lewin. A series of videos. I recommend them to anyone interested in learning some basics about forces, motion and energy. Lewin has a gift, along with an engaging style. It’s nice to see chalk boards and overhead projectors because they are probably no more in use (? young people please advise).

These lectures are not just for iPhone and iTunes people – here is the weblink.

The gift of teaching science is not in accuracy – that’s a given – the gift is in showing the principle via experiment and matching it with a theoretical derivation, and “why this should be so” and thereby producing a conceptual idea in the student.

I haven’t got to Lecture 20: Angular Momentum yet, I’m at about lecture 11. It’s basic stuff but so easy to forget (yes, quite a lot of it has been forgotten). Especially easy to forget how different principles link together and which principle is used to derive the next principle.

What caught my attention for the purposes of this article was how every principle had an equation.

For example, in deriving the work done on an object, Lewin integrates force over the distance traveled and comes up with the equation for kinetic energy.

While investigating the oscillation of a mass on a spring, the equation for its harmonic motion is derived.

Every principle has an equation that can be written down.

Over the last few days, as at many times over the past two years, people have arrived on this blog to explain how radiation from the atmosphere can’t affect the surface temperature because of blah blah blah. Where blah blah blah sounds like it might be some kind of physics but is never accompanied by an equation.

Here’s the equation I find in textbooks.

Energy absorbed from the atmosphere by the surface, E_a:

E_a = αR_L↓ ….[eqn 1]

where α = absorptivity of the surface at these wavelengths, R_L↓ = downward radiation from the atmosphere

And this energy absorbed, once absorbed, is indistinguishable from the energy absorbed from the sun. 1 W/m² absorbed from the atmosphere is identical to 1 W/m² absorbed from the sun.

That’s my equation. I have provided six textbooks to explain this idea in a slightly different way in Amazing Things we Find in Textbooks – The Real Second Law of Thermodynamics.

It’s also produced by Kramm & Dlugi, who think the greenhouse effect is some unproven idea:

Now the equation shown is a pretty simple equation. The equation reproduced in the graphic above from Kramm & Dlugi looks a little more daunting but is simply adding up a number of fluxes at the surface.

Here’s what it says:

Solar radiation absorbed + longwave radiation absorbed – thermal radiation emitted – latent heat emitted – sensible heat emitted + geothermal energy supplied = 0

Or another way of thinking about it is energy in = energy out (written as “energy in – energy out = 0“)

Now one thing is not amazing to me –  of the tens (hundreds?) of concerned citizens commenting on the many articles on this subject who have tried to point out my “basic mistake” and tell me that the atmosphere can’t blah blah blah, not a single one has produced an equation.

The equation might look something like this:

E_a = f(α,T_atm-T_sur).R_L↓ ….[eqn 2]
where T_atm = temperature of the atmosphere, T_sur = temperature of the surface

With the function f being defined like this:

f(α,T_atm-T_sur) = α, when T_atm ≥ T_sur and

f(α,T_atm-T_sur) = 0, when T_atm < T_sur

In English, it says something like energy from the atmosphere absorbed by the surface = 0 when the temperature of the atmosphere is less than the temperature of the surface.

I’m filling in the blanks here. No one has written down such ridiculous unphysical nonsense because it would look like ridiculous unphysical nonsense. Or perhaps I’m being unkind. Another possibility is that no one has written down such ridiculous unphysical nonsense because the proponents have no idea what an equation is, or how one can be constructed.

My Prediction

No one will produce an equation which shows how no atmospheric energy can be absorbed by the surface. Or how atmospheric energy absorbed cannot affect internal energy.

This is because my next questions will be:

1. Please supply a textbook or paper with this equation
2. Please explain from fundamental physics how this can take place

My Challenge

Here’s my challenge to the many people concerned about the “dangerous nonsense” of the atmospheric radiation affecting surface temperature –

Supply an equation.

If you can’t, it is because you don’t understand the subject.

It won’t stop you talking, but everyone who is wondering and reads this article will be able to join the dots together.

The Usual Caveat

If there were only two bodies – the warmer earth and the colder atmosphere (no sun available) – then of course the earth’s temperature would decrease towards that of the atmosphere and the atmosphere’s temperature would increase towards that of the earth until both were at the same temperature – somewhere between the two starting temperatures.

However, the sun does actually exist and the question is simply whether the presence of the (colder) atmosphere affects the surface temperature compared with if no atmosphere existed. It is The Three Body Problem.

My Second Prediction

The people not supplying the equation, the passionate believers in blah blah blah, will not explain why an equation is not necessary or not available. Instead, continue to blah blah blah.

