‘To heat a planetary surface’ for dummies; Part 5a

In 1938, English steam technologist Guy Stewart Callendar wrote what proved to be a seminal – one might even venture to call it the foundational – paper of the entire modern AGW pipe dream movement, with its rather determined effort at postulating what we today call the “Radiative (Atmospheric) Greenhouse Effect” (rGHE), or as some people would prefer it: the “Callendar Effect”.

In his paper – “The Artificial Production of Carbon Dioxide and Its Influence on Temperature” – Callendar argued that the increase in global atmospheric CO2  concentration due to our industrial endeavours would (and did) warm the world because of the alleged augmenting influence of this IR-active molecule on the so-called “sky radiation” (what we today call “(atmospheric) downwelling longwave radiation” (DLR, DWLWIR), more commonly known simply as “back radiation”):

“Few of those familiar with the natural heat exchanges of the atmosphere, which go into the making of our climates and weather, would be prepared to admit that the activities of man could have any influence upon phenomena of so vast a scale.

In the following paper I hope to show that such influence is not only possible, but is actually occurring at the present time.”

Notice here how Callendar was well aware that with his hypothesis, he was challenging a generally accepted scientific paradigm of his time, one which held that our climate and weather are natural phenomena with purely natural drivers, which can not in any meaningful way be influenced (globally, at least) by human activity.

Callendar claimed that it can. And that it does. He even went so far as to claim he could show it …

Well, then; by all means bring it on! To quote Carl Sagan:

“Extraordinary claims require extraordinary evidence.”

Callendar makes an extraordinary claim, that he can somehow show the ‘null hypothesis’ to be no longer valid. In AGW terms, the ‘null hypothesis’ would be that humans cannot and do not affect global climate. Callendar claims that we can and that we do. Which means that the onus is on him to show his claim to be correct. He will have to provide direct empirical evidence of a causal link between human activity and a global change in climate. It is not enough to simply produce evidence of a global change in climate. It is also not enough to hypothesize about mechanisms, i.e. about how human activity could conceivably cause a global change in climate, and after that simply go out and point to a global change in climate.

In such case, you’re assuming your premise to validate your conclusion and at the same time your conclusion to validate your premise – a classical circular argument.

So let’s have a look at what Callendar has to offer in terms of ‘extraordinary evidence’, shall we?

Here is (some of) what he says about “sky radiation”:

“For normal conditions near the earth’s surface, with a clear sky the downward radiation varies between three and four fifths of that from the surface, the proportion being greatest when the air is warm and carries much water vapour.

The method used to calculate the sky radiation from the absorption coefficients of water vapour and carbon dioxide is simple but laborious. It consists of dividing the air into horizontal layers of known mean temperature, water vapour, and carbon dioxide content, and summing the absorbing power of these layers on the different wave bands, in conjunction with the spectrum distribution of energy at the surface temperature. In this way the perpendicular component of sky radiation is obtained.”

In other words, Callendar starts out by simply presupposing the reality of his downward “sky radiation” as some kind of distinct macroscopic (bulk) transfer of energy to the ground. Even though admitting there is no way such a ‘thing’ could ever be measured directly (as in ‘separately physically detected’); you will have to derive it from your assumptions and, based on these, from particular radiative formulas using other – actual, physically observed – parameters as input.

Undeterred, here is how he explains the theoretical influence of CO2 on this inferred “sky radiation” phenomenon:

“When radiation takes place from a thick layer of gas, the average depth within that layer from which the radiation comes will depend upon the density of the gas. Thus if the density of the atmospheric carbon dioxide is altered it will alter the altitude from which the sky radiation of this gas originates. An increase of carbon dioxide will lower the mean radiation focus, and because the temperature is higher near the surface the radiation is increased, without allowing for any increased absorption by a greater total thickness of the gas.

The change of sky radiation with carbon dioxide depends largely upon this change in the altitude of the radiation focus, because the present quantity in the atmosphere (equal to a layer of 2 m. at N.T.P. [‘normal temperature and pressure’: 20°C and 1 atm respectively]) can absorb nearly the maximum of which this gas is capable. The latter assumption depends upon the exponents used, but it is probable that great thicknesses of carbon dioxide would absorb on other wave lengths besides those of the primary bands.


From the figures in Table V it will be seen that an increase of carbon dioxide causes the radiation to be concentrated from the lowest air layers, whilst the amount from the cold upper layers is still further screened off, the net effect being a small increase in the total sky radiation.”

