Archive for the ‘Basic Science’ Category

In The “Greenhouse” Effect Explained in Simple Terms I list, and briefly explain, the main items that create the “greenhouse” effect. I also explain why more CO2 (and other GHGs) will, all other things remaining equal, increase the surface temperature. I recommend that article as the place to go for the straightforward explanation of the “greenhouse” effect. It also highlights that the radiative balance higher up in the troposphere is the most important component of the “greenhouse” effect.

However, someone recently commented on my first Kramm & Dlugi article and said I was “plainly wrong”. Kramm & Dlugi were in complete agreement with Gerlich and Tscheuschner because they both claim the “purported greenhouse effect simply doesn’t exist in the real world”.

If it’s just about flying a flag or wearing a football jersey then I couldn’t agree more. However, science does rely on tedious detail and “facts” rather than football jerseys. As I pointed out in New Theory Proves AGW Wrong! two contradictory theories don’t add up to two theories making the same case..

In the case of the first Kramm & Dlugi article I highlighted one point only. It wasn’t their main point. It wasn’t their minor point. They weren’t even making a point of it at all.

Many people believe the “greenhouse” effect violates the second law of thermodynamics, these are herein called “the illuminati”.

Kramm & Dlugi’s equation demonstrates that the illuminati are wrong. I thought this was worth pointing out.

The “illuminati” don’t understand entropy, can’t provide an equation for entropy, or even demonstrate the flaw in the simplest example of why the greenhouse effect is not in violation of the second law of thermodynamics. Therefore, it is necessary to highlight the (published) disagreement between celebrated champions of the illuminati – even if their demonstration of the disagreement was unintentional.

Let’s take a look.

Here is the one of the most popular G&T graphics in the blogosphere:

From Gerlich & Tscheuschner

From Gerlich & Tscheuschner

Figure 1

It’s difficult to know how to criticize an imaginary diagram. We could, for example, point out that it is imaginary. But that would be picky.

We could say that no one draws this diagram in atmospheric physics. That should be sufficient. But as so many of the illuminati have learnt their application of the second law of thermodynamics to the atmosphere from this fictitious diagram I feel the need to press forward a little.

Here is an extract from a widely-used undergraduate textbook on heat transfer, with a little annotation (red & blue):

From Incropera & DeWitt (2007)

From “Fundamentals of Heat and Mass Transfer” by Incropera & DeWitt (2007)

Figure 2

This is the actual textbook, before the Gerlich manoeuvre as I would like to describe it. We can see in the diagram and in the text that radiation travels both ways and there is a net transfer which is from the hotter to the colder. The term “net” is not really capable of being confused. It means one minus the other, “x-y”. Not “x”. (For extracts from six heat transfer textbooks and their equations read Amazing Things we Find in Textbooks – The Real Second Law of Thermodynamics).

Now let’s apply the Gerlich manoeuvre (compare fig. 2):


Not from “Fundamentals of Heat and Mass Transfer”, or from any textbook ever

Figure 3

So hopefully that’s clear. Proof by parody. This is “now” a perpetual motion machine and so heat transfer textbooks are wrong. All of them. Somehow.

Just for comparison, we can review the globally annually averaged values of energy transfer in the atmosphere, including radiation, from Kiehl & Trenberth (I use the 1997 version because it is so familiar even though values were updated more recently):

From Kiehl & Trenberth (1997)

From Kiehl & Trenberth (1997)

Figure 4

It should be clear that the radiation from the hotter surface is higher than the radiation from the colder atmosphere. If anyone wants this explained, please ask.

I could apply the Gerlich manoeuvre to this diagram but they’ve already done that in their paper (as shown above in figure 1).

So lastly, we return to Kramm & Dlugi, and their “not even tiny point”, which nevertheless makes a useful point. They don’t provide a diagram, they provide an equation for energy balance at the surface – and I highlight each term in the equation to assist the less mathematically inclined:



Figure 5

The equation says, the sum of all fluxes – at one point on the surface = 0. This is an application of the famous first law of thermodynamics, that is, energy cannot be created or destroyed.

The red term – absorbed atmospheric radiation – is the radiation from the colder atmosphere absorbed by the hotter surface. This is also known as “DLR” or “downward longwave radiation, and as “back-radiation”.

Now, let’s assume that the atmospheric radiation increases in intensity over a small period. What happens?

The only way this equation can continue to be true is for one or more of the last 4 terms to increase.

  • The emitted surface radiation – can only increase if the surface temperature increases
  • The latent heat transfer – can only increase if there is an increase in wind speed or in the humidity differential between the surface and the atmosphere just above
  • The sensible heat transfer – can only increase if there is an increase in wind speed or in the temperature differential between the surface and the atmosphere just above
  • The heat transfer into the ground – can only increase if the surface temperature increases or the temperature below ground spontaneously cools

So, when atmospheric radiation increases the surface temperature must increase (or amazingly the humidity differential spontaneously increases to balance, but without a surface temperature change). According to G&T and the illuminati this surface temperature increase is impossible. According to Kramm & Dlugi, this is inevitable.

I would love it for Gerlich or Tscheuschner to show up and confirm (or deny?):

  • yes the atmosphere does emit thermal radiation
  • yes the surface of the earth does absorb atmospheric thermal radiation
  • yes this energy does not disappear (1st law of thermodynamics)
  • yes this energy must increase the temperature of the earth’s surface above what it would be if this radiation did not exist (1st law of thermodynamics)

Or even, which one of the above is wrong. That would be outstanding.

Of course, I know they won’t do that – even though I’m certain they believe all of the above points. (Likewise, Kramm & Dlugi won’t answer the question I have posed of them).

Well, we all know why

Hopefully, the illuminati can contact Kramm & Dlugi and explain to them where they went wrong. I have my doubts that any of the illuminati have grasped the first law of thermodynamics or the equation for temperature change and heat capacity, but who could say.

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Over the last few years I’ve written lots of articles relating to the inappropriately-named “greenhouse” effect and covered some topics in great depth. I’ve also seen lots of comments and questions which has helped me understand common confusion and misunderstandings.

This article, with huge apologies to regular long-suffering readers, covers familiar ground in simple terms. It’s a reference article. I’ve referenced other articles and series as places to go to understand a particular topic in more detail.

One of the challenges of writing a short simple explanation is it opens you up to the criticism of having omitted important technical details that you left out in order to keep it short. Remember this is the simple version..


First of all, the “greenhouse” effect is not AGW. In maths, physics, engineering and other hard sciences, one block is built upon another block. AGW is built upon the “greenhouse” effect. If AGW is wrong, it doesn’t invalidate the greenhouse effect. If the greenhouse effect is wrong, it does invalidate AGW.

The greenhouse effect is built on very basic physics, proven for 100 years or so, that is not in any dispute in scientific circles. Fantasy climate blogs of course do dispute it.

Second, common experience of linearity in everyday life cause many people to question how a tiny proportion of “radiatively-active” molecules can have such a profound effect. Common experience is not a useful guide. Non-linearity is the norm in real science. Since the enlightenment at least, scientists have measured things rather than just assumed consequences based on everyday experience.

The Elements of the “Greenhouse” Effect

Atmospheric Absorption

1. The “radiatively-active” gases in the atmosphere:

  • water vapor
  • CO2
  • CH4
  • N2O
  • O3
  • and others

absorb radiation from the surface and transfer this energy via collision to the local atmosphere. Oxygen and nitrogen absorb such a tiny amount of terrestrial radiation that even though they constitute an overwhelming proportion of the atmosphere their radiative influence is insignificant (note 1).

How do we know all this? It’s basic spectroscopy, as detailed in exciting journals like the Journal of Quantitative Spectroscopy and Radiative Transfer over many decades. Shine radiation of a specific wavelength through a gas and measure the absorption. Simple stuff and irrefutable.

Atmospheric Emission

2. The “radiatively-active” gases in the atmosphere also emit radiation. Gases that absorb at a wavelength also emit at that wavelength. Gases that don’t absorb at that wavelength don’t emit at that wavelength. This is a consequence of Kirchhoff’s law.

The intensity of emission of radiation from a local portion of the atmosphere is set by the atmospheric emissivity and the temperature.


3. The transfer of heat within the troposphere is mostly by convection. The sun heats the surface of the earth through the (mostly) transparent atmosphere (note 2). The temperature profile, known as the “lapse rate”, is around 6K/km in the tropics. The lapse rate is principally determined by non-radiative factors – as a parcel of air ascends it expands into the lower pressure and cools during that expansion (note 3).

The important point is that the atmosphere is cooler the higher you go (within the troposphere).

Energy Balance

4. The overall energy in the climate system is determined by the absorbed solar radiation and the emitted radiation from the climate system. The absorbed solar radiation – globally annually averaged – is approximately 240 W/m² (note 4). Unsurprisingly, the emitted radiation from the climate system is also (globally annually averaged) approximately 240 W/m². Any change in this and the climate is cooling or warming.

Emission to Space

5. Most of the emission of radiation to space by the climate system is from the atmosphere, not from the surface of the earth. This is a key element of the “greenhouse” effect. The intensity of emission depends on the local atmosphere. So the temperature of the atmosphere from which the emission originates determines the amount of radiation.

If the place of emission of radiation – on average – moves upward for some reason then the intensity decreases. Why? Because it is cooler the higher up you go in the troposphere. Likewise, if the place of emission – on average – moves downward for some reason, then the intensity increases (note 5).

More GHGs

6. If we add more radiatively-active gases (like water vapor and CO2) then the atmosphere becomes more “opaque” to terrestrial radiation and the consequence is the emission to space from the atmosphere moves higher up (on average). Higher up is colder. See note 6.

So this reduces the intensity of emission of radiation, which reduces the outgoing radiation, which therefore adds energy into the climate system. And so the climate system warms (see note 7).

That’s it!

It’s as simple as that. The end.

A Few Common Questions

CO2 is Already Saturated

There are almost 315,000 individual absorption lines for CO2 recorded in the HITRAN database. Some absorption lines are stronger than others. At the strongest point of absorption – 14.98 μm (667.5 cm-1), 95% of radiation is absorbed in only 1m of the atmosphere (at standard temperature and pressure at the surface). That’s pretty impressive.