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In Kramm & Dlugi On Illuminating the Confusion of the Unclear I pointed out that the authors of Scrutinizing the atmospheric greenhouse effect and its climatic impact are in agreement with climate science on the subject of “back radiation” from the atmosphere contributing to the surface temperature.

No surprise to people familiar with the basics of radiative heat transfer. However, Kramm & Dlugi are apparently “in support of” Gerlich & Tscheuschner, who famously proposed that radiation from the atmosphere affecting the temperature of the ground was a violation of the second law of thermodynamics. A perpetual motion machine or something. (Or they were having a big laugh). For more on the exciting adventures of Gerlich & Tscheuschner, read On the Miseducation of the Uninformed..

The first article on the Kramm & Dlugi paper was short, highlighting that one essential point.

Given the enthusiasm that new papers which “cast doubt” on the inappropriately-named “greenhouse” effect are lapped up by the blogosphere, I thought it was worth explaining a few things from their complete paper.

If I sum it up in simple terms, it is a paper which will annoy climate scientists and add confusion to scientifically less clear folk who wonder about the “greenhouse” effect.

And mostly, I have to say, without actually being wrong – or not technically wrong (note 1). This is its genius. Let’s see how they “dodge the bullet” of apparently slaying the “greenhouse” effect without actually contradicting anything of real significance in climate science.

Goody & Yung’s Big Mistake

Regular readers of this blog will know that I have a huge respect for Richard M. Goody, who wrote the seminal Atmospheric Radiation: Theoretical Basis in 1964. (The 2nd edition from 1989 is coauthored by Goody & Yung).

However, they have a mistake in a graph on p.4:

Kramm & Dlugi say:

..This figure also shows the atmospheric absorption spectrum for a solar beam reaching the ground level (b) and the same for a beam reaching the temperate tropopause (c) adopted from Goody and Yung [30]. Part (a) of Figure 5 completely differs from the original twin-peak diagram of Goody and Yung. We share the argument of Gerlich and Tscheuschner [2,4] that the original one is physically misleading..

I have the same argument about this one graph from Goody & Yung’s textbook. You can see my equivalent graph in 4th & 5th figures of The Sun and Max Planck Agree – Part Two.

There is nothing in the development of theory by Goody & Yung that depends on this graph. Kramm & Dlugi don’t demonstrate anything else in error from Goody & Yung. However, I’m sure that someone who wants to devote enough time to the subject will probably find another error in their book, or at least, an incautious statement that could imply that they have carelessly tossed away their knowledge of basic physics. This is left as an exercise for the interested reader..

To clarify the idea for readers – the energy emitted by the climate system to space is approximately equal to the energy absorbed from the sun by the climate system. This is not in dispute.

Kramm & Dlugi point out that one should be careful when attempting to plot equal areas on logarithmic graphs. Nice point.

Kepler & Milankovitch

Kramm & Dugli spend some time deriving the equations of planetary motion. These had been lost by climate science so it is good to see them recovered.

They also comment on Milankovitch’s theory in terms that are interesting:

Thus, on long-term scales of many thousands of years (expressed in kyr) we have to pay attention to Milankovitch’s [33] astronomical theory of climatic variations that ranks as the most important achievement in the theory of climate in the 20th century [10].

The theory definitely has a lot of mainstream support as being the explanation for the ice ages. However, as a comment to be developed one day when I understand enough to write about it, there isn’t one Milankovitch theory, there are many, and of necessity they contradict each other.

Interesting as well to suggest it as the most important achievement in the theory of climate last century – as the consequence of accepting Milankovitch’s theory is that climate is very sensitive to small peturbations in radiative changes in particular regions at particular times. In essence, the Milankovitch theory appears to rely on quite a high climate sensitivity.

Anyway, I’m not criticizing Kramm & Dugli or saying they are wrong. It’s just an interesting comment. And excellent that Kepler’s theories are no longer lost to the world of climate science.

Energy Conversion in the Atmosphere & at the Surface

The authors devote some time to this study (with no apparent differences to standard climate science) with the conclusion:

..Note that the local flux quantities like Q(θ, φ), H(θ, φ), G(θ, φ) and R_L↑(θ, φ) are required to calculate global averages of these fluxes, but not global averages of respective values of temperature and humidity.

An important point.

They also confirm – as noted in Kramm & Dlugi On Illuminating the Confusion of the Unclear – that the energy balance at the surface is affected by the energy radiated by the atmosphere. Just helping out the many blog writers and blog commenters – be sure to strike Kramm & Dlugi off your list of advocates of the imaginary second law of thermodynamics.