What is so fascinating about these particular passages is how they seem to carry within them not only the seed, but pretty much the entire, fully grown stem of the currently favoured explanation of the working mechanism of “greenhouse warming”, the one about the raised ‘effective radiating level’ (ERL), where some specified gassy layer 5.1 km up in the mid-troposphere allegedly emits Earth’s entire radiative flux to space as if it were a solid blackbody surface, by virtue of a mean physical temperature of 255K, and from which you can apparently draw down the 6.5 K/km lapse rate to produce the actual surface temperature of 288K, giving a radiative-convective “greenhouse effect” of [288 – 255 =] 33K.

The only difference between the two explanations is that Callendar’s addresses alleged radiation down to the surface (his “sky radiation”) while the ERL one concerns Earth’s upward radiation, to space. The principle behind both, however, is exactly the same: The specific temperature of the layer of air representing “the average depth within [the atmosphere] from which the radiation comes” (either up or down) determines the intensity of the radiative flux.

Straight from the Stefan-Boltzmann law (plus a bit of reversed deduction).

Callendar argues – based solely on select theoretical considerations – that the denser the concentration of an IR-active (absorbing/emitting) gas, the lower (and hence warmer) the ‘mean focus’ for downward radiation. Thus resulting in increased “sky radiation” intensity to the surface.

If you then shift your aim 180 degrees and look up instead, then you simply flip the argument around and say: “The denser the concentration of an IR-active (absorbing/emitting) gas, the higher (and hence cooler) the ‘mean focus’ for upward radiation. Thus resulting in reduced “earth radiation” intensity to space.

That’s the ERL argument right there … And why the atmosphere apparently (according to those famous global Earth energy budget diagrams as presented by the climate movement) emits a mere ~240 W/m2 UP (to space) and a full ~345 W/m2 DOWN (to Earth’s surface).

Anyway. Let’s move on.

Callendar, finally, on the effect of the “sky radiation” on surface temperature:

“If the whole surface of the earth is considered as a unit upon which a certain amount of heat falls each day, it is obvious that the mean temperature will depend upon the rate at which this heat can escape by radiation, because no other type of heat exchange is possible. For simplicity the reflection loss from clouds and ice surfaces is assumed to be a constant factor.

The radiation loss from the surface and clouds depends upon the fourth power of the absolute temperature and is proportional to the difference between the surface and sky radiation:

H = σ * T4 * (1 – S) … … … … (4)


H = radiation heat loss from surface

σ = radiation constant; [1.17 x 10-7 cal/cm2/day/K4 or 5.6704 x 10-8 W/m2/K4]

T = temperature of surface, Abs.

S = sky radiation, as proportion of that from the surface.

Suppose that the sky radiation is changed from S1 to S2 whilst H remains constant. Then:

T2 = T1√[(1 – S1)/(1 – S2)] … … … … (5)

From this relation it will be seen that the change of temperature for a given change of sky radiation increases rapidly as the latter approaches that from the surface, it being always assumed that the heat supply and loss are constant.


Small changes of atmospheric carbon dioxide do not affect the amount of sun heat which reaches the surface, because the CO2 absorption bands lie well outside the wave lengths, 0.25 to 1.5 μ[m], on which nearly all the sun energy is carried. Consequently a change of sky radiation due to this gas can have its full effect upon low level temperatures, provided it does not increase the temperature differences on which the atmospheric circulation depends.”

So Callendar is essentially employing the classic ‘bidirectional flow’ model of radiative heat transfer (where two oppositely directed, macroscopically defined* transfers of energy are imagined to operate simultaneously and to occupy the exact same section of space, but still doing their work independently of one another, as if the opposing one weren’t there, as if each constituted a completely separate process; basically two distinct transfers in one) to explain how the already solar-heated surface will statically warm beyond a purely solar steady state from its total ‘radiative heating’ increasing with the extra input of energy as ‘heat’ to the warm surface from the cooler atmosphere, not from the hot Sun, its actual (and only) source of energy:

(*As a classically thermodynamic, ordered, averaged out, unidirected ‘flux’ (flow) of energy, like a proper ‘heat flux’, detected and described macroscopically; as opposed to the complete disorder and randomness characterizing the minute inner workings of the microscopic/quantum realm.)


Figure 1.

The “(extra) heating by back radiation” explanation of “greenhouse warming”.

So what does Callendar do next?

He assumes – without empirical evidence of any kind – that this, the theoretical basis of his hypothesis, is correct: More CO2 in the cool atmosphere WILL necessarily make the warm surface even warmer. By intensifying the “sky radiation” to the ground. ‘All Else Being Equal.’

And armed with this self-deduced and approved ‘fact’ as his warrant, he then goes on to show that there has in fact been warming over the previous decades:

Callendar 1938

Figure 2: The lower half of Callendar’s Figure 4.