By contrast, from 570 – 600 cm-1 (16.7 – 17.5 μm) and 730 – 770 cm-1 (13.0 – 13.7 μm) the CO2 absorption through the atmosphere is nowhere near “saturated”. It’s more like 30% absorbed through a 1km path.

You can see the complexity of these results in many graphs in Atmospheric Radiation and the “Greenhouse” Effect – Part Nine – calculations of CO2 transmittance vs wavelength in the atmosphere using the 300,000 absorption lines from the HITRAN database, and see also Part Eight – interesting actual absorption values of CO2 in the atmosphere from Grant Petty’s book

The complete result combining absorption and emission is calculated in Visualizing Atmospheric Radiation – Part Seven – CO2 increases – changes to TOA in flux and spectrum as CO2 concentration is increased

CO2 Can’t Absorb Anything of Note Because it is Only .04% of the Atmosphere

See the point above. Many spectroscopy professionals have measured the absorptivity of CO2. It has a huge variability in absorption, but the most impressive is that 95% of 14.98 μm radiation is absorbed in just 1m. How can that happen? Are spectroscopy professionals charlatans? You need evidence, not incredulity. Science involves measuring things and this has definitely been done. See the HITRAN database.

Water Vapor Overwhelms CO2

This is an interesting point, although not correct when we consider energy balance for the climate. See Visualizing Atmospheric Radiation – Part Four – Water Vapor – results of surface (downward) radiation and upward radiation at TOA as water vapor is changed.

The key point behind all the detail is that the top of atmosphere radiation change (as CO2 changes) is the important one. The surface change (forcing) from increasing CO2 is not important, is definitely much weaker and is often insignificant. Surface radiation changes from CO2 will, in many cases, be overwhelmed by water vapor.

Water vapor does not overwhelm CO2 high up in the atmosphere because there is very little water vapor there – and the radiative effect of water vapor is dramatically impacted by its concentration, due to the “water vapor continuum”.

The Calculation of the “Greenhouse” Effect is based on “Average Surface Temperature” and there is No Such Thing

Simplified calculations of the “greenhouse” effect use some averages to make some points. They help to create a conceptual model.

Real calculations, using the equations of radiative transfer, don’t use an “average” surface temperature and don’t rely on a 33K “greenhouse” effect. Would the temperature decrease 33K if all of the GHGs were removed from the atmosphere? Almost certainly not. Because of feedbacks. We don’t know the effect of all of the feedbacks. But would the climate be colder? Definitely.

See The Rotational Effect – why the rotation of the earth has absolutely no effect on climate, or so a parody article explains..

The Second Law of Thermodynamics Prohibits the Greenhouse Effect, or so some Physicists Demonstrated..

See The Three Body Problem – a simple example with three bodies to demonstrate how a “with atmosphere” earth vs a “without atmosphere earth” will generate different equilibrium temperatures. Please review the entropy calculations and explain (you will be the first) where they are wrong or perhaps, or perhaps explain why entropy doesn’t matter (and revolutionize the field).

See Gerlich & Tscheuschner for the switch and bait routine by this operatic duo.

And see Kramm & Dlugi On Dodging the “Greenhouse” Bullet – Kramm & Dlugi demonstrate that the “greenhouse” effect doesn’t exist by writing a few words in a conclusion but carefully dodging the actual main point throughout their entire paper. However, they do recover Kepler’s laws and point out a few errors in a few websites. And note that one of the authors kindly showed up to comment on this article but never answered the important question asked of him. Probably just too busy.. Kramm & Dlugi also helpfully (unintentionally) explain that G&T were wrong, see Kramm & Dlugi On Illuminating the Confusion of the Unclear – Kramm & Dlugi step up as skeptics of the “greenhouse” effect, fans of Gerlich & Tscheuschner and yet clarify that colder atmospheric radiation is absorbed by the warmer earth..

And for more on that exciting subject, see Confusion over the Basics under the sub-heading The Second Law of Thermodynamics.

Feedbacks overwhelm the Greenhouse Effect

This is a totally different question. The “greenhouse” effect is the “greenhouse” effect. If the effect of more CO2 is totally countered by some feedback then that will be wonderful. But that is actually nothing to do with the “greenhouse” effect. It would be a consequence of increasing temperature.

As noted in the preamble, it is important to separate out the different building blocks in understanding climate.

Miskolczi proved that the Greenhouse Effect has no Effect

Miskolczi claimed that the greenhouse effect was true. He also claimed that more CO2 was balanced out by a corresponding decrease in water vapor. See the Miskolczi series for a tedious refutation of his paper that was based on imaginary laws of thermodynamics and questionable experimental evidence.

Once again, it is important to be able to separate out two ideas. Is the greenhouse effect false? Or is the greenhouse effect true but wiped out by a feedback?

If you don’t care, so long as you get the right result you will be in ‘good’ company (well, you will join an extremely large company of people). But this blog is about science. Not wishful thinking. Don’t mix the two up..

Convection “Short-Circuits” the Greenhouse Effect

Let’s assume that regardless of the amount of energy arriving at the earth’s surface, that the lapse rate stays constant and so the more heat arriving, the more heat leaves. That is, the temperature profile stays constant. (It’s a questionable assumption that also impacts the AGW question).

It doesn’t change the fact that with more GHGs, the radiation to space will be from a higher altitude. A higher altitude will be colder. Less radiation to space and so the climate warms – even with this “short-circuit”.

In a climate without convection, the surface temperature will start off higher, and the GHG effect from doubling CO2 will be higher. See Radiative Atmospheres with no Convection.

In summary, this isn’t an argument against the greenhouse effect, this is possibly an argument about feedbacks. The issue about feedbacks is a critical question in AGW, not a critical question for the “greenhouse” effect. Who can say whether the lapse rate will be constant in a warmer world?


Note 1 – An important exception is O2 absorbing solar radiation high up above the troposphere (lower atmosphere). But O2 does not absorb significant amounts of terrestrial radiation.

Note 2 – 99% of solar radiation has a wavelength <4μm. In these wavelengths, actually about 1/3 of solar radiation is absorbed in the atmosphere. By contrast, most of the terrestrial radiation, with a wavelength >4μm, is absorbed in the atmosphere.

Note 3 – see:

Density, Stability and Motion in Fluids – some basics about instability
Potential Temperature – explaining “potential temperature” and why the “potential temperature” increases with altitude
Temperature Profile in the Atmosphere – The Lapse Rate – lots more about the temperature profile in the atmosphere

Note 4 – see Earth’s Energy Budget – a series on the basics of the energy budget

Note 5 – the “place of emission” is a useful conceptual tool but in reality the emission of radiation takes place from everywhere between the surface and the stratosphere. See Visualizing Atmospheric Radiation – Part Three – Average Height of Emission – the complex subject of where the TOA radiation originated from, what is the “Average Height of Emission” and other questions.

Also, take a look at the complete series: Visualizing Atmospheric Radiation.

Note 6 – the balance between emission and absorption are found in the equations of radiative transfer. These are derived from fundamental physics – see Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations – the equations of radiative transfer including the plane parallel assumption and it’s nothing to do with blackbodies. The fundamental physics is not just proven in the lab, spectral measurements at top of atmosphere and the surface match the calculated values using the radiative transfer equations – see Theory and Experiment – Atmospheric Radiation – real values of total flux and spectra compared with the theory.

Also, take a look at the complete series: Atmospheric Radiation and the “Greenhouse” Effect

Note 7 – this calculation is under the assumption of “all other things being equal”. Of course, in the real climate system, all other things are not equal. However, to understand an effect “pre-feedback” we need to separate it from the responses to the system.

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If we open an introductory atmospheric physics textbook, we find that the temperature profile in the troposphere (lower atmosphere) is mostly explained by convection. (See for example, Things Climate Science has Totally Missed? – Convection)

We also find that the temperature profile in the stratosphere is mostly determined by radiation. And that the overall energy balance of the climate system is determined by radiation.

Many textbooks introduce the subject of convection in this way:

  • what would the temperature profile be like if there was no convection, only radiation for heat transfer
  • why is the temperature profile actually different
  • how does pressure reduce with height
  • what happens to air when it rises and expands in the lower pressure environment
  • derivation of the “adiabatic lapse rate”, which in layman’s terms is the temperature change when we have relatively rapid movements of air
  • how the real world temperature profile (lapse rate) compares with the calculated adiabatic lapse rate and why

We looked at the last four points in some detail in a few articles:

Density, Stability and Motion in Fluids – some basics about instability
Potential Temperature – explaining “potential temperature” and why the “potential temperature” increases with altitude
Temperature Profile in the Atmosphere – The Lapse Rate – lots more about the temperature profile in the atmosphere

In this article we will look at the first point.

All of the atmospheric physics textbooks I have seen use a very simple model for explaining the temperature profile in a fictitious “radiation only” environment. The simple model is great for giving insight into how radiation travels.

Physics textbooks, good ones anyway, try and use the simplest models to explain a phenomenon.

The simple model, in brief, is the “semi-gray approximation”. This says the atmosphere is completely transparent to solar radiation, but opaque to terrestrial radiation. Its main simplification is having a constant absorption with wavelength. This makes the problem nice and simple analytically – which means we can rewrite the starting equations and plot a nice graph of the result.

However, atmospheric absorption is the total opposite of constant. Here is an example of the absorption vs wavelength of a minor “greenhouse” gas:

From Vardavas & Taylor (2007)

From Vardavas & Taylor (2007)

Figure 1

So from time to time I’ve wondered what the “no convection” atmosphere would look like with real GHG absorption lines. I also thought it would be especially interesting to see the effect of doubling CO2 in this fictitious environment.

This article is for curiosity value only, and for helping people understand radiative transfer a little better.

We will use the Matlab program seen in the series Visualizing Atmospheric Radiation. This does a line by line calculation of radiative transfer for all of the GHGs, pulling the absorption data out of the HITRAN database.

