Guy Callendar: Precis of his foundational paper on Global Warming

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Earlier this week the inestimable Ed Hawkins reminded the world that February 16th was the 83rd anniversary of a breathtaking publication in 1938 by Guy Callendar in the Quarterly Journal of the Royal Meteorological Society.

You can read the 18-page paper here: The Artificial Production of Carbon Dioxide and Its Influence on Temperature

A year or two ago I wrote extensive notes on the paper intending to write about it on this blog, but somehow in the chaos of my retirement those notes have disappeared and I no longer have the fortitude to attempt that again.

But it is such a singular paper that it is worth pointing out its general structure and one or two of its highlights.

But before we get onto the paper, it is worth mentioning Guy Callendar’s job title: Steam Technologist to the British Electrical and Allied Industries Research Association . In short his foundational paper on what we now call global warming involved expertise way outside his ‘day job’.

The Abstract

The abstract is short and clear.

  • He points out that in the 50 years from 1887 to 1937 humanity had put 150,000 million tonnes (150 gigatons (GT)) of carbon dioxide into the atmosphere and that most of it was probably still there.
  • He then calculates the effect of this extra carbon dioxide in terms of the extra “sky radiation” that falls on to the Earth.
    • I don’t know if his use of the term ‘sky radiation’ was its first use, but clearly it was not standard terminology.
    • He estimated the entire surface of the Earth was warming by 0.003 °C per year, or 0.15 °C over the previous 50 years.
  • He then points out that meteorological measurements are consistent with his claim.

In short, he understood the entirety of the mechanism underlying global warming, and had the insight to realise how it might be detectable.

And a recent review of his paper using modern techniques has confirmed its accuracy.

The Start

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I particularly like the beginning where he states the basic problem.

The scale of the Earth’s natural weather systems are so large and the amount of energy involved so enormous that it is difficult to conceive that any human intervention could possibly have any effect.

Today this still remains astonishing. The energy that humanity uses collectively each day – all the electricity and gas and oil burning – is (roughly) only 1 part in 10,000 of the natural daily flux of energy on and off the planet.

So the assertion that changes in the atmospheric concentration of an unreactive gas present only in trace quantities could possibly have any effect  seems similarly astounding.

But here he states it directly up front: this is what he intends to show.

The Structure of the Paper

He makes his argument in 6 sections

  1. The Rate of Accumulation of Atmospheric Carbon Dioxide
  2. Infra-Red Absorption by Carbon Dioxide and Water Vapour
  3. Sky Radiation
  4. The Effect of Carbon Dioxide on Sky Radiation
  5. The Relation between Sky Radiation and Temperature
  6. The Observed Temperature Variations of the Earth

I do not have energy to follow through the details of his arguments, parts of which are subtle and complex.

So instead I will highlight just a few features in each of these sections which delight me.

1. The Rate of Accumulation of Atmospheric Carbon Dioxide

In the early part of the 20th Century, measuring the atmospheric concentration of carbon dioxide was a major challenge.

But Callendar takes what few measurements there were from 1905 and 1930-36 and notes that the atmospheric concentration of carbon dioxide appears to have increased.

He then compares the measured increase with what he would have expected to observe based on known emissions from burning coal and oil (which would increase the atmospheric concentration), and the expected rate at which carbon dioxide would dissolve in the oceans (which would decrease it).

He gets good agreement between the measurements and his calculations but modestly observes:

“Such close agreement with the calculated increase is, of course, partly accidental.”

Comments such as this endear him to me.

2. Infra-Red Absorption by Carbon Dioxide and Water Vapour

This is a very technical section covering transmission of infrared light through the atmosphere. Measurements in those days were crude by modern standards.

But he correctly identifies the critical roles played by both water vapour and carbon dioxide in absorbing infrared light of different wavelengths.

The end result is a table showing the fractions of energy emitted by the Earth in different infrared wavebands for three different temperatures of the Earth.

When attempted in full, this calculation is enormously complex. A few years ago I spent five (!) blog articles describing the calculation!