The Gulags for Everyone? – Climatology Loses Its Rational Basis

The authors cite this extract from the WMO website about the “greenhouse” effect:

In the atmosphere, not all radiation emitted by the Earth surface reaches the outer space. Part of it is reflected back to the Earth surface by the atmosphere (greenhouse effect) leading to a global average temperature of about 14°C well above –19°C which would have been felt without this effect.

This website statement is incorrect as the radiation emitted by the Earth’s surface is absorbed and re-emitted by the atmosphere – not reflected. This is a very basic error.

Kramm & Dlugi say:

Note that the argument that “part of it is reflected back to the Earth surface by the atmosphere” is completely irrational from a physical point of view. Such an argument also indicates that the discipline of climatology has lost its rational basis. Thus, the explanation of the WMO is rejected..

[Emphasis added]

Well, we could argue that if one person writing a website for one body writes one thing that is not technically correct then that whole discipline has lost its rational basis. We could.

Seems uncharitable to me. Although I have to confess that on occasion I am a little bit uncharitable. I wrote that Gerlich & Tscheuschner had lost their marbles, or were having a big laugh, with their many ridiculous and unfounded statements. We all have our off days.

I think if we want to uphold high standards of defendable technical accuracy we would say that the person that wrote this website and the person that reviewed this website are not technically sound as far as the specifics of radiative physics go. I’m hard pressed to think it is justified to cast stones at say Prof. Richard M Goody for this particular travesty. Or Prof. R. Lindzen. Or Prof. V. Ramanathan. Or Prof. F.W. Taylor. Otherwise it might be a bit like Stalin with the Gulag. Everyone and their mother gets tarred with the sins of the fellow down the road and 30 million people wind up digging rocks out of the ground in a very cold place..

But let’s stay on topic. If indeed there is one.

The Main Point

Now that we have found a graph in Goody that is wrong, a website that has a mistake and have rediscovered Kepler’s equations of motion, we turn to the main course.

Kramm & Dlugi turn to perhaps their main point, about the surface temperature of the earth with and without radiatively-active gases.

As a clarification for newcomers, average temperature has many problems. Due to the non-linearity of radiative physics, if we calculate the average radiation from the average temperature we will get a different answer compared with calculating the radiation from the temperature at each location/time and then taking the average.

For more on this basic topic see under the subheading How to Average in Why Global Mean Surface Temperature Should be Relegated, Or Mostly Ignored

First citing Lacis et al:

The difference between the nominal global mean surface temperature (TS = 288 K) and the global mean effective temperature (TE = 255 K) is a common measure of the terrestrial greenhouse effect (GT = TS – TE = 33 K).

The authors develop some maths, of which this is just a sample:

Using Eq. 3.8 and ignoring G(θ,φ) will lead to:

<T_s> = 2^3/2T_e/5 ≈ 144K (3.9)

for a non-rotating Earth in the absence of its atmosphere, if S = 1367 W/m² , α (Θ₀, θ, φ) = α_E = 0.30 and ε(θ, φ) = ε = 1 are assumed [2]

T_s = 153 K if α_E = 0.12 and T_s = 155 K if α_E = 0.07

It might surprise readers that these particular points are not something novel or in contradiction to the “greenhouse” effect. In fact, you can see similar points in two articles (at least) on this blog:

– In The Hoover Incident we had a look at what would happen to the climate if all the radiatively-active gases (= “greenhouse” gases) were removed from the atmosphere. Here is an extract:

..And depending on the ice sheet extent and whether any clouds still existed the value of outgoing radiation might be around 1.0 – 1.5 x 10¹⁷ W. This upper value would depend on the ice sheets not growing and all the clouds disappearing which seems impossible, but it’s just for illustration.

Remember that nothing in all this time can stop the emitted radiation from the surface making it to space. So the only changes in the energy balance can come from changes to the earth’s albedo (affecting absorbed solar radiation).

And given that when objects emit more energy than they absorb they cool down, the earth will certainly cool. The atmosphere cannot emit any radiation so any atmospheric changes will only change the distribution of energy around the climate system.

What would the temperature of the earth be? I have no idea..

Notice the heresy that without “greenhouse” gases we can’t say for sure what the surface temperature would be.. (It’s definitely going to be significantly lower though).

– In Atmospheric Radiation and the “Greenhouse” Effect – Part One:

..The average for 2009 [of outgoing longwave radiation] is 239 W/m². This average includes days, nights and weekends. The average can be converted to the total energy emitted from the climate system over a year like this:

Total energy radiated by the climate system into space in one year = 239 x number of seconds in a year x area of the earth in meters squared..