I updated the program in a few subtle ways. Mainly the different treatment of the stratosphere – the place where convection stops – was removed. Because, in this fictitious world there is no convection in the lower atmosphere either.

Here is a simulation based on 380 ppm CO2, 1775 ppb CH4, 319 ppb N2O and 50% relative humidity all through the atmosphere. Top of atmosphere was 100 mbar and the atmosphere was divided into 40 layers of equal pressure. Absorbed solar radiation was set to 240 W/m² with no solar absorption in the atmosphere. That is (unlike in the real world), the atmosphere has been made totally transparent to solar radiation.

The starting point was a surface temperature of 288K (15ºC) and a lapse rate of 6.5K/km – with no special treatment of the stratosphere. The final surface temperature was 326K (53ºC), an increase of 38ºC:


Figure 2

The ocean depth was only 5m. This just helps get to a new equilibrium faster. If we change the heat capacity of a system like this the end result is the same, the only difference is the time taken.

Water vapor was set at a relative humidity of 50%. For these first results I didn’t get the simulation to update the absolute humidity as the temperature changed. So the starting temperature was used to calculate absolute humidity and that mixing ratio was kept constant:


Figure 3

The lapse rate, or temperature drop per km of altitude:


Figure 4

The flux down and flux up vs altitude:


Figure 5

The top of atmosphere upward flux is 240 W/m² (actually at the 500 day point it was 239.5 W/m²) – the same as the absorbed solar radiation (note 1). The simulation doesn’t “force” the TOA flux to be this value. Instead, any imbalance in flux in each layer causes a temperature change, moving the surface and each part of the atmosphere into a new equilibrium.

A bit more technically for interested readers.. For a given layer we sum:

  • upward flux at the bottom of a layer minus upward flux at the top of a layer
  • downward flux at the top of a layer minus downward flux at the bottom of a layer

This sum equates to the “heating rate” of the layer. We then use the heat capacity and time to work out the temperature change. Then the next iteration of the simulation redoes the calculation.

And even more technically:

  • the upwards flux at the top of a layer = the upwards flux at the bottom of the layer x transmissivity of the layer plus the emission of that layer
  • the downwards flux at the bottom of a layer = the downwards flux at the top of the layer x transmissivity of the layer plus the emission of that layer

End of “more technically”..

Anyway, the main result is the surface is much hotter and the temperature drop per km of altitude is much greater than the real atmosphere. This is because it is “harder” for heat to travel through the atmosphere when radiation is the only mechanism. As the atmosphere thins out, which means less GHGs, radiation becomes progressively more effective at transferring heat. This is why the lapse rate is lower higher up in the atmosphere.

Now let’s have a look at what happens when we double CO2 from its current value (380ppm -> 760 ppm):


Figure 6 – with CO2 doubled instantaneously from 380ppm at 500 days

The final surface temperature is 329.4, increased from 326.2K. This is an increase (no feedback of 3.2K).

The “pseudo-radiative forcing” = 18.9 W/m² (which doesn’t include any change to solar absorption). This radiative forcing is the immediate change in the TOA forcing. (It isn’t directly comparable to the IPCC standard definition which is at the tropopause and after the stratosphere has come back into equilibrium – none of these have much meaning in a world without convection).

Let’s also look at the “standard case” of an increase from pre-industrial CO2 of 280 ppm to a doubling of 560 ppm. I ran this one for longer – 1000 days before doubling CO2 and 2000 days in total- because the starting point was less in balance. At the start, the TOA flux (outgoing longwave radiation) = 248 W/m². This means the climate was cooling quite a bit with the starting point we gave it.

At 180 ppm CO2, 1775 ppb CH4, 319 ppb N2O and 50% relative humidity (set at the starting point of 288K and 6.5K/km lapse rate), the surface temperature after 1,000 days = 323.9 K. At this point the TOA flux was 240.0 W/m². So overall the climate has cooled from its initial starting point but the surface is hotter.

This might seem surprising at first sight – the climate cools but the surface heats up? It’s simply that the “radiation-only” atmosphere has made it much harder for heat to get out. So the temperature drop per km of height is now much greater than it is in a convection atmosphere. Remember that we started with a temperature profile of 6.5K/km – a typical convection atmosphere.

After CO2 doubles to 560 ppm (and all other factors stay the same, including absolute humidity), the immediate effect is the TOA flux drops to 221 W/m² (once again a radiative forcing of about 19 W/m²). This is because the atmosphere is now even more “resistant” to the escape of heat by radiation. The atmosphere is more opaque and so the average emission of radiation of space moves to a higher and colder part of the atmosphere. Colder parts of the atmosphere emit less radiation than warmer parts of the atmosphere.

After the climate moves back into balance – a TOA flux of 240 W/m² – the surface temperature = 327.0 K – an increase (pre-feedback) of 3.1 K.

Compare this with the standard IPCC “with convection” no-feedback forcing of 3.7 W/m² and a “no feedback” temperature rise of about 1.2 K.


Figure 7 – with CO2 doubled instantaneously from 280ppm at 1000 days

Then I introduced a more realistic model with solar absorption by water vapor in the atmosphere (changed parameter ‘solaratm’ in the Matlab program from ‘false’ to ‘true’). Unfortunately this part of the radiative transfer program is not done by radiative transfer, only by a very crude parameterization, just to get roughly the right amount of heating by solar radiation in roughly the right parts of the atmosphere.

The equilibrium surface temperature at 280 ppm CO2 was now “only” 302.7 K (almost 30ºC). Doubling CO2 to 560 ppm created a radiative forcing of 11 W/m², and a final surface temperature of 305.5K – that is, an increase of 2.8K.

Why is the surface temperature lower? Because in the “no solar absorption in the atmosphere” model, all of the solar radiation is absorbed by the ground and has to “fight its way out” from the surface up. Once you absorb solar radiation higher up than the surface, it’s easier for this heat to get out.


One of the common themes of fantasy climate blogs is that the results of radiative physics are invalidated by convection, which “short-circuits” radiation in the troposphere. No one in climate science is confused about the fact that convection dominates heat transfer in the lower atmosphere.

We can see in this set of calculations that when we have a radiation-only atmosphere the surface temperature is a lot higher than any current climate – at least when we consider a “one-dimensional” climate.

Of course, the whole world would be different and there are many questions about the amount of water vapor and the effect of circulation (or lack of it) on moving heat around the surface of the planet via the atmosphere and the ocean.

When we double CO2 from its pre-industrial value the radiative forcing is much greater in a “radiation-only atmosphere” than in a “radiative-convective atmosphere”, with the pre-feedback temperature rise 3ºC vs 1ºC.

So it is definitely true that convection short-circuits radiation in the troposphere. But the whole climate system can only gain and lose energy by radiation and this radiation balance still has to be calculated. That’s what current climate models do.

It’s often stated as a kind of major simplification (a “teaching model”) that with increases in GHGs the “average height of emission” moves up, and therefore the emission is from a colder part of the atmosphere. This idea is explained in more detail and less simplifications in Visualizing Atmospheric Radiation – Part Three – Average Height of Emission – the complex subject of where the TOA radiation originated from, what is the “Average Height of Emission” and other questions.

A legitimate criticism of current atmospheric physics is that convection is poorly understood in contrast to subjects like radiation. This is true. And everyone knows it. But it’s not true to say that convection is ignored. And it’s not true to say that because “convection short-circuits radiation” in the troposphere that somehow more GHGs will have no effect.

On the other hand I don’t want to suggest that because more GHGs in the atmosphere mean that there is a “pre-feedback” temperature rise of about 1K, that somehow the problem is all nicely solved. On the contrary, climate is very complicated. Radiation is very simple by comparison.

All the standard radiative-convective calculation says is: “all other things being equal, an doubling of CO2 from pre-industrial levels, would lead to a 1K increase in surface temperature”

All other things are not equal. But the complication is not that somehow atmospheric physics has just missed out convection. Hilarious. Of course, I realize most people learn their criticisms of climate science from people who have never read a textbook on the subject. Surprisingly, this doesn’t lead to quality criticism..

On more complexity  – I was also interested to see what happens if we readjust absolute humidity due to the significant temperature changes, i.e. we keep relative humidity constant. This led to some surprising results, so I will post them in a followup article.


Note 1 – The boundary conditions are important if you want to understand radiative heat transfer in the atmosphere.

First of all, the downward longwave radiation at TOA (top of atmosphere) = 0. Why? Because there is no “longwave”, i.e., terrestrial radiation, from outside the climate system. So at the top of the atmosphere the downward flux = 0. As we move down through the atmosphere the flux gradually increases. This is because the atmosphere emits radiation. We can divide up the atmosphere into fictitious “layers”. This is how all numerical (finite element analysis) programs actually work. Each layer emits and each layer also absorbs. The balance depends on the temperature of the source radiation vs the temperature of the layer of the atmosphere we are considering.

At the bottom of the atmosphere, i.e., at the surface, the upwards longwave radiation is the surface emission. This emission is given by the Stefan-Boltzmann equation with an emissivity of 1.0 if we consider the surface as a blackbody which is a reasonable approximation for most surface types – for more on this, see Visualizing Atmospheric Radiation – Part Thirteen – Surface Emissivity – what happens when the earth’s surface is not a black body – useful to understand seeing as it isn’t..

At TOA, the upwards emission needs to equal the absorbed solar radiation, otherwise the climate system has an imbalance – either cooling or warming.

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As a friend of mine in Florida says:

You can’t kill stupid, but you can dull it with a 4×2

Some ideas are so comically stupid that I thought there was no point writing about them. And yet, one after another, people who can type are putting forward these ideas on this blog.. At first I wondered if I was the object of a practical joke. Some kind of parody. Perhaps the joke is on me. But, just in case I was wrong about the practical joke..


If you pick up a textbook on heat transfer that includes a treatment of radiative heat transfer you find no mention of Arrhenius.

If you pick up a textbook on atmospheric physics none of the equations come from Arrhenius.