Note the dashed straight, upward-tilting line labelled “CO2 Effect”. That’s Callendar’s inferred causal correlation between the rise in global temps over the period in question and the (quite crudely) estimated coincident rise in ‘global’ atmospheric  CO2 concentration:

“Since calculating the figures in Table I, I have seen a report of a great number of observations on atmospheric CO2, taken recently in the eastern U.S.A. The mean of 1,156 “free air” readings taken in the years 1930 to 1936 was 310 parts in 10,000 by volume. For the measurements at Kew in 1898 to 1901 the mean of 92 free air values was 292, including a number of rather high values affected by local combustion, etc.; and assuming that a similar proportion of the American readings are affected in the same way, the difference is equal to an increase of 6 per cent. Such close agreement with the calculated increase is, of course, partly accidental.”

And voilà! There you have it! Callendar’s extraordinary evidence …

He does exactly what I pointed out he couldn’t do according to the scientific method: Using his own hypothesis as evidence for it. Callendar is simply “Begging the question”. He assumes a priori the empirical reality of his hypothesized ‘mechanism>effect’ relation (+CO2 atm ⇨ +Tsfc). He can thereby simply let his premise confirm his conclusion and his conclusion confirm his premise:

‘It has become warmer and CO2 has increased. Therefore, since we ‘know’ (through our hypothesis) that more CO2 will make it warmer, we can conclude that it’s the increase in CO2 that made it warmer. This in turn also confirms our original hypothesis, that rising CO2 will make it warmer, since CO2 has risen and it has become warmer.’

This is the same kind of mindless pseudoscientific approach to the real world – where you have already established before you set out on your search what you’re going to find – as what we see in full operation today whenever you try to discuss anything to do with climate and weather with the warmists. They are utterly incapable of seeing it themselves, how fundamentally circular their entire line of argument is. (It’s not a line. It’s a circle.) A complete blind spot.

Courtesy of the ‘Climate Establishment’ …

In the discussion following Callendar’s exposition of his hypothesis, long-time head of the British MetOffice and fellow of the Royal Society, Sir George Simpson, pointed out the following:

“(…) he [Simpson] would like to mention a few points which Mr. Callendar might wish to reconsider.

In the first place he thought it was not sufficiently realised by non-meteorologists who came for the first time to help the [Meteorological] Society in its study, that it was impossible to solve the problem of the temperature distribution in the atmosphere by working out the radiation. The atmosphere was not in a state of radiative equilibrium, and it also received heat by transfer from one part to another.

In the second place, one had to remember that the temperature distribution in the atmosphere was determined almost entirely by the movement of the air up and down. This forced the atmosphere into a temperature distribution which was quite out of balance with the radiation. One could not, therefore, calculate the effect of changing any one factor in the atmosphere, and he felt that the actual numerical results which Mr. Callendar had obtained could not be used to give a definite indication of the order of magnitude of the effect.”

Callendar’s response:

“(…) Mr. G.S. CALLENDAR said he realized the extreme complexity of the temperature control at any particular region of the earth’s surface, and also that radiative equilibrium was not actually established, but if any substance is added to the atmosphere which delays the transfer of low temperature radiation, without interfering with the arrival or distribution of the heat supply, some rise of temperature appears to be inevitable in those parts which are furthest from outer space.


The sky radiation is calculated as a proportion of that from the surface, hence, at constant heat supply, a change of sky “temperature” involves an equilibrium change of surface temperature as in expression (5).”

It appears from this that Callendar isn’t really addressing the point(s) Simpson is making at all. He simply stands by his original supposition that all other processes of heat exchange within the climate system will remain unchanged while an increasing concentration of atmospheric CO2 is allowed to quietly and gradually intensify the “sky radiation” to the surface, thus forcing it to warm.

This is what the entire AGW argument boils down to: ALL ELSE BEING EQUAL.

Problem is, it isn’t. For one, the Earth system as a whole does not constitute one static, homogeneous reservoir inside a rigid outer black body surface to space. But that’s essentially how they model it …

What Simpson is effectively pointing out to Callendar is this:

On Earth, you cannot under any circumstance look at a radiative budget alone and determine surface temps. Not regionally. And not globally.

The rGHE hypothesis seeks to derive directly the temperature of the surface purely from an atmospheric radiative balance (the lapse rate down functioning only as its extended arm).

The total energy content (the ‘internal energy’) of a thermodynamic system – like the Earth system – is certainly determined by the balance between its total energy input and output, in the context of the Earth system, simply the balance struck between SW in and LW out through the ToA. Energy content being an extensive property.

However, the specific temperature (an intensive property) of different subsystems inside a vastly heterogeneous overall system like Earth can by no means be derived from this same balance (or – in the special case of the AGW hypothesis (really just an rGHE spin-off product) – imbalance). The empirical tropical dry/wet region comparison is a good case in point. This is where the rGHE hypothesis goes wrong.