  1. Light Transmission through the atmosphere
  2. Light Transmission through a gas
  3. Light Transmission through the atmosphere
  4. Feedback and Climate Models
  5. What was that all about

Sadly, Callendar did not have access to MODTRAN

3. Sky Radiation

If we stand on the Earth then on a clear night we can look out to space using our eyes, and the transparency of the atmosphere to visible light allows us to see the stars.

But it is different for infrared light.

The key point of Section 2 was that at certain infrared wavelengths, the atmosphere is opaque. If we could see in these wavelengths the atmosphere would look like a mist.

Also, in the infrared, the Earth is not dark but glows with a brightness that depends upon how hot it is.

Because  the atmosphere is partially opaque in the infrared, some of the infrared glow from the Earth is absorbed by the atmosphere and re-radiated back to the Earth’s surface, warming it. This is what Callendar calls “Sky Radiation”.

“Sky radiation” is analogous to the way visible light is scattered back to its source in a mist.

  • In a very dense mist shining headlights into a fog can dazzle the driver because lots of light is returned within a short distance in the direction it started out in.
  • In a less dense mist, the light can travel quite a distance and the reflection back to the driver is not so bright.

Callender calculates the fraction of the infrared light radiated by the Earth that is returned as ‘sky radiation’.

He considers many factors that affect the amount of sky radiation received back on Earth.

  • Altitude: mountains
  • Latitude: he considers the poles, temperate and tropical locations
  • Angle: he considers the effect of radiation from near the horizon and radiation from directly above, the zenith.
  • The composition of the atmosphere – the nearly constant concentration of carbon dioxide, and the highly variable concentration of water vapour.

He then significantly underplays the difficulty of the calculation.

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4. The Effect of Carbon Dioxide on Sky Radiation

This is another very technical section, but the gist of it is simple.

Having calculated previously (Section 3) how much ‘sky radiation’ was being returned to the Earth, in this section he calculates how this would be affected by changes in the concentration of carbon dioxide.

He has several key insights.

First he considers only infrared light with wavelengths between 0.013 mm and 0.016 mm. This is because in this waveband the Earth’s infrared glow is at its brightest, and it also corresponds to a range where carbon dioxide absorbs strongly. So it is in this waveband that changes in the atmospheric concentration of carbon dioxide will have their greatest effect.

Secondly, he notes that the atmosphere is already totally opaque to infrared light in this waveband. So the effect of increasing the absorption further (by adding more carbon dioxide) is to lower the effective height above the Earth from which the ‘Sky radiation’ is returned to the Earth. Lower parts of the atmosphere are warmer and so re-radiate more ‘sky radiation’.

He writes:

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His calculation is summarised in his Table 5 which I have annotated below

Click for larger version. Annotated version of Callendar’s Table 5. The small net increase in ‘sky radiation’ on doubling the atmospheric concentration of carbon dioxide arises from an increase from the lowest atmospheric layers and decrease from the upper atmospheric layers

His calculations indicate that doubling the concentration of carbon dioxide in the atmosphere will give rise to a 0.58% net increase in the amount of sky radiation in the waveband between 0.013 mm and 0.016 mm.

5. The Relation between Sky Radiation and Temperature

Now we come to the key question:

What amount of warming might we expect from this apparently tiny 0.58% increase in the amount of sky radiation in the waveband between 0.013 mm and 0.016 mm caused by doubling the amount of carbon dioxide in the atmosphere?

Callendar states the key insight clearly at the start.

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The warming of the Earth by the Sun is apparent and obvious to all. The more subtle question is where does that heat go?

Ultimately, if the temperature of the Earth is constant, then ALL the solar radiation which warms the Earth must be re-radiated out into space. As Callendar puts it:

…because no other type of heat exchange is possible.

After some subtle arguments about the role of water vapour, Callendar summarises his calculation with a graph which I have annotated below.

Click for larger version.  I have drawn in red the current concentration of atmospheric carbon dioxide (417 ppm as I write in February 2021) and so the predicted temperature rise since 1938, is roughly 0.8 °C.

The graph shows the expected change in the mean surface temperature of the Earth as the concentration of atmospheric carbon dioxide changes.