Yet there is a steady stream of entertaining “papers” which describe “where Arrhenius went wrong”, “Arrhenius and his debates with Fourier”. Who cares?

Likewise, if you study equations of motion in a rotating frame there is no discussion of where Newton went wrong, or where he got it right, or debates he got right or wrong with contemporaries. Who knows? Who cares?

History is fascinating. But if you want to study physics you can study it pretty well without reading about obscure debates between people who were in the formulation stages of the field.

Here are the building blocks of atmospheric radiation:

  • The emission of radiation – described by Nobel prize winner Max Planck’s equation and modified by the material property called emissivity (this is wavelength dependent)
  • The absorption of radiation by a surface – described by the material property called absorptivity (this is wavelength dependent and equal at the same wavelength and direction to emissivity)
  • The Beer-Lambert law of absorption of radiation by a gas
  • The spectral absorption characteristics of gases – currently contained in the HITRAN database – and based on work carried out over many decades and written up in journals like Journal of Quantitative Spectroscopy and Radiative Transfer
  • The theory of radiative transfer – the Schwarzschild equation – which was well documented by Nobel prize winner Subrahmanyan Chandrasekhar in his 1952 book Radiative Transfer (and by many physicists since)

The steady stream of stupidity will undoubtedly continue, but if you are interested in learning about science then you can rule out blogs that promote papers which earnestly explain “where Arrhenius went wrong”.

Hit them with a 4 by 2.

Or, ask the writer where Subrahmanyan Chandrasekhar went wrong in his 1952 work Radiative Transfer. Ask the writer where Richard M. Goody went wrong. He wrote the seminal Atmospheric Radiation: Theoretical Basis in 1964.

They won’t even know these books exist and will have never read them. These books contain equations that are thoroughly proven over the last 100 years. There is no debate about them in the world of physics. In the world of fantasy blogs, maybe.

There is also a steady stream of people who believe an idea yet more amazing. Somehow basic atmospheric physics is proven wrong because of the last 15 years of temperature history.

The idea seems to be:

More CO2 is believed to have some radiative effect in the climate because of the last 100 years of temperature history, climate scientists saw some link and tried to explain it using CO2, but now there has been no significant temperature increase for the last x years this obviously demonstrates the original idea was false..

If you think this, please go and find a piece of 4×2 and ask a friend to hit you across the forehead with it. Repeat. I can’t account for this level of stupidity but I have seen that it exists.

An alternative idea, that I will put forward, one that has evidence, is that scientists discovered that they can reliably predict:

  • emission of radiation from a surface
  • emission of radiation from a gas
  • absorption of radiation by a surface
  • absorption of radiation by a gas
  • how to add up, subtract, divide and multiply, raise numbers to the power of, and other ninja mathematics

The question I have for the people with these comical ideas:

Do you think that decades of spectroscopy professionals have just failed to measure absorption? Their experiments were some kind of farce? No one noticed they made up all the results?

Do you think Max Planck was wrong?

It is possible that climate is slightly complicated and temperature history relies upon more than one variable?

Did someone teach you that the absorption and emission of radiation was only “developed” by someone analyzing temperature vs CO2 since 1970 and not a single scientist thought to do any other measurements? Why did you believe them?

Bring out the 4×2.

Note – this article is a placeholder so I don’t have to bother typing out a subset of these points for the next entertaining commenter..

Update July 10th with the story of Fred the Charlatan

Let’s take the analogy of a small boat crossing the Atlantic.

Analogies don’t prove anything, they are for illustration. For proof, please review Theory and Experiment – Atmospheric Radiation.

We’ve done a few crossings and it’s taken 45 days, 42 days and 46 days (I have no idea what the right time is, I’m not a nautical person).

We measure the engine output – the torque of the propellors. We want to get across quicker. So Fred the engine guy makes a few adjustments and we remeasure the torque at 5% higher. We also do Fred’s standardized test, which is to zip across a local sheltered bay with no currents, no waves and no wind – the time taken for Fred’s standarized test is 4% faster. Nice.

So we all set out on our journey across the Atlantic. Winds, rain, waves, ocean currents. We have our books to read, Belgian beer and red wine and the time flies. Oh no, when we get to our final destination, it’s actually taken 47 days.

Clearly Fred is some kind of charlatan! No need to check his measurements or review the time across the bay. We didn’t make it across the Atlantic in less time and clearly the ONLY variable involved in that expedition was the output of the propellor.

Well, there’s no point trying to use more powerful engines to get across the Atlantic (or any ocean) faster. Torque has no relationship to speed. Case closed.

Analogy over.


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In Part Three we had a very brief look at the orbital factors that affect solar insolation.

Here we will look at these factors in more detail. We start with the current situation.

Seasonal Distribution of Incoming Solar Radiation

The earth is tilted on its axis (relative to the plane of orbit) so that in July the north pole “faces” the sun, while in January the south pole “faces” the sun.

Here are the TOA graphs for average incident solar radiation at different latitudes by month:

From Vardavas & Taylor (2007)

From Vardavas & Taylor (2007)

Figure 1

And now the average values first by latitude for the year, then by month for northern hemisphere, southern hemisphere and the globe:


Figure 2

We can see that the southern hemisphere has a higher peak value – this is because the earth is closest to the sun (perihelion) on January 3rd, during the southern hemisphere summer.

This is also reflected in the global value which varies between 330 W/m² at aphelion (furthest away from the sun) to 352 W/m² at perihelion.


There is a good introduction to planetary orbits in Wikipedia. I was saved from the tedium of having to work out how to implement an elliptical orbit vs time by the Matlab code kindly supplied by Jonathan Levine. He also supplied the solution to the much more difficult problem of insolation vs latitude at any day in the Quaternary period, which we will look at later.

Here is the the TOA solar insolation by day of the year, as a function of the eccentricity of the orbit:


Figure 3 – Updated

The earth’s orbit currently has an eccentricity of 0.0167. This means that the maximum variation in solar radiation is 6.9%.

Perihelion is 147.1 million km, while aphelion is 152.1 million km. The amount of solar radiation we receive is “the inverse square law”, which means if you move twice as far away, the solar radiation reduces by a factor of four. So to calculate the difference between the min and max you simply calculate: (152.1/147.1)² = 1.069 or a change of 6.9%.

Over the past million or more years the earth’s orbit has changed its eccentricity, from a low close to zero, to a maximum of about 0.055. The period of each cycle is about 100,000 years.

Here is my calculation of change in total annual TOA solar radiation with eccentricity:


Figure 4

Looking at figure 1 of Imbrie & Imbrie (1980), just to get a rule of thumb, eccentricity changed from 0.05 to 0.02 over a 50,000 year period (about 220k years ago to 170k years ago). This means that the annual solar insolation dropped by 0.1% over 50,000 years or 3 mW/m² per century. (This value is an over-estimate because it is the peak value with sun overhead, if instead we take the summer months at high latitude the change becomes  0.8 mW/m² per century)

It’s a staggering drop, and no wonder the strong 100,000 year cycle in climate history matching the Milankovitch eccentricity cycles is such a difficult theory to put together.

Obliquity & Precession

To understand those basics of these changes take a look at the Milankovitch article. Neither of these two effects, precession and obliquity, changes the total annual TOA incident solar radiation. They just change its distribution.

Here is the last 250,000 years of solar radiation on July 1st – for a few different latitudes:


Figure 5 – Click for a larger image

Notice that the equatorial insolation is of course lower than the mid-summer polar insolation.

Here is the same plot but for October 1st. Now the equatorial value is higher:


Figure 6 – Click for a larger image

Let’s take a look at the values for 65ºN, often implicated in ice age studies, but this time for the beginning of each month of the year (so the legend is now 1 = January 1st, 2 = Feb 1st, etc):


Figure 7 - Click for a larger image

And just for interest I marked one date for the last inter-glacial – the Eemian inter-glacial as it is known.

Come up with a theory:

  • peak insolation at 65ºN
  • fastest rate of change
  • minimum insolation
  • average of summer months
  • average of winter half year
  • average autumn 3 months

Then pick from the graph and let’s start cooking.. Having trouble? Pick a different latitude. Southern Hemisphere – no problem, also welcome.

As we will see, there are a lot of theories, all of which call themselves “Milankovitch” but each one is apparently incompatible with other similarly-named “Milankovitch” theories.

At least we have a tool, kindly supplied by Jonathan Levine, which allows us to compute any value. So if any readers have an output request, just ask.

One word of caution for budding theorists of ice ages (hopefully we have many already) from Kukla et al (2002):

..The marine isotope record is commonly tuned to astronomic chronology, represented by June insolation at the top of the atmosphere at 60′ or 65′ north latitude. This was deemed justified because the frequency of the Pleistocene gross global climate states matches the frequency of orbital variations..

..The mechanism of the climate response to insolation remains unclear and the role of insolation in the high latitudes as opposed to that in the low latitudes is still debated..

..In either case, the link between global climates and orbital variations appears to be complicated and not directly controlled by June insolation at latitude 65’N. We strongly discourage dating local climate proxies by unsubstantiated links to astronomic variations..

[Emphasis added].

I’m a novice with the historical records and how they have been constructed, but I understand that SPECMAP is tuned to a Milankovitch theory, i.e., the dates of peak glacials and peak inter-glacials are set by astronomical values.