Internal temperatures would be set rather by differing subsystem ‘heat capacities’ and the intricate dynamics of the ‘internal movement’ of energy between its initial absorption by and final emission from the system as a whole. The internal movement of energy between subsystems, regions and levels inside the total Earth system is governed almost exclusively by the process of convection/advection – mass transfer, oceanic and atmospheric circulation.

This is why Callendar (like today’s ‘Climate Establishment’), with his simplistic, one-variable approach to the global climate, would forever be groping around in darkness for his answers. Getting nowhere.

Radiative balance at the ToA simply isn’t it. Internal transport of energy is.

Which brings us to Part 5b: What processes really determine Earth’s mean global surface temperature, beside the solar input …?

13 comments on “‘To heat a planetary surface’ for dummies; Part 5a

  1. Peter Shaw says:

    Credit where credit is due: Callendar clearly articulates that “back-radiation” (however construed) is a *temperature* effect mediated by greenhouse gases. We have many contemporaries who haven’t quite grasped this yet. It indicates that any GHG effects must be considered together with all other temperature effects (so presenting “all else equal” as a magical weasel-clause).

    Where he goes astray (as you indicate) is in treating the “back-radiation” in isolation. As support of your argument (here and earlier posts) I offer a quotation: “It is as absurd to consider the emission of light without its subsequent absorption, as it is to consider the absorption of light absent its prior emission.” (said a century ago, by a chemist – there’s progress…)
    My take – light is (somehow!) a *transaction*, and you can’t understand a transaction by studying half of it.

    ps – If you have a handy engineering-compliant correction of your Fig 1, adding it would ensure that even casual readers won’t misconstrue.

    • okulaer says:

      Peter, you say: “My take – light is (somehow!) a *transaction*, and you can’t understand a transaction by studying half of it.”

      My opinion exactly. It is a hopeless (and highly misleading) approach, conceptually splitting the ONE transfer of radiant heat between two regions at different temperatures into two and treating each of them as a separate transfer, independent of the other one. But this is what the bidirectional model allows you to do. In fact, it is what it tells you to do.

  2. Christopher says:

    Claes Johnson treats the two-stream radiative (heat) transfer due to Schwarzschild in his latest blog post today.


    Not very surprisingly, the result is, as to be expected for pseudophysics, a catastrophe for the two-stream approach 😉

  3. Kristian,
    Claes Johnson seems to off on a tangent that will lead only to the Willis’ Steel greenhouse, which is also incorrect.; The false assumption is that surface radiation maintains the actual atmospheric temperature. (rethermalization). If this were the case, the measured lapse rate would be minus 13-17 degree Celsius per km of altitude. Dry LR is -10 degree/km with saturated LR half that. All of the troposphere is at a higher temperature than would occur via EMR alone. This leads to the notion that something other than EMR determines atmospheric temperature. That something is to the right of your fig. 1. Water vapor adds sensible heat while condensing. This along with thermostatic gravitational compression and a we bit of surface EMR sets everything. Atmospheric exit flux to space constantly accumulates all the way to 220km. No EMR to a higher temperature is needed nor does such exist. However it is the variable WV that dominates all temperature. Atmospheric WV amount is in turn dominated by low level wind speed. I hope your part 5B clearly shows what determines wind speed at every location. 🙂

    • markstoval says:

      Will J.,

      I am under the impression that we are in substantial agreement on climate matters. I wonder if you are of the same belief that I am on the odds of modern science figuring it all out.

      I believe that modern science will not be able to leave the “CO2 is a warm blanket” paradigm for at least one more generation and more than likely it will be at least three generations.

      Even so-called skeptics will not consider the idea that there is no warming via “back-radiation” heating up the surface of the planet. Even though the moon gets much hotter without an atmosphere, they claim the earth must have one with “greenhouse gasses” to keep from freezing into a ball of ice. The so-called skeptics and the alarmists differ only in degree and not in kind.

      At least that is my take on it.

      • Mark
        I would go further to state, that the thermal control system of this Earth, is by design unknowable by any critter on or above the Earth surface. Not to sure about sea critters. Be careful of learning too much!! The designers are still watching with inconceivable weapons! 🙂

  4. Mr. Pettersen says:

    The international space station have a surface temp well over 200 C on the outside when its on the sunny side of the earth.
    And it orbits faster than our planet so it should be colder. Both the spacestation and the moon tells us the earth without an atmosphere would be a lot hotter……

    • markstoval says:

      How can that be?

      People who teach physics in college tell me that without CO2 the earth would be a frozen ball of ice. So I think the space station must be real cold and have to have heaters to help the sun out. (well unless it is a steel greenhouse I guess)


  5. markstoval says:

    “Which brings us to Part 5b: What processes really determine Earth’s mean global surface temperature, beside the solar input …?”

    At my advanced age, I am hoping you get to this sooner rather than later. 🙂

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