E_TOA= 3.8 x 10²⁴ J

The reason for calculating the total energy in 2009 is because many people have realized that there is a problem with average temperatures and imagine that this problem is carried over to average radiation. Not true. We can take average radiation and convert it into total energy with no problem..

[Emphasis added]

The point here is that the total emitted top of atmosphere radiation is much lower than the total surface emitted radiation. It can be calculated. In that article I haven’t actually attempted to do it accurately – it would require some work (spatial and temporal temperature across a year and the longwave emissivity of the surface around the globe) – it is a straightforward yet tedious calculation. (See note 2).

A note in passing that this difference between the top of atmosphere radiation and the surface radiation is also derided by the internet imaginary second law advocates as being a physical impossibility because it “creates energy”.

Now I am not in any way a “representative of climate science” despite the many claims to this effect, it’s just that the basics are.. the basics. And radiative transfer in the atmosphere is a technical yet simple subject which can be easily solved with the aid of some decent computing power. So I have no quarrel with anything of substance that I have so far read in textbooks or papers on radiative physics. Yet I appear to have stated similar points to Kramm & Dlugi.

Perhaps Kramm & Dlugi have not yet stated anything controversial on the inappropriately-named “greenhouse” effect.

They take issue with what I would call the “introduction to the greenhouse effect” where a simple comparison is drawn. This is where the “greenhouse” effect is highlighted as “effective temperature”.

It could more accurately be highlighted as “difference in average flux between surface and TOA” or “difference in total flux between surface and TOA”

Is it of consequence to anything in climate science if we agreed that the difference between the TOA radiation to space and the upward surface radiation is a better measure of the “greenhouse” effect?

Kramm & Dlugi comment on a paper by Ramanathan et al:

“At a surface temperature of 288 K the long-wave emission by the surface is about 390 W/m², whereas the outgoing long-wave radiation at the top of the atmosphere is only 236 W/m² (see Figure 2 [here presented as Figure 17]). Thus the intervening atmosphere causes a significant reduction in the long-wave emission to space. This reduction in the long-wave emission to space is referred to as the greenhouse effect”

As discussed before, applying the power law of Stefan and Boltzmann to a globally averaged temperature cannot be justified by physical and mathematical reasons.

Thus, the argument that at a surface temperature of 288 K the long-wave emission by the surface is about 390 W/m² is meaningless.

Just for interest here is how Ramanathan et al described their paper:

The two primary objectives of this review paper are (1) to describe the new scientific challenges posed by the trace gas climate problem and to summarize current strategies for meeting these challenges and (2) to make an assessment 0f the trace gas effects on troposphere-stratosphere temperature trends for the period covering the pre-industrial era to the present and for the next several decades. We will rely heavily on the numerous reports..

We could assume they don’t understand science basics, despite their many excellent papers demonstrating otherwise. Or we could assume that someone writing their 100th paper in the field of climate science doesn’t need to demonstrate that something called the “greenhouse” effect exists, or quantify it accurately in some specific way unless that is necessary for the specific purpose of the paper.

However, this is the genius of Kramm & Dlugi’s paper..

Dodging the Bullet

Casual readers of this paper (and people who rely on the statements of others about this paper) might think that they had demonstrated that the “greenhouse” effect doesn’t exist. They make a claim in their conclusion, of course, but they haven’t proven anything of the sort.

Instead they have written a paper explaining what everyone in climate science already knows.

So, to clarify matters, what is the emission of radiation from the top of atmosphere to space in one year?

E_TOA= 3.8 x 10²⁴ J

What is the emission of radiation from the surface in one year?

E_surface = ?

My questions to Kramm & Dlugi:

Is  E_surface significantly greater than E_TOA ?

Obviously I believe Kramm & Dlugi will answer “Yes” to this question. This confirms the existence of the greenhouse effect, which they haven’t actually disputed except in their few words at the conclusion of their paper.

Hopefully, the authors will show up and confirm these important points.

Conclusion

The authors have shown us:

• that a graph in the seminal Goody & Yung textbook is wrong
• Kepler’s laws of planetary motion
• that a website describes the “greenhouse” effect inaccurately
• that without any “greenhouse” gases the effective albedo of the earth would be different
• the average temperature of the earth’s surface can’t be used to calculate the average upward surface radiation

However, the important calculations of “radiative forcing” and various effects of increasing concentrations of radiatively-active gases are all done without using the “33K greenhouse effect”.