Articles in the Series

Part One – An introduction

Part Two – Lorenz – one point of view from the exceptional E.N. Lorenz

Part Three – Hays, Imbrie & Shackleton – how everyone got onto the Milankovitch theory

Part Five – Obliquity & Precession Changes – and in a bit more detail

Part Six – “Hypotheses Abound” – lots of different theories that confusingly go by the same name

Part Seven – GCM I – early work with climate models to try and get “perennial snow cover” at high latitudes to start an ice age around 116,000 years ago

Part Seven and a Half – Mindmap – my mind map at that time, with many of the papers I have been reviewing and categorizing plus key extracts from those papers

Part Eight – GCM II – more recent work from the “noughties” – GCM results plus EMIC (earth models of intermediate complexity) again trying to produce perennial snow cover

Part Nine – GCM III – very recent work from 2012, a full GCM, with reduced spatial resolution and speeding up external forcings by a factors of 10, modeling the last 120 kyrs

Part Ten – GCM IV – very recent work from 2012, a high resolution GCM called CCSM4, producing glacial inception at 115 kyrs

Pop Quiz: End of An Ice Age – a chance for people to test their ideas about whether solar insolation is the factor that ended the last ice age

Eleven – End of the Last Ice age – latest data showing relationship between Southern Hemisphere temperatures, global temperatures and CO2

Twelve – GCM V – Ice Age Termination – very recent work from He et al 2013, using a high resolution GCM (CCSM3) to analyze the end of the last ice age and the complex link between Antarctic and Greenland

Thirteen – Terminator II – looking at the date of Termination II, the end of the penultimate ice age – and implications for the cause of Termination II


Last Interglacial Climates, Kukla et al, Quaternary Research (2002)

Modeling the Climatic Response to Orbital Variations, John Imbrie & John Z. Imbrie, Science (1980)

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Measurements of outgoing longwave radiation (OLR) are essential for understanding many aspects of climate. Many people are confused about the factors that affect OLR. And its rich variability is often not appreciated.

There have been a number of satellite projects since the late 1970’s, with the highlight (prior to 2001) being the five year period of ERBE.

AIRS & CERES were launched on the NASA AQUA satellite in May 2002. These provide much better quality data, with much better accuracy and resolution.

CERES has three instruments:

  • Solar Reflected Radiation (Shortwave): 0.3 – 5.0 μm
  • Window: 8 – 12 μm
  • Total: 0.3 to > 100 μm

AIRS is an infrared spectrometer/radiometer that covers the 3.7–15.4 μm spectral range with 2378 spectral channels. It runs alongside two microwave instruments (better viewing through clouds): AMSU is a 15-channel microwave radiometer operating between 23 and 89 GHz; HSB is a four-channel microwave radiometer that makes measurements between 150 and 190 GHz.

From Aumann et al (2003):

The simultaneous use of the data from the three instruments provides both new and improved measurements of cloud properties, atmospheric temperature and humidity, and land and ocean skin temperatures, with the accuracy, resolution, and coverage required by numerical weather prediction and climate models.

Among the important datasets that AIRS will contribute to climate studies are as follows:

  • atmospheric temperature profiles;
  • sea-surface temperature;
  • land-surface temperature and emissivity;
  • relative humidity profiles and total precipitable water vapor;
  • fractional cloud cover;
  • cloud spectral IR emissivity;
  • cloud-top pressure and temperature;
  • total ozone burden of the atmosphere;
  • column abundances of minor atmospheric gases such as CO, CH, CO, and N2O;
  • outgoing longwave radiation and longwave cloud radiative forcing;
  • precipitation rate

More about AIRS = Atmospheric Infrared Sounder, at Wikipedia, plus the AIRS website.

More about CERES = Clouds and the Earth’s Radiant Energy System, at Wikipedia, plus the CERES website – where you can select and view or download your own data.

How do CERES & AIRS compare?

CERES and AIRS have different jobs. CERES directly measures OLR. AIRS measures lots of spectral channels that don’t cover the complete range needed to just “add up” OLR. Instead, OLR can be calculated from AIRS data by deriving surface temperature, water vapour concentration vs height, CO2 concentration, etc and using a radiative transfer algorithm to determine OLR.

Here is a comparison of the two measurement systems from Susskind et al (2012) over almost a decade:


From Susskind et al (2012)

Figure 1

The second thing to observe is that the measurements have a bias between the two datasets. But because we have two high accuracy measurement systems on the same satellite we do have a reasonable opportunity to identify the source of the bias (total OLR as shown in the graph is made of many components). If we only had one satellite, and then a new satellite took over with a small time overlap any biases would be much more difficult to identify. Of course, that doesn’t stop many people from trying but success would be much harder to judge.

In this paper, as we might expect, the error sources between the two datasets get considerable discussion. One important point is that version 6 AIRS data (prototyped at the time the paper was written) is much closer to CERES. The second point, probably more interesting, is that once we look at anomaly data the results are very close. We’ll see a number of comparisons as we review what the paper shows.

The authors comment:

Behavior of OLR over this short time period should not be taken in any way as being indicative of what long-term trends might be. The ability to begin to draw potential conclusions as to whether there are long-term drifts with regard to the Earth’s OLR, beyond the effects of normal interannual variability, would require consistent calibrated global observations for a time period of at least 20 years, if not longer. Nevertheless, a very close agreement of the 8-year, 10-month OLR anomaly time series derived using two different instruments in two very different manners is an encouraging result.

It demonstrates that one can have confidence in the 1° x 1° OLR anomaly time series as observed by each instrument over the same time period. The second objective of the paper is to explain why recent values of global mean, and especially tropical mean, OLR have been strongly correlated with El Niño/La Niña variability and why both have decreased over the time period under study.

Why Has OLR Varied?

The authors define the average rate of change (ARC) of an anomaly time series as “the slope of the linear least squares fit of the anomaly time series”.


We can see excellent correlation between the two datasets and we can see that OLR has, on average, decreased over this time period.

Below is a comparison with the El Nino index.

We define the term El Niño Index as the difference of the NOAA monthly mean oceanic Sea Surface Temperature (SST), averaged over the NOAA Niño-4 spatial area 5°N to 5°S latitude and 150°W westward to 160°E longitude, from an 8-year NOAA Niño-4 SST monthly mean climatology which we generated based on use of the same 8 years that we used in the generation of the OLR climatologies.

From Susskind et al (2012)

From Susskind et al (2012)

Figure 2

It gets interesting when we look at the geographical distribution of the OLR changes over this time period:

From Susskind et al (2012)

From Susskind et al (2012)

Figure 3 – Click to Enlarge

We see that the tropics have the larger changes (also seen clearly in figure 2) but that some regions of the tropics have strong positive values and other regions have strong negative values. The grey square square centered on 180 longitude is the Nino-4 region. Values as large as +4 W/m²/decade are found in this region. And values as large as -3 W/m²/decade are found over Indonesia (WPMC region).

Let’s look at the time series to see how these changes in OLR took place:


Figure 4 – Click to Enlarge

The main parameters which affect changes in OLR month to month and year to year are a) surface temperatures b) humidity c) clouds. As temperature increases, OLR increases. As humidity and clouds increase, OLR decreases.

Here are the changes in surface temperature, specific humidity at 500mbar and cloud fraction:

From Susskind (2012)

From Susskind (2012)

Figure 5 – Click to Enlarge

So, focusing again on the Nino-4 region, we might expect to find that OLR has decreased because of the surface temperature decrease (lower emission of surface radiation) – or we might expect to find that the OLR has increased because the specific humidity and cloud fraction have decreased (thus allowing more surface and lower atmosphere radiation to make it through to TOA). These are mechanisms pulling in opposite directions.

In fact we see that the reduced specific humidity and cloud fraction have outweighed the effect of the surface temperature decrease. So the physics should be clear (still considering the Nino-4 region) – if surface temperature has decreased and OLR has increased then the explanation is the reduction in “greenhouse” gases (in this case water vapor) and clouds, which contain water.


We can see similar relationships through correlations.

The term ENC in the graphs stands for El Nino Correlation. This is essentially the correlation of the time-series data with time-series temperature change in the Nino-4 region (more specifically the Nino-4 temperature less the global temperature).

As the Nino-4 temperature declined over the period in question, a positive correlation means the value declined, while a negative correlation means the value increased.

The first graph below is the geographical distribution of rate of change of surface temperature. Of course we see that the Nino-4 region has been declining in temperature (as already seen in figure 2). The second graph shows this as well, but also indicates that the regions west and east of the Nino-4 region have  a stronger (negative) correlation than  other areas of larger temperature change (like the arctic region).

The third graph shows that 500 mb humidity has been decreasing in the Nino-4 region, and increasing to the west and east of this region. Likewise for the cloud fraction. And all of these are strongly correlated to the Nino-4 time-series temperature:

From Susskind (2012)

From Susskind et al (2012)

Figure 6 – Click to expand

For OLR correlations with Nino-4 temperature we find a strong negative correlation, meaning the OLR has increased in the Nino-4 region. And the opposite – a strong positive correlation – in the highlighted regions to east and west of Nino-4:

From Susskind (2012)

From Susskind (2012)

Figure 7 – Click to expand

Note the two highlighted regions

  • to the west: WPMC, Warm Pool Maritime Continent;
  • and to the east: EEMA, Equatorial Eastern Pacific and Atlantic Region

We can see the correlations between the global & tropical OLR and the OLR changes in these regions:


Figure 8 – Click to expand

Both WPMC and EEPA regions together explain the reduction over 10 years in OLR. Without these two regions the change is indistinguishable from zero.


This article is interesting for a number of reasons.

It shows the amazing variability of climate – we can see adjacent regions in the tropics with completely opposite changes over 10 years.

It shows that CERES gets almost identical anomaly results (changes in OLR) to AIRS. CERES directly measures OLR, while AIRS retrieves surface temperature, humidity profiles, cloud fractions and “greenhouse” gas concentrations and uses these to calculate OLR.

AIRS results demonstrate how surface temperature, humidity and cloud fraction affect OLR.

OLR has – over the globe – decreased over 10 years. This is a result of the El-Nino phase – at the start of the measurement period we were coming out of a large El-Nino event, and at the end of the measurement period we were in a La Nina event.

The reduction in OLR is explained by the change in the two regions identified, which are themselves strongly correlated to the Nino-4 region.


Interannual variability of outgoing longwave radiation as observed by AIRS and CERES, Susskind et al, Journal of Geophysical Research (2012) – paywall paper

AIRS/AMSU/HSB on the Aqua Mission: Design, Science Objectives, Data Products, and Processing Systems, Aumann et al, IEEE Transactions on Geoscience and Remote Sensing (2003) – free paper

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This could be considered as a continuation of the earlier series – Atmospheric Radiation and the “Greenhouse” Effect – but I’ve elected to start a new series.