The curve allows Callendar both to look ahead to suggest the magnitude of future warming, and to look back to see whether warming has taken place in the previous 50 years

Looking back is the focus of the final section of the paper, but in this  section he looks ahead to future centuries.

In Table 6 he summarises his expectations based on annual carbon dioxide emissions of 4.3 gigatonnes.

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I have sketched his expectations from Table 6 (above) on the figure below.

In fact carbon dioxide emissions are currently growing 8 times faster than he anticipated, and at this rate a century of Callendar’s anticipated changes takes only 12.5 years.

Click for larger version. The graph shows atmospheric concentration of carbon dioxide in parts per million versus year. The green circles show Callendar’s estimate of future concentrations based on 4.3 gigatonnes of emissions per year. Actual emissions are currently around 35 gigatonnes of carbon dioxide. The black curve shows modern best estimates of historical carbon dioxide concentrations.

6. The Observed Temperature Variations of the Earth

While clever calculations and insightful fancies about infrared radiation in the atmosphere are one thing, and bold predictions about the temperature of the entire Earth are another – actually determining whether the average temperature of the Earth’s surface had warmed by a few tenths of a degree Celsius is quite another.

Callendar set about the task by consulting a tome published by the US Smithsonian Institute : World Weather Records

The problems with the strategy are obvious:

  • There is a great deal of natural variability in weather records with time scales of days, weeks, months, years (obviously) and decades!
  • Not all records are reliable.
  • Very few records are continuous across the period of interest and few are of a long length.
  • Some locations on Earth have very little data and so warming or cooling may be either under or over represented.
  • The local environment around many stations has changed over decades due to urban growth which might give rise to spurious warming

But Callendar understood that there were strategies for getting a reliable result in the face of all these difficulties.

Most critically he understood that because each station samples its local environment differently from each other station, that one should look at only changes (so-called anomalies) of each station record with respect to itself.

In other words he asked how the 10 year average from weather station 1 had changed over decades, and how the 10 year average from weather station 2 had changed over decades – he didn’t try to average the raw data from the weather stations. Using anomalies eliminates many possible systematic errors.

He also had a big advantage. The climate change he was looking was global! Thus he expected a similar trend from ALL tropical stations, ALL temperate stations, and ALL polar stations. This allowed him to compare trends deduced from different combinations of stations to see if the trends he saw were really present everywhere, or just statistical artefacts.

After extensive testing and tabulation he came up with the graph below.

Click for larger version. Estimates of changes (anomalies) in the temperature of the Northern and Southern temperate zones, the tropics, and of the whole Earth. These estimates are based on analysis of data from 147 weather stations.

Like all good scientists, Callendar includes a table of data with his final result. This has enabled me to overplot his estimate (in green) with modern re-analysis of many more stations by the Berkeley Earth team.

Click for larger version. The Berkeley Earth estimate of the Global Average temperature from 1850 to 2018. Overplotted in green is Callendar’s estimate of the changes of Global Average temperature from 1880 to 1935. I have offset Callendar’s data by -0.4 °C to take account of the use of different baselines.

Actually – the result is pretty good. The failure to detect the exceptionally warm years of 1876 and 1877 was probably due to poor coverage by weather stations.


What impresses me most about his paper is the completeness of his understanding from the basics, through the multiple competing processes at play in the atmosphere, to the likely climatological consequences.

At that time, papers were ‘read’ aloud (I think) and members of the Royal Meteorological Society asked questions which were minuted and included in the paper

Callendar was clearly aware of many of the detailed criticisms raised by his interlocuters, but he does not get lost in those details. His response begins beautifully:

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Here he points out that the details don’t matter. ANYTHING that makes the atmosphere more opaque to infrared radiation MUST warm the Earth no matter how complex the mechanism.

In response to a request for details of the natural movements he responds that he has written a paper on this but it was 8 times longer than the present paper!

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So his astonishing insight and endeavour was communicated with modesty in the face of what I read to be quite a polite but unwelcoming reception by meteorologists who likely thought “What does this Steam Man know about meteorology!

The challenge with any precis is to actually use less words than the original document. With that in mind I must stop writing now. My hope is that this article may help you make your own way through the paper. I will let Guy Callendar’s conclusion be my own.

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