Without using the 33K “greenhouse” effect, we can derive all the equations of radiative transfer, solve them using the data for atmospheric temperature profiles, concentration of “greenhouse” gases, spectral line data from the HITRAN database and get:

• the correct flux and spectral intensity at top of atmosphere
• the correct flux and spectral intensity of downward radiation at the surface

We can also do this for changes in concentrations of various gases and find out the changes in top of atmosphere and downward surface flux. (Feedback and natural climate variations are the tricky part).

The discussions about average temperature are an amusing sideshow.

They are of no consequence for deriving the “greenhouse” effect or for determining the changes that might take place in the climate from increases or decreases in these gases.

Notes

Note 1: I didn’t check everything, so there could be mistakes. As the full article makes clear, not much need to check. I don’t endorse their last paragraph, as my conclusion – and article – makes clear.

Note 2: The calculation in that article for total annual global surface radiation doesn’t take into account surface emissivity. The value of ocean emissivity is incorrectly stated (see Emissivity of the Ocean). There are probably numerous other errors which I will fix one day if someone points them out.

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Many people are confused about science basics when it comes to the inappropriately-named “greenhouse” effect.

This can be easily demonstrated in many blogs around the internet where commenters, and even blog owners, embrace multiple theories that contradict each other but are somehow against the “greenhouse” effect.

Recently a new paper: Scrutinizing the atmospheric greenhouse effect and its climatic impact by Gerhard Kramm & Ralph Dlugi was published in the journal Natural Science.

Because of their favorable comments about Gerlich & Tscheuschner and the fact that they are sort of against something called the “greenhouse” effect I thought it might be useful for many readers to find out what was actually in the paper and what Kramm & Dlugi actually do believe about the “greenhouse” effect.

Much of the comments on blogs about the “greenhouse” effect are centered around the idea that this effect cannot be true because it would somehow violate the second law of thermodynamics. If there was a scientific idea in Gerlich & Tscheuschner, this was probably the main one. Or at least the most celebrated.

So it might surprise readers who haven’t opened up this paper that the authors are thoroughly 100% with mainstream climate science (and heat transfer basics) on this topic.

It didn’t surprise me because before reading this paper I read another paper by Kramm – A case study on wintertime inversions in Interior Alaska with WRF, Mölders & Kramm, Atmospheric Research (2010).

This 2010 paper is very interesting and evaluates models vs observations of the temperature inversions that take place in polar climates (where the temperature at the ground in wintertime is cooler than the atmosphere above). Nothing revolutionary (as with 99.99% of papers) and so of course the model used includes a radiation scheme from CAM3 (=Community Atmospheric Model) that is well used in standard climate science modeling.

Here is an important equation from Kramm & Dlugi’s recent paper for the energy balance at the earth’s surface.

Lots of blogs “against the greenhouse effect” don’t believe this equation:

Figure 1

The highlighted term is the downward radiation from the atmosphere multiplied by the absorptivity of the earth’s surface (its ability to absorb the radiation). This downward radiation (DLR) has also become known as “back radiation”.

In simple terms, the energy balance of Kramm & Dlugi adds up the absorbed portions of the solar radiation and atmospheric longwave radiation and equates them to the emitted longwave radiation plus the latent and sensible heat.

So the temperature of the surface is determined by solar radiation and “back radiation” and both are treated equally. It is also determined of course by the latent and sensible heat flux. (And see note 1).

As so many people on blogs around the internet believe this idea violates the second law of thermodynamics I thought it would be helpful to these readers to let them know to put Kramm & Dlugi 2011 on their “wrong about the 2nd law” list.

Of course, many people “against the greenhouse thing” also – or alternatively – believe that “back radiation” is negligible. Yet Kramm & Dlugi reproduce the standard diagram from Trenberth, Fasullo & Kiehl (2009) and don’t make any claim about “back radiation” being different in value from this paper.

“Back radiation” is real, measurable and affects the temperature of the surface – clearly Kramm & Dlugi are AGW wolves in sheeps’ clothing!

I look forward to the forthcoming rebuttal by Gerlich & Tscheuschner.

In the followup article, Kramm & Dlugi On Dodging the “Greenhouse” Bullet, I will attempt to point out the actual items of consequence from their paper.

Further reading –  Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part One and New Theory Proves AGW Wrong!

Note 1 – The surface energy balance isn’t what ultimately determines the surface temperature. The actual inappropriately-named “greenhouse” effect is determined by:

• the effective emission height to space of outgoing longwave radiation which is determined by the opacity of the atmosphere (for example, due to increases in CO2 or water vapor)
• the temperature difference between the surface and the effective emission height which is determined by the lapse rate

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