It’s clear that many people have conceptual problems with the subject of what is, in technical terms called radiative transfer. That is, how radiation travels through the atmosphere and is affected by the atmosphere.

Radiation and Gas in a Box

First, let’s consider what happens as we shine an intense beam of infrared radiation at a narrow range of wavelengths (let’s say somewhere in the region of 15μm) through a box of CO2 gas at room temperature:


Figure 1

The red arrow on the left is the incident radiation. The graph indicates the spectrum. The spectrum on the right is made up of two main parts:

  • the transmitted radiation – the incident radiation attenuated by the absorbing gas
  • the emitted radiation due to the temperature and emissivity of the gas at these wavelengths

The yellow spectrum shows what we would measure from one of the sides. Note that the transmitted radiation that goes from left to right has no effect on this yellow spectrum (except in so far as absorption of the incident radiation affects the temperature of the gas).

If we increase the length of the box (left to right) – and keep the density the same – the transmitted radiation from the right side would decrease in intensity. If we reduce the length of the box (again, same density) the transmitted radiation from the right would increase in intensity.

But the emitted radiation from the top is only dependent on the temperature of the gas and its emission/absorption lines.

And the temperature of the gas is of course affected by the balance between absorbed and emitted radiation as well as any heat transfer from the surroundings via convection and conduction.

Hopefully, this is clear. If anyone thinks this simple picture is wrong, now is the time to make a comment. Confusion over this part means that you can’t make any progress in understanding atmospheric radiation.

Scattering is insignificant for longwave radiation (4μm and up). Stimulated emission is insignificant for intensities seen in the atmosphere.

Radiation in the Atmosphere

How does radiation travel through the atmosphere?


Figure 1

The idea shown here is a spectrum of radiation at different wavelengths incident on a “layer” of the atmosphere (see note 1). The atmosphere has lots of absorption lines of many different strengths. As a result the transmitted radiation making it out of the other side is some proportion of the incident radiation. The proportion varies with the wavelength.

The atmosphere also emits radiation, and the emission lines are the same as the absorption lines. More about that in Planck, Stefan-Boltzmann, Kirchhoff and LTE.

However, the emission depends on the temperature of the gas in the layer (as well as the absorption/emission lines). But the absorption depends on the intensity of incident radiation (as well as the absorption/emission lines), which in turn depends on the temperature of the source of the radiation.

So in almost every case, the sum of transmitted plus emitted radiation is not equal to the incident radiation. By the way, the spectrum at the top is just a raggedy freehand drawing to signify that the outgoing spectrum is not like the incoming spectrum. It’s not meant to be representative of actual intensity vs wavelength.

And – it’s a two way street. I only showed one half of the story in figure 1. The same physics affects downward radiation in exactly the same way.

Considering One Wavelength at a Time

To calculate the actual transmission of radiation through the layer we simply work out the transmissivity, tλ, of the layer at each wavelength, λ (tλ simply indicates that t will vary for each value of λ we consider). We do that by looking up values calculated by spectroscopic professionals. These values are per molecule, or per kg of particular molecules so we need to find out how much of each absorbing gas is present.

1. The incident radiation making it through the layer = Iλ x tλ – for example, it could be 90% making it through, or 20%.

2. The “new” radiation emitted from each side of the layer equals the “Planck blackbody function at the temperature of the layer and the wavelength of interest” x Emissivity of the gas at that wavelength.

In case people are interested this can be written as Bλ(T).ελ, where ελ = emissivity at that wavelength, and Bλ(T) is the “Planck function” at that temperature and wavelength. Well, emissivity = absorptivity (at the same wavelength) and absorptivity = 1-transmissivity, so the same equation can be written as Bλ(T).(1-tλ).


Perhaps (the Planck function showing up in an equation) this is where many blogs (Parady blogs?) get the idea, and promote and endorse the idea, that climate science depends on the assumption that the atmosphere emits as a blackbody. There are some cases where the atmospheric emission is not far from the “blackbody assumption” (e.g., in clouds), but that is due to reality not assumption. There is no “blackbody assumption for the atmosphere” in climate science. But there is a movement of people who believe it to be true.

Misleadingly, they like to be known as “skeptics”.

End of digression..

Doing the Calculation

So it’s not really that hard to understand how radiation travels through the atmosphere. It is difficult to calculate it, mostly due to having to read a million absorption lines, figure out the correct units, get a model of the atmosphere (temperature profile + concentration of different “greenhouse” gases at each height), write a finite element program and work out a solution.

But that is just tedious details, it’s not as hard as having to understand general relativity or potential vorticity.

One important point – it is not possible to do this calculation in your head. If you think you have done it in your head, even to a close approximation, please go back and read this section again, then look up all of the absorption lines.

Still convinced – post your answer in a comment here.

In the next article I’ll explain radiative-convective models and show some results from the atmospheric model I built in MATLAB which uses the HITRAN database. Now that we have a model which calculates realistic values for emission, absorption and transmission we can slice and dice the results any way we want.

Does water vapor mask out the effects of CO2? What proportion of radiation is transmitted through the atmospheric window? What is the average emission height to space?

Related Articles

Part Two – some early results from a model with absorption and emission from basic physics and the HITRAN database

Part Three – Average Height of Emission – the complex subject of where the TOA radiation originated from, what is the “Average Height of Emission” and other questions

Part Four – Water Vapor – results of surface (downward) radiation and upward radiation at TOA as water vapor is changed

Part Five – The Code – code can be downloaded, includes some notes on each release

Part Six – Technical on Line Shapes – absorption lines get thineer as we move up through the atmosphere..

Part Seven – CO2 increases – changes to TOA in flux and spectrum as CO2 concentration is increased

Part Eight – CO2 Under Pressure – how the line width reduces (as we go up through the atmosphere) and what impact that has on CO2 increases

Part Nine – Reaching Equilibrium – when we start from some arbitrary point, how the climate model brings us back to equilibrium (for that case), and how the energy moves through the system

Part Ten – “Back Radiation” – calculations and expectations for surface radiation as CO2 is increased

Part Eleven – Stratospheric Cooling – why the stratosphere is expected to cool as CO2 increases

Part Twelve – Heating Rates – heating rate (‘C/day) for various levels in the atmosphere – especially useful for comparisons with other models.


Note 1 – What is a layer of atmosphere? Isn’t the thickness of this layer somewhat arbitrary? What if we change the thickness? And doesn’t radiation go in all directions, not just up?

These are all good questions.

In typical physics terms the actual equation of “radiative transfer” is a differential equation, which expresses continual change. In practical terms, solving a differential equation in most real world cases requires a numerical solution which has finite thicknesses for each layer.

People trying to solve these kind of problems usually check what happens to the solution as they go for more of thinner layers vs less of thicker layers. There is a trade-off between accuracy and speed.

Radiation does go in all directions. The plane parallel assumption has very strong justification and – in simple terms – mathematically resolves to a vertical solution with a correction factor. You can see the plane parallel assumption and the derivation of the equations of radiative transfer in Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations.

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In Atmospheric Circulation – Part One we saw how the pressure “slopes down” from the tropics to the poles creating S→N winds in the northern hemisphere.

In The Coriolis Effect and Geostrophic Motion we saw that on a rotating planet winds get deflected off to the side  (from the point of view of someone on the rotating planet). This means that winds flowing from the tropics to the north pole will get deflected “to the right”.

Taylor Columns

Strange things happen to fluids in rotating frames. To illustrate let’s take a look at Taylor columns.

From Marshall & Plumb (2008)

Figure 1

The static image is quite beautiful, but the video illustrates it better. Compare the video of the non-rotating tank with the rotating tank.

Now to stretch the mind we have a rotating tank with an obstacle on the base – in this case a hockey puck. The height of the puck is small compared with the depth of the fluid. The fluid flow has come into equilibrium with the tank rotation.

We slow down the rotation slightly. We sprinkle paper dots on the surface of the water. Amazingly the dots show that the surface of the fluid is acting as if the puck extended right up to the surface – the flow moves around the obstacle at the base (of course) and the flow moves “around” the obstacle at the surface. Even though the obstacle doesn’t exist at the surface!

Take a look at the video, but here are a few snapshots:

Figure 2

This occurs when:

  • the flow is slow and steady
  • friction is negligible
  • there is no temperature gradient (barotropic)

Under the first two conditions the flow is geostrophic which was covered with examples in The Coriolis Effect and Geostrophic Motion.

And under the final condition, with  no temperature gradient the density is uniform (only a function of pressure).

“Thermal Wind”

Now let’s look at an experiment with a “cold pole” and “warm tropics”:

From Marshall & Plumb (2008)

Figure 3

The result:

Figure 4

Even better - take a look at the video.

This experiment shows that once there is a N-S temperature gradient the E-W winds increase with altitude.

Which is kind of what we find in the real atmosphere:

From Marshall & Plumb (2008)

Figure 5

Why does this happen? I found it hard to understand conceptually for a while, but it’s actually really simple:

From Stull (1999)

Figure 6

So the ever increasing pressure gradient with height (due to the temperature gradient) induces a stronger geostrophic wind with height.

Here is an instantaneous measurement of E-W winds, along with temperature in a N-S section:

From Marshall & Plumb (2008)

Figure 8

The measurement demonstrates that the change in E-W wind vs height depends on the variation in N-S temperature.

The equation for this effect for the E-W winds can be written a few different ways, here is the easiest to understand:

∂u/∂z = (αg/f) . ∂T/∂y

where ∂u/∂z = change in E-W wind with height, α = thermal coefficient of expansion of air, g = acceleration due to gravity, f = coriolis parameter at that latitude, T = temperature, y = N-S direction

It can also be written in vector calculus notation:

u/∂z = (αg/f)z x ∇T

where u = wind velocity (u, v, w), = unit vector in vertical

In the next article we will look at why the maximum effect in the average, the jet stream, occurs in the subtropics rather than at the poles.


Meteorology for Scientists and Engineers, Ronald Stull, 2nd edition – Free (partial) resource

Atmosphere, Ocean and Climate Dynamics – An Introductory Text, Marshall & Plumb, Academic Press (2008)

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This is a tricky but essential subject and it’s hard to know where to begin.

Geopotential Height – The Height of a Given Atmospheric Pressure

Let’s start with something called the geopotential height. This is the height above the earth’s surface of a particular atmospheric pressure. In the example below we are looking at the 500 mbar surface. For reference, the surface of the earth is at about 1000 mbar and the top of the troposphere is at 200 mbar.

From Marshall & Plumb (2008)

Figure 1

At the pole the 500 mbar height is just under 5 km, and in the topics it is almost 6 km.

Why is this?

Here is another view of the same subject, this time the annual average latitudinal value (expressed as difference from the global average):

From Marshall & Plumb (2008)

Figure 2

See how the geopotential height increases in the tropics compared with the poles. And see how the difference increases with height.

The tropics are warmer than the poles – warm air expands and cool air contracts.

There is a mathematical equation which results from the ideal gas law and the hydrostatic equation:

z(p) = R/g ∫(T/p)dp

where z(p) = height of pressure p, R = gas constant, g = acceleration due to gravity, T = temperature

This is (oversimplified) like saying that the height of a “geopotential surface” is proportional to the sum of the temperatures of each layer between the surface and that pressure.

At 500 mbar, a 40ºC change in temperature leads to a height difference of just over 800 m.

North-South Winds

Because of the pressure gradient at altitude between the tropics and the poles, there is a force (at altitude) pushing air from the tropics to the poles.

From Goody (1972)

If the earth was rotating extremely slowly, the result might look something like this:

From Marshall & Plumb (2008)

Figure 3

However, the climate is not so simple. Here are 3 samples of the north-south circulation for annual, winter and summer:

From Marshall & Plumb (2008)

Figure 4

So instead of a circulation extending all the way to the poles we see a circulation from the tropics into the subtropics (note especially the DJF & JJA averages).

Here is an experiment shown in Goody (1972) to help understand the processes we see in the atmosphere:

Figure 5

Note that the first example is with slow rotation and the second example is with fast rotation.

And here is a similar experiment shown in Marshall & Plumb, but they come with videos, which help immensely. First the slow rotation experiment:

Figure 6

And second, the fast rotation experiment:

Figure 7

In both of the above links, make sure to watch the videos.

The reason the circulation breaks down from a large equator-polar cell to the actual climate with an equator-subtropical cell plus eddies is complex. We’ll explore more in the next article.

As a starter, take a look at the west-east winds:

From Marshall & Plumb (2008)

Figure 8

In the next article we will look at the thermal wind and try and make sense out of our observations.

Update – now published:

Atmospheric Circulation – Part Two – Thermal Wind


Atmosphere, Ocean and Climate Dynamics – An Introductory Text, Marshall & Plumb, Academic Press (2008)

Atmospheres, Goody & Walker, Prentice Hall (1972)

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Here is an article from Leonard Weinstein. (It has also been posted in slightly different form at The Air Vent).

Readers who have been around for a while will remember the interesting discussion Convection, Venus, Thought Experiments and Tall Rooms Full of Gas – A Discussion in which myself, Arthur Smith and Leonard all put forward a point of view on a challenging topic.

With this article, first I post Leonard’s article (plus some graphics I added for illustration), then my comments and finally Leonard’s response to my comments.

Why Back-Radiation is not a Source of Surface Heating

Leonard Weinstein, July 18, 2012

The argument is frequently made that back radiation from optically absorbing gases heats a surface more than it would be heated without back radiation, and this is the basis of the so-called Greenhouse Effect on Earth.

The first thing that has to be made clear is that a suitably radiation absorbing and radiating atmosphere does radiate energy out based on its temperature, and some of this radiation does go downward, where it is absorbed by the surface (i.e., there is back radiation, and it does transfer energy to the surface). However, heat (which is the net transfer of energy, not the individual transfers) is only transferred down if the ground is cooler than the atmosphere, and this applies to all forms of heat transfer.

While it is true that the atmosphere containing suitably optically absorbing gases is warmer than the local surface in some special cases, on average the surface is warmer than the integrated atmosphere effect contributing to back radiation, and so average heat transfer is from the surface up. The misunderstanding of the distinction between energy transfer, and heat transfer (net energy transfer) seems to be the cause of much of the confusion about back radiation effects.

Simplest Model

Before going on with the back radiation argument, first examine a few ideal heat transfer examples, which emphasize what is trying to be shown. These include an internally uniformly heated ball with either a thermally insulated surface or a radiation-shielded surface. The ball is placed in space, with distant temperatures near absolute zero, and zero gravity. Assume all emissivity and absorption coefficients for the following examples are 1 for simplicity.

The bare ball surface temperature at equilibrium is found from the balance of input energy into the ball and radiated energy to the external wall:

T= (P/σ)0.25 ….(1)

Where To (K) is absolute temperature, P (Wm-2) is input power per area of the ball, and σ = 5.67×10-8 (Wm-2T-4) is the Stefan-Boltzmann constant.

Ball with Insulation Layer

Now consider the same case with a relatively thin layer (compared to the size of the ball) of thermally insulating material coated directly onto the surface of the ball. Assume the insulator material is opaque to radiation, so that the only heat transfer is by conduction. The energy generated by input power heats the surface of the ball, and this energy is conducted to the external surface of the insulator, where the energy is radiated away from the surface. The assumption of a thin insulation layer implies the total surface area is about the same as the initial ball area.

Figure 1 – Ball with Insulation

The temperature of the external surface then has to be the same (=T) as the bare ball was, to balance power in and radiated energy out. However, in order to transmit the energy from the surface of the ball to the external surface of the insulator there had to be a temperature gradient through the insulation layer based on the conductivity of the insulator and thickness of the insulation layer.

For the simplified case described, Fourier’s conduction law gives:

qx=-k(dT/dx) ….(2)

where qx (Wm-2) is the local heat transfer, k (Wm-1T-1) is the conductivity, and x is distance outward of the insulator from the surface of the ball. The equilibrium case is a linear temperature variation, so we can substitute ΔT/h for dT/dx, where h is the insulator thickness, and ΔT is the temperature difference between outer surface of insulator and surface of ball (temperature decreasing outward).

Now qx has to be the same as P, so from (2):

ΔT = (To-T’) = -Ph/k ….(3)

Where T’ is the ball surface temperature under the insulation, and thus we get:

T’ = (Ph/k)+To ….(4)

The new ball surface temperature is now found by combining (1) + (4):

T’ = (Ph/k)+(P/σ)0.25 ….(5)

The point to all of the above is that the surface of the ball was made hotter for the same input energy to the ball by adding the insulation layer. The increased temperature did not come from the insulation heating the surface, it came from the reduced rate of surface energy removal at the initial temperature (thermal resistance), and thus the internal surface temperature had to increase to transmit the required power.

There was no added heat and no back heat transfer!

Ball with Shell & Conducting Gas

An alternate version of the insulated surface can be found by adding a thin conducting enclosing shell spaced a small distance from the wall of the ball, and filling the gap with a highly optically absorbing dense gas. Assume the gas is completely opaque to the thermal wavelengths at very short distances, so that he heat transfer would be totally dominated by diffusion (no convection, since zero gravity).

The result would be exactly the same as the solid insulation case with the correct thermal conductivity, k, used (derived from the diffusion equations).

It should be noted that the gas molecules have a range of speeds, even at a specific temperature (Maxwell distribution). The heat is transferred only by molecular collisions with the wall for this case. Now the variation in speed of the molecules, even at a single temperature, assures that some of the molecules hitting the ball wall will have higher energy going in that leaving the wall. Likewise, some of the molecules hitting the outer shell will have lower speeds than when they leave inward. That is, some energy is transmitted from the colder outer wall to the gas, and some energy is transmitted from the gas to the hotter ball wall. However, when all collisions are included, the net effect is that the ball transfers heat (=P) to the outer shell, which then radiates P to space.

Again, the gas layer did not result in the ball surface heating any more than for the solid insulation case. It resulted in heating due to the resistance to heat transfer at the lower temperature, and thus resulted in the temperature of the ball increasing. The fact that energy transferred both ways is not a cause of the heating.

Ball with Shell & Vacuum

Next we look at the bare ball, but with an enclosure of a very small thickness conductor placed a small distance above the entire surface of the ball (so the surface area of the enclosure is still essentially the same as for the bare ball), but with a high vacuum between the surface of the ball and the enclosed layer.

Now only radiation heat transfer can occur in the system. The ball is heated with the same power as before, and radiates, but the enclosure layer absorbs all of the emitted radiation from the ball. The absorbed energy heats the enclosure wall up until it radiated outward the full input power P.

The final temperature of the enclosure wall now is To, the same as the value in equation (1).

Figure 2 – Ball with Radiation Shield separated by vacuum

However, it is also radiating inward at the same power P. Since the only energy absorbed by the enclosure is that radiated by the ball, the ball has to radiate 2P to get the net transmitted power out to equal P. Since the only input power is P, the other P was absorbed energy from the enclosure. Does this mean the enclosure is heating the ball with back radiation? NO. Heat transfer is NET energy transfer, and the ball is radiating 2P, but absorbing P, so is radiating a NET radiation heat transfer of P. This type of effect is shown in radiation equations by:

Pnet = σ(Thot4-Tcold4) ….(6)

That is, the net radiation heat transfer is determined by both the emitting and absorbing surfaces. There is radiation energy both ways, but the radiation heat transfer is one way.

This is not heating by back radiation, but is commonly also considered a radiation resistance effect.

There is initially a decrease in net radiation heat transfer forcing the temperature to adjust to a new level for a given power transfer level. This is directly analogous to the thermal insulation effect on the ball, where radiation is not even a factor between the ball and insulator, or the opaque gas in the enclosed layer, where there is no radiation transfer, but some energy is transmitted both ways, and net energy (heat transfer) is only outward. The hotter surface of the ball is due to a resistance to direct radiation to space in all of these cases.

Ball with Multiple Shells

If a large number of concentric radiation enclosures were used (still assuming the total exit area is close to the same for simplicity), the ball temperature would get even hotter. In fact, each layer inward would have to radiate a net P outward to transfer the power from the ball to the external final radiator. For N layers, this means that the ball surface would have to radiate:

P’ = (N+1)Po ….(7)

Now from (1), this means the relative ball surface temperature would increase by:

T’/To = (N+1)0.25 ….(8)

Some example are shown to give an idea how the number of layers changes relative absolute temperature:

N       T’/To

1       1.19
10      1.82
100    3.16

Change in N clearly has a large effect, but the relationship is a semi-log like effect.

Lapse Rate Effect

Planetary atmospheres are much more complex than either a simple conduction insulating layer or radiation insulation layer or multiple layers. This is due to the presence of several mechanisms to transport energy that was absorbed from the Sun, either at the surface or directly in the atmosphere, up through the atmosphere, and also due to the effect called the lapse rate.

The lapse rate results from the convective mixing of the atmosphere combined with the adiabatic cooling due to expansion at decreasing pressure with increasing altitude. The lapse rate depends on the specific heat of the atmospheric gases, gravity, and by any latent heat release, and may be affected by local temperature variations due to radiation from the surface directly to space. The simple theoretical value of that variation in a dry adiabatic atmosphere is about -9.8 C per km altitude on Earth. The effect of water evaporation and partial condensation at altitude, drops the size of this average to about -6.5 C per km, which is the called the environmental lapse rate.

The absorbed solar energy is carried up in the atmosphere by a combination of evapotransporation followed by condensation, thermal convection and radiation (including direct radiation to space, and absorbed and emitted atmospheric radiation). Eventually the conducted, convected, and radiated energy reaches high enough in the atmosphere where it radiates directly to space. This does require absorbing and radiating gases and/or clouds. The sum of all the energy radiated to space from the different altitudes has to equal the absorbed solar energy for the equilibrium case.

The key point is that the outgoing radiation average location is raised significantly above the surface. A single average altitude for outgoing radiation generally is used to replace the outgoing radiation altitude range. The temperature of the atmosphere at this average altitude then is calculated by matching the outgoing radiation to the absorbed solar radiation. The environmental lapse rate, combined with the temperature at the average altitude required to balance incoming and outgoing energy, allows the surface temperature to be then calculated.

The equation for the effect is:

T’ = To -ΓH ….(9)

Where To is the average surface temperature for the non-absorbing atmospheric gases case, with all radiation to space directly from the surface, Γ is the lapse rate (negative as shown), and H is the effective average altitude of outgoing radiation to space. The combined methods that transport energy up so that it radiated to space, are variations of energy transport resistance compared to direct radiation from the surface. In the end, the only factors that raise ground temperature to be higher than the case with no greenhouse gas is the increase in average altitude of outgoing radiation and the lapse rate. That is all there is to the so-called greenhouse effect. If the lapse rate or albedo is changed by addition of specific gases, this is a separate effect, and is not included here.

The case of Venus is a clear example of this effect. The average altitude where radiation to space occurs is about 50 km. The average lapse rate on Venus is about 9 C per km. The surface temperature increase over the case with the same albedo and absorbed insolation but no absorbing or cloud blocking gases, would be about 450 C, so the lapse rate fully explains the increase in temperature.

It is not directly due to the pressure or density alone of the atmosphere, but the resulting increase in altitude of outgoing radiation to space. Changing CO2 concentration (or other absorbing gases) might change the outgoing altitude, but that altitude change would be the only cause of a change in surface temperature, with the lapse rate times the new altitude as the increase in temperature over the case with no absorbing gases.

One point to note is that the net energy transfer (from combined radiation and other transport means) from the surface or from a location in the atmosphere where solar energy was absorbed is always exactly the same whatever the local temperature. For example, the hot surface of Venus radiated up (a very short distance) over 16 kWm-2. However, the total energy transfer up is just the order of absorbed solar energy, or about 17 Wm-2, and some of the energy carried up is by conduction and convection. Thus the net radiation heat transfer is <17 Wm-2, and thus back radiation has to be almost exactly the same as radiation up. The back radiation is not heating the surface; the thermal heat transfer resistance from all causes, including that resulting from back radiation reducing net radiation, results in the excess heating.

In the end, it does not matter what the cause of resistance to heat transfer is. The total energy balance and thermal heat transfer resistance defines the process. For planets with enough atmosphere, the lapse rate defines the lower atmosphere temperature gradient, and if the lapse rate is not changed, the distance the location of outgoing radiation is moved up by addition of absorbing gases determines the increase in temperature effect. It should be clear the back radiation did not do the heating; it is a result of the effect, not the cause.

—— End of section 1 ——

My Response

I agree with Leonard. Now for his rebuttal..

Ok, a few words of clarification. I agree with Leonard about the greenhouse mechanism, the physics and the maths but see a semantic issue about back radiation. It’s always possible it’s a point of substance disguised as a semantic issue but I think that is unlikely.

A large number of people are unhappy about climate science basics but are unencumbered by any knowledge of radiative heat transfer theory as taught in heat transfer textbooks. This group of people claim that back radiation has no effect on the surface temperature. I’ll call them Group Zero. Because of this entertaining and passionate group of people I have spent much time explaining back radiation and physics basics. Perhaps this has led others to the idea that I have a different idea about the mechanism of the inappropriately-named “greenhouse” effect.

Group Zero are saying something completely different from Leonard. Here’s my graphic of Leonard’s explanation from one of his simplified scenarios:

Figure 2 – again

From the maths it is clear that the downward radiation from the shell (shield) is absorbed by the surface and re-emitted. Here the usual graphic presented by the Group Zero position, replete with all necessary equations:

Figure 3 – how can you argue with this?

And here’s an interpretation of a Group Zero concept, pieced together by me from many happy hours of fruitless discussion:

Figure 4 – Group Z?

In this case P, the internal heating, is still a known value. But Y and X are unknown, which is why I have changed them from the solution values shown in figure 2.

Now we have to figure out what they are. Let’s make the assumption that the shell radiates equally inwards and outwards, which is true if it is thin (and so upper and lower surfaces will be at the same temperature) and has the same emissivity both sides. That is why we see the upward flux and the downward flux from the shell both = Y.

Because, according to Group Zero, the downward radiation from a colder atmosphere cannot “have any effect on” the surface, I’m going to assume their same approach to the radiation shield (the “shell”). So the surface only has the energy source P. Group Zero never really explain what happens to Y when it “reaches the ground” but that’s another story. (Although it would be quite interesting to find out along with an equation).

So at the surface, energy in = energy out.

P=X ….(10)

And at the shell, energy in = energy out.

X = 2Y ….(11)

In figure 2, by using real physics we see that the surface emission of radiation by the ball = 2P. This means the surface temperature, T’ = (2P/σ)0.25.

In figure 4, by using invented physics we see that the surface emission of radiation by the ball = P. This means the surface temperature, T'(invented) = (P/σ)0.25.

So the real surface temperature, T’ is 1.19 times larger than T'(invented). Because 20.25 = 1.19.

And back to the important point about the “greenhouse” effect. Because the atmosphere is quite opaque to radiation due to radiatively-active gases like water vapor and CO2 the emission of radiation to space from the climate system is from some altitude. And because temperature reduces with height due to other physics the surface must be warmer than the effective radiating point of the atmosphere. This means the surface temperature of the earth is higher than it would be if there were no radiatively-active gases. (The actual maths of the complete explanation takes up a lot more room than this paragraph). This means I completely agree with Leonard about the “greenhouse” effect.

If back radiation were not absorbed by the surface lots of climate effects would be different because the laws of physics would be different. I’m pretty sure that Leonard completely agrees with me on this.

—— End of section 2 ——

Leonard’s Final Comment

I think we are getting very close to agreement on most of the discussion, but I still sense a bit of disagreement to my basic point. However, this seems to be mainly based on difference in semantics, not the logic of the physics. The frequent use of the statement of heat being transferred from the cold to hot surface (like in back radiation), is the main source of the misuse of a term. Energy can be transferred both ways, but heat transfer has a specific meaning. An example of a version of the second law of thermodynamics, which defines limitations in heat transfer, is from the German scientist Rudolf Clausius, who laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work. His formulation of the second law, which was published in German in 1854, may be stated as: “No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.”

The specific fact of back radiation and resulting energy transfer does result in the lower surface of the cases with radiation resistance going to a higher temperature. However, this is not due to heat being transferred by back radiation, but by the internal supplied power driving the wall to a higher temperature to transfer the same power. The examples of the solid insulation and opaque gas do exactly the same thing, and back heat transfer or even back energy transport is not the cause of the wall going to the higher temperature for those cases. There is no need to invoke a different effect that heat transfer resistance for the radiation case.

An example can give some insight on how small radiation heat transfer can be even in the presence of huge forward and back radiation effects. For this example we use an example with surface temperature like that found on Venus.

Choose a ball with a small gap with a vacuum, followed by an insulation layer large enough to cause a large temperature variation. The internal surface power to be radiated then conducted out is 17 Wm-2 (similar to absorbed solar surface heating on Venus). The insulation layer is selected thick enough and low enough thermal conductivity so that the bottom of the insulation the wall is 723K (similar to the surface temperature on Venus). The outside insulation surface would only be at 131.6K for this case.

The question is: what is the surface temperature of the ball under the gap?

From my equation (6), the surface of the ball would be 723.2K. The radiation gap caused an increase in surface temperature of 0.2K, which is only 0.033% of the temperature increase. The radiation from the surface of the ball had increased from 17 Wm-2 (for no insulation) to 15,510 Wm-2 due to the combined radiation gap and insulation, and back radiation to the ball is 15,503 Wm-2. This resulted in the net 17 Wm-2 heat transfer. However, the only source of the net energy causing the final wall temperature was the resistance to heat transfer causing the supplied 17 Wm-2 to continually raise the wall temperature until the net out was 17 Wm-2. Nowhere did the back radiation add net energy to the ball wall, even though the back radiation absorbed was huge.

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